Luquitas Figal Garone Agradecemos a Marcelo Leiras que nos envío esta reseña.

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The Stata Journal (2009)

9, Number 2, pp. 315–320

A statistician’s perspective on “Mostly Harmless Econometrics: An Empiricist’s Companion”,

by Joshua D. Angrist and J¨rn-Steﬀen Pischkeo

Andrew Gelman, Department of Statistics and Department of Political Science Columbia University, gelman@stat.columbia.edu

Abstract. This article reviews Mostly Harmless Econometrics: An Empiricist’s

Companion, by Joshua D. Angrist and J¨rn-Steﬀen Pischke.o

Keywords: gn0046, experimentation, causal inference, ordinary least-squares re-

gression, instrumental variables, diﬀerence in diﬀerences, ﬁxed eﬀects, discontinu-

ity analyses, mhe

1.Introduction

Joshua D. Angrist and J¨rn-Steﬀen Pischke, two leading researchers on the practicalo

use of instrumental variables in econometrics, have come out with a new book, suitable

for students, applied researchers, and researchers such as myself who work in adjacent

disciplines such as political science and statistics. The book’s eight chapters begin with

a conceptual overview of experimentation and causal inference, then cover ordinary

least-squares regression, instrumental variables, and a few models such as diﬀerence

in diﬀerences, ﬁxed eﬀects, and discontinuity analyses, which can be viewed as special

cases of regression adapted to particular forms of natural experiments. The book closes

with some more-technical discussion of quantile regression and calculations of standard

errors.

Despite its broad title, the book’s coverage is limited to one corner of econometrics.

The data structures considered are cross-sectional, with no time series and virtually no

panel or time-series cross-sectional data. And, in the world of Angrist and Pischke, the

problems of interest are all causal: there is no forecasting, no descriptive modeling, and

no theory testing. Finally, when it comes to methods, the book is all about least-squares

estimation of regression coeﬃcients: there is little to nothing about nonparametric

methods, Bayesian inference, or models other than linear regression.

That said, the corner of econometrics covered by Angrist and Pischke’s book is

important and perhaps deserves more emphasis, given that much of the theoretical lit-

erature in econometrics and statistics focuses on issues of standard errors, robustness,

and asymptotics. It can be debated whether Mostly Harmless Econometrics is indeed

mostly harmless, but it is certainly well adapted to the econometric issues that re-

searchers in labor economics, program evaluation, and political science are concerned

with in their applied work.

The book is focused, which has got to be a good thing: it is only 300 pages, and the

pages themselves are pretty small. It is written in a conversational style (except for the

theorems; more on that below) and is informative and pleasant to read.

I will now give a statistician’s impression of the book. My own research is on statisti-

cal methods with applications in political science and public health, and I have written

books on Bayesian data analysis and applied regression/multilevel modeling. I have

done some work on causal inference (including estimating the advantage of incumbency

in congressional elections, an example discussed in Angrist and Pischke’s book), and I

hope this review will be of interest in revealing some of the similarities and diﬀerences

between statisticians’ and econometricians’ attitudes.

2. Nothing on model building

The book’s perspective is as follows: you want to do a causal inference, you already

have an outcome measure and a treatment indicator—in their examples, the outcome

is almost always continuous and the treatment is almost always binary—and you also

probably have some pretreatment measures. And then you run a regression. Angrist

and Pischke explain how direct regression works, and then they discuss how various

methods such as instrumental variables and discontinuity analysis can help you make

use of any quasi-experimental structure in your data. My main criticism of the book is

that, in keeping their sharp focus, the authors spend almost no time discussing model

building. They discuss the idea of the conditional expectation function, E(y | x), right

away, but they seem to imply that the model is prespeciﬁed or that the researcher has

designed the study so well ahead of time that he or she can simply take all available

variables and do nothing to them but throw them in. Realistically, in the many examples

of regression analyses I have seen, there can be a lot of transformation and combination of variables.

In particular, the book does not mention interactions at all (except in the special case

of their use to create a saturated model with discrete predictors), a point to which I shall return below. From my perspective, these omissions are not a problem, because model building and interactions are standard material in any statistical textbook on regression methods. But I am a little worried that students and researchers in economics might be misled by Angrist and Pischke’s conversational yet authoritative tone into thinking that the model and predictors come to the researchers fully formed.

Also here are some things that are not in the book, or, at least, words that are

entirely missing from the index:

• forecasting

• time series

• Bayes

• mediation

• multilevel (or hierarchical)

• sampling

Again this is no criticism—but I would have liked to have seen a few sentences near

the beginning or the end of the book bounding their topics, so that students would have

a better sense of what else is out there.

To defend Angrist and Pischke here, I might say that statisticians such as myself are

all too concerned about modeling the data, enough so that they (we) shortchange the

ultimately more important goal of causal inference. Angrist and Pischke are keeping

the focus where it counts. With its focus on practical tips and understanding of models,

Angrist and Pischke’s book is much closer to my sensibility than Wooldridge (2002), for

example, which is of very high quality but is structured much more around theoretical

results. And in many ways, there is something refreshing to me about the economists’

(and econometricians’) focus on estimating one “beta” using all means necessary. On

the other hand, I think there is a big gap in practice when there is no discussion of how

to set up the model, an implicit assumption that variables are just dumped raw into

the regression.

Maybe students of econometrics could read a statistics text (that is, a book more

focused on model building) as a supplement.

3. Treatment interactions

In keeping with the econometric and statistical literature on causal inference, Angrist

and Pischke spend a bit of time discussing concepts such as the local average treatment

eﬀect. The idea is that, in any experiment or observational study, the inference about

the treatment eﬀect applies only to the people who could have had the treatment or the control done to them, with various designs and estimation strategies corresponding to diﬀerent estimands (the eﬀect of the treatment on the treated, and so forth).

All this is important, but it seems funny to me for it to be considered in isolation

of the model being ﬁt. In particular, were the treatment eﬀect truly constant across

all units, we could just speak of “the treatment eﬀect” without having to specify which

cases we are averaging over. Any discussion of particular average treatment eﬀects is rel-evant because treatment eﬀects vary; that is, the treatment interacts with pretreatment variables.

Given that, I think it can be important to model such interactions. This is done

in econometrics (see, for example, Dehejia [2005]), so I am not proposing anything

revolutionary here. What I am saying is that in a 300-page book on econometrics,

where there is much discussion of average treatment eﬀects, I would like to see some

discussion and examples of models with treatment interactions. This is one area where

statisticians’ more open-ended philosophy of “modeling the data” might have some

advantage over econometricians’ often laser-like focus on average treatment eﬀects.

4. Which comes ﬁrst, the causal question or the natural experiment?

The other day, I was discussing Angrist and Pischke’s book with a colleague, and I

mentioned my struggle with instrumental variables: where do they come from, and

doesn’t it seem awkward when you see someone studying a causal question and looking

around for an instrument?

And my colleague said: No, it goes the other way. What Angrist and his colleagues

do is to ﬁnd the instrument ﬁrst, and then they go from there. They might see something in the newspaper or hear something on the radio and think, Hey—there is a natural experiment—it could make a good instrument! And then they go from there.

This sounded wrong at ﬁrst, but now that I think about it, I actually prefer this to the

usual presentation of instrumental variables. The “ﬁnd the instrumental variables ﬁrst”

approach is cleaner: in this story, all causation ﬂows from the instrumental variable,

which has various consequences. So if you have a few key researchers such as Angrist

keeping their ears open, hearing of instrumental variables, then you will learn some

things.

This approach also ﬁts in with a more general approach in which you focus on the

direct eﬀect of the instrument. Suppose z is your instrument, T is your treatment, and

y is your outcome. So the causal model is z → T → y. The trick is to think of (T, y)

as a joint outcome and to think of the eﬀect of z on each. For example, an increase

of 1 in z is associated with an increase of 0.8 in T and an increase of 10 in y. The

usual “instrumental variables” summary is just to say the estimated eﬀect of T on y is

10/0.8 = 12.5, but I would rather just keep it separate and report the eﬀects on T and

y separately.

Sometimes the approach of leading with the natural experiment can lead to mis-

steps, as illustrated by Angrist and Pischke’s overinterpretation of David Lee’s work

on incumbency in elections. (In my opinion, Lee is estimating the “incumbent party

advantage” rather than the advantage of individual incumbency.) But, generally, it

seems like the way to go, much better than the standard approach of starting with a

causal goal of interest and then looking around for an instrumental variable. My only

complaint with Angrist and Pischke on this point is that they frame the identiﬁcation

problem as one of looking for a good instrument or discontinuity, even though it might

make more sense to consider the natural experiment as coming ﬁrst.

5. Other impressions

Reading this enjoyable book provoked various additional thoughts:

Psychological experimentation: The authors discuss Milgram’s famous experiment

on obedience to authority but then suggest that it would have been “better left on the

drawing board”. Why do they say this—because somebody said that the participants of

that study might have been upset by it? My impression is that the Milgram experiment

was a great contribution and that, as a society, we are better oﬀ that it was done. I can see that some people might be skeptical about Milgram’s result, but as an empirical

researcher, I appreciate those people like Milgram who go to the trouble to get the data

that the rest of us analyze.

Thinking in terms of interventions: In introducing the foundations of experimen-

tation and causal inference, I wish Angrist and Pischke would discuss potential inter-

ventions as a way to understand causality. For example, they give an example of a

“fundamentally unidentiﬁed question” that I would actually call a fundamentally unde-

ﬁned question. In their example, why not just consider potential interventions such as

sending a given kid to ﬁrst grade at age 5, 6, or 7? The causal inference all ﬂows from

this.

Matching and regression: The authors provide a useful discussion of matching and

regression and the essential unity of these methods. In a second edition, I recommend

that they more clearly distinguish between two diﬀerent (but related) goals of matching:

balance and overlap (for example, see chapter 10 of Gelman and Hill [2007] for some

graphs that illustrate these concepts). Also they should make more clear the two-step

process: do matching to get comparable groups, and then do regression for further

adjustment and for modeling interactions. A casual reader of the book might be left

with the unfortunate impression that matching is a competitor to regression rather than

a tool for making regression more eﬀective.

Weighting: When discussing weighted regression, it would have been good if Angrist

and Pischke had pointed out that if you include as regression predictors the variables

that aﬀect the treatment assignment, then there is no need to weight for them in the

regression. Weighting is intended to correct for variables that have not been included in

the model. Making this point would have uniﬁed the book’s presentation of weighting,

instead of presenting it more as a matter of taste as they do here.

Mathematical style: As a statistician, I trace my descent from R. A. Fisher, who

wrote books (notably, Statistical Methods for Research Workers) with methods and

examples and discussions but no theorems. Statistics books such as Fisher’s (and, I

hope, mine) have a logical ﬂow but are not in the theorem/proof style. In contrast,

Angrist and Pischke, despite their conversational style, here and there slip in pages of

theorems and formulas. It does not make a lot of sense to me, but there you go. I

suppose it is how econometricians communicate.

Writing style: Throughout, the authors use too many abbreviations for my taste

(and, I suspect, for many students’ tastes as well). It is a well-written book, but the constant barrage of acronyms disrupts the ﬂow of the book. One or two abbreviations

(for example, OLS and IV) are okay, but it gets out of control when they start with the

more obscure acronyms such as HIE, CEF, LDV, CIA, OVB, MD, CQF, DD, LIML, ACR,

and so forth.

Presentation of results: I like their use of graphs. I would have liked some scatterplots of raw data, but I know that is not economists’ style. Overall, I feel the presentation is excellent.

6. Summary

I like Mostly Harmless Econometrics a lot and hope it is widely read, not just by

economists but also by statisticians, political scientists, and other social researchers. If

the book does do any harm, then it would be in misleading readers into thinking that

causal inference is a bit too cut-and-dried, a misunderstanding that will be avoided as

long as a more traditional book on statistical modeling is read at the same time. Much

will be learned by students who go back and forth between the two books and ask their

hapless instructors to explain the diﬀerences.

7. Acknowledgments

I thank the National Science Foundation for partial support of this research and Jennifer

Hill and several others for helpful suggestions.

8. References

Dehejia, R. H. 2005. Program evaluation as a decision problem. Journal of Econometrics

125: 141–173.

Gelman, A., and J. Hill. 2007.Data Analysis Using Regression and Multi-

level/Hierarchical Models. New York: Cambridge University Press.

Wooldridge, J. M. 2002. Econometric Analysis of Cross Section and Panel Data. Cam-

bridge, MA: MIT Press.

About the author

Andrew Gelman is a professor of statistics and political science at Columbia University. His

books include Bayesian Data Analysis (with John B. Carlin, Hal S. Stern, and Donald B.

Rubin), Teaching Statistics: A Bag of Tricks (with Deborah Nolan), Data Analysis Using

Regression and Multilevel/Hierarchical Models (with Jennifer Hill), and, most recently, Red

State, Blue State, Rich State, Poor State: Why Americans Vote the Way They Do (with David

Park, Boris Shor, Joseph Bafumi, and Jeronimo Cortina).

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