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Estimating Average and Local Average American Economic Association Estimating Average and Local Average Treatment Effects of Education When Compulsory Schooling Laws Really Matter Author(s): Philip Oreopoulos Source: The American Economic Review, Vol. 96, No. 1 (Mar., 2006), pp. 152-175 Published by: American Economic Association Stable URL: http://www.jstor.org/stable/30034359 Accessed: 09/05/2010 13:51 Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at http://www.jstor.org/page/info/about/policies/terms.jsp. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, non-commercial use. Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at http://www.jstor.org/action/showPublisher?publisherCode=aea. Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed page of such transmission. JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact [email protected]. American Economic Association is collaborating with JSTOR to digitize, preserve and extend access to The American Economic Review. http://www.jstor.org EstimatingAverage and LocalAverage Treatment Effects of Educationwhen CompulsorySchooling Laws ReallyMatter By PHILIPOREOPOULOS* The change to the minimumschool-leaving age in the United Kingdomfrom 14 to 15 had a powerful and immediateeffect that redirectedalmost half the population of 14-year-olds in the mid-twentiethcentury to stay in school for one more year. The magnitudeof this impactprovides a rare opportunityto (a) estimate local average treatment effects (LATE) of high school that come close to population average treatmenteffects (ATE); and (b) estimate returns to education using a regression discontinuitydesign insteadof previous estimatesthat rely on difference-in-differences methodology or relatively weak instruments.Comparing LATE estimates for the United States and Canada, where very few students were affected by compulsory school laws, to the United Kingdom estimates provides a test as to whether instrumentalvariables (IV) returnsto schooling often exceed ordinaryleast squares (OLS) because gains are high only for small and peculiar groups among the more general population. I find, instead, that the benefitsfrom compulsoryschooling are very large whether these laws have an impact on a majority or minority of those exposed. (JEL 120, 121, 128) Researchers routinely use the IV method to how to interpretestimated treatmenteffects us- evaluate programsand estimate consistent treat- ing IV. When the treatmentbeing evaluatedhas ment effects. A valid instrumental variable, the same effect for everyone, any valid instru- which helps determinewhether an individual is ment will identify this unique parameter.But treated,but does not determineother factors that when responses to treatmentvary, different in- affect the outcomes of interest, can overcome strumentsmeasure different effects. Guido W. estimationbiases thatoften arise when using the Imbens and Joshua D. Angrist (1994) point out OLS method. Recent work in this field clarifies that, in this more realistic environment,the only effect we can be sure that this method estimates is the treatmenteffect those who * average among Departmentof Economics, University of Toronto, 140 alter their treatmentstatus because react to Toronto M55 and National they St. George Street, 3G6, Canada, the call this the Bureau of Economic Research (e-mail: oreo@economics. instrument; they parameter utoronto.ca). I am very grateful to Joshua Angrist, Enrico LATE. In some cases, the LATE also equals the Moretti, and staff membersfrom the U.K. Data Archive for average treatmenteffect among those exposed providing me with necessary data for this project. Seminar to the treatment,but only when persons do not and conference participantsat UC-Berkeley, the London make decisions to react to the instrumentbased School of Economics, the Federal Reserve, Chicago Royal on factors that also determine treatment Holloway, Duke University, McGill University, Queens gains University, NBER Summer Institute, IZA/SOLE Transat- (James J. Heckman, 1997). lantic Meetings, and the universities of Toronto, British In the returnto schooling literature,research- Columbia, and Guelph provided helpful discussion. I am ers use IV. Some often-cited exam- to frequently especially thankful George Akerlof, JoshuaAngrist, Alan include studies that measure the LATE Auerbach,David Autor, Michael Baker, GregoryBesharov, ples David Card, Liz Cascio, Stacey Chen, Botond Koszegi, among persons who attendcollege because they John Quigley, Marco Manacorda, Rob McMillan, Justin live close to college (David Card, 1995); per- McCrary,Costas Meghir, Mathew Rabin, Jesse Rothstein, sons who attend because tuition is low Van college Emmanuel Saez, Aloysius Siow, Alois Stutzer, Jo J. Kane and Cecilia Elena Rouse, Biesebroeck, Ian Walker,and three referees for (Thomas anonymous and to in school many helpful comments and discussions. I am solely re- 1995) persons obliged stay sponsible for this paper's contents. longer because they face more restrictivecom- 152 VOL. 96 NO. 1 OREOPOULOS:ESTIMATING ATE AND LATEWITH COMPULSORY SCHOOLING LAWS 153 pulsory school laws (Angrist and Alan B. realize at a glance of the figure that the mini- Krueger, 1991; Daron Acemoglu and Angrist, mum school-leaving age in Britain increased 2001). These instrumentstypically affect fewer from 14 to 15 in 1947. Within two years of this than 10 percentof the populationexposed to the policy change, the portion of 14-year-oldsleav- instrumentand often generate treatmenteffects ing school fell from 57 percent to less than 10 that exceed those generated from OLS. Card percent. The trend for the fraction of children (2001) and Lang (1993) suggest that the higher dropping out at age 15 or less, however, re- IV results could occur because they approxi- mained intact-it appears virtually everyone mate average effects among a small and pecu- who would have left school at age 14 left at age liar group, whereas OLS estimates, in the 15 after the change. I found an equally dramatic absence of omitted variables and measurement response to an increase in the minimum legal error biases, approximate average effects school-leavingage in NorthernIreland (see Figure among everyone. In a model where individuals 2), wherethe law changeoccurred ten years later. weigh costs and benefits from attaining addi- I use these two U.K. experiences to make two tional school, LATE estimates from IV could contributionsto the returns-to-schoolinglitera- exceed OLS estimates for a variety of reasons, ture. First, I estimate average returns to high for example, because individualsaffected by the school from instrumentalvariables that affect instruments are more credit constrained, have almost half the population. The magnitude of greaterimmediate need to work, or have greater the response from these policies provides a test distaste for school.' to whetherprevious IV estimates often match or PreviousLATE estimateshave providedlittle exceed OLS estimates because they identify inkling about what the gains to schooling are for average returnsto schooling for a select group a more general population. An alternative pa- in the population. I demonstrate this test by rameter that captures this is the ATE, the comparing the results with LATE estimates expected gain from schooling among all indi- from compulsory schooling laws in the United viduals (or all individuals with a given set of States and Canada,where very few studentsleft covariates). Unlike the LATE, it does not de- early, to the U.K. estimates.If high school drop- pend on a particularinstrument or on who gets outs have more to gain than high school grad- treated. The ATE offers a theoretically more uates from staying on an extra year, the local stableparameter when consideringpotential gains average treatmenteffect of compulsory educa- for anyonereceiving an extrayear of schoolingor tion will be higher than the average treatment college study. A comparisonbetween ATE and effect for the total population.2As the fraction previous LATE estimates would help determine affectedby compulsoryeducation increases, how- whetherthe earlierLATE results are anomalies, or ever, the LATEand ATE convergesince the ATE whetherthe effects of educationare by and large includes the population of would-be dropouts. similaracross a wider population. Whenthe fractionaffected by compulsoryschool- In this paper, I exploit historicallyhigh drop- ing increases, we can use the gradientof these out rates in the United Kingdom to estimate the estimatesto determinethe ATE population.This LATE for secondaryschooling. The result is an approachis similar in spirit to one proposedby IV estimate that is probably closer to the ATE Heckmanand EdwardVytlacil (2001). than any previously reported.I focus on a pe- My second contributionis to adopt a regres- riod when legislative changes had a remarkable sion discontinuity (RD) design to estimate av- effect on overall education attainment.
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