Mastering ’Metrics: The Path from Cause to Effect

1 Chapter 1 Randomized TrialsKwai Chang Caine:What happens in a man s life is alreadywritten. A man must move through life as his destiny man:Yet each is free to live as he chooses. Though they seemopposite, both are Fu,PilotOur PathOur path begins with experimentalrandom assignment,both as a framework for causal questions and a bench-mark by which the results from other methods arejudged. We illustrate the awesome power of random assign-ment through two randomized evaluations of the effects ofhealth insurance . The appendix to this chapter also uses theexperimental framework to review the concepts and methodsof statistical In Sickness and in Health ( insurance )The Affordable Care Act (ACA) has proven to be one of themost controversial and interesting policy innovations we veseen. The ACA requires Americans to buy health insurance ,with a tax penalty for those who don t voluntarily buy in. Thequestion of the proper role of government in the market forhealth care has many angles.

2 One is the causal Effect of healthinsurance on health. The United States spends more of its GDPon health care than do other developed nations, yet Americansare surprisingly unhealthy. For example, Americans are morelikely to be overweight and die sooner than their Canadiancousins, who spend only about two-thirds as much on care. Copyright, Princeton University Press. No part of this book may be distributed, posted, or reproduced in any form by digital or mechanical means without prior written permission of the publisher. For general queries, contact Chapter 1 America is also unusual among developed countries in havingno universal health insurance scheme. Perhaps there s a causalconnection Americans are covered by a federal program calledMedicare, while some poor Americans (including most singlemothers, their children, and many other poor children) arecovered by Medicaid. Many of the working, prime-age poor,however, have long been uninsured.

3 In fact, many uninsuredAmericans have chosen not to participate in an employer-provided insurance workers, perhaps correctly,count on hospital emergency departments, which cannot turnthem away, to address their health-care needs. But the emer-gency department might not be the best place to treat, say,the flu, or to manage chronic conditions like diabetes andhypertension that are so pervasive among poor Americans. Theemergency department is not required to provide long-termcare. It therefore stands to reason that government-mandatedhealth insurance might yield a health dividend. The push forsubsidized universal health insurance stems in part from thebelief that it paribusquestion in this context contrasts thehealth of someone with insurance coverage to the health ofthe same person were they without insurance (other than anemergency department backstop). This contrast highlights afundamental empirical conundrum: people are either insuredor not.

4 We don t get to see them both ways, at least not at thesame time in exactly the same his celebrated poem, The Road Not Taken, RobertFrost used the metaphor of a crossroads to describe the causaleffects of personal choice:Two roads diverged in a yellow wood,And sorry I could not travel bothAnd be one traveler, long I stoodAnd looked down one as far as I couldTo where it bent in the undergrowth;1 For more on this surprising fact, see Jonathan Gruber, Covering theUninsured in the United States, Journal of Economic Literature, vol. 46,no. 3, September 2008, pages 571 606. Copyright, Princeton University Press. No part of this book may be distributed, posted, or reproduced in any form by digital or mechanical means without prior written permission of the publisher. For general queries, contact Trials 3 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 traveler claims his choice has mattered, but, being onlyone person, he can t be sure.

5 A later trip or a report by othertravelers won t nail it down for him, either. Our narrator mightbe older and wiser the second time around, while other trav-elers might have different experiences on the same road. So itis with any choice, including those related to health insurance :would uninsured men with heart disease be disease-free if theyhad insurance ? In the novelLight Years,James Salter s irreso-lute narrator observes: Acts demolish their alternatives, thatis the paradox. We can t know what lies at the end of the roadnot can t know, but evidence can be brought to bear on thequestion. This chapter takes you through some of the evidencerelated to paths involving health insurance . The starting pointis the National Health Interview Survey (NHIS), an annualsurvey of the population with detailed information onhealth and health insurance . Among many other things, theNHIS asks: Would you say your health in general is excellent,very good, good, fair, or poor?

6 We used this question to codean index that assigns 5 to excellent health and 1 to poor healthin a sample of married 2009 NHIS respondents who may ormay not be index is ouroutcome:a measurewe re interested in studying. The causal relation of interesthere is determined by a variable that indicates coverage byprivate health insurance . We call this variable thetreatment,borrowing from the literature on medical trials, although thetreatments we re interested in need not be medical treatmentslike drugs or surgery. In this context, those with insurance canbe thought of as thetreatment group;those without insurancemake up thecomparisonorcontrol good controlgroup reveals the fate of the treated in a counterfactual worldwhere they are not sample is aged 26 59 and therefore does not yet qualify for Medicare. Copyright, Princeton University Press. No part of this book may be distributed, posted, or reproduced in any form by digital or mechanical means without prior written permission of the publisher.

7 For general queries, contact Chapter 1 The first row of Table compares the average health indexof insured and uninsured Americans, with statistics tabulatedseparately for husbands and with health insur-ance are indeed healthier than those without, a gap of in the index for men and .4 in the index for women. Theseare large differences when measured against the standard de-viation of the health index, which is about 1. (Standard de-viations, reported in square brackets in Table , measurevariability in data. The chapter appendix reviews the relevantformula.) These large gaps might be the health dividend we relooking and Fruitful ComparisonsSimple comparisons, such as those at the top of Table , areoften cited as evidence of causal effects. More often than not,however, such comparisons are misleading. Once again theproblem isother things equal,or lack thereof. Comparisonsof people with and without health insurance are not apples toapples; such contrasts are apples to oranges, or other differences, those with health insurance arebetter educated, have higher income, and are more likely tobe working than the uninsured.

8 This can be seen in panel Bof Table , which reports the average characteristics ofNHIS respondents who do and don t have health of the differences in the table are large (for example,a nearly 3-year schooling gap); most are statistically preciseenough to rule out the hypothesis that these discrepancies aremerely chance findings (see the chapter appendix for a re-fresher on statistical significance). It won t surprise you tolearn that most variables tabulated here are highly correlatedwith health as well as with health insurance status. More-educated people, for example, tend to be healthier as well asbeing overrepresented in the insured group. This may be be- Cause more-educated people exercise more, smoke less, andare more likely to wear seat belts. It stands to reason thatthe difference in health between insured and uninsured NHIS3An Empirical Notes section after the last chapter gives detailed notes forthis table and most of the other tables and figures in the book.

9 Copyright, Princeton University Press. No part of this book may be distributed, posted, or reproduced in any form by digital or mechanical means without prior written permission of the publisher. For general queries, contact Trials and demographic characteristics of insured and uninsuredcouples in the NHISH usbandsWivesSome HI No HI Difference Some HI No HI Difference(1)(2)(3)(4)(5)(6)A. HealthHealth [.93][ ](.03)[.92][ ](.04)B..02(.01)(.01) (.29)(.30) (.10)(.11)Family ..43(.05)(.05) (.01)(.02)Family income 106,467 45,65660,810106,212 46,38559,828(1,355)(1,406)Sample size8,1141,2818,2641,131 Notes:This table reports average characteristics for insured and uninsured marriedcouples 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 (3) and (6) report the difference between the average characteristic for individualswith and without health insurance (HI).

10 Standard deviations are in brackets; standard errorsare reported in parentheses. Copyright, Princeton University Press. No part of this book may be distributed, posted, or reproduced in any form by digital or mechanical means without prior written permission of the publisher. For general queries, contact Chapter 1respondents at least partly reflects the extra schooling of effort to understand the causal connection between in-surance and health is aided by fleshing out Frost s two-roadsmetaphor. We use the letterYas shorthand for health, theoutcome variable of interest. To make it clear when we retalking about specific people, we use subscripts as a stand-in for names:Yiis the health of individuali. The outcomeYiisrecorded in our data. But, facing the choice of whether to payfor health insurance , personihas twopotential outcomes,onlyone of which is observed. To distinguish one potential outcomefrom another, we add a second subscript: The road taken with-out health insurance leads toY0i(read this as y-zero-i ) forpersoni, while the road with health insurance leads toY1i(readthis as y-one i ) for personi.