Mastering 'Metrics

The Path from Cause to Effect

Joshua D. Angrist, Jörn-Steffen Pischke

• Publisher: Princeton University Press
• Year: 2014
• ISBN:
  9781400852383
• Topic: Economía
• Subtopic: Econometría

From Joshua Angrist, winner of the Nobel Prize in Economics, and Jörn-Steffen Pischke, an accessible and fun guide to the essential tools of econometric research Applied econometrics, known to aficionados as 'metrics, is the original data science. 'Metrics encompasses the statistical methods economists use to untangle cause and effect in human affairs. Through accessible discussion and with a dose of kung fu–themed humor, Mastering 'Metrics presents the essential tools of econometric research and demonstrates why econometrics is exciting and useful.The five most valuable econometric methods, or what the authors call the Furious Five--random assignment, regression, instrumental variables, regression discontinuity designs, and differences in differences--are illustrated through well-crafted real-world examples (vetted for awesomeness by Kung Fu Panda's Jade Palace). Does health insurance make you healthier? Randomized experiments provide answers. Are expensive private colleges and selective public high schools better than more pedestrian institutions? Regression analysis and a regression discontinuity design reveal the surprising truth. When private banks teeter, and depositors take their money and run, should central banks step in to save them? Differences-in-differences analysis of a Depression-era banking crisis offers a response. Could arresting O. J. Simpson have saved his ex-wife's life? Instrumental variables methods instruct law enforcement authorities in how best to respond to domestic abuse.Wielding econometric tools with skill and confidence, Mastering 'Metrics uses data and statistics to illuminate the path from cause to effect.

• Shows why econometrics is important
• Explains econometric research through humorous and accessible discussion
• Outlines empirical methods central to modern econometric practice
• Works through interesting and relevant real-world examples

Chapter 1

Randomized Trials

KWAI CHANG CAINE: What happens in a man’s life is already written. A man must move through life as his destiny wills.

OLD MAN: Yet each is free to live as he chooses. Though they seem opposite, both are true.

Kung Fu, Pilot

Our Path

Our path begins with experimental random assignment, both as a framework for causal questions and a benchmark by which the results from other methods are judged. We illustrate the awesome power of random assignment through two randomized evaluations of the effects of health insurance. The appendix to this chapter also uses the experimental framework to review the concepts and methods of statistical inference.

1.1 In Sickness and in Health (Insurance)

The Affordable Care Act (ACA) has proven to be one of the most controversial and interesting policy innovations we’ve seen. The ACA requires Americans to buy health insurance, with a tax penalty for those who don’t voluntarily buy in. The question of the proper role of government in the market for health care has many angles. One is the causal effect of health insurance on health. The United States spends more of its GDP on health care than do other developed nations, yet Americans are surprisingly unhealthy. For example, Americans are more likely to be overweight and die sooner than their Canadian cousins, who spend only about two-thirds as much on care. America is also unusual among developed countries in having no universal health insurance scheme. Perhaps there’s a causal connection here.

Elderly Americans are covered by a federal program called Medicare, while some poor Americans (including most single mothers, their children, and many other poor children) are covered by Medicaid. Many of the working, prime-age poor, however, have long been uninsured. In fact, many uninsured Americans have chosen not to participate in an employer-provided insurance plan.¹ These workers, perhaps correctly, count on hospital emergency departments, which cannot turn them away, to address their health-care needs. But the emergency department might not be the best place to treat, say, the flu, or to manage chronic conditions like diabetes and hypertension that are so pervasive among poor Americans. The emergency department is not required to provide long-term care. It therefore stands to reason that government-mandated health insurance might yield a health dividend. The push for subsidized universal health insurance stems in part from the belief that it does.

The ceteris paribus question in this context contrasts the health of someone with insurance coverage to the health of the same person were they without insurance (other than an emergency department backstop). This contrast highlights a fundamental empirical conundrum: people are either insured or not. We don’t get to see them both ways, at least not at the same time in exactly the same circumstances.

In his celebrated poem, “The Road Not Taken,” Robert Frost used the metaphor of a crossroads to describe the causal effects of personal choice:

Two roads diverged in a yellow wood,

And sorry I could not travel both

And be one traveler, long I stood

And looked down one as far as I could

To where it bent in the undergrowth;

Frost’s traveler concludes:

Two roads diverged in a wood, and I—

I took the one less traveled by,

And that has made all the difference.

The traveler claims his choice has mattered, but, being only one person, he can’t be sure. A later trip or a report by other travelers won’t nail it down for him, either. Our narrator might be older and wiser the second time around, while other travelers might have different experiences on the same road. So it is with any choice, including those related to health insurance: would uninsured men with heart disease be disease-free if they had insurance? In the novel Light Years, James Salter’s irresolute narrator observes: “Acts demolish their alternatives, that is the paradox.” We can’t know what lies at the end of the road not taken.

We can’t know, but evidence can be brought to bear on the question. This chapter takes you through some of the evidence related to paths involving health insurance. The starting point is the National Health Interview Survey (NHIS), an annual survey of the U.S. population with detailed information on health and health insurance. Among many other things, the NHIS asks: “Would you say your health in general is excellent, very good, good, fair, or poor?” We used this question to code an index that assigns 5 to excellent health and 1 to poor health in a sample of married 2009 NHIS respondents who may or may not be insured.² This index is our outcome: a measure we’re interested in studying. The causal relation of interest here is determined by a variable that indicates coverage by private health insurance. We call this variable the treatment, borrowing from the literature on medical trials, although the treatments we’re interested in need not be medical treatments like drugs or surgery. In this context, those with insurance can be thought of as the treatment group; those without insurance make up the comparison or control group. A good control group reveals the fate of the treated in a counterfactual world where they are not treated.

The first row of Table 1.1 compares the average health index of insured and uninsured Americans, with statistics tabulated separately for husbands and wives.³ Those with health insurance are indeed healthier than those without, a gap of about .3 in the index for men and .4 in the index for women. These are large differences when measured against the standard deviation of the health index, which is about 1. (Standard deviations, reported in square brackets in Table 1.1, measure variability in data. The chapter appendix reviews the relevant formula.) These large gaps might be the health dividend we’re looking for.

Fruitless and Fruitful Comparisons

Simple comparisons, such as those at the top of Table 1.1, are often cited as evidence of causal effects. More often than not, however, such comparisons are misleading. Once again the problem is other things equal, or lack thereof. Comparisons of people with and without health insurance are not apples to apples; such contrasts are apples to oranges, or worse.

Among other differences, those with health insurance are better educated, have higher income, and are more likely to be working than the uninsured. This can be seen in panel B of Table 1.1, which reports the average characteristics of NHIS respondents who do and don’t have health insurance. Many of the differences in the table are large (for example, a nearly 3-year schooling gap); most are statistically precise enough to rule out the hypothesis that these discrepancies are merely chance findings (see the chapter appendix for a refresher on statistical significance). It won’t surprise you to learn that most variables tabulated here are highly correlated with health as well as with health insurance status. More-educated people, for example, tend to be healthier as well as being overrepresented in the insured group. This may be because more-educated people exercise more, smoke less, and are more likely to wear seat belts. It stands to reason that the difference in health between insured and uninsured NHIS respondents at least partly reflects the extra schooling of the insured.

TABLE 1.1
Health and demographic characteristics of insured and uninsured couples in the NHIS

Notes: This table reports average characteristics for insured and uninsured married couples in the 2009 National Health Interview Survey (NHIS). Columns (1), (2), (4), and (5) show average characteristics of the group of individuals specified by the column heading. Columns (3) and (6) report the difference between the average characteristic for individuals with and without health insurance (HI). Standard devi...