This did not work out. The empirical evidence, always slight, was emphatically refuted by the randomized controlled trial revolution. There is definite utility to having lenders around, but the marginal impact of adding more was dominated by a cash transfer. This does not mean that credit constraints do not exist. They do, and the decisions of farmers and entrepreneurs in the developing world are substantially distorted away from what is optimal. Neither does this mean that there is no scope for international aid to take forms other than simple cash transfer. There is room for a balanced portfolio of charitable interventions.

This essay will survey the effects of microfinance, why the initial revolution failed, and what we can do about it, including how changes in contractual structure can improve welfare. We will then discuss whether international aid should seek to change people’s actions, and whether common interventions to share risk, internalize externalities, and induce investments are better than cash transfers.

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The explosion of microfinance in the 1990s was in part due to technological innovations on the part of Mohammed Yunus and the Grameen Bank. He had founded the bank in 1976, lending money to the poorest of the poor in Bangladesh, with the motto that credit is a human right. With ineffective rule of law, lenders would normally find the cost of people running away with the money too high. The innovation was giving group loans to neighbors, almost all women, and having everyone be a guarantor of the loan. The neighbors would refuse to agree if they believed their neighbors to be a rotten apple, and they would be able to pressure each other into making a good-faith effort to pay it back. This basic model started spreading around the world – to Bolivia with the Banco-Sol, to Indonesia with the Bank Rakyat and the Bank Kredit Desa, and to India, where a patchwork of moneylenders developed in the 2000s.

International aid being not a hand out, but a hand up, was very popular with donors. In 1997, the Microcredit Summit, headlined by Hillary Clinton and other notables, started a drive to raise $20 billion and reach 100 million people by 2005. The peak of the movement’s influence was in 2006, when the Nobel Peace Prize was awarded to Mohammed Yunus and the Grameen bank. At that time, they had served 7 million people, and disbursed 6 billion dollars.

The Grameen Bank charged interest for their loans, and did have a high rate of repayment, but it still ran at a loss. It needed support from international donors for continued operation. So why support it? One theory is that the poor people are in a poverty trap. Suppose that people produce output by physical exertion. When one is famished, they are not capable of working as hard as they could, and produce just enough to survive. When they are well-nourished, then they can produce much more output. For this to be a poverty trap, there must be a region where adding a bit more food has only a small gain, less than the cost of buying more food, but with a big enough investment, you could get to the higher equilibrium of producing while well-nourished. Or for an alternative story, suppose that borrowing is impossible, there exist large and indivisible productive investments, but that if one accumulates savings they will face unbearable pressure to share from impecunious relatives. Borrowing allows you to shift to an asset which is more difficult for others to take. (I am going to defer a fuller discussion of this to an article next week, which will be linked here once that is complete).

To complete the story for the intervention of outsiders, we need some way for lending to be suboptimally low. This is where Stiglitz-Weiss (1981) (and in the same line of logic, Mankiw (1986)) come in. Suppose that borrowers possess private information about the riskiness of a project, or perhaps whether they intend to run away with the money. When the project fails and they are unable to pay back the loan, the lender is limited in how much they can get back. Raising the interest rate causes the people with safer investments to exit, forcing the interest rate to be even higher; in some cases, there will be no interest rate which is able to clear the market. The role of the donor is to eat the loss long enough to get people to jump out of the bad equilibria. If credit does exist, it will be rationed, and people will be prevented from buying as much as they wanted at the prices they want. This part definitely exists, and it is striking how much microfinance is viewed not as a reduction in the price of what you borrow, but of the amount which you can borrow.

The evidence base for microfinance being effective was always extremely thin. Morduch (1999), in an otherwise hopeful article on the development of microfinance, could not help but note the paucity of the available evidence that it was actually doing anything. The best evidence cited at the time for the Grameen Bank was Pitt and Khandker (1998), who used an eligibility requirement to infer the effect of the loans. However, they skip over the obvious approach in favor of considerably more complicated estimators. Simply running standard estimators, as Morduch and Roodman (2012) do, does not replicate the findings. Pitt and Khandker responded, but it’s almost beside the point – if you have $20 billion in aid money riding on it, you don’t want its utility to depend on involved arguments about what the correct estimator to use on a single dataset is. The comparison is to simply give people money – an action which we now know has substantial multipliers, and at the very least can’t harm anyone.

So by the later part of the 2000s, a movement to test microcredit with randomized controlled trials developed. A randomized controlled trial (an RCT) is one where the treatment – in this case, access to microfinance – has been randomized, and data is collected on the control group who was never offered the treatment. What randomization does for you is get rid of selection. The people who are likely to seek out loans may systematically differ from the population at large, and simply controlling for the things you can observe is unlikely to fix. For example, imagine that people who discover a profitable idea would pay for it out of savings without microfinance, but if loans are available will seek a loan. Thus, you would observe that people who go on to have higher incomes are more likely to obtain loans, without the loans having had any actual causal influence on the outcomes. With randomization, you would observe that there is no difference in investment or income between the groups, and thus correctly infer that the offer of a loan had no effect.

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Things came to a head in a special issue of the AEJ:Applied in 2015, which featured six randomized controlled trials in Morocco, Bosnia-Herzegovina, Mexico, Mongolia, Ethiopia, and India. These trials were deliberately designed to be similar enough to aggregate together, and Rafe Meager (2019), conducting a meta-analysis on these and also Karlan and Zinman (2011) found that the average effects were simply nothing. The RCTs, even in very different contexts and with different methods, had similar null effects. The only light for microfinance was that Meager (2022), interested in if there were different impacts among subgroups, found that households with prior business experience were overrepresented in the tail of outcomes.

There are two ways to conduct an RCT on microfinance, randomizing at the individual level and randomizing at the village level. These have different tradeoffs. Randomizing at the village level means that you capture the interpersonal spillovers which individual randomization would miss. For instance, if people live in households, then it might not matter if one member of the family was not offered if somebody else got a loan and shared it. In a more negative sense, some people receiving money in a village and consuming more might increase the prices of goods, and reduce the consumption of others.

Randomizing at the village level captures the general equilibrium spillovers from person to person, but it is possible that the control group is contaminated. Lending is offered for profit. It stands to reason that profit-seeking firms will choose to locate themselves where the researchers are not competing. This would bias the effect toward zero, as untreated groups are secretly treated.

An immediate objection is that the RCTs are estimating something different from credit constraints, particularly the studies which are randomized at the individual level. The natural thing to point out is that lending is useful both for investment and mitigating risk, and what actually matters for the latter is the credible promise to be able to borrow. Of course take-up is extremely low for one time offers – not everyone has investment opportunities just waiting to go. What we need is for lenders to stand ready when an investment opportunity does come along. Unfortunately, we were able to test it, and it once again failed.

In 2001, the newly elected Thaksin Shinawatra government announced the Million Baht Initiative. One million baht, about $25,000, was transferred to each of the 77,000 villages in Thailand in order to start a village bank. These banks lent out most of the principal at rates matching prevailing interest rates, and the loans were not systematically looted through default. By all accounts, it was implemented in a fair and evenhanded manner.

The results were puzzling. We might have expected people to use the loans to finance investment, but there was no change in investment. Neither was there any change in the price of credit. What happened is that total consumption rose dollar for dollar with the amount available to the villagers to borrow, which is difficult to reconcile with the lack of change of the price of credit and the low default rate. It’s not even consistent with a cash transfer, because people would save a portion of the transfer and spend the interest.

Kaboski and Townsend (2011) try to fit the facts with a macro model. Each household has declining marginal utility of consumption in a given period, and so would like to consume the same amount in each period. Since they discount the future, though, they will not spend exactly the same amount, but consume more now at the cost of consumption later. Each household faces both permanent income and transitory income shocks in each period, drawn from an unknown distribution, and likewise are stochastically presented with the opportunity to invest into a randomly sized, lumpy investment. They can borrow up to a limit, denoted s, at an interest rate r, and if they are unable to pay back the loan default to a minimum level of consumption c. Lastly, there is measurement error in income, which we will estimate, and there is a return to investment which is plugged in from elsewhere (as there is not enough investment in the sample to tidily identify it).

The objective is to choose a set of parameters which will match the period before the intervention. If our model is correct, then that same set of parameters – properly modified to account for the change in the borrowing limit, and the general upward trend after the East Asian financial crisis of 1997 – should replicate the outcomes afterwards.

We find those parameters with the method of simulated moments, which is an extension of generalized method of moments. A brief aside on what those are. Generalized method of moments works by slowly converging to some set of parameters which match the outcomes in the data, or “moments”. You take a guess, solve, and see how far off you are. How far you are updates what you guess next, and eventually you converge to something which comes close enough to matching. The simulation aspect comes in for the inner loop, where you “solve”. The model which they sketch out does not have a tidy solution. Instead, they simulate what agents would do under the parameters with random shocks many times, and take the average. The results from the inner loop can be compared to the outcomes of interest, and you crawl around finding the values that fit.

To evaluate the counterfactual, they change the borrowing constraint s. Because one million baht was given to each of the villages, regardless of size, the variation in the borrowing constraint is plausibly exogenous to what was going on. Consumption increased equal to the amount of credit that was available in each village, and investment was unchanged, although investment was rare enough in the data that failing to observe a significant increase was not puzzling.

Key to understanding the puzzling result is that ex ante identical households which face different shocks will behave very differently. Those households which are living hand-to-mouth, and face a negative temporary income shock, will use the credit to smooth consumption. Their consumption will naturally rise. The more interesting thing is the consumption of people who have positive income shocks. They do not borrow, yet still benefit from the change in the borrowing limit because they can reduce the stock of precautionary savings which they would have held. Meanwhile, people who are insolvent are actually worse off – raising the borrowing limit leaves them more in debt, and they have to pay the interest in the next period. Finally, people who face investment opportunities may borrow to finance it, with ambiguous effects on consumption. Because of the fixed size of the investments, families might reduce their consumption to add to the new borrowing limit.

I think it’s important to point out the role that the default level of consumption c is playing. If default was impossible, and you could always lose more money, then the expanded borrowing limit would always be strictly better. However, with the bound on consumption, the borrowing limit is essentially how much the lender can hold you to from period to period. A higher borrowing limit essentially reduces how much you can default on the debt.

We can then evaluate what would happen if, instead of a loan program, they had simply transferred a sum of money which raised utility by as much. Earnings are in the model – simply move it up, and simulate. They find that a cash transfer could have produced the same increase in utility for 70% of the cost. And yes, that is fully accounting for the credit offerings being permanent. With the risk of having to pay interest for a long time, they would prefer a smaller cash transfer.

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I would not suggest that lending services are not effective. Breza and Kinnan (2021) study the government of Andhra Pradesh’s abrupt interruption of moneylending services in 2010 on consumption, wages, and employment. The government in Andhra Pradesh claimed that it was for consumer protection, but this was of course nonsense; it was more akin to medieval kings periodically expropriating the moneylenders. Breza and Kinnan are not studying the direct effect of no longer being able to access loans in Andhra Pradesh, which would be hopelessly contaminated with changes over time and have only one observation. Rather, they have data from 25 providers of microfinance across multiple districts. Their exposure to Andhra Pradesh, where borrowers were able to default at will, varied, and so the places that saw bigger losses had to reduce their lending in other districts. From this variation, we can get the effect on wages and consumption.

It was not good! The places which saw reductions in lending activity also saw reductions in wages, earnings, and consumption, with employment showing a null effect. Agricultural wages went down 4%, non-agricultural wages went down 8%, and household consumption went down 5%. These losses did not show up immediately – only in the next year, when the banks could not make the loans they had made the previous year in view of their financial losses. Screwing the moneylenders is good exactly one time, and then you pay for it forever. Also, at a larger scale, Bau and Matray (2023) show that India removing the constraints on access to foreign capital which it had until the early 2000s caused firms which had higher marginal revenue products of capital to greatly increase revenue and investment.

The evaluations thus far are the short-run impact. Unfortunately, we can’t expect for the long-run impacts to be better, and in fact we should expect them to be worse. Buera, Kaboski, and Shin (2021) trace out the incentives, but the basic finding can be found from considering what happens if people draw down their buffer stock savings. With lower savings rates, the real interest rate rises in the long run, and the village accumulates less capital. To be clear, total consumption is sure to go up, and as a corollary, income is actually redistributed to labor through higher wages at the expense of less capital. But the rise in immediate consumption is a sugar high from being able to use one’s savings now, and does not stick around.

Nor have we been able to find much evidence of the poverty traps which microfinance would solve. A poverty trap is not merely “things are bad”. It is very specifically the idea that if you give people a substantial enough amount of money, they will be able to start building up toward a higher equilibrium on their own. We just have not found it. The story of people restricted by calories, for instance? Outside of maybe active famine, it just doesn’t make sense – calories are so astonishingly cheap now. Kraay and McKenzie (2014) survey with a sympathetic eye, and can’t find anything. It goes to show just how starved we are for poverty traps that a paper showing one example in rural Bangladesh gets a trumpeting paper – nevermind that, as Karlan, Raswan and Udry (2026) pointed out a couple weeks ago, none of the other instances of this program showed the same effect, and the one that does it probably just correlated geography.

The RCTs, combined with the structural evaluations of the general equilibrium effects, marked the end of microfinance as a charity darling. If you cannot beat a simple cash transfer, then you have no argument for existing.

Some mysteries remain. How do we reconcile the ineffectiveness of microfinance in the RCTs with the rate of return appearing to be well over the prevailing market interest rate? Just because microfinance was ineffective does not mean that credit constraints do not exist, or that decisions are distorted due to risk. Perhaps we need not to discard the spirit, but change the letter.

The second part of this article will cover whether poverty traps exist, microfinance with different loan structures, insurance for farmers, the utility of public health interventions, subsidizing education, subsidizing migration, and summing up.

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What this calls into question is the assumption that firms and consumers are rational, profit-maximizing agents. Standard practice across a range of models is to assume that firms are making the optimal decisions given information and costs which we cannot observe, and then to infer what those costs must be in order to rationalize the observed behavior. This is believable when optimal behavior is easy to solve for when costs/benefits are known, even if inference is difficult, but difficult to believe when the problem which must be solved by both firm and econometrician is difficult. Airlines are a demonstrable break of this assumption – as I will show, it implicates a large class of problems.

In particular, antitrust authorities will naturally be interested in regulating the airline industry, and preventing the abuse of market power. But what market power? What do we actually know about the conduct of airlines? How can we regulate an industry when not even the participants know entirely what they are doing? And in regulating an industry to minimize distortions in a static model, do we raise the possibility that we might make the existence of airlines unsustainable?

Rationality is probably the most attacked assumption in economics by people from outside. If you talk to businessmen, they do not say “we generate a forecast of demand given uncertainty, and then choose the optimal course of action”, nor do people choose bananas one day and apples the next as part of deliberate calculation. People describe the decisions they make in very broad, heuristic terms.

Economists defend themselves with a somewhat unsatisfactory two part gambit. The first part is to say that what we mean by rationality is far narrower than what you might expect – that it means nothing more than each agent possessing a complete and well-ordered set of preferences. The second part is to defend people being calculating on an “as-if” basis. People may not literally undertake enormous calculations to find how much to spend on groceries every week, but they behave as if they do. Armen Alchian (1950) famously argued for profit maximization as the result of evolution and natural selection – although I should point out that there is no reason to expect that natural selection should lead to profit maximization over survival.

Dealing with uncertainty and imperfection in decision making is absorbed in the model. If we say that firms are uncertain about demand, we assume they either know the distribution from which demand is drawn, or if we want to be more complicated, they possess beliefs about the distribution and learn over time. A firm persistently deviating from what is implied by rationality is a form of model misspecification. If you want to make counterfactual predictions, it is not enough to know that the firm’s beliefs are wrong – you have to know the exact way in which they are wrong.

It is not a good idea to start by presuming that firms are getting it wrong. But in some cases, they are demonstrably wrong. I source what follows from Hortascu, Natan, Parsley, Schwieg, and Williams (2024), who have extraordinary access to the internal decisionmaking processes of a major U.S. airline. (It’s either Delta, American, or United). They consider only the routes along which the carrier has a nonstop monopoly, to avoid having to care about the possible responses of carriers. Even without competition, they find that the airline could raise revenue by 18% simply by having its various departments work together. A brief excursion, though, on the history of airlines.

Airlines were deregulated in 1978, allowing for actual price competition. Before then, prices and routes were regulated by the Civil Aeronautical Board, a body which existed in practice to hold up fares and prevent undercutting. They possessed remarkably broad powers, which they abused – between its formation in 1938 and its dissolution, they granted not one single new route. With firms unable to alter fares, they competed on frequency and amenities, frittering away the supracompetitive rents on half-empty airplanes. (The CAB targeted a load factor of 55%. By comparison, load factors are now around 85% and have been for years).

There were a few entrants before 1978, but they were restricted to running routes within states. Notably, Southwest Airlines ran routes around Texas, often at half the price of routes between states. After deregulation, fares plummeted and many new companies entered as fast as they could.

This is in spite of the fact that airlines are a notoriously bad business for investors. I suggest Warren Buffett’s comments on the airline industry as extremely entertaining reading along these lines – he characterizes airlines as a bottomless pit into which investors shovel money out of misguided optimism. And it is a tough business – one puts out large capital outlays to buy the aircraft, but then has small marginal costs to either enter a new route or to sell an additional ticket. After considering the cost of capital, airlines seem to have actively lost money. I had Claude plot out profits over time. Even in the best times, they’re only getting a 4% margin, and they get obliterated by disasters.

It is partially for this reason that so many airlines have gone bankrupt. I should note, though, that bankruptcy is not as serious as one would think. Employees are governed by the Railway Labor Act, and you cannot renegotiate contracts in the event of a negative shock to demand without bankruptcy. It’s really more of a negotiating device, and all of the major airlines have done it at some point.

As stands now, there are three major carriers, United, American, and Delta, which operate across the country, plus Southwest, which is the largest of the low cost carriers (although it is increasingly becoming like the major carriers). Alaska Airlines is a quarter of the revenue of the major carriers, and then there is a tail of low-cost and ultra-low-cost carriers. The business models differ, where the major carriers focus on offering higher quality service, combined with rewards points through their own credit cards in order to make it harder to switch. The low cost carriers differ by unbundling every component of the flying process, and charging a fee for each of them.

The airline sets the network, then a menu of prices, then estimates demand for each of the fare classes. The network is generally of a hub-and-spoke form, with a few central nodes of the network branching out to many destinations. This has numerous advantages, the biggest of which is that it makes many flights possible. There isn’t enough demand to offer a flight from Boise to whatever the 50 different cities passengers from there want to go to, but there is enough demand to put them on a flight to Denver, and then onwards to whatever their destination is. Hubs also make it easier to repair all planes in a central location, makes it easier to hire crew (because they can guarantee a return to one’s home city), and makes a network more resilient to disruptions. If you recall the 2022 Southwest holiday meltdown, that was on account of Southwest running point-to-point flights. When flights were grounded in one airport, it caused a cascade of cancellations in all of the airports which they were due to fly to. It is my understanding that activist shareholders are seeking to make Southwest like the other airlines, which is why they have recently gotten rid of the unusual features like free checked bags and unassigned seating. Later in the article, we will be able to put explicit numbers on the economies of density from hubbing.

Given a network, optimizing which aircraft go on which routes, the schedules, and crew are solved algorithmically, the details of which I am not particularly interested in. Hortascu, Natan, Parsley, Schwieg, and Williams take the network as given, on the grounds that the adjustment process is slow. The network is chosen as marginal additions to an existing network, rather than a complete redesign. You consider what the likely demand for the flight is from the distance and size of the cities, and what the frequency and quality of other competitors on the route is. As far as I can tell, though, this is done remarkably heuristically. Routes are added as part of large initiatives, not as detailed optimization.

With the network, the pricing department chooses a set of fares. These are buckets for fares to be allocated, which the revenue management department does after forecasting demand. They assume that it is low-willingness-to-pay consumers who arrive first, with willingness-to-pay rising as we get closer to the day of the flight. This corresponds to leisure travelers being much more flexible over both when and where they travel, while business travelers have their itinerary taken out of their hands. As the tickets are sold, the price of the remaining tickets increases, and as we get closer to the date of the flight, the prices are also hiked.

In the simplest case, suppose that we have two classes of tickets, high and low. In that case, we want to be indifferent between selling a ticket now at the lower price, and holding back the ticket to sell at the higher price. It’s just like sliding down a demand curve until marginal cost equals marginal revenue.

With two classes of tickets, this is the optimal rule. But with multiple classes of tickets, finding the optimum across all of them is too complicated to do, so instead airlines use the EMSR-b algorithm (where EMSR stands for Expected Marginal Seat Revenue). You collapse all of the fares above your lowest price into one fare, then optimize the number of seats at the lowest level given your demand forecast. You then repeat this exercise for the next fare class, and so on until you run out of fare classes.

Explicitly estimating demand like this was a really big deal. Smith, Leimkuhler, and Darrow (1992), in an article crowing about the innovations which they introduced at American Airlines, credit it with yielding at least $500 million a year in revenue. And when we trace out load factors – the percentage of seats filled – we see that they grew steadily ever since deregulation began, until holding steady around 80% since the 2000s.

The algorithm itself is not optimal because it collapses all of the information of higher tiers into a single number, but it’s very close to optimal. The far bigger problem is that it does not consider how customers with a higher willingness-to-pay will buy the cheaper tickets if they are available. The model assumes that all of the low demand consumers arrive, and then all of the high demand arrive. If they arrive at the same time at all, then you are unable to see how protecting more seats will raise revenue. If you simply estimate demand like this, you will underestimate the true willingness-to-pay, a problem which the revenue management department partially solves by systematically inflating all of their demand forecasts. Further, HNPSW are able to see that the particular algorithm this company uses does not consider substitution across flights, even their own. If there are two flights two hours apart, then selling a ticket on the earlier flight should affect the measure of demand for the other flight.

Perhaps remarkably, these departments are not in coordination with each other, and indeed barely appear to communicate with each other at all. In an illustrative example, the revenue management department persistently assigns tickets to fare classes which do not exist. This is not disastrous, because the fares will default to a different class, but it says something that a stupid bug lasts for two years without any apparent change.

Far more consequentially, though, the pricing department sets its menu of prices largely without the knowledge of the demand estimates for their own product. Their fares are set based upon what other firms are doing, not what they are capable of doing. Remember, HNPSW have restricted themselves to routes where the airline is the only non-stop carrier, so the fares of other firms on other routes is useful only as a vague heuristic.

HNPSW can do better. They possess all of the information the firm does – including, in something of particular importance for this type of good, all of the customers who considered purchasing but ended up not – but unlike the firm, they’re gonna do this right.

Their model has two types of consumers, business and leisure. They arrive over time according to a Poisson process, choose whether or not to buy at the posted price, and depart. They are assumed to be unaware of the number of remaining seats, which prevents needing to consider the level of inventory. They recover the latent demand using variation people stochastically arriving – if you show up 3 weeks before the flight to buy a ticket, sometimes all the cheap tickets will have been bought, and other times cheap tickets remain – as well as shifts at arbitrary dates of the costs. With the demand estimates, you can resolve for what would have been the optimal prices, and the optimal bins.

The prices are set too low. Many of the fares are set in the inelastic portion of the demand curve – in other words, raising the price by 1% reduces the number of tickets bought by less than one percent. If they listened to the revenue management department and repriced, they could raise profitability by 18%. The revenue management department inflating their demand forecasts above what their algorithms actually found is not sufficient to undo the bias, although if they inflated it even more, they could partially offset the losses.

It is important to note that the changes which could be implemented by the firm raise profits, but they do reduce efficiency. While price discrimination, and dynamic pricing more generally, can raise efficiency – Kevin Williams has earlier work showing that it does do this in the airline market – it does not here. The gains are from a firm realizing the market power which it has, and finally exploiting it. It is possible, of course, that there is something in the model which we are not capturing. Given the importance of credit cards to airlines, they may want to maintain brand presence in the public mind, and not reduce the number of seats sold through higher prices, or there may be unobserved costs to consumer goodwill.

Yet, I find it difficult to believe that that is the correct model, and not a model where the firms just don’t know what their optimum is. How else can you explain the persistent lack of communication? How else can you explain the company giving this truly comprehensive data over to the economists, if they do not intend to use this in their work? Firms have to learn about the conditions which they face. The existence of consultants is proof positive that this is costly and not perfect.

A standard method in industrial organization is to, in the absence of knowledge of the costs facing a decision maker, infer what the costs must have been in order to justify the behavior. If firms are not at their optimal behavior already, however, then we might reasonably be concerned our estimates are not stable, and cannot predict much at all.

Some classic studies like this concern the entry decisions of businesses, including airlines, into different markets. Bresnahan and Reiss (1991) show that it is possible to infer something about the degree of competition in markets as a function of the number of competitors, despite lacking any information on price or quantity. In the American West, there are enormous swathes of isolated towns, with no population for dozens of miles. Each of these is their own market – people are unlikely to drive a hundred miles to get their car repaired. We assume that firms pay a fixed cost to enter, and then produce at constant marginal costs. In order to enter, they must charge a markup sufficient to pay back the fixed cost.

When we look at the ratio of population to competitors, we can observe that the first firm requires only a very small population to enter, and that getting the next firm requires more than the former. Each additional firm requires more people to enter than the firm before, although the rate at which these additional people grow slows down. We can infer that market competition must decrease the markup needed to pay back the fixed cost, and that the degree to which the markup is reduced falls as more firms are added.

In Bresnahan and Reiss, firms are assumed to be identical, both in fixed costs and marginal costs. Steven Berry (1992), studying airlines, keeps the identical marginal costs, but allows the fixed cost to vary depending on which airports they already have a presence at. This is of immense practical importance, because of the hub and spoke structure of most networks. We have some practical difficulties, however, which are best thought of as a sequence of problems. First, we now need to care about the identity of firms. We resolve this by first identifying the number of firms that will enter on average, and then imposing a condition on the order in which firms will enter. (In this case, by profitability). There are unobserved shocks to costs drawn from a type I extreme value distribution, which you will recall from demand estimation. The probability that a given number of firms will enter are the combinations of the integrals of the probabilities of each given firm, with which 26 potential entrants easily gives us millions of terms. So, instead we use simulation. We observe the actual number of firms which entered, so for each guess of the cost parameters, we draw a few hundred random draws and see how accurate they are.

Ciliberto and Tamer (2009) extend firm heterogeneity even further. Now, the firms can have impacts on the variable profits of other airlines. What we give up, when we do this, is a determinate equilibrium. Since everybody competed for people just the same conditional upon entering in Berry, there exists only one number of firms; however, in Ciliberto and Tamer, it could be possible for there to exist multiple numbers of firms which are equilibria that no one can deviate profitably from. Put concretely, maybe two small companies have the same effect on other’s profits as one large company, and which prevails is a matter of unmodeled beliefs.

So what we use are called “moment inequalities”, and they’re becoming a workhorse in some of the more involved areas of industrial organization. An intuitive example might come from grocery stores, and whether putting them close together allows them to be more efficient (Holmes, 2011). If we observe how much business opening a store takes from the other stores you own, then the gains from opening grocery stores close together must have been bigger than this. However, the gains must not be so large that you would open up another store. The true value must lie between these points. In Ciliberto and Tamer, the things we are putting bounds on are parameters which deliver the equilibria that we observe in the data.

All of this is predicated on the idea that firms do not make unprofitable moves. But if we demonstrate that firms are systematically deviating from profit maximization, and may make moves that lose them money, where are we left? Unfortunately, I have been unable to make progress on this question. It introduces radical uncertainty about our estimates, but not any clear bias. It might lead on the one hand to too many firms entering and then losing money, or too few firms entering and leaving money on the table. The only bound that comes to mind is a bankruptcy bound. As Gary Becker (1962) showed, you can get market outcomes without utility maximization, but it’s going to take you a very long time to get there.

Antitrust policy in the airline market has been in the news lately. In 2024, the DoJ blocked the proposed merger of Spirit Airlines with JetBlue. Now Spirit has gone entirely bankrupt, and unlike other restructurings, this one is for real. It’s not coming back.

The argument behind the blocking of the merger was that Spirit was an important “maverick” which held down fares everywhere by threatening to take the bottom of the market, even if they don’t actually enter. There is evidence for this, largely from Southwest. Goolsbee and Syverson (2008) showed that Southwest caused fares to decline once they began serving two airports, even before they began flying the route themselves. For instance, if they fly from Dallas Love Field to Cleveland, then opening a route from Dallas Love Field to Washington Dulles causes fare from Dulles to Cleveland to fall, before they actually enter the market.

I do not have a definite answer to whether the merger should have been allowed or not. I certainly don’t have a general answer to antitrust actions in the airline sector. But this is because no one really does. Not even the airlines know what optimal behavior looks like. How could the government possibly know?

This need for caution is especially strong in the other main area of interest for antitrust authorities, collusion. We broadly think that firms are not setting their prices as low as they could go. With fares and details being public on homogenized goods, the conditions are certainly ripe for it, and we do indeed have substantial circumstantial evidence.

There have been some papers formally testing the “conduct” of the airline market. That bit of jargon, “conduct”, is the way in which firms compete with each other. More technically, it’s a matrix of values that spits out marginal costs given prices, quantities, and the demand curve. If firms are colluding with each other, that means they are pricing as if they placed a weight on the profits of other firms equal to their own. The current method is this: we take the demand curve, the estimation of which we will skip over. Given some model of conduct, the marginal costs must be x, y, and z. The markups are thus price minus marginal cost. You possess some set of instrumental variables which shift the markup, but are uncorrelated with marginal costs. If your model of conduct is wrong, the marginal costs will be correlated with the instrumental variables.

I am not, however, terribly enthused by the prospect of testing conduct in the airline industry. Here’s the problem – conduct is going to be correlated with demand shocks, and this holds under many conditions. Suppose that firms are not able to directly bind themselves to colluding through a contract. Instead, they can do so only with a Green and Porter (1984) style punishment strategy. The idea is simple: if you can’t monitor the output of the company you’re competing with, you’re unsure whether a fall in demand for your product is due to demand falling, or due to the competing company defecting on the agreement. So, whenever demand falls, you go from colluding to the default competition. At the other extreme, when they can perfectly observe competing firm output as in Rotemberg and Saloner (1986), defection occurs during booms, because the gains from cheating are larger. Either way, your conduct is going to be bound up with changes in the demand curve. This definitely wrecks the old-school method of measuring conduct, which is to measure the conduct parameter theta as a multiple of the maximum price possible. Even for modern methods, it implies that we cannot summarize the result of a dynamic game as a single conduct parameter.

The best work takes this seriously, but in doing so they limit what they can say. Ciliberto and Williams (2014) cannot say anything about the level of collusion, but they can say that there is more collusion as firms have more contact with each other across markets. This fall simply out of the Green and Porter story, because being involved across more markets increases the amount that one can be punished for defecting.

There is also circumstantial evidence. For instance, the airlines seem to communicate with their competitors through earnings calls. When everybody talks about the need for “capacity discipline” in a particular market, Aryal, Ciliberto, and Leyden (2022) show that the number of seats offered in the next period falls by 2%. Notably, this only happens when all of the carriers talk about it, and there is no unilateral fall in capacity when they are the only ones doing so.

The mandate of the antitrust authorities is clear. Collusion is illegal under the law, whether or not it involves an explicit agreement. But, in principle, should we always try to restrict collusion? Airlines seem like an example of an “empty core” game, where there could be no stable market. David Oks recently argued this, in an essay which inspired this whole choice of topic. Firms may enter in the expectation of being able to collude later, and if we restrict this, we lose out on entry.

An easy way to see why this might be the case is to observe that later entrants do not enter where demand is low. They enter where demand is high. But how do they know that demand is high? Well, they know it because one of their competitors took on the risk of entering when demand conditions were unknown, and now find themselves charging high prices. Not enough firms will enter, because nobody wants to be the first one to move. (I realize, after consulting with Claude, that I have reinvented Chamley-Gale (1994) from first principles). This is how the Civil Aviation Board was justified. I don’t think that those justifications were born out, but it does suggest that perhaps a little collusion need not be so bad.

The new big thing in airline pricing is using steadily improved algorithms to set prices. There has been much recent work on “algorithmic collusion”, and the pretty robust conclusion is that multiple algorithms will converge on supracompetitive prices, and even “dumb” human players can be forced to go along with the higher prices, if algorithms can change prices faster than humans can (Brown and MacKay, 2026). The Department of Justice is interested in pursuing cases against their use. Should they do so? I don’t know. But with so much uncertainty over what is optimal, and knowing that profits tend to induce entry and innovation in the long run, we should perhaps be less eager to intervene.

I should substantiate the claims about traders in Kenya, lest I be accused of libel. In Kenya, as with much of East Africa, corn is a staple crop. It is sold to the consumer in bulk with the kernels removed from the cob and dried, to be ground into flour when needed (flour does not keep as long as the kernels do), or simply boiled and served in another dish. Farmers do not sell directly to the consumer, but to intermediaries, who then bring the corn to market. Entry is constrained by the high cost of trucks – buying one takes 21 times annual per capita GDP, and simply renting one for a day would set you back $250, or 18% of annual income. Everybody knows everyone else, even when they might visit multiple markets.

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The conditions are certainly ripe for collusion. There are no publicly posted prices, and everything is done via negotiation. Nevertheless, these negotiations are public, and everyone can hear what the prices you offer are. The ability to secretly deviate and undercut your rivals is anathema to collusive cartels. They would prefer everything out in the open. Read Genesove and Mullin (2001) on the sugar cartel – what held it together was not explicit collusion on prices and quantities, but obsessive rules on standardizing the product and making it impossible to give secret discounts.

We face a difficulty, however: estimating “conduct” — which is just the way in which firms are competing against each other, or perhaps colluding — is normally very difficult with observational data. Most studies in industrial organization do not attempt it. Suppose that you have estimated the demand curve, at considerable effort. In order to recover the degree of market power which firms have, one needs the marginal cost of producing an additional unit. The marginal cost and the mode of conduct are not separately identified – for every mode of conduct, I can give you a marginal cost which justifies it. The normal method, then, is to assume the mode of conduct, and spit out the marginal costs and markups that way.

In principle, however, the form of conduct can be identified with an additional exogenous variable. You have one exogenous variable shift the supply curve along the demand curve, which traces out its shape; and the other exogenous variable rotates the demand curve. You might get this from something like the entry of an alternative good which makes demand more elastic now that there is a close substitute available. With the demand curve rotating, firms which are colluding or otherwise charging a markup will increase the amount they supply, while firms charging at marginal cost will see no change in output.

The original implementation, due to Timothy Bresnahan, doesn’t quite work if firms are colluding on a price which is not the joint profit maximizing price. This can be reached quite easily, if the firms are colluding through a Green and Porter (1984) style strategy where they revert back to competition whenever they detect a decrease in their demand. This muddles matters, and biases the conduct parameter to perfect competition.

The modern method is due to Berry and Haile (2014). Rather than estimate a single conduct parameter, you can test particular models of conduct, and see if they deliver the behavior necessary for them to be correct. If your model of conduct is correct, then after subtracting out markups, the marginal costs must be uncorrelated with another set of instrumental variables which you did not use in estimating demand, like demographics. To see it put in action, read Backus, Conlon, and Sinkinson (2021).

Lauren Falcao Bergquist and Michael Dinerstein (2020) run a beautiful series of experiments to systematically pin down everything you would need to know about the markets. First, we are going to estimate passthrough by giving traders a per unit subsidy. There are three groups, corresponding to no subsidy, a low subsidy, and a high subsidy. Only around 20% of the subsidy is passed on to the consumer, and perhaps remarkably, this holds no matter the size of the subsidy, the number of traders in the market, or the degree of market access (proxied for by things like whether the roads are paved).

We can rule out pure price competition (Bertrand competition), which would imply 100% passthrough of the subsidy. We can’t separate out the type of imperfect competition without knowing the demand curve, though. For any given passthrough under a monopoly, increasing the curvature of the demand curve to make it more concave could replicate it under partial competition.

So Bergquist and Dinerstein have a second experiment, where they manipulate the price that consumers face directly. Consumers negotiate a quantity at a given price, then the enumerators of the experiment come along and draw a random subsidy. The consumer is then free to choose a new quantity at the new price (with the seller having agreed in advance to not revoke the agreement and try to renegotiate). Tracing out the demand curve, competition where traders choose the quantities they will bring to market, and then choose price (Cournot competition) would imply a pass through of 46%, comfortably outside the 95% confidence intervals. Instead, the pricing behavior is essentially indistinguishable from a perfect monopoly.

So what can we do about it? The obvious thing would be to encourage entry. Perhaps someone who is not privy to the collusive arrangement would cause the whole thing to break down. We are also uncertain whether the markups represent something necessary to make back the genuinely high fixed costs, or whether they represent excess profits extracted from the consumer.

So Bergquist and Dinerstein test this. They offer traders money to go to new markets. The take up rate – which is altogether low – allows us to infer the fixed cost to entering a new market. Then, we can look at how prices change. Strikingly, if the traders were already familiar with the new entrant, there is no change in prices. It is only when the traders were unfamiliar to the existing traders that prices are impacted.

We know that intermediaries possess considerable market power in Africa. Atkin and Donaldson (2015), in an extraordinary feat of data collection, collect detailed prices on homogenous branded goods as one gets further away from distribution hubs. When prices fall at the port, that doesn’t mean people inland see the gains. It’s getting absorbed by the intermediaries. What Bergquist and Dinerstein are able to do is finally understand why.

We sadly lack a lot of evidence on collusion, as opposed to more generic sources of market power. I know of only one other study credibly measuring conduct – Garima Sharma’s working paper on Indian textile mills, who proposes some heuristic methods of determining collusion along the lines of Bresnahan, and then validates it with the “full-IO” approach.

She is working with data from Indian textile mills, where she has uncovered a startling regularity. Members of the Tirupur Exporters’ Association pay their workers exactly the minimum wage. Not around the minimum wage – because deviations below what is legal are ubiquitous, this is possible – exactly the minimum wage. She argues that this is due to the members of the association exerting pressure on each other to hold the line on the wages. Like with intermediaries in Africa, this is a place where entry is constrained. It is notoriously difficult to hire and fire workers in India – for example, if you have more than 100 employees, you need to get government permission to change hours, wages, or employment status. It is difficult, then, to profitably defect from existing arrangements.

Sharma has a simple test. Under any form of earnest competition, a shock to the demand for a competitor’s products will increase their demand for labor, reducing the number of people that you are able to hire and forcing you to increase wages. If you were previously in a collusive agreement, however, wages rise, but so too does employment. Because these textile plants are generally producing for one single major firm, like Nike or Zara, a change in the demand for those particular brands creates a demand shock that is genuinely idiosyncratic.

Naturally, the firms are colluding with each other. Positive demand shocks increase employment and wages, before the wages eventually settle back down around the minimum wage as the collusive agreement is re-established.

I suspect that this sort of collusion is common. Humans are social creatures, who are capable of sustaining cooperative agreements within their community. Many contracts are not enforced through law, but through social pressure and norms. What breaks it down is “capitalism” – trade, globalization, market access, anonymous profit-seeking by alienated individuals. All this is good.

It leads one to believe that the gains from trade are understated. The normal way to quickly estimate the gains from trade can be borrowed from Arkolakis, Costinot, and Rodriguez-Clare (2012) – all of the standard models, whether Eaton-Kortum (gains from comparative advantage) or Melitz (gains from reallocating to more efficient firms) can be summarized by the share of domestic expenditures, raised to the elasticity of trade with respect to costs. The key to their equivalence is that markups are a constant proportion of marginal costs. Having trade make collusive agreements unsustainable breaks the ACR equivalence. The gains from trade can be much larger than they would appear, because they are really the gains from modernity.

A lot of people dislike this. They believe that college should be strictly ordered by merit. This is bound up with affirmative action and racial preferences – the people on twitter who advocate for this tend to be right-wing and think there should be more Asians and Whites instead of Black people in elite colleges – but there is a genuine belief that college admissions should be more objective. For instance, the SAT should not be top-coded, but should instead ask harder questions to distinguish between students; and admissions committees should have much less power to consider soft criteria from hard evidence of academic capability.

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This article will teach you urban economics from the beginning to the very cutting edge. We will first cover the foundational models of spatial general equilibrium, then show how developments first developed for the study of international trade gave them empirical relevance. We shall then take a tour of all the wonderful things you can do with quantitative spatial equilibrium models, and conclude with what policy lessons they have for us. In particular, I believe that we should spend more on all forms of transport infrastructure, including and particularly highway infrastructure.

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The first model of economic activity in space is that of Heinrich von Thunen’s, way back in 1826. In Paul Samuelson’s view, von Thunen’s “The Isolated State” was a tremendous achievement – containing the first articulation of a general equilibrium model, the birth of marginalism, and much modern trade theory – and places him in the “inner ring of Valhalla” alongside Walras, Mill, and Smith. Mr. von Thunen was an autodidact, who worked out his ideas over many decades while working as manager of land in Mecklenburg. Much of the book is concerned with practical matters of cultivation, and his better remembered theoretical contributions to economics were made in the effort of making actual empirical predictions. Nevertheless, we shall skip those. (I say this only to note that I came away extremely impressed with his work while doing research for this post). While he was one of the first to use calculus to derive equilibrium (the first?), its essentials can be understood without algebraic encumbrances.

Imagine a town upon a flat, featureless plain (or perhaps plane). Farmland extends in a circle around the town, allowing us to only care about one measure of distance, and can be used to produce grain. Meanwhile, in the town, people may produce cloth. Everyone has identical, homothetic tastes for grain and cloth – for simplicity’s sake, each person prefers half grain and half cloth. People may locate themselves wherever they may. Grain is produced as a function of land and labor, with decreasing marginal returns – each additional person on a plot produces less grain than the person added before him. Finally, trade is costly and is a linear function of distance. (Samuelson notes that this prefigures his device of iceberg trade costs, by imagining that the oxen eat the grain which they are being used to transport).

So that is the setup. This delivers a striking prediction – in equilibrium, the marginal utility of living in any given place must equal that of every other place. The further outside the town you get, the more expensive cloth becomes. To live out there, one must have a higher wage in grain. To get such a wage, the population has to be correspondingly thinner. In the limit, the rent falls to nothing, and there are no people. Further, and remarkably, prices, wages, rents, and population densities are all uniquely determined by the ratio of grain to cloth inside the town.

You can extend this by having multiple types of crops. For example, you might have vegetables that can be grown for personal consumption, or transported at a much higher cost. The only place where they can be economically grown as the only good is close to the town, where they are traded for cloth on the one hand and grain on the other. Further away from the city, we have a region of grain and vegetables. We must be precise about the production technology – to get the specialization we intuitively expect we would have needed to say something earlier in the model – but you get something which broadly matches the use of agricultural land around a city, especially in pre-modern times.

Later models of the city keep the circular setup. In the Alonso-Muth-Mills model, production occurs only in the center. The question is where people reside, and how large their residences are. The same basic principles apply – all people commute to the center, paying a linear cost to do so, and so in order to balance the marginal utilities across all places, the price of housing must decrease as you get further away. When we extend it to different types of production, then we get sorting of uses depending on how important it is that companies be close to other companies. It predicts commerce in the city center, manufacturing in a ring around the outside, residences in another ring, and then back to agriculture further out.

This leaves open the question of why the city exists at all. The standard answer is an agglomeration force, where being nearer to other people allows for cheaper production. This naturally makes us wonder why we do not then all collapse into one mega-city (or perhaps a black hole), and it is that which Henderson (1974) answers. The force of agglomeration must be balanced out by congestion. We are at equilibrium when the congestion forces people out of the city into others. You can thus explain the existence of multiple cities. Its main empirical prediction is that cities will be too large, because each person moving does not consider the congestion externalities they impose on others, and no one is individually incentivized to create a new city.

We have left it vague what this agglomerative force is. Paul Krugman (1991) is an incredibly elegant explanation for this and where economic production will be located. It is, along with the Alonso-Muth-Mills model, one of the only two models which Ed Glaeser required Harvard Ph.D. students to be able to reproduce from memory, equation by equation. We will, as before, go in less detail than that, but pay attention.

There exist two regions, A and B, and two sectors, agriculture and manufactures. Agriculture is a homogenous good, while the manufacturing side consists of many goods. Each firm produces one good, paying a fixed cost to enter, and charges a markup over marginal cost. The consumer benefits from having more goods. (This device – Dixit-Stiglitz preferences – was earlier used by Krugman to explain why trade often occurs within industry, rather than according to what would be predicted by comparative advantage). The degree to which consumers care about gains from variety is given by sigma σ, and the share spent on manufactures is given by mu μ.

Agricultural workers are spread thin over both regions, and cannot move. Meanwhile, manufacturing may place itself wherever it may. Trade within a region is free, while trade between regions faces a cost τ, which is the fraction of goods shipped which survive the journey.

There are three forces which affect where firms will decide to locate. Two press for concentration: as a manufacturing firm moves to a region, the workers they bring with them demand more products produced in that region, making locating there more attractive to manufacturing firms. And likewise, as more firms locate in a region, workers locating there will find themselves able to buy more. What holds back the snowball is the competition for the rural peasantry.

If transportation costs are zero, then manufacturing can be located anywhere; as we start turning on transportation costs, it would take a very low share spent on manufactures μ, or very low scale economies from σ, to have firms be dispersed. As it continues rising, eventually the losses from manufacturing only happening in one region are too high to be ignored, and firms will disperse themselves to sell to the peasantry.

Now, where will manufacturing firms place themselves? We actually can’t say. What we can test is whether a given arrangement is at equilibrium or not – whether individual firms, if they were all placed in region A, are incentivized to move to region B. Unfortunately, this makes these models unable to make the jump to empirical work for exactly this reason. It is very difficult to sort out how much of the value of a place is due to the natural amenities of living there, versus the gains from having other people located there already. Consider that if all of the firms being in region A is an equilibrium, then so too are having all of the firms in region B!

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The empirical work which we did see took the economic geography literature more as inspiration than blueprint. Some of this work is quite excellent. Davis and Weinstein (2002), for instance, is able to make some real progress on whether cities exist where they do because of the natural amenities or because of agglomeration by using the bombing of Japanese cities during the Second World War. Since the cities remarkably returned to their former rank ordering by size after being unevenly obliterated, it suggests that the natural features of the city were of primary importance for the relative size of cities. On the other hand, several studies show how arbitrary events of history lead to permanently altered locations of cities – e.g. Bleakley and Lin (2012) on East Coast cities being located along river rapids which formerly necessitated cargo being unloaded but are now irrelevant, or Michaels and Rauch (2018) on how the total collapse of the Roman state in Britain allowed cities to reset to being on waterways rather than on old Roman roads, while in France they remained stuck in the wrong locations. Without a universal answer, it is difficult to get even broad policy prescriptions. Krugman saw his model as telling the story of how manufacturing in America was at first dispersed when transportation costs were prohibitive, then concentrated as they fell, then dispersed again as they fell still further; but this is economic theory as a parable.

We don’t want parables. We want to actually estimate things. And so that brings us to Ahlfeldt-Redding-Sturm-Wolf (2015).

ARSW take Eaton-Kortum (2002) and apply it to city blocks instead of countries. I have already exhaustively discussed the problems which Eaton and Kortum were solving several weeks ago on the blog; we will thus have only an abbreviated coverage. The trouble with trade is that there are too many varieties of goods. Finding exactly which goods are traded by who and for what other goods depends upon the prices and quantities of every other good in every other country. This is not feasible to calculate, much less get data on. Instead, we abstract away from the specific goods, and have each country draw their productivity at producing a good from a Frechet distribution. The reason for assuming this very particular distribution is that if you take a bunch of draws for a bunch of countries, the distribution of the least cost producers is itself a Frechet distribution, even if countries have different levels of productivity. This property lets us cleanly add together results, which makes the computations necessary possible.

We observe even less about why people choose to reside in some blocks and work in others, so the abstracted approach is particularly useful. There are a lot of symbols, and everything in this will look more intimidating than it actually is.

Each worker has utility for each pair of residences and workplaces. They receive a household amenity B for their residence, multiplied by a wage w. This is divided by the residential floor price, raised to 1 minus the share of expenditures on housing, multiplied by the cost of commuting between the two pairs. This gives us a probability of choosing a given pair which is this, raised to the power of the shape parameter ε. (This gives us the variance in idiosyncratic utilities). When they commute to their job, they produce a single good through a constant returns to scale production technology, with the productivity allowed to vary by block. This productivity is dependent both on the production fundamentals, and on agglomeration externalities.

We observe how many jobs are in each block, as well as how many people live in each block. We observe the price of a square foot of housing in each block, and we observe how much land and space there is. We calculate – in their case, from detailed maps of public transport – a matrix with the time to travel between each of the city blocks, and the commuting flows between each residence and each place. We can use this to calculate the implied cost of commuting. This last step, the gravity equation, is based around how people will trade more with closer-by places, and with more productive places. It is also the most sensitive to specification choices by the researcher – there is no a priori reason to expect a linear, quadratic, or some higher order polynomial fit for people’s preferences over travel time.

What we do not observe are the wages (and thus, income), the externalities from having more residents around, the natural amenities of living in a place, the agglomeration externality which affects production, the underlying productive capacity of each block, and how much floor space exists in each block. Perhaps remarkably, we can recover all of these unobserved parameters like a zipper, one after the other.

1. The wages in each city block have to justify the commuting decisions of people. There exists one vector of wages which clears the market. The reason this works without knowing what anything else is is that once you fix the residence, someone’s choice of workplace is dependent only on the wages and the cost of getting there. Computing the real income of a place, and the value of the jobs someone has access to from every given place, follows simply.

2. Now with the wages, we can find the combined values of the externalities from residents and the fundamentals of living in a place, and the combined values of the production externalities and the production fundamentals. We need an exogenous shock here which shifts density without changing the natural features. Once we have this, we can see how much people and production shift, and infer the value of the externalities; the locational fundamentals are whatever is left over.

3. Given the value of being in a place implied by everything we’ve found so far, and given our observed floor prices for housing and commercial buildings, we can infer the amount of floor space needed to justify the prices. This step here is often one which we can validate, by comparing to known measures of housing stock, but it is not necessary.

ARSW uses a particularly convenient exogenous shock – the partition of Berlin into East and West by the Berlin Wall – which makes it simpler to figure out exactly how many blocks one should include into the matrix. Their main result you can see (if you squint a little) from a map of land prices. The Berlin Wall cut through what was once a serious commercial center; the part that was left in West Berlin ceased to be a major commercial center, and economic activity drifted over to the now more centrally located western parts. This is the same result, in miniature, as Redding and Sturm (2008) found – the cities along the border now had worsened market access, and less economic activity.

The need for a believable exogenous shock is a bit of a constraint on doing this approach right. If you’re willing to believe it, though, you can simply plug in the estimates from other cities and get the fundamentals that way. Many studies, in fact, simply take the estimates from ARSW and call it a day, and everybody who estimates the elasticities defends their estimates by pointing out how it’s similar to what ARSW did.

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Still, concern over circularity in the parameter estimates aside, the full general equilibrium model is a substantial improvement over the prior reduced form studies mentioned earlier. Consider the case of Japanese cities. Davis and Weinstein (2002) argued that Japanese cities returning to their prior relative status, despite some being destroyed and others left unscathed, is evidence that the location of cities is driven by the locational fundamentals. Using a more modern approach, though, Kohei Takeda and Atsushi Yamagishi (2025) argue that, at least in the case of Hiroshima, the city returning to its prior shape was simply one equilibrium of many. People simply expected for the city to reform, and so it did.

You can then use the full model to evaluate counterfactuals. The most exciting set of counterfactuals, to me, are those that involve the evaluation of transport infrastructure. Questions which simply quantify the effects of a prior change are relatively uninteresting to me, because they do not suggest an obvious lever which we should press upon. I thus skip over such excellent studies as Heblich, Redding, and Sturm (2020), who show that the steam engine and railroads were absolutely essential for the growth of the city of London, or Donaldson and Hornbeck (2016) who show that the railroad was essential for American agricultural growth.

There are two ways of going about computing a counterfactual. The first, the “covariates approach”, is what we did earlier with Ahlfeldt, Redding, Sturm, and Wolf. You completely solve the model, estimate how the event would change the travel time matrix (and possibly change the amenities directly), then resolve for equilibrium.

The alternative approach is called “exact-hat algebra”, after the little “hats” which denote variables representing a change in underlying variables. Rather than completely re-solve the model, you rewrite the outcomes as a function of the things you change, then get out the changes in the outcome variables.

These two methods represent opposite ends of a bias-variance tradeoff. The drawback of exact-hat algebra is that, if you have a sample which is too small, then random measurement error from the small sample will bury anything of substance in your data. The drawback of the covariates approach is that any misspecification in the gravity equation passes through to the model outcomes. For urban contexts, the covariate approach is better, largely because any pairs of blocks with zero flows break the model. You can’t multiply it by a change in variables because it will still be zero no matter what, as Dingel and Tintelnot (2026) point out. I am going to skip over the details of dealing with this as too in the weeds even for this blog, but Bas Sanders (2026) gives a general framework which can nest the solutions Dingel and Tintelnot propose.

(Attentive readers will note that this tradeoff between bias and variance is similar to the tradeoff between nested fixed point methods and conditional choice probability methods in discrete choice models, as we covered earlier. I am also under the impression that local projections and VARs are similar, although I know very little about that area).

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An excellent study evaluating infrastructure with a full ARSW model is that of Nick Tsivanidis (2026), who studied the implementation of bus rapid transit in Bogota, Colombia. Methodologically, the main advancement is the use of sufficient statistics – quantifying the welfare gains when the change has already happened is a simpler task than forecasting the future benefits. You can just make an exogeneity assumption for the exact routing, supported by planned routes that fell through not growing, and get the welfare effects from changes in rents, residents, employment, and commercial rents. You can also get the sufficient statistic elasticities from other cities, if you’re willing to believe that, or extrapolate from experiments in other parts of the city.

Turning to the results, the bus system can explain somewhere between 3 and 14% of the GDP growth of the city, and 30% of the population growth, well exceeding the cost of building. If we had used better models to guide where the networks were placed, it would be possible to increase welfare by 44%, holding the resources spent constant.

Conventional measures of the value gained would badly understate things. In an efficient economy, and when the change in infrastructure is sufficiently small, the gain is approximated by the number of commuters times the amount of time saved times the value of the time saved. If you are familiar with standard supply and demand diagrams, there is a large rectangle under the demand curve when the supply shifts. That is the gain to the people who were already using it, though – standard approximations are unable to take into account how people change their commuting, residence, and production decisions in response to the infrastructure change. You absolutely need the full model.

In contrast to bus rapid transit, Chris Severen’s study of the Los Angeles metro finds that it is a massive waste. Annual benefits are a bit over a tenth of the annualized costs, and even adding in reduced congestion (for which there is substantial quasi-experimental evidence from when the LA Metro workers went on strike – see Michael Anderson (2014)) does not get us close to covering the costs. LA is not a very good city for transit, which works better when there is one central business district to which the routes can point, and the routes were placed such that they affected only 2% of the population. One hopeful note for urbanists, though – if places near urban transit had been allowed to build up by just 10%, the gains from the Metro would have doubled.

The main difficulty for evaluating these models is the commuting flow data. The United States has LODES, but you cannot expect to get it in the developing world. This is particularly bad when it is the developing world which might expect to see bigger gains from program evaluation. We have a few ways around this, the most promising being cell phone data. Some of the studies which we will cover in the forthcoming sections use extensive cellphone data in slightly different models. It can also support extensions of the model which are otherwise impossible – for instance, Miyauchi, Nakajima, and Redding (2021) allow for people to take multi-part itineraries, and show that it better predicts the observed impact of a subway line.

Also, Ahlfeldt, Redding, Sturm, and Wolf (2015) are not the last word in estimating infrastructure counterfactuals. As we zoom out, we can go from evaluating infrastructure within a city to evaluating infrastructure between regions. We will drop evaluating pairs of residences and businesses, and instead have people choose a region to live and work. Treb Allen and Costas Arkolakis (2014) establish conditions for a unique equilibrium (agglomeration must be small enough, or natural advantages large enough – when we are considering large regions of the United States, having one equilibrium is far more believable than city blocks. Put formally, the spectral radius of a matrix is less than one) and evaluate the buildout of highway infrastructure in America. It more than paid for itself. Allen and Arkolakis (2022) add in traffic congestion, and allow you to evaluate the gains from any single link – again, highways are extremely worth it, although there is variance from link to link.

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There is one final type of paper which we are going to cover, which goes beyond solving for marginal changes in the infrastructure system and finds the overall optimum. Fajgelbaum and Schaal (2020) is a critical paper in this literature. With convex costs of shipping – in other words, congestion – we can guarantee that investments into capacity along the existing network have a single optimum. They argue that the EU has substantially underinvested in highway links across cities and regions.

Kreindler, Gaduh, Graff, Hanna, and Olken (2023) set themselves the task of finding the optimal public bus network in Jakarta, the world’s largest city. With buses, unlike with trains or even bus rapid transit routes, we are much less concerned with finding the value of one additional link, and can completely reshuffle the lines however we want. They possess data from cell phones, showing where people commute, along with tap cards showing willingness to pay for different fares. They use changes in commuting costs from new bus routes opening, frequencies being changed, or prices being hiked, to infer consumer demand. When it comes time to pick the best combinations of routes, they cannot hope to find the single best model, so instead they have the social planner try to choose a network that maximizes utility subject to an idiosyncratic shock. It is worth pointing out that finding the single best transport network is often not necessary, because we can at least compare all of the proposals, and then choose the best one.

It is difficult to say what generalizable lessons we can draw from one particular city’s bus network. Their results push us to prefer bus routes which serve a wider area, even at the expense of wait time, and that there should be fewer buses in the center city where there are already enough buses to keep wait times low. However, this may be the case in a poor, developing country, while not the case in a richer one.

Two final studies. Olivia Bordeu (2025) and Yuyang Jiang (2026) both show considerable distortions from optimal transportation networks due to divided governments. The local governments care less about residents of other towns than they do their own constituents, leading them to underinvest in transport links which serve mainly to ferry goods and passengers through. (Although I note that whether municipalities would over or under invest is not determined a priori – while the municipalities don’t gain from between town links, they do gain from within town links that serve to draw taxpayers away from other municipalities). Otherwise identical routes which pass between towns or states take substantially longer than those which are entirely contained within the municipality. Bordeu estimates a full ARSW model for the city of Santiago, skipping over some of the less exciting parameters by adding in parameters estimated elsewhere, and finds large gains possible from centralizing. Likewise, Jiang estimates that leaving highway building in the hands of the states causes a welfare loss equal to 30% of the total spending on the highway system, and an underinvestment of 15%.

These studies differ widely in what they study and how they study it. The only consistent throughline is this – we invest too little into transport infrastructure. The standard methods of infrastructure evaluation tend to underestimate the gains from investment because they do not take into account that people can adjust.

Most people on twitter would likely interpret this as a call for more investment into trains. I would like us to not get stuck on that. Highways are, by any measure, a consistent improver of welfare. We must not lose sight of the fact that, while it may be perhaps unfair that highways are subsidized at the expense of rail systems, they are nevertheless extremely good. In fact, the only study we covered on contemporary rail investments found that it was a terrible waste.

Finally, the status quo of infrastructure evaluation is lagging behind what is possible. This is not like antitrust, where tight time constraints require implementing simpler models. Infrastructure takes a notoriously long time to develop, and is planned for years. We do not have to restrict ourselves to multiplying the number of commuters and the time saved. We can fully evaluate how people will reallocate themselves across space.

But the rot runs deeper. Everywhere I look, I am unimpressed by the candidates on offer in serious races. In the California gubernatorial race, the crowded field ended up settling around Xavier Becerra, who is notable only for being Hispanic and an intellectual lightweight. Patrick Wolff, who I endorsed, looks likely to get no more than 10%, despite being obviously more competent than everyone else. And this is, of course, even more so the case for congressional Republicans, whose election of Andy Ogles guarantees that Platner cannot be the most odious member of Congress if elected.

We seem unable to elect people who will simply be sound, competent managers. It is difficult to believe that electing the boards of management consulting firms or taking a random draw of professors of economics would not get us better policy. Instead, we elect people who, according to Matt Yglesias, just know very little about public policy issues. It’s just not that important a part of their job.

I see two basic explanations for this. First, the supply of competent individuals is constrained. People who have high outside options have no interest in running for office when they could make much more money – with far more security – elsewhere. Second, the low-information voters who might be swayed by crude bravado are much more persuadable than the high-information voters who, aside from wanting competence, also have ideological preferences which keep them from voting for different parties.

But before questioning mechanisms, we should ask if leaders matter at all.

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It is shocking that we do this when a cure exists. With a kidney transplant, none of this is needed. The patient will live a longer, better life, without needing to spend what remains of their life in a clinic chair. It also costs much less – the spending on kidney transplant patients is about about a third of the total spending on patients undergoing dialysis.

The trouble is that there are not enough kidneys to go around. In America, as in most of the world, you cannot buy a kidney. They must be donated by a living donor, or sourced from a recently deceased individual. There is universal agreement among economists that allowing kidneys to be bought and sold, or at the very least having donation be subsidized by the government, would be far better, but people are repulsed by the thought of others selling their body.

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We cannot implement the best solution, but there are ways in which we can do things better. The improvement of kidney donation is one of the most important uses of mechanism design in real life. It has saved the lives of hundreds of people already, and if it is allowed to spread around the world, it could save many more. What’s more, you can participate in this. Your actions can save lives.

The first problem we need to overcome is that people might be altruistic only for one person, but not all kidneys are substitutable. Perhaps someone’s wife would like to donate to their husband, but she is not compatible. This might be because the blood types are incompatible, or because the tissue types cause an immune reaction in the recipient. We can imagine that there are many couples like this. We would like to find a mechanism which pairs compatible people so that everyone can end up with a kidney.

The simplest is to find bilateral trades. However, because of the many different ways in which people can be incompatible with each other, this is no guarantee of anything close to efficiency if one were restricted to only these.

What we can do instead is have an exchange. There are two basic types, a cycle and a chain. The cycle allows for us to resolve loops of people, none of whom are able to make a trade with each other, with the optimal combinations found via algorithms (covered in Ashlagi and Roth (2020)).

When agents are arriving over time, it is possible that waiting longer for agents to arrive enables better matches, at the cost of agents departing unserved because they waited too long. Akbarpour, Li, and Oveis Gharan (2020) show that waiting can be better only if the planner is able to identify who is about to leave, so that they can match them in a hurry. To my knowledge, we are reasonably able to predict how likely a person is to exit the market from their medical condition. However, in practice this concern has not led to different practices.

The drawback of the cycle is the need to do everything simultaneously. The law does not allow people to sign binding contracts to donate kidneys, and so we cannot guarantee that someone will not pull out after their recipient has received a kidney, but before they donate. It is costly to have the capacity to do many simultaneous surgeries. The size of the cycles is in practice capped at three for this reason (eight operating rooms and eight surgical teams in one hospital would be quite a lot). Thankfully, the efficiency losses are negligible when one is only concerned about blood types, although they become worse when we are more concerned about tissue type. In addition, if any part of the cycle vetoes their donor because they believe they could get a higher quality one, the whole cycle is broken and we need to make another set of offers.

This is where a chain of donors comes in. If you have someone who is donating without expecting anything in return, then you can get a chain of arbitrary length which requires nobody to donate before their recipient gets a kidney, and ends only when someone reneges (a prospect which is rarer than we might fear) or when the kidney is implanted in someone on the cadaver waiting list. This becomes more important as people become harder to match.

Were you able to break the simultaneity constraint, outcomes would be substantially improved. If you put recipients whose donor donated a kidney at the top of the queue for inclusion in any future pairings, you could (at least in France) increase the match rate from below 40% to 63%, and reduce the average waiting time by 50 days. But alas, that is not allowed.

There is one big thing for us to do to improve living donor transplantation. There are multiple donor exchanges, which are all largely siloed from each other. Many donations are arranged locally by the hospitals themselves, who do not pass on the information to others. We end up matching too many O’s to AB’s, when they could be used to start a larger, useful cycle. Agarwal, Ashlagi, Azevedo, Featherstone, and Karaduman (2019) estimate that forcing hospitals to share donors to the central exchange would increase transplants by somewhere between 240 and 500 a year.

We can also improve the allocation of deceased donor kidneys. Unlike with living donors, the surgery cannot be scheduled in advance. Someone must be made an offer, decide whether to take it, and do the surgery at the drop of a hat. These offers must be made sequentially – since we don’t have money, and these are not repeated transactions, we cannot use auction mechanisms like Feeding America used for food banks. The combination of sequential offers, plus kidneys degrading in quality over time, means that we cannot guarantee that every kidney gets used, nor that they will be allocated to the best person.

Finding a better way to order the offers of kidneys is what Agarwal, Ashlagi, Rees, Somaini, and Waldinger (2021) set out to do. They have data from New York City and environs, with around 5,000 people on the waiting list. 1,400 people join the list every year, while only 200 cadaver kidneys are recovered. The list is in a steady state only because people are dying before they can get a transplant.

Both the old and new system ranked the patients with points for tissue-type similarity, being a pediatric patient, how hard they would be to match, and importantly, waiting time. This element of waiting time encourages patients to refuse the offer they are given, because they will expect to receive further, possibly better, offers in the future. The mechanism that reduces wastage would be to make it first come, last served, but as we shall see, this is not actually the best.

It is not enough to simply simulate, given the current observed choices, what would happen under a different mechanism. People are strategic and respond to incentives. Instead, we must estimate the demand for kidneys, which they do using a conditional choice probability model in continuous time.

Conditional choice probability estimation usually resides in discrete time. You have a finite number of states, which are simply combinations of variables, and you observe the choices of each person in each state, plus the probability of transitioning forward to any given state. You can therefore estimate the expected value of being in a particular state by simulating forward many times. Discrete time requires you to pick how long the period length is, as well as figure out what happens when multiple kidneys, so instead they operate in continuous time.

With the estimates of consumer demand, we can try out different policies. If we try out the first come, last served policy, we see that it would reduce the fraction of kidneys discarded by a quarter, but create such a mismatch between patients and kidney characteristics that welfare goes down by the equivalent of a 55% decrease in the arrival rate of kidneys.

If you knew each person’s preferences, then you could raise welfare by the equivalent of a 33% increase in the arrival rate of kidneys, while reducing wastage by 14%. (Note that you don’t actually want to reduce wastage by 100% – not every kidney from a dead person is worth implanting, even with the enormous backlog). The optimal one which can be reasonably implemented creates an increase in welfare that is equivalent to an 18% increase in the arrival rate.

Unfortunately, the recommendations do not appear to have been adopted. Perhaps they were too complicated – they cannot be summed up as a set of simple rules, but are more of an estimation technique for getting rules specific to a market – but it is only with difficulty that economists can get their recommendations adopted.

This is one thing which bugs me about kidney donation. It is excellent that we have tools for better allocating the kidneys that we do have. It is good to do good things. The only reason we have to be so concerned with allocation, though, is that we have chosen not to do the best thing. The problem is that there are not enough to go around. If we could incentivize people to donate their kidney through money, we would have a lot more kidneys! The magnitude of this dwarfs the possible gains from better systems. Consider the paper on cadaveric donations in New York. An 18% increase in the arrival rate of kidneys is only an increase of 36 kidneys more a year. That’s a big deal for the 36 people who get them – but there are 5,000 people on the wait list!

This is a general problem with mechanism design. The solution is generally just prices. Mechanism design is often useful only when, for no particularly good reason, we choose not to use the best mechanism. We can do a lot of work trying to solve the problem of double coincidence of wants in a barter market, or we can use the tool we invented in ages immemorial for exactly this purpose. The original uses of the trading cycles were for exchanging housing in communist Moscow – why are we trying to do communism marginally better when we could just not do communism at all?

The best examples of useful mechanism design where the problem is not one that we created for ourselves are in allocating resources for the first time. Because of asymmetric information, we cannot simply give out the resources and expect them to be reallocated to the right uses. The initial auction mechanism matters, especially when the simplified assumptions for simple auctions are broken and we need to take into account people having valuations for multiple goods, risk aversion, and other complications. The FCC spectrum auctions are beautiful to me for this reason.

Al Roth would argue that repugnance is just as real a constraint as asymmetric information. I don’t really like this. It seems too conciliatory to the anti-market savages. But if we must live in an imperfect world, there is nevertheless something which you can do. You can donate your kidney. The National Kidney Foundation is, to my knowledge, the best place to do this. I would like to personally encourage you to sign up.

I went through the screening process in the spring of 2023. It was not unpleasant – I collected a large jug of urine, gave a lot of blood for testing, and had a long morning in the Georgetown University Hospital system. Unfortunately, I cannot speak to the experience of actually undergoing the surgery, because I was rejected. (In fact, I learned that I was just on the border of having pre-diabetes, and that I was at risk of kidney failure in the future).

I feel embarrassed to tell others this! I fear that people will think that I chickened out. I did not! They just didn’t want me.

I don’t know what the right way to sell donating a kidney is. All I can give are the facts – it will create a lot of consumer surplus. You won’t capture it, but it is nevertheless good to create consumer surplus. So sign up today!

Because there are reasons to believe that unionization will reduce wages for workers. In the United States, a firm becomes unionized when 50% or more of a workplace votes for it. The remaining workers are forced to be represented by the union, whether they like it or not. Since unions compress the payscale, such that better workers are paid less and worse workers are paid more, people could be voting for unions in order to redistribute from their coworkers to themselves. Employees might also vote for a union which will redistribute to them, at the cost of the company being more likely to go bankrupt long after they retire.

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My best read of the evidence is that a union raises wages by around 7% for currently unionized employees. The wage gains from a redistribution of rents evenly across workers. Wage compression exists, but redistribution from worker to worker is only a small part. These are the current effects – unionizing more of the economy will have declining marginal returns, and will likely turn negative quickly — and take into account both the reduction of productivity by unions, which biases estimates up, and the spillovers to other firms’ wages, which biases estimates down.

I do not believe that unionization is efficient. While precise figures are lacking, it is unlikely to be a better method of supporting the poor or working class, both because union workers are not disproportionately poor, and also because their methods of extracting surplus are not restricted to just wages. I will note that while the best paper on the effects of unions on productivity finds a positive partial equilibrium effect, but that is only for some markets, does not benefit the consumer, and the aggregate effects are likely negative. I believe that unions reduce total welfare.

Understanding what the real effects of unions are is extremely difficult. Everything is endogenous, which will invalidate the basic exercises which we would have hoped were possible. Consider simply regressing wages on union membership. We will naturally need to control for things which might systematically vary with both income and union membership, like education and skills. Doing so gives you a premium of about 13-15% of wages. Firms which are unionized are also substantially more productive than those which are not. These controls are clearly insufficient, though – the decision to unionize is not a random one. Employees unionize precisely when the gains are expected to be largest, which will bias our estimates of the wage premium upwards. How do we get around this?

One appealing method is to use a regression-discontinuity approach at the 50% threshold for unionization. The idea is that a vote which passed by 51% is probably awful similar to a vote which failed with only 49% of the vote. Dinardo and Lee (2004) are the first to do this, and rather surprisingly find no effect on anything. There’s no increase in firm exit, no change in employment, and most surprisingly of all, no change in wages.

But this is also not good enough, for two reasons. The first is that the key assumption – that votes at 51% are awful similar to votes at 49% – does not actually hold in the data. Frandsen (2021) finds that close union elections get systematically tampered with depending on which party is in office, leading to close elections actually being substantially different in characteristics. The “tampering” which we’re talking about might be, for instance, waiting until after the election results are known to take up the argument that the “workplace” was improperly defined, and some votes should not be counted. This will make the firms which had a close election that passed substantially different from those whose vote just failed.

After correcting this, Frandsen finds that the wage effect is still zero. The firms, however, are badly affected. They employ fewer people, pay workers less, and are more likely to exit.

The other issue is more fundamental. With a regression discontinuity, you identify the local average treatment effect. You see what the gain to being unionized is, if your union is right on the threshold of being beneficial to workers. If the union were obviously promising to workers, then we would expect it to pass by a wide margin. We are going to badly underestimate the firm wage premium using only close elections. There is suggestive evidence for this in Lee and Mas (2012) – unionization reduces stock prices by much more when the union vote is won by a wide margin.

To get the average treatment effect, we use the Abowd-Kramarz-Margolis decomposition instead. This is the framework for modern labor economics, and you should understand what it is. Some workers, even after controlling for everything that you can see about them, are going to earn more. Likewise, some firms are going to pay more. In the cross-section, you cannot tell these apart. You don’t know whether high-paying firms are like that because they are high-paying firms, or because they simply attract higher paying workers.

So what you use are moves of workers from firm to firm. Worker Q moves from Firm A to Firm B, and his wage drops. You get a little bit of information indicating that Firm A is a higher paying firm than Firm B. In your data, which are administrative payroll or tax records, you observe millions of moves, enough to link together all of the firms. You estimate fixed effects, one for each worker and one for each firm, and that’s it.

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An aside on matrix algebra. A fixed effect allows you to estimate a separate intercept for each person and each firm. How this works, concretely, is that you have a very large matrix Z. The rows are person-years, and the columns are equal to the number of workers and the number of firms. Each row has exactly two 1’s, ticking off which worker this is and in which firm they worked. Your formula for the slope is (Z’Z)^-1 times Z’y, where y is the outcome – wages – and Z’ is the transpose matrix. What we’re aiming for is the covariance of x and y, or how much they change together, divided by the variance of x. The first term takes Z multiplied by the transpose Z’ in order to make it invertible. (The matrix needs to be square and linearly independent to be invertible). Z’y is the covariance of Z with wages in logs. Multiplying by an inverted matrix is linear algebra’s way of dividing. The 1’s and 0’s for the fixed effects mean that you solve for the intercepts of just the group, but you get the slope from all of the observations together, at the bottom of the matrix, left over from multiplying.

This is too large to invert. We have tens of millions of workers, and hundreds of thousands of firms. So instead, we make use of the Frisch-Waugh-Lovell theorem, with a modification. With a single fixed effect per row, you can simply subtract the group’s average value, then wipe out the fixed effects. This is like sliding down every data point to be related to the origin. With two fixed effects, firm and worker, this does not neatly resolve in a single operation. However, we can reach the same result by iteratively subtracting the group mean of workers, then the group mean of firms, then back and forth until there is nothing more to subtract.

Now that you have the fixed effects, you can see how much variance goes away when you apply each one. How much variance disappears when you apply worker fixed effects? That’s how much of high pay is due to the unobserved characteristics of the workers. The variance that disappears when you apply firm fixed effects is the wage premium of high-paying firms. You’re also able to describe the sorting of high wage workers to high wage firms. To get the effect of the union, you look at what happens when workers change in and out of union jobs. You then subtract out the component which is attributable to unionized firms being more productive, and what remains is the union wage premium.

There are a few difficulties for these AKM estimates working. First, there must be no match-specific effects. The wage is simply the result of combining the firm wage premium and the worker wage premium (plus error). This wage premium must be portable from firm to firm. Second, workers moving from firm to firm has to be exogenous, and cannot be due to unobserved changes in skill. Third, what we are measuring is the variance explained. Since our sample is finite, noise will lead to us understating the percentage of variance explained. Fourth, specific to the union context, we are unable to account for the union’s possible effect on productivity. Only rarely do we observe a firm change union status, and when we do, we cannot exclude that the unionization decision was related to future prospects. If unions target productive firms, and then make them worse, we will misread the welfare consequences.

We have solutions for each of these. But perhaps it’s better to get to the papers, of which Beauregard, Lemieux, Messacar, and Saggio (2025) will be a seminal one. They have detailed data from Canada for the year 2001 through 2019, which contains every worker and every job. Dropping the firms for which we lack sufficient linkages and workers whose wages are not consistent with full time work, we are left with about 1 million firms and 17 million workers.

They find that unionized jobs pay 19 log points more in wages. Union workers are also more experienced, so conditional on observed worker characteristics, the premium is 15.5 log points. Unionized firms are then 28 log points more productive. Adjusting for this allows us to attribute 60% of the premium – 9 percentage points – to rent-extraction from the employer, and the remainder to unionized firms being more productive (without taking a stand on why they are more productive).

Unions not only raise the wages of workers, but they also compress them. Especially capable workers are less able to renegotiate their terms of employment. BLMS are able to capture this by allowing the worker fixed effect to vary depending on whether they are in a union or non-union job. 40% of the union sample switches back and forth between a union and non-union job at some point, allowing us to identify if the union premium systematically differs across workers, and the firm effects are identified from companies which hire both union and non-union labor. The remaining 60% of their sample is imputed by matching on everything we can observe about the workers, and assuming their union premiums would be the same.

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After adjusting for wages at the first job, this looks less like redistribution from top to bottom, but a soft wage cap for the most skilled workers. This tracks with how the amount of rent extracted does not increase with productivity, but seems a one time amount distributed evenly across workers.

So how do they deal with the four challenges? The easy one to deal with is the limited sample bias. They follow best practices from Kline, Saggio, and Solvsten (2020), who show how to deal with bias by reestimating the equation leaving out each firm-worker pair (with a computational trick to avoid having to redo their work hundreds of millions of times). But more importantly, this doesn’t matter for estimating specifically the union wage premium. Sure, worker and firm effects explain too much, but both union and non-union jobs are biased the same. The difference is unaffected.

They allow for complementarity in a limited manner. The current gold standard for estimating complementarity in AKM models is Bonhomme-Lamadon-Manresa (2019), who bunch firms into groups with k-means clustering based on the distribution of wages, and then look at wage effects when workers move within a cluster of firms versus when they move across clusters of firms. BLMS only allow complementarity of people with union or non-union jobs, but they do not find substantial effects. They can take comfort, though, in how Bonhomme-Lamadon-Manresa estimate a minuscule change in aggregate variance explained from complementarities.

The big concern is that moves are not exogenous. It’s always been a bit hard for me, to be frank, to make economic sense of the exogenous job movements requirement. People are maximizing agents, and they don’t have to leave for a job that pays them less, if nothing has changed. Imagine people are searching for jobs while on the job. They will naturally only leave if their wage is better than before!

The counter that BLMS have – and really, the entirety of the literature since Card, Heining, and Kline (2013) has – is pretrends around an event study, and the symmetry of moves up and down. In the figure below, people moving up or down do not appear to be responding to changes in their productivity which show up in wages before the event. (Although we still cannot rule out sudden shocks to productivity! As we saw during the inflation period after the pandemic, wages were stuck at current employer and rose mainly through switching job to job).

Further, the wage gains and losses from moving between different quartiles of firms are symmetric.

The deeper reason for this is that the labor market should converge to a steady state where everything balances out. Otherwise, everyone’s wage would be increasing just through searching and searching for better jobs. We can get respectable estimates of the firm wage premiums in this way. Notably, though, we cannot reliably believe the same about moves in and out of unions.

They deal with the concerns about unions affecting productivity with a sample of firms which changed unionization status, matched against counterfactual firms which were otherwise very similar. They rule out anything greater than a 5% decrease in value added per worker. Unfortunately, they do not report the local average treatment effect of changing to a unionized firm, which would be extremely important for answering whether expanding unionization actually raises wages.

The last concern for the union wage premium are threat effects. If workers and companies expect wages to rise with unionization, then companies are incentivized to buy off their workers so as to prevent unionization. This will push down the estimate of the firm wage premium. Farber, Herbst, Kuziemko, and Naidu (2021) show that unions, for instance, mainly reduce inequality through spillovers onto non-union members.

BLMS do not deal with these. This would bias their estimate of the firm wage premium down, and so they are safe ignoring it, and letting the union wage premium in their paper stand as a conservative estimate.

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There is another superb working paper, Derononcourt, Gerard, Lagos, and Montialoux (2025) who explore not just the average effect, but the heterogeneity across unions. I am not going to go into it in as much detail as BLMS, in the interest of space and since the labor situation in Brazil is arguably less applicable to the United States, but it is excellent. They have broadly similar results to BLMS.

My initial headline figure is based on disbelieving the perfect exogeneity of worker moves, and believing that it biases wages up, as well as at least a substantially negative effect on productivity, combining to slightly overwhelm the bias from threat effects.

So those are the effects on worker wages. But what about the effect on the real economy? As with any question that naturally involves the development of technology and new techniques, it is quite hard to answer. The evidence gets really thin. There is one truly exceptional paper, and some other bits of suggestive evidence.

Dodini, Stansbury, and Willen (2026) have the universe of workers in Norway. Between 2002 and 2010, Norway changed the tax deduction rules for union dues, which made it cheaper to join a union, but only if the union dues were previously above the cap. This gives us differential exposure, and we can get a cleanly exogenous change in unionization.

In specifically manufacturing, productivity rose. Since DSW estimate production functions, we can exclude that this is simply employment falling while capital is fixed in the short term. Employment and output rise. However, prices rise by more than the cost of labor. The markups of firms rose. So what’s going on?

The most plausible story is this. Suppose large firms have market power over labor, and small firms don’t. Unionization is a shock to the cost of labor for all firms, one which large manufacturing firms can absorb but small ones cannot. Small firms reduce their business, increasing the market share of the large firms. In a basic model where firms are engaged in quantity competition, market shares map directly onto markups. This is supported by the response of the private sector more broadly, which find the expected decrease in productivity. So be careful in how you interpret findings of productivity from unions!

In close election designs, Frandsen (2021) finds sharp declines in employment, payroll, earnings, survival, and productivity after unionization. (Note that his productivity figure is going to be overestimated, because holding capital fixed, reducing employment increases output per worker). Similarly, Bradley, Kim, and Tian (2021) find a reduction in patenting after unionization, and Kini, Shen, Shenoy, and Subramaniam (2021) find a decline in product quality.

Considering the broader spectrum of unions, Maksimovic and Yang (2023) note that unionized plants have lower and less effective incentives. There is a long literature on the effect of good management practices – notably including “paying people for doing their job well” – and unionized plants do worse on this and productivity in general, as identified by changes in state right to work laws. Lastly, Dustmann et al (2025) gives us an example of how really badly designed collective bargaining can indeed be worse for workers – Northern and Southern Italy are practically different countries, and forcing Palermo to have the same wage rates as Milan is obviously going to be bad for Palermo.

For redistribution, the relevant thing to compare to is the same redistribution implemented through the tax system. I do not think that question is tractable at the moment. We would have to know the degree of distortion across many different markets. Nevertheless, it is difficult to believe that unions are the most efficient way.

If we want to limit the damage that a union can do, a simple means would be through limiting what unions can bargain over. Rather than only bargain over wages, unions often impose rules on how many people must be used in a production process. Numerous examples of these are given in section 2.1 of Bridgman (2015), and often include people who are required to stand around doing nothing for a job to be done. These practices are rampant in public sector construction unions, most notoriously in subway tunnel digging. By requiring someone to show up to a job at which they are completely unproductive, such rules are necessarily worse than the same amount of money simply delivered as a transfer.

Finally, there is no good case for public sector unions. There is no plausible labor market inefficiency which they are fixing. Governments are not profit maximizing entities, and are not choosing their labor quantity based on utility maximization. Public sector unions are justified only if it’s better for redistribution on the basis of marginal utility to come attached to skilled jobs which the poorest of the poor are inequipped to hold. I do not think this is the case.

He gave an example with two countries, Portugal and England, and two goods, cloth and wine. We suppose that the two are fixed so as to trade at the same price. Portugal needs 90 workers to produce a unit of cloth and 80 to produce a unit of wine, while England needs 100 and 120 workers, respectively, to produce the same. If we want to maximize the total number of goods produced, we should have England just produce cloth, and Portugal just produce wine. It is as if one “produces” wine at the least cost in England by making cloth and shipping it to Portugal, in the same sense that Nebraska “produces” cars by growing corn, and then transporting it to Japan.

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There are a lot of unstated assumptions here. We cannot determine who produces what without some notion of preferences and wages. Let’s assume, as is usual, that people have “Cobb-Douglas preferences”, which means nothing more than that they’d prefer the same fraction of goods at all levels of income, with smoothly declining utility as they get away from this optinal fraction. This means that trade will happen – otherwise, Portugal would simply consume only wine, if there were even the slightest cost to trade, and England would consume only cloth. It is therefore the wage which determines who produces what. (The following borrows heavily from “Putting Ricardo to Work”, by Eaton and Kortum).

Set the Portuguese wage to 1, and set England’s relative wage to w. Since England’s workers are less productive, they would have to earn a lower wage than Portugal’s. Specifically, if their wage was above .9, then they would all be unemployed. This is not an equilibrium, so the wage would fall to nine tenths — ultimately because an English worker would produce only nine tenths the cloth. Likewise, at the other extreme, if the English wage were less than two thirds the Portuguese one, then Portugal would be completely unemployed, as England produces both wine and cloth. If the wage lies between the points and the countries are the same size, then you get complete specialization; if England is larger than Portugal, then it is possible for England to produce both goods.

Let’s add a third good. Suppose that linen is something England is as good at producing as Portugal is, with a ratio of 100 to 100 workers. As England gets bigger, its wages will fall because it saturates the demand for the products it’s good at, and has to start producing the goods it’s relatively less good at. We can visualize this with the following diagram. As the population increases, its wage rate falls when both countries are completely specialized, and stays flat as both England and Portugal produce the goods. This gives you a pattern of treads and risers.

This is really hard to make meaningful. You are not able to say whether any particular change will make wages higher or lower without complete knowledge of the demand for all goods and the production functions of all goods in the world. Because actually finding meaningful predictions was so hard, trade theory after Ricardo (as exposited by Mill, 1848) shifted over to focusing on factors of production, as in the Heckscher-Ohlin model. Countries are endowed with things like capital, land and labor. Countries export the things which are produced with the factors they have relatively more of, and import what is produced with the goods they have relatively less of. The United States, having lots of capital, should be exporting those goods, and importing goods which take lots of labor. This allows us to make predictions like the Stolper-Samuelson theorem, where a fall in trade costs can harm the owners of a factor of production, although it must be on net beneficial.

Making use of this turned out to be really hard. The assumptions were just too strong, and scaling up to empirically realistic contexts was unsolvable. The production technology has to be identical everywhere, which is just, obviously wrong; and in the 1950s, empirical explorations by Wassily Leontief showed that countries were exporting the wrong goods. The capital abundant United States was exporting labor intensive goods.

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So the next breakthrough in trade theory was Dornbusch, Fischer, and Samuelson (1977). They deal with the problem of too many goods by saying that there are in fact an infinite number of goods. Don’t worry about whether a change in size takes place over a flat or rising part – there are so many goods that any change is going to affect both. What assuming an infinite number of goods – a continuum of them – buys you that it’s a line, and lines play nicely.

Let’s order all of them by the ratio of productivity to the other country. Since it’s a ratio, the other country’s line must be the opposite of ours. Now, if there was a shock to the raw technological ability of a country, we can think of this as just like a demand shock. The curve shifts, and we have both higher wages and more varieties produced in England.

We have not said anything about trade costs so far, to keep things cleaner. Adding in trade costs implies that the prices of goods will no longer be the same in all countries. Instead, there will be a wedge in the Dornbusch-Fischer-Samuelson graph – goods will be produced by Portugal that should have been produced by England, and vice versa.The usual form of trade costs are “iceberg” ones, where we assume that some fraction of the value of the goods is lost in transit, as if it had melted like an iceberg. The reason for this is that if the trade cost were a constant, then the effects of trade cost would depend on total income. Everything would break, pretty much. We will explore models which relax this assumption, but for now we keep it.

Something remarkable happens when we add trade costs, though. When trade costs fall, more trade occurs. When a country gets bigger, or more productive, there is also more trade. If trade costs are related to distance, then which countries will trade with who looks remarkably like gravity. Aggregate trade flows will be equal to the product of GDP of two countries, divided by distance.

The Dornbusch-Fischer-Samuelson model is for two countries. There are more than two countries in the world. Unfortunately, we cannot extend it to many countries by simply adding dimensions. The ranking of goods by relative productivities is simple enough when there are two countries, but it breaks down when we add more. The relative productivities depend upon the prices and productivities of every other country, and so there is no simple formula you can plug things into. You would have to find it with some sort of iteration, and as you might have learned from my article on Rust (1987), these sort of many dimensional environments are essentially impossible to solve for.

Into the void step Eaton and Kortum. As with DFS, there is a continuum of goods. Their contribution is to say that productivities for each good from a given country is drawn from one particular distribution.

What makes it work is that productivities are drawn from a very particular distribution indeed. It’s called the Frechet distribution – if you are familiar with the logit errors common to industrial organization, this is the same but in logs. Having the Frechet distribution has a reasonable microfoundation if you believe that a country’s productive technology is the result of researchers repeatedly sampling a distribution of research ideas, as Kortum (1997) showed. It’s related to e, so finding the derivative as you need to estimate maximums is stable. You get a neat little expression – the probability that any given country produces at the lowest cost is equivalent to its share of global technology, multiplied by its trade cost, and when you take.

We can boil down the distributions into two parameters, the technology parameter T, and the shape parameter θ, or theta. The technology parameter T gives us the absolute productivity of a country, while the shape parameter theta gives us the variance of the distribution. T is unique to each country, and theta is shared across the world. An increase in either productivity or variance, when trade is possible, increases welfare. (Note that the variance is pi over 6 theta, such that a decrease in theta increases variance). That a shift to the right of productivity raises productivity is obvious; the gains from increasing variance is that it increases the gains which are possible through trade. Suppose that the variance were zero, and a country was as good at producing every product as every other. If they faced even the most trivial cost to trade with another country, they simply would not do it at all. Widening the distribution allows a country to produce only the goods for which its advantage is greatest.

Each country buys each good from the country that produces it for the cheapest, inclusive of trade costs. More productive countries will thus export more, and closer countries will engage in more trade.

We cannot, just looking at this, tell apart trade costs from the dispersion of productivities. Eaton and Kortum have several different identification strategies. The most believable of them is to use price data on commonly traded goods. The price difference between different countries pins down the trade cost. Theta is given by the ratio of the highest price to the second highest. Believe it or not, this is all you need to do to get theta, because we made an assumption about the distribution. They also get an estimate of theta from arguably exogenous variation in wages, and directly estimate the effect of distance by controlling for a pile of observable characteristics.

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The accuracy of this estimate is a bit shaky, and many papers which follow pass off responsibility for accurately estimating the productivity dispersion by citing estimates “common in the literature”. All three methods give substantially different results. For the first method, Eaton and Kortum have the prices of 50 goods in 19 countries, which means that, ultimately, you only have 50 data points underlying the results, because the countries are only useful . Simonovska and Waugh (2014) shows that this leads you to consistently overestimate the trade costs, because whether a good is exported from one country to another changes discontinuously as trade costs fall. Resimulating Eaton and Kortum’s data, they put theta at 4 instead of 8, doubling the gains from trade. Costinot, Donaldson, and Komunjer (2012) directly observe the distribution of productivities, using R&D as an instrument, getting a theta 6.53. I don’t particularly believe any of them, but you need something.

But for all the quibbles about parameterizing the model, Eaton and Kortum’s paper is a remarkable achievement. Better to estimate the wrong parameters than have no parameters to estimate. They use this to estimate the gains from removing all trade barriers – “large” – but you can use it for precise answers across many contexts.

Suppose, for instance, you want to know about the impact of transportation improvements. The ordinary way would be to run some sort of regression. There is a railroad here, there is no railroad there, we compare incomes in both places before and after and attribute the difference in changes to the railroad.

Obviously you can pursue this with increasing econometric sophistication. You need some reason to believe that the placement of the railroad is exogenous, but perhaps a read through the motives of the company or the government accords with that, or perhaps when you consider railroads which were planned but never built (a “placebo test”) you do not get spurious changes in outcomes. But that leaves you unsure of why incomes rose. Perhaps it was just due to the government, having decided to place a railroad hither to thither, investing more in the location. We really would like to say whether this was due to trade or not. Thanks to Eaton-Kortum, we can.

Go back to the parameter theta, which governs the dispersion of productivity. This also has the property of being the elasticity of trade with respect to trade costs. If the distribution is not very wide, then a fall in trade costs would make little difference in what a place buys. Its purchasing would still largely be of its own goods, with wages determined by its level of technology T. If, however, it is wide, then you would get a large change in expenditures on domestic goods.

Thus, the gains from a fall in trade costs can be identified from the change in domestic expenditures, given how elastic they are to the trade cost. Now you can measure the entire effect of the railroad that was due to trade, aside from everything else. Dave Donaldson’s “Railroads of the Raj” (2018) does this in India, where the British Empire built an enormous network between 1870 and 1930.

Since he has a formula, he can approach this like a cook getting every ingredient. We need domestic expenditures — okay, simply digitize tens of thousands of records covering output and trade and weather. We need trade costs — okay, there are certain types of salt which are made in only one district but sold around the country. Take the price differences as a direct measure of trade costs where we observe pairs, then use a detailed GIS map of India to fill in what the most likely costs are. We need the level of technology — okay, let’s digitize daily rainfall records for hundreds of districts and tell you how much a positive rainfall shock increases output.

With all three pieces, T, theta, and trade costs, we can say the railroad led to an 11% increase in income due to gains from trade. This compares with a 22% percent increase from the reduced form results. Likely, we are underestimating the gains from trade, because the ability to smooth consumption in the face of risk allows them to take on riskier crops. And the consumption smoothing enabled by the railroad was very important — Burgess and Donaldson (2012) show that it was the railroad that effectively extinguished famine in India.

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We can also use it to evaluate the effects of trade agreements. Caliendo and Parro (2015) is an excellent example of this, and worth going in depth as a “complete” paper. They are studying the impact of NAFTA on welfare in Mexico, the United States, and Canada. There is absolutely no guarantee that the agreement benefit all of the countries party to the agreement at all, and that is indeed what they found – Mexico had a very large gain in income, while Canada saw a slight decrease as Mexican goods outcompeted them in the United States. (This reverses when we consider contemporaneous changes in world tariffs – Canada was the best off of our three countries. Trade is good, all in all).

In Eaton and Kortum, we assumed a single theta for the variance of productivity of all goods. Casual inspection of the world suggests that that is not the case, and instead the variance of productivity will differ by sector. Remember that since theta gives us the trade elasticity, we can directly estimate theta if we have exogenous variation in trade costs, just like how we would estimate anything else in economics.

They are also able to model the impact of intermediate goods on welfare, without treating them all as homogenous. The sectors are linked through input-output tables compiled by the BEA. Including these is extremely important to the results – if you dropped them, the gains from trade would be less than half of what we observe.

The complication that sectoral linkages adds is that solving for equilibrium is difficult. The methodological core of the paper is in section 3.1.7, where they popularized “exact hat algebra”. The changes in tariffs were heterogenous by sector, as some tariffs started higher than others. The idea of exact hat algebra is that, rather than completely resolve for equilibrium – which will depend on many things which you will have difficulty estimating – you solve only for the changes in wages, prices, and trade shares. The baseline is an equilibrium, so the change allows you to subtract out the fundamental productivity in each sector. You then guess and check vectors of wages until you find a set of wages that imply the trade shares observed in the data.

Eaton and Kortum’s framework is also able to trace out the distributional impact of trade. Modern critics of trade have often focused on the unequal gains and losses, and the possibility that manufacturing workers in particular will lose their jobs to foreign competition. Famously, Autor-Dorn-Hanson (2013) attribute 25% of the decline in manufacturing employment in the United States between 1990 and 2007 to increased competition from China.

But their approach, which is based on comparing the different shares of employment, and thus the exposure of labor markets to the particular set of industries which China got good at, is inappropriate for determining the general equilibrium impacts. They can only say that there were fewer jobs in the more exposed areas relative to the less exposed areas. If trade with China increased the total number of manufacturing jobs, all else equal, but increased it less in the more exposed areas, we would get the wrong effect.

Caliendo, Dvorkin, and Parro (2019) show that the job losses were much less than implied by ADH. Their addition to the usual trade model with sectors are households, who can choose to stay, move, or change jobs. Ordinarily, with 50 “states” (not states in the usual dynamic discrete choice sense, US states), 22 sectors, and 38 countries, there’d be far too many combinations of variables to possibly come to an answer. They can repurpose the exact hat algebra from their prior paper, though, to get rid of local productivities and endowments, the cost of moving, the cost of trade, and whatever the utility of being unemployed is. Their approach is sorta like differences-in-differences, for the path of an entire economy.

Even though manufacturing employment falls – they attribute 16% of the contemporaneous fall to the China Shock – welfare rises. People left to do other jobs, like construction. However, these welfare gains took a while to materialize, and there was a considerable dispersion of gains by labor markets, with many suffering losses.

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That is the current cutting edge of what can be done with Eaton Kortum. It is not the only path to modeling the gains from trade. At the same time that Dornbusch, Fisher, and Samuelson (1977) were resurrecting Ricardian trade, a young graduate student by the name of Paul Krugman was figuring out what to write a paper on. In 1977, Avinash Dixit and Joseph Stiglitz published a little paper called “Monopolistic Competition and Optimum Product Diversity”. We’re going to skip over the algebra, which due to the unfortunate proliferation of symbols looks more complicated than it is; readers who want a full derivation can turn to Jonathan Dingel’s lecture notes.

We assume that, as with the Cobb-Douglas preferences we used in the case of England and Portugal, we want an equal share of every good. We also assume that every good is as good as any other. Each firm pays a fixed cost to enter, and can produce exactly one product at the same marginal cost as every other firm. Since every good is as good as another, there’s no reason to produce the same as some other firm. Each firm then charges a price which is a fixed multiple of the cost of producing the unit, with is the same as the elasticity of substitution that consumers have to other products. Intuitively, each firm occupies a little bit of space all to their own, and raises their prices up until the point that someone would go to someone else’s firm instead. We reach equilibrium when the profits from the “markup” (the difference between price and marginal cost) exactly equal the fixed cost of entry.

Krugman recognized that this little model could be used to tractably analyze trade, and along the way, explain some puzzles. Why is it, after all, that Japan exports automobiles to the United States, when we export automobiles to them too? Well, since the portion of the total cost which the fixed cost takes up is continuously falling as production increases, having more customers is always better.

He gets a few clean predictions out of this. In Krugman (1980), he shows that the larger country will export more. If you’re a producer, you want to locate there because you will pay the transport cost on less of your production. If preferences differ across countries, then there will be a home-market effect, where the countries with more demand for a product also export more of it. (This was empirically tested by Costinot, Donaldson, Kyle, and Williams (2019), using demographic characteristics to shift demand). Krugman (1981) shows that if countries produce goods with more than one factor of production, then whether trade benefits everyone depends on the relative proportion of the gains from trade coming from increasing returns versus comparative advantage. If countries are identical, then all gains from trade must be from increasing returns and thus everyone benefits; if they are due to comparative advantage, it is possible for us to be in the world of Stolper-Samuelson.

Thus far, we have been treating countries as homogenous units, which might be the case if all firms were identical to each other. This is obviously not the case. Firms are different from each other. It is plausible that there is another source of gains from trade — expanded markets reallocate production from unproductive firms to productive ones — and that was what Melitz (2003) was first to formalize.

The way Melitz does it is one little trick, but it gets the job done. Firms start out not knowing their productivity, but do know the distribution they will receive their productivity from. This productivity can be thought of as a constant marginal cost. Firms can pay a fixed cost to draw that productivity, and then decide whether they want to produce at all. This gives a realistic distribution of firm sizes, and also fits the fact that less productive firms produce less and exit earlier.

How can trade increase productivity? Simple. They have to pay another fixed cost to export, except this time they now know their productivity. Only the most efficient firms choose to export, so they gain a larger market share, and the average cost goes down. You can combine the two models relatively, as in Bernard, Eaton, Jensen, and Kortum (2003).

That trade increases the productivity of firms has found considerable empirical support. In fact, the estimates of the effect of trade on productivity from reallocation alone are smaller than what we observe in the data, which is generally an increase in total factor productivity, likely due to managerial slack.

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It was, I think, therefore something of a shock when Costas Arkolakis, Arnaud Costinot, and Andres Rodriguez-Clare showed in “New Trade Models, Same Old Gains?” (2012) that all of these trade models were exactly the same. Under the assumptions which were made so that they could be analyzed, they all deliver the same gains from trade. The welfare formula that Dave Donaldson used in “Railroads of the Raj” proves to be remarkably general – the change in welfare of any change in trade costs is simply the change in real income, raised to the power of 1 over the elasticity of trade with respect to trade costs.

I think everybody’s reaction to ACR 2012 was that we have got to be missing something. The estimated gains from trade were too low. There are three assumptions which drive the result, two of them consequential, which are as follows:

1. Trade is balanced. No deficits, no surpluses. This should hold in the long-run, if you are properly valuing everything.

2. The trade elasticity is the same at all levels, across all goods, and across all sectors. In Eaton-Kortum, this made possible by the Frechet distribution of country productivities; in CES models like Melitz, this is made possible by the distribution of firm productivities being Pareto.

3. Aggregate profits, as a percentage of revenue, are constant. Eaton and Kortum (2002) assume perfect competition, such that profits are zero. CES demand models imply profits which are a constant multiple of the cost. Notably, this rules out the possibility of a change in competition.

The simplest solution is just to deny that the trade elasticity is the same at all levels. Melitz and Redding (2015) show that bounding the Pareto distribution of firm productivities can cause arbitrary increases in the gains from trade. The formula we gave above rules out intermediate goods, and including them – in the form of a multiple on the trade elasticity – will also arbitrarily expand the gains from trade, as we saw in the multisector models earlier.

An intuitively appealing channel for trade to increase productivity is through competition – not merely reallocation of production, but actively lowering the markups which firms charge. So far, we’ve ruled this out. The third pillar of trade theory has firms engaged in oligpolistic competition and charging variable markups, with their markups related to their market size.

The treatment of competition where firms choose their quantity instead of their price begins with Brander and Krugman (1983), who show how it is possible for opening trade to actually reduce welfare. They have two countries, A and B, who each have one firm in the market, which consists of one good. Each firm choose a monopoly markup in each country, and collects excess profits. There exists a cost to send a good from A to B. If this cost is relaxed, the two companies will find it worthwhile to send goods from one country to another, even though this erases their margins and causes what were formerly profits to be wasted on the transport costs from place to place.

Atkeson and Burstein (2008) is the key modern paper. Their motivation is that the fluctuations in the relative price of goods is nowhere near as much as fluctuations in the real exchange rates between countries. Their solution multiple levels of aggregation. In every sector, a small number of producers produce goods. The goods within the sector have some elasticity of substitution, and then the sectors as a whole have a different elasticity of substitution. What makes the whole model tick is that the elasticity of substitution is higher within the sector than without.

Imagine you’re a firm. The markup that you can charge is a weighted average of how much the price increase would cause consumers to shift to other goods in the sector, and how much it would cause them to shift away from the sector entirely. When a firm is small, people to switch to very similar products, and so it can charge only very small markups; as it gets larger, though, people would have to switch to entirely different sectors, and markups get larger.

Edmond, Midrigan, and Xu (2015) take this, and show that the gains from trade are importantly dependent on the cross-country correlation in sectoral productivity. If they are similar, then the number of competitors increases and markups go down. Otherwise, the more productive country simply displaces the native producers entirely, with no gain from competition. In their particular application, though – Taiwan – including the gains from competition doubles the gains from trade relative to a constant markups.

There is an important negative result for the competition story from Arkolakis, Costinot, Donaldson, and Rodriguez-Clare (2019). Here they get variable markups from having consumers with non-homothetic preferences – rather than prefer exactly the same fraction of goods as income increases, which would be homothetic preferences, they change as income increases. Opening up trade to a foreign country decreases the markups of companies in both countries, but it reallocates which goods people buy to the firms with relatively higher markups. In their calibrations, this latter effect actually outweighs the decrease in markups, and so allowing for competition decreases the gains from trade. There is considerable degree for choice

The next step is to then directly measure markups from production data, rather than impose the markups as the result of the demand system. De Loecker, Goldberg, Khandelwal, and Pavcnik (2016) directly estimate the production functions of firms, then count up the increase in profits from falling marginal costs to the firms, as well as the decrease in markups due to competition. They found that, on net, markups rose – while trade is good, it was not amplified by a reduction in misallocation.

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Finally, we might argue that there is something completely outside the model which generates larger gains from trade. Generally, this is the dispersion of ideas through contact, or simply scale economies of production. I have found this line of literature to be weaker than we would have hoped – Atkin, Khandelwal, and Osman (2017), who have a randomized controlled trial giving Egyptian carpet makers the opportunity to export, is essentially the best evidence we have for learning by doing through exporting, and gets cited all the time, despite the questionable ability for single artisans to inform our knowledge of what happens if large textile firms got greater market access.

The studies which do explicitly model the flow of ideas across countries have always just struck me as incredibly squishy. They have abstractions over abstractions. I think their work is often admirable – for example, I think Buera and Oberfield (2020) is good. They build off of the discovery of ideas process discussed in Kortum (1997), and show that things still generalize well to the Eaton-Kortum framework. But the assumptions they need to infer the value of governing the diffusion of ideas are just completely unbelievable. Even if we did get a believable number, we have no idea how to evaluate counterfactuals because we don’t know how to map policies onto the parameter. At least in Eaton Kortum, we could get a decent guess at how much a tariff change is as a fraction of the total cost of trade with additional empirical work. Here, we have no idea how much “the internet is invented” or “new university is founded” increases the diffusion rate.

There is also a line of literature which essentially just says “we don’t know why it is the case that the gains from trade are an underestimate, but they definitely are” and documents changes in productivity which cannot be explained by mere reallocation alone. James Schmitz (2005) is in this line, where exposure to competition from Brazil caused Minnesotan and Canadian iron ore mines to, bluntly, stop screwing around and actually produce iron ore efficiently. I think this, along with numerous other studies showing the persistent effect of competition on total factor productivity, is important, but it is not systematizable. We should simply remember that estimates of the gains from trade are likely to be underestimates.

I think the deepest criticism of trade theory is that it is in some sense useless. We know that trade is good. Arbitrary tariffs are bad. Why do we need to say how good it is? But this is wrong. There are many contexts where it is indispensable – in particular, infrastructure. Trade costs can be reduced by expenditure on infrastructure. We have no idea whether this expenditure is worth it without being able to actually quantify the gains from trade.

The main question which trade theory faces is whether it should, strictly speaking, be the study of international trade. I believe it is choosing not to be. As we get more data about products, we can explicitly model their characteristics without aggregating. Looking at, for instance, recent studies assessing the impact of the Trump tariffs, we see that they are mostly measuring the passthrough of the taxes to the consumer, often using data from the bar code level. It is industrial organization, which just happened to travel over a boundary.

Instead, the tools of trade theory are becoming applied to the study of arbitrary trade in space – commuting flows, household locations, and the placement of industry. Ahlfeldt-Redding-Sturm-Wolf (2015), also a Frisch Medal winner, and which will be the subject of a companion essay, is essentially Eaton-Kortum but with city blocks instead of countries. If it is infrastructure improvements that we care about most, then the future of trade is spatial. I’ll see you next week.

I would like to make a few general observations. First, scientific research has indivisibilities. Giving a few thousand dollars to a poor person will produce more utility than paying a scientist the same sum, but paying scientists a million dollars will likely create more utility than paying poor people the same amount. With the sums involved, the foundations will subsidize a lot of scientific research.

Second, there are three ways of inducing people to do scientific research. We can subsidize their accumulation of skill; we can subsidize them to work at some process which stochastically generates advancements we do not need to specify in advance; or we can offer a prize for the production of a good we specify in advance. Given our current funding levels of each, a change in the forces which advantage one over another identifies which we should fund more of.

It is highly unlikely that they should subsidize the accumulation of skill. With AI, we are less sure what the relevant skills are, and it is easier for an amateur to task an AI agent to answer a question of interest.

We should therefore either fund researchers, or fund prizes. The former is better when we can specify what working is, without knowing what the end result will be. It becomes better as workers become more risk-averse, and it becomes worse when workers possess more private information about their chance of success. Conversely, funding prizes becomes better when we can specify what the outcome in advance, without knowing how to get there. It becomes less effective as people become more risk-averse, and more effective as people possess more private information about their own aptitude.

The AI foundations will not be subject matter experts in everything. They will lack the detailed knowledge needed to differentiate genuine workers from flim-flam man. They will, however, be able to produce a list of problems which they would like solved, and attach a dollar value to it.

I expect the size of the future AI foundations to make it so we have to do less to specify what the output is. If a charity promises a single prize with vague criteria, people will be less willing to undertake costly effort to find it. By maintaining a reputation for fair-dealing, the AI foundations will be able to propose prizes for vaguer questions.

There is an argument that a higher level of material wealth would make people less risk-averse. I do not think that this will be important, but it would point toward prizes over funding.

If we are going to have prizes, then we must decide whether to have many prizes or one. Theory clearly points us to many prizes, for several reasons. To the extent that people are risk-averse, we will want several prizes; if the cost function of producing effort is convex – and we would expect it to be at the relevant margin – then we should offer several prizes (Moldovanu-Sela, 2001); and if the research effort of someone makes subsequent research toward that prize cheaper, then we want to include prizes for people with partial answers.

I cannot tell you the details of what the AI foundations should do in advance. They should hire a few good managers to decide that. What I can tell you is that the direction of funding should point toward prizes.

Mr. Harold Zurcher is the superintendent of maintenance for the Madison Metropolitan Bus Company. The Bus Company possesses 162 buses, largely purchased from the General Motors Corporation, all of which are diesel powered and run for about 5000 miles every month. Mr. Zurcher’s goal is to maintain the buses in such a way as to maximize the profits of the Bus Company, bearing in mind not only the cost of repairing or replacing the engines, but also minimizing the loss of consumer goodwill which a breakdown would cause. The data we have are monthly readings of the odometer, and a record of the date, mileage, and maintenance actions when the bus went into the shop. Our task is to infer the underlying cost functions using only his decision to replace and not replace.

You might ask why we do not simply phone the General Motors Corporation and ask them ourselves what the cost of replacing a bus engine would be. We will need to do something like this, in order to convert our measurements of ratios into dollars, but just doing this would be missing the point. Here, we might have an answer key, although of course the engine itself is only part of the cost of taking the bus out of service, and Mr. Zurcher generally rebuilds a new engine completely out of parts. In many other contexts, we will not have this. We need to find the underlying cost functions using the data which we have, not the data we wish we had.

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I will give the high-level overview of solving the problem first, and then expand upon each of the details. Every month, Mr. Zurcher decides whether to replace the bus engine, or to continue to the next period without replacement.. We can see immediately that any model with a deterministic stopping point at which the engine is replaced would be rejected. The exact mileage at replacement varies considerably. Note that we are chunking the mileage into 90 bins, one for every 5,000 miles.

What we will instead do is allow for there to be idiosyncratic shocks to Mr. Zurcher’s decision to replace the bus. He is an expert in the ways of buses, so it stands to reason that sometimes he will see that an engine is holding up well, and other times it isn’t. These are errors are not correlated with each other over time, but drawn anew each time the bus comes into the shop.

These shocks have a very particular structure – Type I extreme value errors, called logit. Why this? Why not a normal distribution? Put plainly, it makes computation more simple later on. More specifically, because the logit distribution is built around e, the probability that an engine is replaced is equal to e to the power of the value of replacing, divided by the sum of all e to the power of every other option. This gives you a number between 0 and 1, which you can read off as a probability. A normal distribution for idiosyncratic shocks would require some extraordinarily nasty integrals.

So once again, we take a guess at the outside parameters. We impose a discount factor, so that Mr. Zurcher values the future a little bit less than the present, and try a replacement cost RC, and a function of ongoing costs as a function of mileage. This will converge to a fixed point, a set of 90 values, one for each bin, with a percentage likelihood of replacement which maximizes Mr. Zurcher’s expected utility. We can then compare the optimal replacement, given these costs, to the actual replacement. If they aren’t close enough, we try a new set of costs, and do this iteration over and over again until we have an answer.

I think we should be clear about what this fixed point is that we’re iterating to. A fixed point is simply some value which, when plugged into an equation, returns itself. For instance, the function f(x) = x^2 has fixed points at 0 and 1. We’re looking for a set of 90 numbers, one for each bin and denoting the present discounted value of being in that state, which when fed into the Bellman operator gives us the same vector of 90 numbers.

What is this Bellman operator? We hand it the vector, and it considers the possibility you land in each future state. (We get this from the data – this just means what the mileage will be a month from now). For each of these, we have our current guess of the expected value of being in that state. We use the logit error formula to get the value of being in each state, given optimal play, then weight going from state to state by the likelihood of doing so in the data.

These guesses will almost certainly be wrong! They are wrong because they are inconsistent with each other. If costs are increasing as a function of mileage, for instance, the value of being in lower mileage states should be higher. But we can use them to find the right guesses.

We take our current guess. We plug it into the Bellman operator. It spits out what the “real” value of being in that state would be, given what our other guesses is. We subtract the “real” values from the first guess, and are left over with a residual. This residual tells you how off you are at each guess.

Each state has a connection to every other state, so there are 90 by 90 values denoting exactly how much each state affects every other state. If you take the inverse of this matrix, the Jacobian, you can multiply it by the vector of leftover values – the residual – and after subtracting this new, updated matrix from the current guess, you get a new guess. The Jacobian is translating that residual into a coordinate update of all of the cells at once. You compute a new Jacobian each time, and the stuff you did in calculating the likelihood of going from state to state provides weighting for each cell in the Jacobian. Every time you do this operation, you double the number of correct digits, and converge very close to the correct answer with only a few iterations.

The results do not currently live in the form of dollars, but as ratios of each other. We can convert them into dollars by speaking to Mr. Zurcher, and asking him what he thinks the cost of replacing the bus engine is, which gives us the RC.

There are some things we cannot do with this. We need for there to be some discounting of the future, in order for the expected future value of being in every state to not be infinite. We also cannot identify the discount factor separately from the replacement cost, as any change in the discount factor can be offset by a corresponding change in the replacement cost.

Above all, we are limited in the number of variables we can have, largely because of needing to invert the matrix. Suppose that we wanted to keep track of the age of the bus. For the sake of argument, if we binned it into 90 chunks, then we’d have 90 squared, or 8,100, states. This would mean inverting a 8,100 by 8,100 matrix, which is 90^6 computations. Nowadays you could actually do that, although everything would take annoyingly long, but Claude assures me that on the IBM-PC Rust programmed this on would take 8 days to do one single matrix inversion – little surprise, since it would take about 700,000 times more computation.

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You might be wondering to yourself – why? Why do we need all this complex math and incredibly fiddly computation, when we could just solve this with a regression? Take the likelihood of the engine being replaced as a function of mileage, draw a line through it, and call it a day. This might be useful for some applications, but you will find yourself completely unable to answer counterfactuals. What happens if the cost of replacing a bus engine increases, or falls?

Your regression has nothing to say about it. You’ve never seen the bus engine cost vary, so your regression slope is totally uninformative. If you want to accurately assess situations which are not exactly like the variation you see in your data, you need the underlying costs which drive behavior.

Let’s take a look at Vincent Rollet’s job market paper, “Zoning and the Dynamics of Urban Development”. Zoning restricts what types of buildings can be built on different plots of land, in particular the size. Many people have proposed that if we upzoned neighborhoods, rents would fall and welfare would rise. We could measure the effect of upzoning by looking at prices and quantities

But this is such a narrow problem to solve. If we want to evaluate the effects of a rezoning, we would be unable to unless another rezoning of similar characteristics had happened earlier in the data. What’s worse, these small scale regressions cannot actually identify welfare – they can measure change in price, and they can measure change in population, but they cannot really account for building housing in New York will affect the demand for housing across the country.

So instead, Rollet solves for the complete supply and demand system. The demand side is given by a quantitative spatial model, in the vein of Ahfeldt, Redding, Sturm, and Wolf (2015); it, too, won a Frisch medal, and so I will skip over the details in the interest of time.

To get the supply side, Rollet solves an extension of Rust’s model, with an additional loop, to get the building choices of developers. They face a cost to build, which includes the cost of tearing down the building which previously resided on the plot, and can choose to exercise the option to build once. Given the costs we guess in the outer loop, we solve the inner loop for whether the plot will be redeveloped. There is then a middle loop, in which they account for how their decisions will affect the supply of housing in the city and its subsequent price (and they’re forced to be consistent with each other), and we can take another shot at the costs.

If the cost functions are correct, then the effects should track what we observe from quasi-experimental estimates. And indeed they do!

Rollet’s model can tell us things that the quasi-experiments can’t. For example, the amount of housing built after a rezoning will tail off as the rezoned area gets more developed. We would not otherwise be incorporating the cost of tearing down a building, and how that both discourages building where development has already happens, and encourages holding onto underdeveloped land for longer. He also predicts that upzoning New York would mainly affect the population of the city, and not so much the rent. It is the places outside NYC which would see a fall in rents, as people move to the Big Apple.

Similarly, we can look at Aradhya Sood’s “Land Market Frictions in Developing Countries”, who is curious how much the small size of plots in India disrupts manufacturing firms. Records of the price of land in India do not exist at scale. Even if they did, the real cost of land includes negotiating and the landowners holding out for better deals. You have to back out the underlying cost functions if you want to have any hope of answering what would happen if the government made it easier for landowners to pool their land together to sell, or for the government to repeal the 2015 eminent domain reforms.

I have cited these excellent recent papers because they address what I believe to be the strongest criticism of the literature of dynamic discrete choice, whether estimated with methods due to Rust specifically or not.. The papers are, very often, simply not answering a question of interest. Either the process of estimation has taken too long and the questions they study have been long since outmoded, or they have chosen a question with easy data but for which there was never any practical interest whatsoever. The prime example of the former must surely be Stephen Ryan (2012). I note that it is an excellent paper doing interesting things, of course, but it is a paper published in 2012 evaluating the effect of a policy change in 1990, long after it would have been policy relevant!

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Rust (1987) is a single agent model. The natural thing to consider is what happens when you have multiple people. (I think this is a reasonable description of the world). To get there, we need to first transform the single agent model into something simpler.

Hotz and Miller (1993) introduced conditional choice probability, or CCP. They skip the inner loop entirely. Instead, we observe that at each state, there is some probability we take an action. We then have some probability of progressing to each different state, and we can say that the payoff being at some state is equivalent to the weighted average of payoffs one would get in all the future states. Because the future is discounted, the contribution to the value of being in the current state that future states have gets smaller and smaller, and when it gets small enough, we stop, which makes the value finite. The weighted average is found by simulating the path a thousand times, and stopping there.

How can we know the flow utility when we don’t have any units? We don’t know the level. We are never going to know the level, but this is the same as Rust – we only know how they relate to each other. We have a function. This is worth considering, because there’s something of a bait and switch in how we treat counterfactuals, including in Rust. If we’re interested in “what happens if the cost of bus engines goes up 20%”, we can evaluate the total cost of replacing the engine going up but we don’t know if that corresponds to GMC’s list price increasing by 20%. We can be agnostic about the costs, but that makes it hard to interpret what the counterfactual change actually was.

The great advantage of this approach is that it handles many variables so much better than Rust. It does not matter how many variables you have. CCP can handle it just fine. You don’t make the number of computations needed scale with a cubic power of the number of states. CCP is also much more parallelizable than Rust. The candidate cost functions in Rust can be run in parallel, but iterating the Bellman equation cannot be. Every part of the CCP algorithm can be run simultaneously on a GPU.

This is not free, obviously, or else Rust would have gone extinct. CCP is sensitive to error, which gets worse as the amount of data we have gets smaller. This is especially dangerous when we see a state with perhaps only a few occurrences and see no one take the action at all. Everything involved with this is in logs, and plugging in a zero to a log model breaks it immediately.

This gives us something of a mixed bag when it comes to handling many variables. We need data on people’s choices in each combination of variables. As you add more variables, the computational difficulty does not change, but the likelihood that pure noise is contaminating your results increases.

An excellent example of CCP in practice in the single-agent context is Benjamin Couillard’s job market paper on housing choice and fertility. The states here are combinations of housing size, the number of children, marital status and so on, smoothed with kernels so that we don’t have 0s and 1s for probability. (A “kernel”, in this context, is basically just an itty-bitty distribution (generally normal) around a data point, normalized so that the integral is 1. When you have a bunch of datapoints with overlapping kernels, you can add them together and get a smooth line, rather than jagged spiked at each datapoint). With a demand side – estimated with modifications of the usual BLP methods so as to , because unlike Vincent Rollet’s paper we care more about the characteristics of housing than the location – we can estimate how much people value children and housing together. He can then find what would happen if we made housing cheaper – each household solves their problem holding rents fixed, we adjust rents to clear the market, households solve for how many kids they want, we adjust rents, and we repeat indefinitely until we converge to an equilibrium.

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The Hotz-Miller approach has also been applied to the study of normally static markets, but I am not convinced by the usefulness of this. Igal Hendel and Aviv Nevo (2006) is the foundational paper here, studying the purchase of laundry detergent. Detergent is storable – you can buy it when it’s on sale, and hold on for it till later. Imagine what would happen if we tried to estimate demand using unexpected sales by the retailer as an instrument. People would buy more, of course. This is not the same thing as what would happen if the price were made permanently lower, though! Storage would lead us to overestimate elasticities.

They deal with this by solving a three step problem. First we estimate what brand people would buy, conditional on size; then we pack everything about the value of each size across all brands into one value, reducing the number of states we need to worry about; then we have households maximizing utility subject to inventory costs, consumption shocks, and the value of each size. Using this they show that simply using variation from sales to trace out demand would leave you with misestimated elasticities.

Why I am not that overwhelmed by it is that you don’t use sales as an exogenous instrumental variable. When you aggregate over time, there is still bias, but it is substantially lessened. The direction of the bias is also known. It’s going to be less elastic in the long run. We’re safe with a heuristic assumption that our results will over or underestimated, and putting bounds on our results.

The Hotz-Miller framework is simple enough that we can apply it to games with many players, through Pat Bajari, Lanier Benkard, and Jonathan Levin (2007). Having multiple players vastly increases the complexity of what we want to estimate. If my actions now affect not only the payoffs of my future actions, but also the payoffs for all the other players, and vice versa, seems unbelievably hard to estimate, even if we know all of the parameters. Backing out the parameters seems impossible!

Now, we have worked out how to solve games with known parameters, with Pakes and McGuire (1994) and its descendants. Each agent has a policy giving its best responses to the actions of other firms. Taking each agent in turn, we solve for their best policy holding the responses of every other agent, then recompute how the state will evolve.

We can do this by imposing a lot of a priori structural assumptions. It is striking, for instance, that our methods for solving games explicitly rule out collusion. If we included past actions, then we’d have separate states for every combination of paths to get somewhere, which blows up. Instead, we only solve the Markov Perfect Equilibrium, where everything depends only on the current state, and you do not exist in the context of all that came before you. We’re also going to cut down the number of agents, which are often firms, to an absolutely bare minimum – the number of states to solve for increases exponentially in the number of firms, so you will have authors liberally claiming that all firms but two are identical, as Panle Jia Barwick (2008) does. We can, in principle, solve. But it’s going to take a really long time to do so.

If we want to find the parameters, we cannot try out candidate values and solve for equilibrium. Instead, we get the policies from the data – firms are observed to make certain choices, we assume they’re rational, these choices must be the best choices available. We can then take a candidate vector of costs and run it through its paces, totaling up costs and benefits from each run. If we simulate that candidate vector many times over, we have the average costs and benefits.

The results must be robust to a deviation from the optimal strategy, so we generate random noise in the equilibrium strategies, and try out each one. If a lot of the randomly changed strategies are better, the candidate vector of costs must be wrong! So it’s back to the drawing board – pick another vector, and do it again. When you do this many times, you’ll have found the set of costs which best justified the behavior to begin with.

We can now estimate things like firms deciding to enter or not enter a market. Stephen Ryan (2012), who was mentioned earlier, shows that not accounting for dynamics misstates the effect of environmental regulation on incumbent firms. The Clean Air Act of 1990 required cement plants to pay a substantial sum in order to be certified as being lower emissions. You would think that a tax on cement firms would decrease their profits, but instead it increased them – deterring entry outweighed the impact of the tax. Allan Collard-Wexler (2013) is able to put numbers on the importance of uncertainty over future demand in the ready-mix concrete industry (note, this is the stuff which cement is mixed into being, and is not cement itself!), and shows that more consistent government procurement would increase the number of firms in the market and increase efficiency. These are both problems which a static measure of supply and demand would be completely unable to answer.

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There have been methodological developments since. Aguirregabiaria and Mira (2002, 2007) strike a middle ground between Rust and Hotz-Miller, where Rust is fully “efficient” and Hotz-Miller computationally cheap, in single agent settings and dynamic games respectively. “Efficient” here just means that it has the lowest possible errors of any estimator. The reason for this is that choices in one state are connected to your choices in all other states through the value equation under Rust, but are separate in Hotz-Miller. The full nested fixed-point loop forces your estimates to be consistent with each other, and so noise in one cell is going to be slightly balanced out in other cells.

Aguirregabiaria and Mira (2002) take the conditional choice probabilities from Hotz-Miller, and have us compute the implied value function that gives those probabilities. Because we observe the choices made, this is a linear function, and can be solved by inverting a matrix. Now that we have the value of being in that state, we can get the expected value of committing to an action before you observe the shocks too. You then get the probability of taking each action in each state, which replaces the old probability. When they stop changing, that means that the value function is consistent with the observed probabilities. We’re doing the same thing as Rust, in forcing the choices to be consistent with every other choice, but since everything in this is linear due to the logit errors, we can solve it simply.

This actually lines up with some stuff in machine learning. In AM, we do have to invert a matrix every time we find the implied value function, which means that increasing the number of states scales unpleasantly. Neural nets solve this. (As do any function approximator, to be clear). There are several recent papers proposing estimators – Hoang Nguyen’s (2026) job market paper, as well as Oguz and Bray (2026) are two examples.

It is too early for me to judge them for their quality, but I am only cautiously optimistic. AM is already asymptotically efficient, and pretty fast. Many contexts do not actually require lots of variables and states. The main question that I think is freed up is collusion. Past history is just a bunch of variables, after all. I also think this might be useful for questions with continuous variables and many conditions. Investment into health comes to mind.

A fundamental difficulty I have with models of dynamic discrete choice is that we assume that firms have already done the work of figuring out what their optimal policies are, and we are simply trying to recover it from the data. This doesn’t seem reasonable – if computation of even a simplified model with common knowledge of all parameters is dauntingly hard, then computing it when firms have partial information about the costs of other firms is totally unbelievable. Firms were doing stuff before computers were invented. Instead, they use heuristics. If we knew what those heuristics were, we could use them to quickly estimate counterfactuals – and this is what Thomas Wollmann (2018) did, where he simply asked a bunch of people in the trucking industry how they decide to introduce a new model and got consistent enough answers to just use it – but if we don’t know exactly what those heuristics are, we’re going to be wrong. We certainly can’t expect heuristics to last outside of the particular context in which they developed!

There have been very few papers testing rationality in structural models, and many of them are based on toy datasets from experiments where external validity is questionable. Bajari and Hortascu (2005) did it for auctions, and Salz and Vespa (2020) do it for dynamic oligopoly. Bajari and Hortascu give students a unique sum of money which they are bidding to win in a first price auction, and recovers what the optimal bids would have been. Bidders are risk-averse, but they behave coherently and approximately optimally.

Meanwhile, Salz and Vespa have players in the laboratory competing in two person games in which the options are enter or exit at various levels of production, and they feed them the particular cost shocks which structural estimation is trying to recover. They find that the inaccuracy from collusion is small, but that the players were not doing a good job reoptimizing over time. This inertia in decision making led to large inaccuracies in the outcomes.

It is difficult to think, though, that the decisions of the undergraduate population of UC Santa Barbara and Houston while competing for lunch money captures the decision making of real firms for high stakes, bright though they are. When we get into the field, the results are not great for rational firms, although not so bad as to make it unworkable as an approximation. Importantly, though, as firms get larger their strategic sophistication increases.

Hortascu and Puller (2008) have exceptionally detailed data on marginal costs in the Texas electricity spot market, allowing them to identify the accuracy of bids directly. The firms which faced large stakes made more accurate bids, and worsened on smaller stakes. Hortascu, Luco, Puller, and Zhu (2019), using the same environment, show that small firms persistently deviate more from optimum bids. Doraszelski, Lewis, and Pakes (2018) directly estimate Markov perfect equilibrium in a newly created electricity market in the UK, and find that choices converge to the “correct” outcomes over time.

No model is going to be perfect. I do not think that we will ever conclusively know that our model is perfectly specified – but on the other hand, we never conclusively know that the exclusion restriction is met and that our instruments are valid. Our choices must be informed by reasoning about what the data generating process is likely to be, same as anywhere else.

What I would like to see, going forward, is dynamic discrete choice becoming a mature field. I believe we are seeing hopeful signs of it doing so, with the job market papers I cited earlier being sterling examples of this. One still gets the sense, though, that many papers are written in part to answer the question of interest, but are more written to demonstrate that answering the question is possible.

This does not accord with my conception of economics. We do this to know things about the world. We want to be able to say, if we change this thing, what will happen going forward? The methods which people develop should be tools in a toolkit, which we return to over and over again. They should not be something fashioned anew for the occasion, and then retired as a museum piece.

I am thus extremely optimistic about the impact of agentic coding tools on its adoption for answering questions of interest. The current flow value of understanding precisely what you want to do with data has never been higher.

The simplest way of thinking about unemployment is to, in some sense, not have it. All you care about are aggregate wages, and aggregate hours. Workers choose between working and leisure, with diminishing marginal returns to both. A negative productivity shock leads to firms offering lower wages, and workers naturally reduce their hours. All unemployment is voluntary.

That works fine for estimating outcomes in the aggregate, but does not really match micro data. Instead, you might imagine this. Workers, whenever they are laid off, search for jobs, which we think of as job offers arriving at some exogenous rate. These job offers are not identical, but are drawn from a distribution. Given this distribution, which we assume is known by everyone, workers decide whether they want to continue searching, or to take the job. The optimal strategy is simply to pick a wage below which you will not work, and continue searching until you get it.

It is important to note that being unemployed, in this framework, is not a loss of utility, any more than a good with a marginal cost above marginal demand not being sold is a loss of utility. In expectation, you have chosen the path that maximizes your utility. Instead of consuming employment, you are consuming leisure. This is a labor search model in the simplest form, as introduced by McCall (1970).

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Ashenfelter uses neither of these. Instead, the worker is constrained. Unemployment occurs because someone would be willing to work at a lower wage, but cannot, and there is no way for them to negotiate for more hours at a lower wage. Not everyone is in this position – some people are on their labor supply curves – but some people are off of it entirely.

You can then get an explanation for unemployment insurance. Since the employed are on their labor supply curve and the unemployed are off it, taking a dollar from them and giving one dollar to someone unemployed raises total utility. We must have diminishing marginal utility, or otherwise people would choose either to only work, or only take leisure. What’s more, we have an exact formula for the welfare loss – it’s one half the slope of the inverse labor supply curve, times the duration of unemployment. The reason why it’s one half is because it’s a triangle, just like the famous Harberger deadweight loss triangles of a monopoly. When someone is made involuntarily unemployed, the leisure they now consume does have some value, and so the first hours of unemployment are really not that bad.

We will not know, a priori, who is constrained and unconstrained, nor which fraction of the population is so constrained. The clever part of the paper is in identifying these with very sparse data. He would have, if he could, used data on the labor supply choices of people in a household, with the argument that if people are unconstrained, and the leisure of the husband is a substitute for the leisure of the wife, then the husband being involuntarily unemployed will induce the wife to seek more employment that she otherwise would. This is 1980, though, and he does not have that sort of detailed individual data.

Instead, we have a regression. If all people are unconstrained, then the amount of consumption will be fully explained by wages and prices. The unemployment rate – really, labor hours – will have no informational content beyond which has already been captured by the wages and consumption. If, however, all people are constrained, then wages and prices will contain no information about consumption. The only margin through which the economy reacts to negative shocks would be through the number of hours worked. If we’re somewhere in between the two, then this allows you to pin down the fraction of workers who are in each state.

When he does this, he naturally comes to an intermediate answer. Somewhere between 30 and 50% of workers are constrained, and thus off their labor supply curve. This does not, mind you, mean that 30 to 50% are unemployed – simply that they would prefer to work more hours, whether more or less, and cannot.

Now, Ashenfelter is stuck having to make some unpleasant assumptions. He uses the time series of aggregate data, so he has to assume that people’s preferences did not drift over time. He could have controlled for things which change over time, and used variation across space, but then he would have had had to assume that everyone in the United States has exactly the same preferences. The results are thus suggestive.

He does, however, have a roundabout way of testing if the Great Depression was different than normal times. The Great Depression was the only time in which unemployment was high, so he tries out unemployment having a quadratic effect on consumption. Since it does, he can argue that the proportion of constrained workers is higher when unemployment is high.

But the question which Ashenfelter has answered has essentially disappeared. Whether workers are on or off their labor supply curve during unemployment has been superseded in both of the literatures which it touches on. In deciding the optimal unemployment insurance tax rate, we do not see redistributive arguments like this. Instead, we argue that people are unable to perfectly insure themselves against negative shocks, and unemployment insurance is filling the incomplete markets. Meanwhile, on the macroeconomic end, the disequilibrium Keynesian approach had fallen out.

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The unemployment insurance question today is dealt with with a labor search model, although rather than having job offers arrive endogenously we will allow for the worker to exert effort into finding a job. The worker has declining marginal utility of consumption in each period, and so would prefer to consume exactly the same amount in each period. Consumption falling upon being laid off, except insofar as being laid off reveals information about your expected lifetime earnings, is thus inefficient, and the worker would have been better off purchasing insurance. We assume, however, that workers possess private information about their likelihood of being laid off, and thus adverse selection prevents anyone from marketing it.

The optimal unemployment insurance policy needs to balance two constraints. On the one hand, if you pay people to be unemployed, they will be unemployed longer. Since the taxes needed to fund unemployment insurance are costly, this moral hazard is inefficient. On the other hand, greater funding allows the worker to search longer than they otherwise would, for a better job. The Baily-Chetty formula allows you to get the optimal level of benefits (as a fraction of wages) very simply from these two things: benefits over wages is equal to the drop in consumption times the coefficient of relative risk aversion (which simply describes how curved the utility gained from consumption is, and thus how much we love from having unequal amounts over time), all divided by how much unemployment duration responds to benefit generosity.

Raj Chetty (2008) simplifies things down even more, and finds whether benefits should be raised or lowered compared to their current level. People have different levels of liquidity when they are laid off – some people have a lot, some people have very little. In addition, some people receive severance upon being laid off, and so definitely should have more liquidity. The people who have more in savings should have longer unemployment durations, and so do the people in states with more generous benefits. If the change in duration is the same, then there’s no moral hazard channel in unemployment insurance. What he actually finds is that 60% of the response is due to liquidity, and benefits should be more generous.

There is a small problem with labor search models generally, which is that we don’t really see increases in wages upon reemployment for people who received more generous UI benefits. Only one study, Nekoi and Weber (2017), finds this, and it’s not an impressive increase. But I leave the study of unemployment insurance behind, and move on to the macroeconomic aspects.

Keynesianism arose to explain the Great Depression. How could it be that, without anything seeming to change, factories could lay idle while workers wait out in the streets begging to be employed? Keynes’ explanation relied upon what we would now call short-run frictions. If there isn’t enough money, aggregate demand, to satisfy the vector of prices for products and labor, goods go unbought and labor goes unsold. Consumption is entirely reliant upon current period income, and we can fix shortfalls just by printing more money.

Why don’t people adjust their wages and prices? There has been some very interesting work, synthesized in Cooper and John (1988), which argued that there are strategic complementarities in price-setting in the presence of increasing returns. (Two such papers I really like are Weitzman (1982) and Diamond (1982)). Everyone would be better off if prices were simultaneously made higher, but it’s in no one’s interest to do so. This is likely right in theory, but analytically intractable. You do not know which equilibrium we are in, nor what equilibria are possible. It has, reasonably I think, been left behind. Keynes had none of that. Instead, there was a Keynesian cross, and you could simply raise supply with more demand.

We have moved beyond the old-school Keynesian models which Ashenfelter was writing in the tradition of. It is very easy to say that we did so because it did not fit the facts. But in macroeconomics, fitting the facts is not really the ground on which models are tested. Every model can be made to fit the facts. Instead, I think the fundamental problem with it was that it was very ad hoc. Parameters like wage stickiness are simply observed in the data, or as Keynes does, simply stated as a heuristic fact of the world. They do not come as the result of rational, optimizing behavior of people given their preferences and the particular costs to each action.

This will land you in trouble whenever you try to do new things. You will find that why people act the way they do is unsettled. You are like an author who does not know his own character’s motivation – as you try to write more you will find it hard to be convincing. When we would like to make predictions about counterfactuals, you cannot use these heuristic observations or generalities. They do not contain anything fundamental about the world, but instead are particular to the policy regime. If you try to make policy interacting with them, you will find that they will turn to dust in your hands, as Lucas (1976) argued.

To give a simple example, suppose that the constraint on workers is that their wages are sticky downwards. When the amount of money decreases, workers are unable to renegotiate to avoid unemployment. When the price level increases, we get a boom of employment instead. And what we found empirically, especially during the era of the gold standard, was that inflation and unemployment were indeed negatively correlated. The famous Phillips Curve shows that when the price level increased, unemployment was noticeably lower.

What economists leapt to, wrongly, was that we could permanently eradicate excess unemployment and inflation by the clever use of monetary and fiscal policy now that we control the money supply, rather than have the money supply vary with gold discoveries. In fact, we could have the economy be permanently producing at its maximum capacity at every moment.

This is not the case. The Phillips curve only holds with unexpected shocks. Once you start trying to exploit inflation to reduce unemployment, wages are no longer sticky like they once were. People account for it already, and now you need sustained inflation just to keep where you were. And so, in the 1970s, the once solid relationship between inflation and unemployment became unglued, and we had a recession with inflation, something which should have been impossible.

This was the collision with the facts which caused us to move away from Keynesianism. But more than anything, it had a collision with the facts precisely because it was not based on sound microfoundations. It is that which the New Keynesian synthesis has tried to solve.

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To give a brief overview, the model posits the existence of a representative consumer, or perhaps a representative household. This household has certain underlying preferences, like risk aversion or the elasticity of labor supply, and they produce using some technology, also with parameters like the rate of depreciation which we will calibrate from as well-identified as possible sources. Given their preferences, the household can solve for its optimal savings and consumption over time, and aggregate outcomes are found by multiplying up to scale.

Into this, we add frictions. We observe that firms do not change their prices instantaneously – thus, the amount of money in the economy can have real impacts on consumption. Since these firms are producing differentiated products with a markup, more money than expected will increase the efficiency of the economy. Last, we add a rule governing the central bank’s response to shocks, which prevents the rate of inflation from becoming arbitrary.

This gives you a graph that looks awfully like supply and demand. A shift in aggregate demand causes a temporary change in output, and then returns to the usual level of output at a higher rate of inflation. These are results which look like the old Keynesian models, but only when shocks are unexpected. Any systematic attempt to exploit the relation will fail.

These models are not perfect. There has been a small resurgence in interest in Keynesianesque models in two ways. The first is that wage stickiness, rather than price stickiness, does a far better job according with what we see in the world. The other is that firms are often constrained on price and quantity, and how much they are constrained is something which firms might well be optimizing over.

First, there has aIso been some recent work on changing what firms optimize. In particular, I would point to the work of Joel Flynn, George Nikokoudis, and Karthik Sastry. In their first paper, “Pricing and Production Without the Invisible Hand”, they say that firms choose both prices and quantities in the face of uncertainty over both their own demand and costs and aggregate demand. The main advantage of this, I think, is that it gives us a sound explanation as to why uncertainty is an economically relevant problem. A greater dispersion of demands for particular goods leads to quadratically increasing deadweight loss. (Uncertainty in the New Keynesian model affects welfare only obliquely).

The other paper, “Organizational Targets in General Equilibrium”, allows for firms to fix prices or quantities at the beginning of each period, and adjust the other to clear the market. This is a much more sensible way to think about firm behavior than the current state of economics, where some fields assume quantity competition, and others price competition, and nobody seems to care that they’re often describing the same markets. There is no disequilibrium, like in the invisible hand paper, but there is a deeply unpleasant implication for monetary policy. While fixing price and adjusting quantity is optimal when one’s own demand is uncertain, fixing quantity and adjusting price is optimal when aggregate demand is uncertain. In other words, monetary policy becomes less effective at precisely the moment it is needed most.

Their research program is still so young that, while we have high hopes for the future, no prediction can be ventured. What we can say something definite about is wage stickiness, which has seen a resurgence. Every central bank targets a positive rate of inflation, generally around 2%. This is strange, though, when we consider what the NK model predicts. Quite robustly, it is 0% inflation which we want. Part of why we choose 2% is that the instrument through which the central bank affects the money supply is the interest rate on loanable funds, and it will become ineffective if it falls below 0, but only using interest rates is a choice we do not have to make. We could use quantitative easing, and literally “print more money”. People don’t cite the zero lower bound when defending 2% inflation, but instead give an intuition based on asymmetrically sticky wages. Workers, we are told, can accept not being given a raise in a year, but cannot accept being given a paycut, even if it should lead them to be laid off entirely.

This contention is absolutely empirically supported, even if the intuition is unsound. It’s unsound because the wages of currently employed workers doesn’t actually matter for aggregate unemployment, only the wages of new hires do, as Pissarides (2009) shows. It is empirically supported, because the wages for new hires are also distorted. Hazell and Taska (2025) is pretty definitive on this point – using ten years of data from Burning Glass, employers simply will not cut wages, even when unemployment in an area surges. (There is also earlier work, like Card and Hyslop (1997), who document an enormous spike at “no nominal change” in what would otherwise be a normal distribution of wage changes).

There have been surprisingly few models which incorporate wage stickiness. However, I believe the field is trending towards doing so, something I welcome. Doing so can handle some specific problems which standard models have difficulty explaining, and as Basil Halperin (2021) argues, the reasons we switched to sticky prices no longer hold up.

Dupraz, Nakamura, and Steinsson (2025) build one to explain the asymmetric tendencies of business cycles – increases in unemployment are undone by recovery back to the maximum level of employment, while increases in employment are not so undone. (The plucking model of Friedman (1964)). The standard New Keynesian model models price changes as symmetric, with some percentage of firms being allowed to change their prices in each period, and importing the machinery of Calvo pricing would not match the data.

Afrouzi, Blanco, Drenik, and Hurst (2026) have wages set by negotiation between employee and employer. This negotiation is costly, and we would prefer to avoid it. When unexpected inflation comes, the real wage erodes. Since negotiation tends to be costlier than quitting for another job, vacancies increase while real wages decline. This is important because otherwise we would interpret an increase in vacancies as evidence of a “tight” labor market, where the demand for workers has increased, and be mystified when workers are absolutely furious about the inflation of the early 2020s.

The newest trend in macroeconomics is incorporating heterogeneity into macroeconomics – instead of the representative agent from earlier, you have heterogenous agents, or HANK. It is striking that these models started with price stickiness, but moved over to wage stickiness because it fit the data better. Auclert, Bardoczy, and Rognlie (2021) show that HANK models face a trilemma. Without frictions on labor supply, you cannot match marginal propensities to consume (MPCs), marginal propensities to earn, and fiscal multipliers without abnormal parameters. The basic intuition is this – if you see a large increase in spending when someone gets an increase in income, why don’t you also see a large increase in hours worked when wages rise, without the workers being constrained in how many hours they can work? You can finagle sticky price parameters to match these two, but then you’ll get smaller fiscal multipliers then we observe.

It’s a bit on the nose, but is it really a surprise that Auclert, Rognlie, and Straub’s most famous paper is “The Intertemporal Keynesian Cross” (2024)? In that, a stimulus does not just cause a change in current period consumption as in Keynes, but causes a whole chain of responses going into the future, where income accruing to high MPC consumers causes persistent changes in inflation. They wrote it in 2018, not anticipating how prescient it would be in explaining how stimulus checks in 2021 might lead to inflation in 2022.

Macroeconomics is not my area of expertise. I am only a tourist in the domain, who comes through sometimes and gawks at the great edifices created by greater minds. All I can say is that I am pleased with where the field is going. Economic models should follow sensible mechanisms of action, and match primitive features of the data, if we are to inform policy changes.

This was the inaugural article in a series discussing every winner of the Frisch Medal, which is given every two years to the best article published in Econometrica. Looking at the past winners is like walking the Hall of Fame. They’re all very good, and are frequently the progenitor of an entire subfield of economics. I think it would be fun to use them as an opportunity to introduce each one to you, my readers, and in some cases learn about them myself. These are not yet all written — your comments and opinions will have some influence over what comes out first.

We could choose that value arbitrarily, but it would be better instead to observe how much people value their own lives and choose a value of a statistical life in line with it. The traditional method of doing this is to use compensating differentials. If there are two jobs which differ only in their mortality, holding the characteristics of the job otherwise fixed, then in order for the market to clear wages must be higher in the more dangerous sector. This gives us values on the order of $7-10 million dollars, or about $100,000 per year of life.

I have never been particularly convinced by this methodology. I’m not so sure that we are going to capture all the relevant characteristics of a job. It certainly seems plausible to me that jobs where you are more likely to die are more unpleasant in ways we cannot observe, which would bias the estimates of the value of a life upwards. More deeply, the differences in mortality risk are quite small. We’ve had a lot of work in behavioral economics with the through line that people simply do not weight small probabilities in a way that is consistent with rational behavior. We are not extracting a single value of life which comes from a coherent underlying set of desires.

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Nor have I been happy with what it is used to imply. Consider medical care. If we take seriously that people place a value of $100,000 per additional year of life, then we would quickly spend well in excess of what people produce in any given year. This is not tenable, and it is no surprise that healthcare systems limit their expenditures to much more cost effective treatments. The NHS cuts off around 30,000 pounds for an additional year in expectation. These are the “death panels” which you might have heard of in the Obamacare debates. The United States seems to have a much higher value, with Medicare statutorily barred from considering cost effectiveness. Sadly, we (being charitable to the consumer) can’t obtain an estimate of how much people value because they presumably face large costs to finding the optimal pattern of healthcare consumption. The trouble (being uncharitable to the consumer) is that they behave like complete morons when they face costs, cutting back things which are effective as much as they cut back things that are ineffective. See, for instance, Brot-Goldberg, Chandra, Handel, and Kolstad (2017).

But lately, there has been a new line of literature, seemingly unrelated to the question of the statistical value of a human life, which has turned up results that actually support the high estimates. In ride-hailing platforms, the perceived quality of a ride depends both upon the price, and the time. If you have plausibly random variation in both, then you can back out a value for time.

Conceivably, this value of time is also the value that people place upon life. What is uncanny is that, if you take the estimates, which cluster around $20 an hour, and multiply it by the amount of time spent awake in a typical human life, you get the same implied statistical values of a human life – 9.34 million dollars, if a person lives 80 years.

I do not think we can identify the value of life from the value of time in the specific contexts which the ride-hailing papers, but I am first going to detour into describing some of these papers. The methods and customs of these papers are completely different from everything else in this essay; I am describing them simply because I think they are cool. The most straightforward of the studies is Goldszmidt, List, Metcalfe, Muir, Smith, and Wang (2020), written when John List was the chief economist at Lyft. The great advantage of being able to control a firm is that you can create your own exogenous variation. Lyft had field experiments in 13 different cities, affecting 3.7 million customers, in which they randomly varied both the price and the time that people had to wait for it. (Never more than four minutes). The estimates from the experiments suggest that people would value a time savings of an hour at $19.38.

But that’s boring. Being able to experimentally vary everything of interest is kind of like cheating at chess – sure you win, but it’s completely uninteresting. In more interesting studies, there’s Bucholz, Doval, Kastl, Matejka, and Salz (2025), as well as Juan Camilo Castillo (2025). The BDKMS is built off of the relatively unusual structure of ridehailing app (Liftago) in Prague, in which the taxi drivers it links are able to bid on price. This is then combined with the expected time it would take for the driver to get there, and submitted to the consumer as up to four options. The expected time to arrive is quasi-random, as taxi drivers do not know exactly where a customer will be ahead of time. There is a concern that the bids drivers place will be correlated with unobserved demand conditions, but they get around this by using the idiosyncratic bidding quirks of drivers across many days. Some drivers place a higher value on their own time, and bid more than others. They get a value of $13.21.

Castillo (2025) uses a similar trick to get the value of time with Uber data in Houston. The distance from the driver it is sent to is presumed to be plausibly exogenous. Meanwhile, the price coefficient is identified from the surge pricing algorithm, which multiplies the base fare by a number rounded to a tenth. So, if the algorithm says 1.04, you get the base fare, but if it says 1.05 you get the fare times 1.1. You can then trace out the demand curve, in theory, from these little shifts.

Unfortunately, these studies do not resolve the value of life. We can expect two main ways in which it is biased, which go in opposite directions. The value that people place on their time in the context of ridehailing is the difference between the value being here and the value being there. It is not the value of existing. We do not measure the value of simply existing as opposed to not existing. On the other hand, people do not call a ridehailing service at a randomly selected moment in their life. They call it precisely when they need to get from place to place the most. We can see this in the Castillo paper (who finds a much, much larger value of time than anyone else) where trips to the airport have an implied value of time of $6.50 per minute. We have no reason to expect these biases to cancel out each other, so we’re back to where we started.

If you couldn’t tell, I started writing this article when I thought that we could back out the value of life from the value of time. I do not think that there exists any good way to find the value of life. This does not mean that we have to give up on humans being rational – there is always a model which will allow us to rationalize the behavior – but we simply know we’re never going to find that ideal model.

Whatever the value of life is, it should almost certainly be lower than it presently is. We face a budget constraint. We cannot spend in excess of what we produce. We should not choose values which obligate us to spend enormous sums which we cannot muster. This applies both to medical care, but also to other fields, like infrastructure investment.

Specifically, in order to convert the achievement tests in Africa to something internationally comparable, we need to make assumptions which are almost certainly not true. The result is that the educational performance of every Francophone African nation is much too high, and that education is more important than we think. Further, countries like India, while performing much worse than the developed world, are not actually on par with sub-Saharan Africa, and it is reasonable to be more optimistic about India’s growth prospects.

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The first attempt to try and link “human capital” to growth was Mankiw, Romer, and Weil (1992), who propose adding it as a factor of production in a Solow model, and seeing how much of growth they can attribute it to the variable. (For more detail on the Solow model, see here). They find it is surprisingly effective at explaining growth, although attributing causality is difficult. (Do countries get rich because they school, or do they have school because they are rich?). However, their measure of education was really bad. It’s just the average percentage of the population 15-19 that was in secondary school between 1960 and 1985, which completely misses variation in primary school. So, later, better data sets would use years of education as the variable.

But of course, even this is inadequate. The point of school is to learn things. Countries can vary in the number of years they spend in school without varying in what they teach in the end, and they can spend the same number of years for vastly different academic outcomes. The ideal measure of skills in a country is measuring skill itself.

Countries do not all take the same tests, unfortunately, although there have been serious attempts to have many countries take the same tests. The OECD sponsors PISA, which is the gold standard for how to do this. The test is written to be the same for each country despite the language changes, with each student receiving a random draw from a bank of questions, allowing them to adjust for bias in a particular question. The tests are linked from year to year by the use of common test items, and the scores are normed such that 500 was the mean when first administered, and 100 the standard deviation. Other measures of learning will also adopt this norm, so please remember that that is what the scores mean.

Not everybody takes this test, though, and countries have been known to withdraw rather than face the music. Consider India, who has only participated in one round of internationally comparable testing, PISA in 2009. It was a disaster and a national embarrassment. India performed much worse than expected, worse than every other country except Kyrgyzstan. They were so embarrassed by this, in fact, that they have pulled out of every subsequent round of testing, pretending to want to come back for 2020 only to claim “Covid disruption” and cancel it again. Still other countries, including basically all of Africa, have never taken PISA at all. Instead, they have regional tests – PASEC for Francophone countries, and SACHEM for Anglophone ones. What to do?

Patrinos and Angrist (2019) try to construct a set of Harmonized Learning Outcomes for the entire world, and certainly make a brave attempt of it. You can see a map of their learning outcomes through Our World In Data. The key to harmonizing the different tests is to look at countries in which the same tests were administered, and then compare the relative performance of the students on the different tests. This then allows them use these “doubloon” countries to convert from one test to another.

So what does this look like in practice? Take Gabon. (Gabon is a Francophone country mostly on the equator. While it notionally has a relatively high-GDP for the region, this is entirely absorbed by the elites, and the country is very poor. We would have no reason to expect their performance to be exceptional). Gabon took PASEC in 2014, so first we need to convert backwards in time to 2006. This is done through Togo. Then, we take their score and use Mauritius to convert from PASEC to SACHEM. That’s still not enough, though, because to make internationally comparable we need to go through Botswana (which did not take PISA, but does take TIMSS, which is similar).

Things get worse than just pure noise, though. Mauritius, while French is common, uses English as the language of instruction. If they do better on the English test than the French test, then the results of every single Francophone country will be biased upwards. And, well…

What possible common factor might lead Senegal to overperform The Gambia, Burkina Faso and Cote D’Ivoire to outperform Ghana, and Cameroon to outperform Nigeria? Who knows, it’s a mystery. If you take this seriously, you would think that Gabon is outperforming not only India, but also China and most of Eastern Europe.

One of those countries (Senegal) did take a variant of PISA, PISA-D, which is designed to be easier so that we can get more differentiation at the very bottom of the testing scale. By this scale, they scored 412 on normalized outcomes; by PISA-D, they got 304, a full standard deviation worse. (And it’s worth noting that the mean for PISA is a bit higher than TIMSS, which calibrates its mean to a worse sample of countries, so it’s actually a bit too high). When you get down this low, the test becomes unable to distinguish how bad learning outcomes are. You start to bump into the floor of just guessing.

I do not think that this approach of converting from country to country using such tenuous links is useful.The best way to do it is from Sandefur and Patel (2020), who give students in Bihar questions from multiple tests in order to directly compare performance with the same sample at the same time. This is excellent, and we should do more of it.

The other takeaway is that countries in sub-Saharan Africa are doing much worse on educational outcomes than you think. India might be doing poorly, but sub-Saharan Africa is barely on the same scale. This biases our measurement of the influence of learning on economic outcomes through two channels. First, since the African nations are largely at the bottom end of both education and economic outcomes, overstating their education will bias the slope of a linear regression down. Second, even pure noise in the x variable, education, will also bias the slope of an ordinary least squares regression down. (This is because OLS is trying to minimize the squared vertical distance from each datapoint to the line. If you shift a data point a little to the right or a little to the left, these do not have equal effects because the distance is then squared. Measurement error in the Y axis does not have this same effect).

This leads me to have a very pessimistic view of the growth prospects of sub-Saharan Africa. I do not think we can expect them to have the same takeoff into sustained growth as the East Asian miracles, or the post-Soviet countries. I think that they are still afflicted by the long reach of geography.

The California Department of Insurance is much worse than you could possibly have imagined. The Commissioner of that Department has, in essence, the ability to set the price of every insurance product except health offered in the state. They have used this authority to essentially drive out insurance altogether. There are millions of people who would have liked to purchase insurance against their home burning down at actuarily fair prices from private companies, but cannot. Offering it would be illegal. Instead, the state is now on the hook for hundreds of billions of dollars in exposure to risk, growing at 20-40% per year.

This all goes back to Proposition 103 in 1988. By a thin margin, the voters made the commissioner an elected position and required every single price change to be approved by that commissioner. (They also required every insurance company to reduce their rates by 20%, which – I suppose you can just pass a law saying “we should take this group’s stuff from them and give it to us”, but you shouldn’t!).

The Insurance Commissioner has terrible incentives. They are generally someone with ambitions for higher office. If they deny a proposed rate increase, they are the hero saving consumers money. If, years down the line, it leads to reductions in coverage and the insolvency of the state, they have already made it up the chain. It’s the next commissioner’s problem.

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As a consequence of this meddling, private insurers are withdrawing from California en masse. Insurance companies have refused to renew policies in high wildfire risk areas by the tens of thousands. (These graphs are from Boomhower, Fowlie, Gellman, and Plantinga (2025). The colors, by order of lightness, represent quantiles of wildfire risk exposure).

This is in spite of the fact that premiums have increased considerably for wildfire prone areas. Just because prices are allowed to rise a bit does not mean that they are able to rise enough to reflect the actual risk which insurers face.

When people are unable to get insurance from private providers, they can go onto the state insurer of last resort, called the FAIR plan. You don’t technically have to buy insurance, but it is a universal requirement of mortgages that you do, so in practice most people must go to the state plan. This is funded by a consortium of all of the insurers in the state. If there is not enough money to pay premiums, then the money is raised by levies on policy holders across the state.

Now, you might ask, why not have the government be the insurer of everyone? What’s the harm? I think this is a fair and important question, and we are better off for thinking clearly through why this is the case. We should not be confused here, though – there is no good case for the state providing wildfire insurance in lieu of private insurers.

The state cannot make the costs of insurance go away. They can only redistribute them. If a catastrophe strikes California, California has to pay those who purchased policies. They can do this either by having accumulated savings from the premiums paid into the system, or by making up the losses with taxes levied on the public.

Both of these options are distortionary. They lead people to make decisions that they would not have otherwise made, and we are worse off for them. The choice we must make, then, is if we would rather this distortion be in where builders choose to place homes, or in people’s labor supply decision. This is an easy choice to make!

When the government insures the risk of wildfire at a rate below the fair cost, they are subsidizing building in areas exposed to wildfires. It creates the risk. When we raise taxes, the things we get are things we don’t want, like people reducing how much they work. When we raise insurance premiums to their actuarily fair level, we get what we want more of – people not moving into dangerous areas, and limiting their exposure to wildfires. It should not be the objective of the government to subsidize people for living in riskier areas at the expense of those in safer ones.

We don’t have evidence of the behavioral distortions directly from fire insurance in California, but we do have analogous work on flood insurance, which has been federally provided since the 1960s. While there is not much evidence on the location of development (this is really hard to identify), Philip Mulder (2021) finds that misclassifying the risk of homes, and charging them the wrong rate as a consequence, reduces social welfare by 138 billion dollars by blunting the incentive to adapt to the risk of floods. Katherine Wagner (2022) finds that raising premiums actually raises welfare, by forcing homeowners to adapt.

There are other problems with government insurance. The government also lacks any real incentive to cut costs. If the plan is overstaffed, there are in fact strong disincentives to cutting them – who wants to be the enemy of a union when they run for office later? And the public insurer has a limited incentive to offer lower rates in exchange for people taking precautionary measures against wildfires. This is one of the main mechanisms in the Mulder paper on flood insurance – the elevation of the building is really effective in reducing flood losses, but because it does not get passed on to the value of the home, as Hovekamp and Wagner (2023) find, it’s underused.

The best argument for these regulations is a bad, selfish one. If prices are set without political interference, the premiums in each state will be determined by the particular risk of that state. If we say that firms must pay a fixed cost to exist as a firm, and then sell in multiple states, then restrictions in one state will cause firms to exit, and rates to rise in the unregulated state. California could profit by immiserating the other states in the union, and that is what Oh, Sen, and Tenekedjieva (2026) find.

Defenders of the status quo will cite billions upon billions in cost savings. They are definitely incorrect about this. When rates are negotiated, a denied rate proposal does not at all mean that companies would have done that. In truth, we have no idea what it would have saved the consumer without detailed knowledge of markups and the relevant demand curve. Remember, there is no way to obviate the costs – they can only be passed around.

This is just not going to get better on its own. What we can do is cut the damages. So, to my Californian readers out there – please do not vote for Jane Kim. She is an astonishingly bad candidate, and is running on a platform of taking from the “greedy corporations”.

Instead, vote for Patrick Wolff. He is a chess grandmaster, who then went on to work in a macro hedge fund. This is his first run for office, and he will not be running for any others. I believe that he will be the candidate most willing to do what is needed to fix California’s insurance markets.

The election is on June 2nd. Make your vote count!

The room is consistently hot, and so the windows are left open. However, below the window runs Memorial Drive, and the sounds of automobiles can be heard. Ordinary traffic is not bad, and passes without event, but sometimes a particularly loud car passes by. When this happens, the professor stands up and shuts the window.

I assert that this is not optimal under some reasonable assumptions. It would be better either to shut the window at the beginning, or to leave it open throughout the class. Choosing to close it conditional upon a negative shock occurring is always worse than one of them.

Consider an idealized case, analogous to this. Suppose that we are flipping a coin. We would like to maximize the number of heads that we have, minus the number of tails. At each point in time, we can choose whether to flip again, or to stop and collect our winnings. We can then choose whether to play again or not. There is no decline in our utility – all we care about is maximizing our number of heads.

What we can see is that, if we must wrap things up in finite time, there is no rule which gets us more heads than tails. We can’t stop whenever we’re up by one, because the next time around we’re as likely to be down by one as up. We can’t break up a series in a way which benefits us, because either way we only care about the running series of heads or tails. What is interesting is that we can guarantee a positive payoff if we grant infinite time – we swear we’re going to keep going until we are positive, and then stop. In infinite time, we will eventually get there. We cannot guarantee it happens in finite time.

The window is not a coin flip, of course. It starts open. Let’s suppose that opening or closing it requires a cost of c. Thus the payoff to always closing it is -c. Let’s say that we receive utility u from the flow of fresh air into the room, and suffer disutility d from a car which arrives with rate λ. Thus the value of always staying open is u – λd.

The value you get from stopping whenever you receive a car, or when you receive k cars, is equivalent to the value of always staying open u – λd times the expected duration, minus the cost of closing the window times the likelihood you do do it. (Always open and always close corresponding to 0 and 1, respectively). If you adopt a rule of reacting to a car arriving, then the probability becomes 1 – e, with e to the power of negative λ times the expected duration. Both of these are controlled by the same λ, however. Because the cars are arriving randomly, the reactive rule is actually just the same as any random opening of the window. There’s no way around it. You don’t learn anything about the world from what you observe, because they are arriving in a Poisson process and are uncorrelated with each other. The only optimal action is to take the expected value of staying open, and seeing whether it exceeds the cost of closing.

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And yet, that is not what we see. We see a consistent reactive rule. Presumably, then, there is something in our basic model which we do not include. Perhaps the process of cars arriving is not memoryless, and a car passing signals more to come; or perhaps the Professor is inattentive and has the cost lowered by the sound of the car. We can propose a specific change to the model, and adduce evidence as to why this particular modification is preferred to other modifications.

A common criticism of models in economics is that they are unrealistic. But you see, they have to be. We need to know what happens in the cleanest, most simplified versions of human behavior in order to understand what exactly we must change in order to get the behavior we observe. For how else are we going to know what we have to change? Simple, unrealistic models are the only way to understand what really causes what.

How about we consider a related problem? Suppose that we are flipping coins again, but this time we care about winning “series”. Define this as a cluster of games – if you have more heads, you get one point, and if you have a cluster of more tails, you lose one point. This game can be played to win with a very simple rule. Whenever you flip a heads, you end the game. Whenever you get a tails, you flip again. This gets you one point half the time, 0 points (because of the tie) a quarter of the time, and you lose one point the remaining quarter.

Ah, but we have a problem! There exists a possibility that the game will go on infinitely – we flip tails over and over again, never being able to stop. This means that the expected points as a function of coin flips is actually 0. What to do?

I want to show you some magic. Change our objective to accumulating points as fast as possible. At each moment, we can choose to stop and collect our point, or we can continue. There is some optimal policy which gives us a long-run average rate of g*. Stopping gives us what we have, and resets, while continuing gives us a fifty:fifty shot of the state increasing by one, or decreasing by one. What continuing also costs us is the average payoff from the optimal policy, whatever it is. The equation we are maximizing is written out below.

We can obviously see that we stop when the state s equals 1. We also know we have to stop at some negative value, which we’ll call b, and continue when it is in some intermediate region between the two. But what should that value be? Rearranging terms and multiplying away the halves, the value of an average period (times two) is equal to h(s + 1) – 2h(s) + h(s – 1). This expression is the same thing as the second derivative of h(s), so g* originally corresponded to a quadratic function. g*s^2 + As + B, where the latter two terms are going to go away when we take derivatives.

This gives us three unknowns. We can solve for each of them. B we normalize to zero, because we set a tie game (equivalently, the state is 0) to equal 0. Get rid of it. We also said that we would stop at s = 1, and get a payoff of 1. Therefore, g*(1) + A(1) = 1, and A = 1 – g*. Substitute 1 – g* every time we see A. Last of all, we stop at -b, so we plug in as before and get that g*b^2 – (1 – g*)b = -1. We now need to get g* alone – skipping over the factoring, we are left with:

So what do we do now? We know that if we want to find the maximum of something, we take the derivative. Skipping over taking the quotient rule, we are left with -b^2 + 2b + 1. If you set it equal to zero, you simply have something to apply the quadratic formula to. The optimal b to stop at, b*, is simply 1 plus the square root of two. If you are forced to only have integers, the optimal policy is to stop after two or three negative flips.

This is called the Bellman equation. It is at the heart of optimizing behavior by people. You will see it again and again. Become familiar with it.

You will not, of course, always get the nice closed-form solution as here. Recall one of the many times which I have discussed Berry-Levinsohn-Pakes, or nested fixed-point loops in general. (See, for instance, this essay on exogenous product characteristics). When we don’t have it, we simply take a guess at what the optimal policy is, and then manually check if it’s accurate. And we could have done that here, too – we could have simulated thousands of different policies, and we would have discovered that stopping after 2 and 3 would slowly pull ahead. But isn’t it beautiful when we don’t need to do that!

Included below are the thresholds which trigger more intensive review. HHI, or the Herfindahl-Hirschman Index, is the sum of squared market shares, out of 10,000 because we are squaring the percentages. Four firms controlling 40, 30, 20, and 10 percent of the market would give you an HHI of 3,000, which is a highly concentrated market. Neatly enough, if you are willing to assume firms with constant marginal costs competing on quantity, then the Lerner index (price minus marginal cost, all divided by price) is equal to HHI over the elasticity of demand.

The antitrust authority is balancing two competing interests. On the one hand, we would not like firms to monopolize a market, reducing total welfare. It is worth noting that, under any mode of competition where firms are earnestly competing with each other, an increase in concentration must increase market power. (Why do I specify that the firms are earnestly competing with each other? Because if they are in collusion, then the sustainability of the agreement is determined both by the number of parties to the agreement, and also by the symmetry of the firms in it. It is possible for mergers to destabilize a collusive cartel – see Igami and Sugaya (2021) for more.) If there are several firms in the market engaged in Cournot competition – such that they set the quantity they would like to produce first, and then choose the price – the markup is equal to 1 over n, where n is the number of firms and 1 is the markup which could be obtained by a monopolist.

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On the other hand, we would not like to encumber advantageous combinations of firms. Firms buy each other for a reason – indeed, there is some reasonable argument that a merger must have efficiencies because otherwise the two firms would not agree to it. They would prefer to continue receiving 2n profits, rather than the profits one firm can attain with one fewer firm. This says nothing, admittedly, about consumer welfare, and breaks the moment we move away from homogenous product Cournot to differentiated product Bertrand.

The law is in a strange state, because it really does push you to the interpretation that no merger, no matter how efficient, can be allowed if it should increase market power. Once a case makes it to trial, efficiencies are no defense. The decision not to challenge is a pragmatic recognition that obviously, preventing any firm from buying another would be absolutely insane.

All this is leading up to a paper I read recently by Nocke and Whinston, who argue that the initial screens used by the FTC are ill-conceived. Remember that the FTC cares about both the level, and the change. Nocke and Whinston argue that this doesn’t make sense – there is simply no role for the level in assessing the anti-competitive effects. In any of the standard models they consider, the level is simply irrelevant to the merger, at least when we are considering the unilateral ability of a firm to affect its own profits. (Things are different if fewer firms are more able to engage in collusion).

This is in line with something that antitrust economists have been hollering about for a while, which is that you cannot simply regress HHI on price and expect it to mean anything. Any observed level of concentration can be consistent with any level of markups, depending upon the particular cost and demand conditions in that market. It’s only once we hold fixed the costs – and hence, only care about the change – that concentration can map onto something meaningful.

Nocke and Whinston then go on to ask – “wait a second, why are these thresholds set where they are?”. The answer is pragmatism – they were written in 1982 without reference to theory, and then revised in 2010 to bring into line with agency practice, but not out of some high minded theory. What they find is that the thresholds are almost certainly set too high, and that there should be more scrutiny of mergers. Even small changes in concentration would require large efficiencies in order to benefit the consumer, which are not in line with what they believe normal efficiencies from mergers to be.

I am somewhat skeptical here of the implicit claim that efficiencies of five percent are so unlikely, however. It just doesn’t seem that big of a change, and the observed price changes after mergers in the consumer packaged goods market (see Bhattacharya, Illanes, and Stillman (2025)) are not inconsistent with substantial reductions in cost.

I would have liked to, here, provide a comprehensive and lengthy overview of what we know about the efficiency gains from mergers. Unfortunately, though comprehensive, it will not be lengthy. Some seemingly obvious, simple methods do not produce satisfactory answers. We cannot simply pool together consummated mergers, and compare to what happened in industries which had mergers denied, or against the consumer price index as a whole. On the first point, the decisions of the FTC/DOJ are not random, and will be correlated with the expected price effects. On the second, suppose that a merger entails paying a fixed cost in order to receive a permanent reduction in marginal cost. Companies will do this if they expect to receive more demand in the future, even after conditioning for everything we can observe about the firms. This is the same reason why we would not expect a fund buying a stock to be what caused it to rise – rather, it was the private information which they had which did it. (I have made this point before, in the context of institutional investors).

Actually measuring the efficiency gains from a merger is extremely hard, generally requiring very detailed data on the actual production of a good. (We can’t use revenue per unit of input, because revenue is itself something which is determined by market power, and thus by concentration). We need to either estimate a complete demand system, impose a model of competition, and back out the marginal costs before and after the merger, or we need to inquire into the particular details of firms and industries. There’s much to be said for the latter because it allows us to say something about why marginal costs changed.

Most of the gains appear to be managerial in origin. People with good ideas for how to use resources buy them from those who don’t know how to use the resources as well. It does not appear to be the case that structural advantages, like avoiding having to duplicate staff, are that important, with a few exceptions. This makes sense, although it is unfortunate that it makes efficiencies close to unforecastable. (The FTC will have no way of telling whether someone will actually be a better manager or not).

Think about why ownership in a firm exists at all. There exists some set of assets. We would like to elicit effort from multiple people – workers, managers, suppliers – in order to put these assets to the most productive use. Ownership, which is just the receipt of profits after incentivizing everyone else, should reside with those whose effort is hardest to describe. If you can exactly describe what must be done, then you simply write out a contract where someone receives payment in exchange for the agreed upon things being provided. It’s much harder for someone to describe in advance an idea – indeed, you can’t describe it without communicating what it is – so instead people who have better ideas for the use of the assets buy the other company.

Let’s first look at some studies which find the marginal costs directly, rather than backing out the marginal costs from a demand system. (I prefer these because they are more likely to allow us to say why the efficiency gains happened). Mert Demirer and Omer Karaduman have a working paper on power plants, which is an excellent industry to study – the good is homogenous, and we can rule out changes in the quality of products or their placement before and after the merger, which keeps things very simple. The striking pattern is that more productive companies buy the underperforming assets of less successful companies, and then bring them up to speed with the average of the company. Robert Kulick (2017) finds something similar in ready-mix concrete plants. Successful plants tend to acquire the poorer performing competitors.Here, physical productivity rises after acquiring, although the net effects are outweighed by changes in market power from the point of view of the consumer. Something we must be cautious about is that a reduction in output caused by an increase in market power might also cause a rise in productivity if there are increasing marginal costs to producing output. Hortascu and Syverson (2007) are also in the ready-mix concrete market, but are concerned with vertical integration between cement manufacturers and concrete plants, which is much less of a concern for antitrust authorities. One might be concerned that the cement plants would use what market power they have to drive out their competitors, but this is not so.

Looking at historical industries, Braguinsky, Ohyama, Okazako, and Syverson (2015) do not find an increase in productivity in early 20th century Japanese cotton spinning mills, conditional upon operating, but they do find that more productive firms keep lower levels of inventories and utilize their capacity better. When they acquire less productive firms, they use their capital to the full extent they’re able to, consistent with more productive firms having better management. If you’ll recall Bloom, Eifert, Mahajan, McKenzie, and Robert’s (2013) famous experiment providing management consulting to Indian textile firms, much of the improvement in output came from implementing inventory management systems. When it comes to mechanisms, this is similar to the Hortascu and Syverson paper discussed earlier, where the gains from mergers came through better logistical coordination of orders, allowing the capacity to be used more efficiently.

Matt Schmitt (2017) looks at hospital mergers between 2000 and 2010, and finds that costs drop by 4 to 7% compared to otherwise similar hospitals which did not merge. These cost reductions cannot be explained as a simple function of changing who the hospitals served. These cost reductions are caused only by acquisitions by multi-hospital chains, and are not found for in-market mergers. In some negative news for mergers, Blonigen and Pierce (2016) apply production function estimation techniques which I have previously discussed at length here to estimate changes in markups across many different mergers of manufacturing firms. They find no evidence that costs fall for merging firms, although I will point out that we will miss improved capital usage under this method.

There have been some excellent studies on mergers in the beer market, including the one which provided the data which Nocke and Whinston used (Miller and Weinberg, 2017). Ashenfelter, Hosken, and Weinberg (2015) is one of the few papers which finds good evidence of predictable efficiencies. In 2008, Miller and Coors, the second and third largest manufacturers of beer in the country, were approved for a joint venture. The main reason to expect this to reduce costs was that Coors was until then only manufactured in Colorado, and then shipped around the country, while Miller had six plants dispersed across the country. Coors would move their beers in Miller plants, cutting the average distance between a local market and a Coors brewery by 364 miles. The change in concentration was offset by the gains in efficiency, if we assume earnest Nash-Bertrant competition. Now, as Miller and Weinberg show, the consolidation enabled coordination between Budweiser and MillerCoors, and the net effect on the consumer was harmful. (Ironic how directly the data on which the Nocke Whinston paper was calibrated contradicts their fundamental assumptions).

I find it frustrating how little we know about the prospective effects of mergers. More, please!

Many people have suggested that this might be a cause of America’s high health care prices. Accordingly, there have been several initiatives to improve price transparency in healthcare markets. In particular, the CMS required that all hospitals in America provide a machine-readable file of all items and services beginning in 2021. Surely, this will reduce healthcare costs?

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We cannot be so sure that this is the case, though. The relationship between information and market outcomes does not have a ready, reliable relationship, and could go either way depending on the circumstances. Suppose there are several sellers of a homogenous good. Under Bertrand competition – which is to say, prices are set first – the price will equal marginal cost. The only way for them to get positive profits is to collude on setting higher prices. Stigler (1964) argued that the great enemy of such collusive behavior are secret price cuts; Green and Porter (1984) showed that collusion is still possible even when you cannot observe prices and quantities, by treating every decrease in demand for your own product as a breakdown of the agreement, but it makes the agreement fragile and imperfect. What the colluders would really like is to know exactly how much every other firm produces and what price they sell it at, even though it’s not in their interest to unilaterally reveal it. Government interventions in favor of price transparency allow the firms to get around their collective action problem – and that’s bad for the rest of us.

There’s a cool case study of the ready-mix concrete industry in Denmark which is relevant here. Concrete – note, not cement – is an extraordinarily non-transportable good. Once you mix it together, it starts hardening, and it must be delivered to the job site within an hour. This means that each concrete mixing plant can serve only a small area, and while there are many plants, each market serves only a small area. In 1993, the Danish government decided that the status quo – rigid posted prices, but frequent secret discounts to bulk buyers – would not do, so they required that each quarter the concrete firms place their prices in the industry newsletter. Prices immediately rose by about 15-20%, and stabilized at a high level. What’s more, there was no more dispersion of prices, strongly suggesting that the firms were using the information to converge upon the same price. Not without some embarrassment, the Danish government repealed the law in 1996.

But what is strange is that it can actually go the other way. Consider the case of the gasoline market. In gasoline, above competitive prices are maintained not through direct collusion at a permanently high level, but through an Edgeworth cycle (1897), which was formalized by Maskin and Tirole (1988). In the simplest case, suppose that there are two firms who set their prices every other day, trading whose day it is back and forth. Suppose the good can be produced at no marginal cost with no cost of storage, and that the optimal price for their own welfare would be 1. Both start with a price of 0, and make no profit. It is therefore a matter of indifference to a firm if their price is at 0 or 1, so one firm chooses to raise their price and goes from 0 profit to 0 profit. The point is that the other firm will follow them by setting their price at just a hair under 1, so that you can undercut them the next day just a hair under what they set, and back and forth until you go down to 0 and the cycle resets. It looks like this:

This figure is from Byrne, de Roos, Lewis, Marx, and Wu (2025) with data from the Australian gasoline market. The gasoline companies received the prices of their competitors, updated every 15 minutes, from a company called Informed Sources. The Australian competition authority disliked this, as they thought that the detailed information was allowing the firms to converge upon supracompetitive prices, and began an investigation. One of the firms, Coles, was in a weaker position and chose to settle before the others, leading to them withdrawing from the platform. The others, which settled later, did not withdraw. Thus, Coles would

What happened is that when Coles raised its prices, enabling others to just undercut it, they would not be able to cut as aggressively as before. Prices were actually higher, and the cycle would last longer. You can see the red line of Coles above the others, and persistently so.

From their calculations, the uninformed firm actually profited, though not as much as the others did. This is in line with other work showing how, when having algorithms setting your price, knowing less about the demand for other products actually allows you to converge to supracompetitive prices when knowing more would lead to the competitive outcome. Cooper, Homem-de-Mello, and Kleywegt (2015) compare what happens when firms don’t know the demand for their own products, and try to discover it with random price experiments. Quantity demanded is dependent upon both one’s own prices, and also on the prices of competitors. Yet, including the prices of competitors into a simple regression model will be less profitable, because it leads to firms converging toward the competitive price, rather than the joint profit maximizing price which observing only your own prices would lead you too. The firm would prefer to be blinded to its opponents’ prices!

Providing information to one party, even in secret, need not necessarily be to their advantage. Zoe Cullen and Bobak Pakzad-Hurson have a paper examining the effects of “Right of Workers to Talk” laws, which establish a protected right of workers to discuss with their fellow workers at a firm what their wages are. It led to an immediate drop in wage by about two percent, concentrated among educated workers who are more likely to have meaningful negotiations about their wages. The channel was that now the firm could credibly say that they can’t pay you anything more, because if they did, they would have to pay everyone else that too. The workers would be better off if they couldn’t know what other people made at the firm, yet they all individually benefit from peeking.

The effects of knowing wages within a firm are not the same as knowing wages across firms, of course. Arnold, Quach, and Taska (2025) exploit legal changes in Colorado requiring that workers include salary information in online job postings. They have data from Lightcast (formerly BurningGlass), which is pretty transparently scraped data from Linkedin, and find that wages increased by 1.3-3.6%. Notably, pay in jobs which were already transparent increased afterwards, consistent with much of the effect being from enabling competition.

I bring these up to illustrate that the relationship between information and prices is incredibly context dependent, and does not imply that more information is always better. So, after the long detour, we return to our original example. Should we mandate price transparency in healthcare markets, or should we not?

On net, it appears that price transparency laws reduce healthcare prices. What is striking, however, is that it does not appear to be due to consumers shopping around, but entirely due to changing the bargaining power of insurers. When price transparency affects prices, it is through the channel of insurers being better informed about the deals that other insurers are getting, and pushing for tougher prices. We need not expect this to raise welfare – and indeed, we could even expect it to reduce it.

One key line of evidence comes from New Hampshire, who was the first state to mandate hospitals report prices for standard imaging tests like X-rays and CAT scans, and whose website for them has been consistently considered the best in the union since then. First Zach Brown (2019) and then Yujie Feng (2025) study the effects on prices, which did indeed fall. However, Feng shows that this is due to the insurers, not consumers. She can show this because only some insurer-procedure combinations get listed (their rollout is staggered), but all of them fall, whether listed on the website or not.

This corresponds with how infrequently the price transparency websites were actually used by the consumer. Given the dispersion of rates, and the fact that checking is free, consumers must be leaving a lot of money on the table by not checking. And yet, they consistently don’t check. Between 2011 and 2013, only 1% of state residents actually used the website. When the state advertised their service, it led to a 700% increase in the number of people using it, yet had no effect on people’s use of lower cost providers. It is worth noting that the results of Kwon and Zhang (2025), who use a similar website in Maine, and do attribute some of the decline to shopping around. It doesn’t fit the narrative, though, so let’s skip over it.

By contrast, when the prices being revealed are more relevant to the shopping consumer, it actually increases prices. Barnes, Glied, Handel, and Kim (2024) conducted an experiment in New York on price transparency in billed charges, which are not the same as the negotiated rates, and are much more relevant to out-of-network consumers who will be actually paying much more of their own bill. Here, they found that prices became less dispersed, and the average price paid actually went up, consistent with some of the providers learning that they were charging too little relative to their peers.

Supposing that price transparency does bring down prices through the insurance channel. How sure are we that this is a good thing? Consider a bilateral monopoly, where one insurance company negotiates with one healthcare provider over the optimal set of payments. The solution is given by the gains from trade, the outside options available, and the bargaining weights to each (which is a reduced form parameter, but you can think of it as the discount rate of each), which gives us a unique division of surplus. If price transparency changes the bargaining weight of the insurer, this has no effect on the price paid by the consumer. This remains the same monopoly price before and after.

Now I must not be too pessimistic. A good deal of the gains from this will be passed on to the consumer, although I do not know how much. I would not say that I am an unquestionable expert here, but I cannot find an estimate of the effect of a shock to bargaining weights alone on premiums. However, I can say with great confidence that it will not “cure” America’s high healthcare prices.