Angrist&Pischke Mostly Harmless Econometrics

Part II

The Core

19

Chapter 3

Making Regression Make Sense
’
Let us think the unthinkable, let us do the undoable.
Let us prepare to grapple with the ine¤able itself,
and see if we may not e¤ it after all.’
Douglas Adams, Dirk Gently’ Holistic Detective Agency (1990)
s
Angrist recounts:
I ran my …rst regression in the summer of 1979 between my freshman and sophomore yearsas a student at Oberlin College. I was working as a research assistant for Allan Meltzer and
Scott Richard, faculty members at Carnegie-Mellon University, near my house in Pittsburgh. I
was still mostly interested in a career in special education, and had planned to go back to work
as an orderly in a state mental hospital, my previous summer job. But Econ 101 had got me
thinking, and I couldalso see that at the same wage rate, a research assistant’ hours and working
s
conditions were better than those of a hospital orderly. My research assistant duties included
data collection and regression analysis, though I did not understand regression or even statistics
at the time.
The paper I was working on that summer (Meltzer and Richard, 1983), is an attempt to
link the size ofgovernments in democracies, measured as government expenditure over GDP, to
income inequality. Most income distributions have a long right tail, which means that average
income tends to be way above the median. When inequality grows, more voters …nd themselves
with below-average incomes.

Annoyed by this, those with incomes between the median and

the average may join those with incomes belowthe median in voting for …scal policies which
- following Robin Hood - take from the rich and give to the poor.

The size of government

consequently increases.
I absorbed the basic theory behind the Meltzer and Richards project, though I didn’ …nd it
t
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CHAPTER 3. MAKING REGRESSION MAKE SENSE
all that plausible, since voter turnout is low for the poor. I also remember arguingwith Alan
Meltzer over whether government expenditure on education should be classi…ed as a public good
(something that bene…ts everyone in society as well as those directly a¤ected) or a private good
publicly supplied, and therefore a form of redistribution like welfare. You might say this project
marked the beginning of my interest in the social returns to education, a topic I went back towith more enthusiasm and understanding in Acemoglu and Angrist (2000).
Today, I understand the Meltzer and Richard (1983) study as an attempt to use regression
to uncover and quantify an interesting causal relation. At the time, however, I was purely a
regression mechanic. Sometimes I found the RA work depressing. Days would go by where I
didn’ talk to anybody but my bosses and theoccasional Carnegie-Mellon Ph.D. student, most
t
of whom spoke little English anyway. The best part of the job was lunch with Alan Meltzer, a
distinguished scholar and a patient and good-natured supervisor, who was happy to chat while
we ate the contents of our brown-bags (this did not take long as Allan ate little and I ate fast).
I remember asking Allan whether he found it satisfying to spend hisdays perusing regression
output, which then came on reams of double-wide green-bar paper. Meltzer laughed and said
there was nothing he would rather be doing.
Now, we too spend our days (at least, the good ones) happily perusing regression output, in the manner

of our teachers and advisors in college and graduate school. This chapter explains why.

3.1

Regression Fundamentals

Theend of the previous chapter introduces regression models as a computational device for the estimation
of treatment-control di¤erences in an experiment, with and without covariates.

Because the regressor of

interest in the class size study discussed in Section 2.3 was randomly assigned, the resulting estimates have
a causal interpretation. In most cases, however, regression is used with...