The Work of Raj Chetty

A comprehensive survey

Raj Chetty is best known for extremely labor-intensive studies, with dozens of research assistants assembling and cleaning datasets to answer enormous questions. This approach can answer questions that nobody else can really answer, because no one else has the data! Who else has the tax records of millions of people, linked to their home address over decades? Archimedes said that with a long enough lever he could move the world; with a detailed enough administrative dataset, one can answer anything. Chetty’s work is much deeper than mere regressions, though. Reading his work, what I was most impressed by was its depth. It is often clever, ingenious, and gives insights far beyond simply answering a specific question.

A theme of his early work is trying to find sufficient statistics. Given a model of the economy with a few assumptions, what is the minimum of facts which we have to find in order to infer the welfare effects of some change? Sufficient statistics are a bridge between what are called structural models, and reduced form strategies. Reduced form strategies are likely the ones you have seen the most of, as it is a term encompassing all of the standard causal methods toolkit which economists use all the time. It is kind of going from the top down, being agnostic about mechanisms, and simply sees what happened when certain things changed. Structural models work from the bottom up, and try to measure deep, underlying parameters about people’s nature and preferences. With those “primitives” in hand, you can plug them into a model and try out counterfactual policies.

That all was a bit abstract, so to make it concrete, let’s take Chetty’s 2008 paper on unemployment insurance and unemployment. Increasing payouts for unemployment do indeed make unemployment spells last longer. However, there are two reasons for this to be so. On the one hand, you have the obvious channel where paying people to be unemployed leads them to be unemployed. On the other hand, let’s imagine that matching with the right job takes time. If households are liquidity constrained, then shortening their unemployment spell is bad. In order to tell whether increasing unemployment insurance is good or bad, we need to tell which effect dominates the other, and by how much.

The primary contribution of the paper is to show that you don’t need to estimate why households have the liquidity constraints or moral hazard that they do. A structural model would go about estimating how constrained people’s borrowing ability is, the curvature of their utility function, and other such “primitives”, at the cost of the estimates being probably unsound. However, since any combination of primitives which results in the same moral hazard and liquidity has the same welfare implications, you don’t need to concern yourself with what they are. And obviously, simply regressing differences in unemployment insurance across states on unemployment cannot answer the question, because a longer spell of unemployment could be either good or bad! It isn't perfect compared to a structural model – you can only answer some questions, and would be unable to convincingly solve for the effects of really big changes – but it’s a lot better than knowing nothing at all.

He finds that it is the liquidity effect which dominates. 60% of the increase in the length of unemployment is owing to removing liquidity constraints, while 40% is due to moral hazard. He shows this in a few ways. First, he compares the change in unemployment duration when benefits increase for constrained and unconstrained households (with constrained being proxied for with asset holdings and such). Second, he uses the receipt of severance upon the end of employment to generate variation in unemployment duration. Obviously, receiving severance is not random, but since it only has an effect on liquidity constrained households we might reasonably infer that removing liquidity constraints pushes us closer to the social optimum. In conclusion, the optimal unemployment benefits would be half of the period wage.

One of the early sufficient statistics papers was Feldstein (1999), who was Chetty’s advisor starting in undergrad. There, we want to identify the deadweight loss from income taxation. There are multiple ways in which we can change our behavior – changing our labor supply, changing how we consume, etc – but since optimization requires that they all have the same utility loss on the margin, we can fully capture the change in behavior from the change in taxable income. Chetty would update this by allowing for the possibility of simply evading taxes by misreporting. The taxable income elasticity is, alas, not a sufficient statistic for welfare in that case. Since some of the elasticity of the richest is simple evasion, higher tax rates aren’t nearly as bad as they seem.

He would also be persistently interested in how we should understand risk aversion. Take “A New Method of Estimating Risk Aversion”, which is actually one of my favorite papers ever written. The simplest way to generate risk aversion is to say that people have declining marginal utility of income. Gaining a thousand dollars when you have a billion is a pittance, while gaining a thousand when you have nothing is life-changing. Thus, if we were given a choice between $500 and 50:50 shot at getting $1000, we would always take the former. The utility gain from the first $500 is larger than the second. We can describe the curvature with the coefficient of relative risk aversion, designated gamma.

Chetty’s insight is to recognize that under this definition, risk aversion, and the behavior of people when their pay increases, are one and the same. If your marginal utility declines as you earn more income, and the disutility from work is constant, then the extent to which you reduce your labor gives us an implied curvature of the utility function, and thus a coefficient of relative risk aversion. He needs to rule out the possibility that consumption and labor are complements, but he can do this fairly easily by looking at how much people reduce consumption when they lose their ability to work. The mean implied value of gamma is below one, and getting it above 2 would require a lower elasticity of labor supply than found in any of the 33 studies he considers as evidence.

This contradicts the finding of risk-aversion drawn from financial markets. One of the common explanations for the “equity premium puzzle” (which is the wide gulf between the return to stocks and the return to bonds) is that people have very high levels of risk aversion. Given that these two methods of estimating risk aversion under the marginal utility framework give us wildly different answers, we are forced to conclude that risk-aversion comes from something other than just the curvature of the utility function.

Risk aversion would be the focus of most of the rest of his early work as well. If risk aversion is due to the curvature of the utility function, and it is strictly concave down, then we have no way to rationalize people both buying insurance and lottery tickets. Chetty and Szeidl (2007) provides sound microfoundations for why marginal utility might be bendy. Conventional analysis of risk assumes that people consume perfectly divisible goods. If this isn’t the case, then people will opt into consumption bundles consisting of indivisible goods, such as a house or a car. Thus, people are quite sensitive to risk over substantial gambles, which would impinge upon their variable consumption, but quite open to risk when it, like a lottery, could transport them into a new level of consumption. This two-good model, one sticky and the other flexible, also well explains apparent habit formation better than standard habit models. In particular, it explains why consumption is affected by anticipated small shocks, but not large shocks; and argues that benefits levels should be lower than the optimum calculated with standard models.

Chetty’s first step into miraculous data access is his paper “Salience and Taxation”, with Adam Looney and Kory Kroft. A fundamental assumption in tax theory is that the incidence of a tax is ultimately determined only by the elasticity of supply and demand, and not on who it is levied on. It shouldn’t matter if a sales tax is paid at the register, or incorporated into the price tag.

They, of course, find that it really does matter how the tax is administered. The first strategy is to compare states with taxes on beer which are levied at the counter or when the supplier buys them, and they of course find substantial differences. The other strategy, though, is getting a major retail chain to try out incorporating sales tax into the price displayed. I do not know how they convinced the supermarket to go along with it — as far as I can tell, they just asked nicely.

I think his greatest paper is the duo of papers with Nathaniel Hendren on intergenerational mobility. (They were once one 143 page behemoth). It combines the ingenuity of methods of early Chetty with the perfect data of later Chetty to reach profound policy implications.

We would like to know how much the place you grew up in affects your outcomes later in life. A starting point would simply be to regress the characteristics of the place you grew up on later in life outcomes. If poor or rich people sort to places with different characteristics, though, then your regression is biased. One can control for the characteristics of the people, but this won’t work for two reasons. First, you are never going to plausibly control for all the characteristics which would affect later outcomes. Second, you are not able to observe many characteristics, nor tell which direction causality ran. Take intelligence, which predicts later income. You can’t directly observe someone’s latent ability, so you would proxy for this with their test scores – but whose to say if the test scores are associated with being in a given area due to people moving, or if the area caused higher test scores? You need exogenous variation in exposure to different areas.

The method they use is simple but genius. Families move together, and children tend to stay with their family until they are grown. If a family moves together, then the younger children will be exposed to the new environment for longer. If everyone moves out at 18, then a family which makes a move with children at 12, 10, and 8 will get 6, 8, and 10 years of exposure to the new neighborhood. Comparing within the family allows you to pick up on everything which is static over time, not just what is easily observable. They also control for income and marital status, which varies over time.

It would still be better to have an exogenous cause of moving. After all, perhaps a move reflects a changed attitude toward work, which also has a linear exposure effect. They use plant closures and natural disasters as a source of variation. Last of all, they wrap things up by seeing if the outcomes of children matches the variation of an area, conditional on exposure. Different places might have the same average incomes, but skewed differently. Alternatively, the effects of places could vary by gender. They find that outcomes do indeed vary in line with the places in the way that you would predict, which shouldn’t happen unless families anticipate not only the average effect but also how it varies by gender.

It is perhaps telling of my biases as an economist that I am almost disinterested in telling you the actual results, in preference to discussing the methods. People converge to the income of the new place at a rate of about 4% per year. The size of the effect is exclusively related to the time treated, and not directly related to the age at which a child moved except insofar as moving earlier allows you to be exposed for longer. This is fairly enormous for policy purposes, which has often fetishized early life interventions. Turns out, we should not expect anything magical about early life.

Part one focused on the effect of place, but without trying to explain why. Part two investigates the effects of counties. The chief difficulty here is that instead of potential outcomes of children being unrelated to the decision to move on average, you now need the condition to hold for 3000 different counties. The innovation over the first paper in the series is measuring the effects of parents who move after their kids have grown. This would be generalized as the “Opportunity Atlas”, which presents the impacts of all census tracts on later in life outcomes.

Chetty, with Hendren and Larry Katz, covers much of the same ground in “The Effects of Exposure to Better Neighborhoods on Children”, trading generalizability for identification. Moving to Opportunity was a government program in the mid-1990s which gave some families on Section 8 housing vouchers money which would only be spent to move to a better neighborhood. Moving has a fixed cost of disruption, and then positive effects related to the length of exposure. This would be replicated by another large-scale experiment in Seattle.

Perhaps another way to improve life outcomes is better education. With data from (not mentioned in paper, but later confirmed in courtroom testimony) New York City, consisting of 2.5 million students and 18 million tests from 1989 to 2009, he can find the value added of teachers to students test scores, and thence the value added of a high quality teacher to lifetime income. This is not a trivial matter, of course. Students and their parents have some influence both over the school they go to, and which teachers they have. Here, controlling for observables is a more plausible approach, and we even have more information than before – they have parental income, which has approximately 0 predictive power. (They find that a $10,000 increase in income leads to a – let me make sure I have the zeroes right – 0.0001 standard deviation increase in teacher value added. That’s the same as moving from a 50th percentile to a 50.0018 percentile teacher.)

We can do better, though. Teachers move from school to school, or quit altogether. A teacher changing to another school with unusually high or low value added would show up as a change in the average value-added for a grade in a year. Chetty, Friedman, and Rockoff’s argument is that, while parents might be able to push for being assigned to some classrooms over others, they are very unlikely to abruptly shift schools based on whether one above or below average in a grade level was over the summer.

The second paper ties test scores to later income. Methodologically this is uninteresting – if you have the value added and the income, your work is done. They argue that replacing a teacher in the bottom 5% of value added with an average teacher increases lifetime income by $250,000. Chetty would later testify to that effect in Vergara v. California, which ruled California’s union rules around teacher hiring and firing unconstitutional.

Their approach of finding teacher value-added is not without criticism. Jesse Rothstein (2017) would argue that teacher switching is not actually exogenous, and this leads to their results to be substantially smaller than otherwise believed, especially the connection to later life income. Prof. Rothstein argued for the defense in Vergara v. California; as Chetty, Friedman, and Rockoff note in their reply, “much of this paper is taken from response letters that we submitted to the American Economic Review during the review process of the CFR papers. In particular, two of Rothstein’s concerns – on imputation and long-term controls – were raised and addressed during the referee process. Rothstein was one of the referees of the CFR papers – a fact that was disclosed during his testimony for the defense in Vergara v. California.” (Footnote 2). CFR argue, in essence, that any bias in the results is very small, and does not substantially upset the results.

Similarly to his work on intergenerational mobility, he (with Friedman, Hilger, Saez, Schanzenbach and Yagan) has a paper studying the same problem with an RCT. Project STAR was an experiment run by the state of Tennessee to test the impacts of small and large classrooms on student outcomes. Conditional upon being within a school, the classroom which you got was randomly assigned, and thus uncorrelated with everything else. Having a small classroom, even for a few years, had positive effects in school, in likelihood of going to college, and thence incomes.

In the interest of space, I will not discuss all of his papers in detail, much though I wish to. I have tried to keep to those papers which are the most thought-provoking, not necessarily those which are most policy important. I will cover them here in rapid-fire format.

He has two enormous papers on the causes of innovation. The first, “Who Becomes an Inventor in America?”, disambiguates the latent ability to invent from having the environment to do so. High-income individuals are much more likely to patent than below average individuals, even after controlling for math scores. In particular, having someone in your family or in your neighborhood patent greatly increases the chance that you do so in the same narrowly defined patent class. Since the determinants of innovation are largely due to career choice driven by prior exposure, tax cuts have only a limited ability to increase innovation, as they show in a follow-up paper.

Racial disparities in income, conditional upon the income of the parent, are entirely explained by differences between black and white males, with no difference for women. There is also considerably more intergenerational mobility among hispanics and whites than for black and Native Americans. Part of the black-white gap is on account of lower marriage rates, so considering individual rather than household outcomes will reduce the gap. The high upward mobility of Asians is entirely driven by first generation immigrants, after which they have similar outcomes.

Card, Chetty, and Weber (2007) is similar in conception to his paper on unemployment insurance, and exploits a quirk in eligibility for severance in the Austrian labor market to estimate how people change their search behavior when they have cash on hand. This again finds that people are meaningfully credit-constrained, and the permanent income hypothesis does not hold perfectly.

I have not covered all of the excellent papers which he has been involved with, as I want to cover them in later blog posts. I think he could be deservedly awarded the Nobel this year; part of me believes that they should not worry about fitting in the old folks, and just award it now. This has been the third part of an ongoing series on the great economists of our time; previously, I covered Duflo, Banerjee, and Kremer, and Paul Krugman.