The workshop’s purpose and themes were as follows:

The general purpose of the workshop is on the one hand to examine the state of the art in the area of asymmetries and irreversibilities relating to commodity market instability and development, with the purpose to first pinpoint gaps in current research, and secondly to highlight promising areas of policy intervention to aid developing countries to manage/cope with market instability. As the topic is very large, and impossible to cover in all of its various aspects, the workshop will restrict its proceedings to a set of specific themes that are judged to have been underemphasized in previous empirical and policy development economics research. While commodity market instability can originate in many ways, the workshop will be restricted to market instability arising from natural or other unpredicted events, as well as unforeseen market developments.

You can find the program and the papers presented at the workshop here by clicking on the relevant tab. The event was an excellent occasion meet with colleagues old and new and discuss a topic which has occupied a sizable proportion of my professional life as well as to receive feedback on the experimental work I have been doing with Yu Na Lee and David Just on price risk preferences.

]]>a variable that is not in itself directly relevant, but that serves in place of an unobservable or immeasurable variable. In order for a variable to be a good proxy, it must have a close correlation, not necessarily linear or positive, with the variable of interest.

For example, we may observe a dummy variable for whether one has started a business as a proxy for entrepreneurial ability. Or we may observe one’s IQ as a proxy for intellectual ability. Or we may observe the frequency of elections as a proxy for democracy. The possibilities here are endless.

For the sake of argument, then let’s denote our proxy variable–what we actually observe in lieu of D–as D*, so that

D* = f(D) + u,

where f(.) is a mapping from D to D* and u is some kind of error term to make the relationship between D and D* stochastic, for if that relationship were deterministic and D* were equal to f(D), then observing the proxy D* would be as good as observing the variable of interest D.

Our ideal goal is to estimate the coefficient c accurately in the regression

(1) Y = a + bX + cD + e,

but the best we can do is to estimate

(2) Y = a* + b*X + c*D* + e*,

where the stars denote that a and a*, b and b*, c and c*, as well as e and e* are different things given the move from (1) to the following equation:

(2′) Y = a* + b*X + c*f(D) + u + e.

If you’ve taken a minimal amount of econometrics, you already know where this is going: We now have to contend with u being in the error term, and so if u is correlated with any of the variables on the right-hand side of (2′), then we are dealing with an endogeneity problem.

An example might be useful here. Suppose we are using a dummy variable D* for whether one has started a business as a proxy for entrepreneurial ability D. In this case, it is reasonable to argue that the proxy is measured with error. Specifically, D* will tend to underestimate entrepreneurial ability. Indeed, many academics are what one would deem “entrepreneurial” in that they undertake risky activities that might have high payoff and are willing to invest in activities where the production function is nonconvex (such risky and nonconvex activities are really what tenure is designed to foster, by the way), but few academics start businesses, save for the occasional consulting business on the side. In this example, D* would tend to understate D, which would lead to a biased estimate of c* (and this discussion implicitly assumes that the correlation between D and D* is “good enough” for D* to pick up any significance that D might have in its relationship with Y).

In the best-case scenario, u is uncorrelated with the variables on the right-hand side of (2′), but that isn’t always the case, and it isn’t even clear that this is frequently the case. And then there care cases where the variable that you use as a proxy really does not have a monotonic relationship with Y, and in which case any statistical test related to c* is unidentified because you don’t know what to test for. Zack Brown and I once won an award for pointing out, using relatively simple micro theory, that wealth is a terrible proxy for risk aversion in applied contract theory–in addition to changing the curvature of a utility function, a change in wealth also changes utility at the margin, which complicates the relationship between contract choice and wealth by making it nonmonotonic in most cases. Here is the abstract of that paper:

Tests of risk sharing in the contracting literature often rely on wealth as a proxy for risk aversion. The intuition behind these tests is that since contract choice is monotonic in the coefficients of risk aversion, which are themselves assumed monotonic in wealth, the effect of a change in wealth on contract choice is clearly identified. We show that tests of risk sharing relying on wealth as a proxy for risk aversion are only identified insofar as the econometrician is willing to assume that (i) the principal is risk-neutral or her preferences exhibit CARA; and (ii) the agent is risk-neutral.

Given the frequent use of proxies, it pays to think carefully about two related questions when doing empirical work:

1. Are any of the variables in the regression of interest proxies for something else? Even a variable like GDP per capita is really only a proxy for standard of living, and it often happens that we treat proxies as being the thing we are really interested in. With all due respect to my poli sci friends, a number of variables used in the international political economy literature to measure “democracy,” “human rights,” etc. strike me as obvious proxies.

2. If any of the variables in the regression a proxy for something else, how might that proxy measure the variable of interest with error? Is this error more like classical measurement error, in which case this causes attenuation bias (i.e., c* is biased towards zero, or what a friend and colleague once called “the good kind of bias”), or is this error systematic, which introduces systematic bias (and not necessarily of the good kind!) in your estimates?

Against 1, I guess the solution is to be honest about what we are truly measuring and use careful language in doing so. In our forthcoming *JDE* article on female genital cutting (FGC), for example, Lindsey Novak, Tara Steinmetz, and I were careful to talk of “respondents *who report* having undergone FGC” rather than of “respondents who have undergone FGC,” because short of interviewers physically verifying FGC status, it is impossible to know whether a woman has actually undergone FGC.

Against 2, the solution is to assess whether there is bias and, if so, what is its direction. In some cases (the “good kind of bias” cases), the bias serves to strengthen a significant result by providing a lower bound (in absolute value) on the true effect. In other cases, it gets trickier. As with any endogeneity problem, one might have to use an instrumental variable to deal in such cases.

]]>It’s the summer, so I have time to read, both for work and for pleasure, and I have time to read books instead of just journal articles and blog posts. This made me realize that while a lot of my thinking has been shaped by things that I have read in journal articles (economics is an article-based field) and in blog posts (there is no better means of spreading important ideas quickly), a large part of my thinking has been shaped by books, which often contain more exciting ideas than journal articles–because they face less strict of a review process, books can be more daring in their claims, and thus have more chances of causing you to change how you view the world.

So I decided to write this series of posts on books that shaped my thinking. I talked about development books three weeks ago; I talked about food and agriculture books two weeks ago; and I talked about economic theory books last week; this week I will talk about econometrics. Some recommendations are very general; others are eminently personal. I just hope you can find one or two that will also shape your own thinking. I’m sure I am forgetting a lot of important books I have read and which have also shaped my thinking, but I made this list by taking quick look at the bookshelves in my office. Conversely, some of the books in this list also appeared in my previous post on The Books that Have Shaped My Thinking.

Josh Angrist and Steve Pischke, *Mastering ‘Metrics*. Perhaps the single, most concise statement of how empirical work is currently being done in applied microeconomics (i.e., labor, development, health, urban, environmental, law economics, etc.) This book is so well written it can be read by economists and noneconomists alike, and any smart undergrad can read it and learn something about how we learn from real-world data in economics.

Josh Angrist and Steve Pischke, *Mostly Harmless Econometrics*. This is Angrist and Pischke’s earlier, more technical book, which essentially presents the same concepts as their more recent book, but with the necessary technical details. Even then, the book is easy to read (for an econometrics text, that is), and highly informative.

Angust Deaton, *The Analysis of Household Surveys*. Though this book isn’t strictly about econometrics, Deaton presents a good review of the core concepts in econometrics. Perhaps more importantly, this book is about how to collect data from household surveys and construct the variables you need. Survey data is messy and is a far cry from the perfect data sets econometrics students are presented with in their classes, and this is the best source to learn how to collect, construct, and analyze survey data.

James Hamilton, *Time Series Analysis*. I’m not really a time series guy. The closest I’ve ever been to one was in my 2015 article on food prices and food riots. Before that, it was when I was doing my Masters in Montreal and took a PhD-level course in time series analysis, for which this book served as the reference text. This thick, heavy book pretty much has all you need to know about time series. If you ever wanted to learn the ins and outs of forecasting time series data, this is the Bible.

Cheng Hsiao, *Analysis of Panel Data*. When I was doing my Masters, I was fortunate enough to take a course on microeconometrics, where we learned about discrete-choice models, hazard models and duration data, and panel data. This was the recommended text for the panel-data part of the course. It contains much more than most applied economists need to know, but it is a valuable reference nevertheless.

Peter Kennedy, *A Guide to Econometrics*. This is hands down my favorite econometrics book. Kennedy splits each chapter in three: First, a big-picture view without any technique. Second, a technical appendix with all the nitty gritty. Third, an appendix with historical details and anecdotes for those who want to know more. This book is what taught me that econometrics was as much art as it was science, and that it could be taught in an intuitive way. I refer to it very often.

Tony Lancaster, *The Econometric Analysis of Transition Data*. This was the reference text for the hazard models and duration data part of the microeconometrics class I took during my Masters. It’s getting a bit old, but no matter–it’s still a good introduction to the topic, which can be supplemented with Nick Keefer’s 1988 JEL article on the topic.

G.S. Maddala, *Limited-Dependent and Qualitative Variables in Econometrics*. This was the reference text for the discrete-choice models part of the microeconometrics class I took during my Masters, and it remains one of my favorite econometrics books. I remember the sense of wonderment I felt when I learned that you could analyze qualitative data using econometrics, and how powerful the tools in this book were. Probit, logit, all kinds of tobit, etc.–this book covers those topics in a nice way.

Stephen L. Morgan and Christopher Winship, *Counterfactuals and Causal Inference: Methods and Principles for Social Research*. This was what I read to get the technical know-how and details related to the potential outcomes framework. Morgan and Winship also have a very nice discussion of regression methods vs. matching methods, which few people seem to understand.

Judea Pearl, *Causality*. I wish I could say I read the whole thing, which is fairly heavy on the technical details. But the appendix, which includes the slides of a talk Pearl gave for the entirety of the UCLA community as an introduction to his research, taught me a lot about causality, and it seriously changed my thinking.

Jeff Wooldridge, *Econometric Analysis of Cross Section and Panel Data*. Perhaps the ultimate reference text for the methods used in applied microeconomics (and more). I remember when I bought my copy in 2002, and how I thought that this book was going to be a game changer after looking at the table of contents and leafing through it. Wooldridge writes very clearly and explains everything very well–more concise than Griffiths et al. (the first econometrics textbook I ever used), a bit more user-friendly than Greene (seen by the older generation as *the* classic).

- Food Policy 1.799
- Food Security 1.495
- American Journal of Agricultural Economics 1.327
- Journal of Agricultural Economics 1.278
- European Review of Agricultural Economics 1.271

The number to the right of each journal name is the journal’s impact factor, which has been calculated on the basis of calendar year 2014 citation numbers.

This has not been a good year for agricultural economics journals–both *Food Policy*, which I edit, and the *American Journal of Agricultural Economics*, at which I serve as associate editor, have seen their impact factor go down. But that seems to be true of a lot of journals. The *Journal of Development Economics*, for example, has a new impact factor of 1.798. If I recall correctly, it used to be well above 2. Moreover, a few journals that I believe to be very good surprisingly did not make the top 5.

But that is only *one* top 5. Bear in mind that the rank ordering might differ significantly depending on what other indicators of quality you look at, or whether you consider reputation. In agricultural and applied economics departments, for example, many people still consider the *AJAE* as the no-contest top journal in the field, no matter what impact factors say.

]]>The main purpose of Canada’s supply management policies, implemented for dairy, poultry and eggs in the 1970s, was to protect farmers from price fluctuations. These policies have three main components: 1) fixing prices, 2) establishing tariff barriers in order to keep lower-priced foreign goods out, and 3) managing supply with quotas so as to avoid price-depressing overproduction.

The beneficiaries of these policies, at least at first glance, are Canada’s 13,500 dairy, poultry, and egg farms, representing about 1/8 of all farms in the country. However, supply management hurts all 35 million Canadian consumers by forcing them to pay consistently more for milk, chicken, and eggs, as well as for other products that use these foodstuffs as ingredients.

Importantly, supply management disproportionately hurts poor Canadians. According to a recent study by researchers from the University of Manitoba, supply management imposes an additional cost of $554 a year on the richest 20% of households, representing 0.47% of their incomes. In contrast, the corresponding burden for the poorest households ($339 a year) represents 2.29% of their incomes. These policies are therefore heavily regressive, hurting poor households almost five times as much as rich households.

… [Y]ou should consider publishing a blog post about how you handle various types of missing data when you are working with secondary data. … I come across data with a lot of [missing] values when analyzing managing household data. I get confusing and contradicting responses when I search on Google as well as when I ask my peers about how to treat missing values. I feel how we handle missing values affects the reproducibility of one’s results hence I wanted to learn if you have any suggestions on how to manage missing values. I am of the view that I may not be the only one who can benefit from learning how you handle this issue when analyzing data for your various research projects.

That is a good question, and its object is something which is not discussed often in econometrics classes, where students are often presented with data sets that have been cleaned and have no missing values. As the email indicates, real-world data is often much messier.

Suppose you have the following regression:

Y = a + bX + cD+ e,

where, as is usual, I use Y to denote the outcome of interest, X to denote control variables, and D to denote the variable of interest, i.e., the treatment variable. The parameters a, b, and c are what we are interested, especially c. To keep things simple, let’s say X is a single variable instead of a vector of control variables.

Suppose you observe D for everyone in your sample, but you have missing data for X. What should you do? Here are a few options:

1. *Ignore the problem*. When I taught at a policy school, I often had remind students that, as much as people in policy schools would like to ignore it, doing nothing is *always* an option in terms of policy. Same thing in econometrics: you can choose to ignore problems. With missing data, there is an implicit assumption that is made when you ignore the problem, viz. that data are missing at random. If you are going to ignore the problem, you should think carefully about whether data are likely to be missing at random. For example, when I asked people in Madagascar whether they had a bank account and, if so, how much they had in it, all in an effort to figure out people’s assets, many people refused to answer. I suspect that the more people had in their bank account, the more likely they were to refuse to answer the question, and so ignoring the problem would lead to a sample that is biased in favor of people who have a higher savings rate, or who are wealthier.

2. *Run a balancing test*. If you want to have an idea of how missing data may bias your sample, you can also run balancing tests. That is, use a t-test to compare the mean of Y for those observations with missing X versus those observations with X present, and do the same for D. If you fail to reject the null hypotheses that (i) the mean of Y is equal for those with X and those with missing X, and (ii) the mean of D is equal for those with X and those with missing X, you can be a bit more confident that your missing values for X appear to leave the sample intact. If you find, say, that there are systematic differences in some variable between those with X and those with missing X, that tells you how those missing values might bias your sample.

3. *Run the sub-regression Y = a + cD + e with and without those observations for which X is missing*. Is c roughly the same across samples? If so, then that is an additional reason not to worry about missing values for X, given that c is the parameter of interest. Of course, if you have missing values for D, that is a different problem.

4. *Use “missing dummies” to keep those observations*. You can create a dummy variable–let’s call it Z–equal to 1 if X is missing and equal to zero otherwise. Then, create a variable X’ equal to X if X is nonmissing and equal to zero otherwise, and estimate

Y = a + bX’ + gZ + cD + e.

This has the advantage of retaining all observations. This is something a reviewer once asked me to do, and though it feels like a bit of a kludge, I think it is fine when presented alongside the results of a regression where you treat the missing values of X as missing at random (UPDATE: A comment on Twitter links to this, noting that this strategy really isn’t great), which brings me to…

5. *“Do both.” *This is pretty much my mantra when it comes to applied econometrics, which is more like rhetoric than dialectic, and in which you need to show that your finding holds over and over in different specifications, building your case for it like a lawyer would build his client’s case in court. So don’t be afraid to do all of 1 to 4 above.

6. Another thing you can do is to impute those missing values. That is, regress X on D and get the predicted values of X, i.e., X hat, and replace missing values of X with the X hats. This also feels like a bit of a kludge, but when used with other methods, and not as your only solution, it should be all right.

7. Finally, should you be lucky enough to have an instrumental variable that (i) is relevant, i.e., it is correlated with missing values, and (ii) is valid, i.e., it only affects Y through X, you can try to estimate a 2SLS or selection correction model, but this seems like a lot of work, and it is rare that we have a good IV for D, not to mention for X.

(UPDATE: 8. Some commenters on Twitter said they missed having “get better data” among my list of proposed solutions. It was missing (heh) on purpose, because it really should go without saying that if you *can *get better data, in most cases, you will.)

The foregoing presupposes that you have a sizable proportion of your sample with missing X. If you only have five cases where X is missing out of 500 observations, I don’t think anyone will seriously mind if you treat those missing values as missing at random. But if, say, more than 5% of your sample is missing, you might want to run through the list above–and even that is an arbitrary rule of thumb. The best thing to do, as always, is to be forthcoming about the problem, explore how it might compromise (i.e., bias) your results, and try to show robustness as best as you can.

]]>It’s the summer, so I have time to read, both for work and for pleasure, and I have time to read books instead of just journal articles and blog posts. This made me realize that while a lot of my thinking has been shaped by things that I have read in journal articles (economics is an article-based field) and in blog posts (there is no better means of spreading important ideas quickly), a large part of my thinking has been shaped by books, which often contain more exciting ideas than journal articles–because they face less strict of a review process, books can be more daring in their claims, and thus have more chances of causing you to change how you view the world.

So I decided to write this series of posts on books that shaped my thinking. I talked about development books two weeks ago; I talked about food and agriculture books last week; this week I will talk about food and agriculture. Some recommendations are very general; others are eminently personal. I just hope you can find one or two that will also shape your own thinking. I’m sure I am forgetting a lot of important books I have read and which have also shaped my thinking, but I made this list by taking quick look at the bookshelves in my office. Conversely, some of the books in this list also appeared in my previous post on The Books that Have Shaped My Thinking.

Pranab Bardhan, *The Economic Theory of Agrarian Institutions*. This one was in my development list. There was a time when development economists took theory seriously, and this book came out of that time. This book is a bit uneven (it’s an edited volume), but the introductory chapter by Joe Stiglitz is probably the single, most important statement ever made about peasants in developing countries being rational. In short: Whenever you find yourself thinking that some behavior you observe in a developing country is stupid, think again. People behave the way they do because they are rational. and If you think they are stupid, it’s because you have failed to recognize a fundamental feature of their economic environment as crucial in how you model their behavior.

Pranab Bardhan and Chris Udry, *Development Microeconomics*. This was also in my development list. This book is getting on in age (it was published in 1999), and it should be supplemented with more recent papers, but as far as concise statements of theory that underlies the study economic underdevelopment at a micro level, it does not get better. In the PhD-level course we co-teach on development microeconomics, Paul Glewwe and I still use this book as the core text. If you are a development student, I encourage you to read and digest the contents of this book. The field of development has been largely a-theoretical for the past 10 years. Something tells me this is changing and we will see the return of theory, because people are starting to care a lot more about the mechanisms through which stuff works or not. Another such book is Kaushik Basu’s *Analytical Development Economics*, which I enjoyed going through when I took Kaushik’s course in grad school, but which is a bit narrower.

Gerard Debreu, *A Theory of Value*. I never liked general equilibrium theory. I think the whole thing is too contrived and unrealistic, and when I learned about it in grad school, I knew I was never going to actually use that knowledge–especially in the form taught to us via Mas-Colell et al.’s textbook (see below). But Debreu’s book is the most concise and elegant statement of the fundamentals of general equilibrium modeling I have seen. It seems weird to write the following, but here goes: This book, which borders on applied math, practically reads like a novel.

Patrick Bolton and Mathias Dewatripont, *Contract Theory*. I became an agricultural and applied economist because I wanted to study the economics of agrarian contracts, and I developed an interest in contract theory as an undergrad at the Université de Montréal. The years while I was writing my dissertation (finally!) saw textbooks on contract theory come out–prior to that, you had to read the foundational papers, which I did when doing fieldwork for my dissertation in Madagascar. I am not a fan of Salanié’s textbook on contract theory, and I don’t like the notation in Laffont and Martimort (2004). Bolton and Dewatripont hit just the right balance for me. (And yes, there seems to be a distinct appeal to contract theory for francophones; Salanié, Laffont, and Martimort are all French; Bolton and Dewatripont are Walloon–French-speaking Belgians).

Robert Ellickson, *Order without Law*. This one was also in my development list. Life in developing countries is often dictated by social norms which we are not familiar with. How do social norms emerge and evolve? Ellickson makes the case that social norms arise to maximize welfare and minimize transaction costs, and that they evolve for the same reasons. He builds his case masterfully and illustrates it with a case study of the cattle ranchers of Shasta County, California. Because Ellikcson is a legal scholar, he writes wonderfully, and this practically reads like a novel.

Marcel Fafchamps, *Market Institutions in sub-Saharan Africa*. Also in my development list. What enables agents to trade with each other in a setting where legal enforcement is often not an option? What institutions develop to sustain transactions in those settings? What is the role of traders? Marcel Fafchamps develops a simple theoretical framework to answer those questions, and he then discusses the evidence. Again, don’t let the title fool you: This is about much more than Africa, as the model and conclusions apply to most if not all developing countries.

Drew Fudenberg and Jean Tirole, *Game Theory*. The book we used to learn game theory in grad school was horrendous. This is really the Bible of game theory, and it is where I gained 95% of my understanding of game theory.

Jack Hirshleifer and John G. Riley, *The Analytics of Uncertainty and Information*. This book is not as well-known as Fudenberg and Tirole for game theory, but it accomplishes the same purpose for risk and uncertainty, which Mas-Colell et al. don’t cover very well. A lot of what I have learned about risk and uncertainty modeling comes from reading this book. There are more modern treatments, including Gollier’s *The Economics of Risk and Time* as well as Gilboa’s The Theory of Decision under Uncertainty. Unfortunately, both Gollier and Gilboa’s books have been sitting on my bookshelf for a long time, entirely unread.

Andreu Mas-Colell, Michael D. Whinston, and Jerry R. Green, *Microeconomic Theory*. The–THE–Bible of microeconomic theory. I understand there might be better books out there now, but this is where I learned it all. The exposition is as elegant as can be. My copy has been highlighted, annotated, and beat up, but in a bad case of Stockholm syndrome, I went from hating micro theory to absolutely loving the beauty and elegance of it once I was done going through this book. (And go through this book we did during my first year of grad school; and then we had to take a four-hour exam on all its contents at the end of the year to merely qualify as doctoral students!)

Nancy Stokey and Robert Lucas, *Recursive Methods in Economic Dynamics*. In my dissertation, I needed to develop a dynamic principal-agent model to account for reverse share tenancy in Madagascar. So I took a half-semester of dynamic programming as part of Cornell’s macro sequence and learned just about enough about dynamic programming to be dangerous. Unfortunately, the model I developed in my dissertation was relegated to an appendix in my 2012 *Land Economics *article–one of those cases where I wish I’d had the courage to stand up to the reviewer who said “get rid of this” by insisting on having the model in the paper instead of in an appendix.

Knut Sydsaeter and Peter Hammond, *Essential Mathematics for Economic Analysis*. I can’t find the actual text we used when I was an undergraduate, but it was by those two. A lot of people swear by Chiang’s text, which is really getting on in age. At Cornell, people swore by Simon and Blume, for obvious reason. But the book by Sydsaeter and Hammond is where I learned how to do math like an economist should.

Hal Varian, Microeconomic Analysis. The production chapters of Mas-Colell et al. are okay at best, so much so that when I took the micro sequence in 2001-2002, we actually learned production theory from Varian’s text, which offers a much better treatment. This book is not as good as Mas-Colell et al.’s, but I list it given that that’s where I learned the theory of the firm, which has guided a good amount of my thinking over the years.

]]>

Hewing to the table of contents in legacy texts, today’s market leaders continue to feature models and assumptions at the expense of empirical applications. Core economic questions are mentioned in passing if at all, and empirical examples are still mostly contrived, as in Studenmund (2011), who introduces empirical regression with a fanciful analysis of the relationship between height and weight. The first empirical application in Hill, Griffiths, and Lim (2011: 49) explores the correlation between food expenditure and income. This potentially interesting relationship is presented without a hint of why or what for. Instead, the discussion here emphasises the fact that “we assume the data… satisfy assumptions SR1-SR5.” An isolated bright spot is Stock and Watson (2011), which opens with a chapter on ‘Economic Questions and Data’ and introduces regression with a discussion of the causal effect of class size on student performance. Alas, Stock and Watson also return repeatedly to more traditional model-based abstraction.

The disconnect between econometric teaching and econometric practice goes beyond questions of tone and illustration. The most disturbing gap here is conceptual. The ascendance of the five core econometric tools–experiments, matching and regression methods, instrumental variables, differences-in-differences and regression discontinuity designs–marks a paradigm shift in empirical economics. In the past, empirical research focused on the estimation of models, presented as tests of economic theories or simply because modelling is what econometrics was thought to be about. Contemporary applied research asks focused questions about economic forces and economic policy.

I have argued in the past in favor of teaching the craft in addition to the technique of econometrics, both here and here. Here is a bit more of Angrist and Pischke’s piece, and I emphasize a bit I disagree with:

The unapologetic focus on causal relationships that’s emblematic of modern applied econometrics emerged gradually in the 1980s and has since accelerated. Today’s econometric applications make heavy use of quasi-experimental research designs and randomized trials of the sort once seen only in medical research. In fact, the notion of a randomized experiment has become a fundamental unifying concept for most applied econometric research. Even where random assignment is impractical,

the notion of the experiment we’d like to run guides our choice of empirical questionsand disciplines our use of non-experimental tools and data.

See an old post of mine titled “Of Gold Standards and Golden Means” for why I don’t think methods should be driving our choice of questions.

]]>As always, suppose you have observational data, and you are interested in estimating the causal effect of your variable interest D on your outcome of interest Y, and you also have access to a vector of control variables X. For the sake of argument, let’s assume there is only one control variable in the equation

(1) Y = a + bX + cD + e.

The parameter of interest is c. If you have observational data, then you know that in most cases E(D’e) is different from zero–that is, D is endogenous to Y in equation 1, and c does not capture the causal effect of D on Y.

But what about X? It often happens that X is also obviously endogenous to Y–say, because X is a decision variable which is determined by each individual respondent’s expectation of Y, which would constitute a case of reverse causality.

In terms of the peer-review process one thing I would not encourage you to do is to try to find an instrumental variable for X. Why is that? To put it simply, if a bit cynically: Because D is your variable of interest, and it is difficult enough to deal with the fact that D is endogenous–that is, how well you do so will determine how well your paper is received by reviewers and editors–that attempting to deal with the endogeneity of your control variable exponentially expands the number of reasons why your reviewers might recommend that your paper be rejected.

Seriously, I still sometimes see papers where the authors are looking at the effect of some variable of interest D on some outcome of interest Y, but where they spend a considerable amount of time trying to deal with X (generally, those authors are also waist-deep in likelihood procedures like the Heckman selection model, too, so dealing with X is only one of a laundry list of things they burden the reader with). But that is really besides the point, because it is D that is the variable of interest, not X.

So how do we deal with endogenous controls? First, let’s think about what an endogenous controls means:

- An endogenous control X means that E(X’e) is different from zero, which obviously means that the estimated b in equation 1 will be biased.
- An endogenous control X also means that the OLS estimator for c–the parameter of interest–will be biased, since X appears in the formula for the OLS estimator of c (see here for the OLS estimator in a simple, two-variable case). Moreover, see this article by Frölich (2008) for a discussion of how both OLS and 2SLS will be inconsistent in the presence of endogenous controls. That is, they do not converge to the true value of the parameter of interest.
- Excluding the endogenous control X means that X is now in the error term e, and so if X is correlated with D, then your estimate of c is
*also*biased.

This suggests the following: If D and X are uncorrelated, then it is better to leave X out of your regression altogether, because in that case, it does not bias your estimate of c, *no matter how much variation in Y is explained by X*.

If D and X are correlated, then you have a problem either way. Omitting X means that you have an omitted variable bias. Including it means that your estimates are inconsistent. (See here for an enlightening, short discussion of bias vs. consistency.) What should you do? I think the middle-of-the-road approach is the usual “do both,” that is to present results both with and without the endogenous control, and see what changes. But even that is not terribly satisfactory, since there is bias in both cases, and “get a better research design” is even less helpful.

Ideally, you would find a good (i.e., valid and relevant) IV for X, but those are difficult to find, and if the IVs used for endogenous variables of interest D in the papers I have seen trying to tackle the of endogenous controls X were usually not the best, the IVs used for those endogenous controls were even worse.

Also see here for a discussion of this issue which I found a bit difficult to follow given the many voices involved (and a few typos, I think). There is also this article by Lechner (2008), but it seems specifically geared towards matching methods.

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