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

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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. Fig- erage returns to schooling. The RD approach ure 1 shows this effect on the fractionof British- differs from previous studies by comparinged- born adults that left full-time education at ages ucation attainmentand adult earnings for stu- 14 or less and 15 or less. It is not difficult to dents just prior to and just after the policy

2 1 Alternatively, IV results might exceed OLS if the in- The term "dropout"is something of a misnomerin the strumentsare invalid. Pedro Carneiro and James J. Heck- United Kingdom, since those who failed to advance to man (2002) criticize the validity of some earlier studies by secondary school were expected to leave at the earliest demonstratingthat some often-used instrumentscorrelate opportunity.I shall occasionally referto U.K. school leavers with proxies for innate ability. as dropoutsfor convenience. 154 THE AMERICANECONOMIC REVIEW MARCH2006

.9 .8 .7 Education .6 .5 Full-Time .4 .3 Leaving .2

Fraction.1 0 1935 1940 1945 1950 1955 1960 1965 YearAged 14 By Age 14 By Age 15

FIGURE1. FRACTIONLEFT FULL-TIME EDUCATION BY YEAR AGED 14 AND 15 (Great Britain) Note: The lower line shows the proportionof British-bornadults aged 32 to 64 from the 1983 to 1998 General Household Surveys who reportleaving full-time education at or before age 14 from 1935 to 1965. The upper line shows the same, but for age 15. The minimum school- leaving age in Great Britain changed in 1947 from 14 to 15. change. The break in education attainmentis so may be related to other factors affecting earn- stark in both Britain and NorthernIreland that ings. Carneiro and Heckman (2002) provide we can show graphically the corresponding some evidence that day of birth also relates to break in earnings and the source of the LATE proxies for early childhood development. identification. Another approachtakes advantage of differ- My analysis addresses some previous con- ences in the timing of compulsory schooling cerns that have been expressed in the literature law changes across regions (e.g., Acemoglu and about the validity of earlier approachesto esti- Angrist, 2001; Lance Lochner and Enrico Mor- mate returnsto compulsory schooling. One ap- etti, 2004; Adriana Lleras-Muney,2005). This proach, introduced by Angrist and Krueger technique uses the same identificationstrategy (1991) uses quarterof birth to identify students as a differences-in-differencesresearch design. allowed to drop out with less education than To estimate consistently the LATE of compul- others because they were born after the school- sory schooling, the timing of the law changes entry cutoff date and waited a full year before must not be correlated with any other policy enteringschool, comparedto those born priorto changes or regional characteristicsthat also re- the cutoff date. John Bound et al. (1995) show late to the outcome variables. These studies that if education attainmentand quarterof birth assume, in the absence of law changes, that are only weakly correlated, estimates can be relative trends in the outcome variables are the biased in the same direction as OLS results are same across regions. biased.3A second concern is that timing of birth

weak instrumentbias that may result from using quarterof 3 Douglas Staiger and James H. Stock (1997) and Luiz birthto estimate returnsto compulsory schooling and arrive M. Cruz and Marcelo J. Moreira (2005) address concerns at generally similar estimates to Angrist and Kureger's about this source of bias. Both attempt to correct for the original study. VOL.96 NO. 1 OREOPOULOS:ESTIMATING ATE AND LATEWITH COMPULSORY SCHOOLING LAWS 155

.9 .8 .7 Education .6 .5 Full-Time .4 .3 Leaving .2

Fraction.1 0 1935 1940 1945 1950 1955 1960 1965 YearAged 14 By Age 14 By Age 15

FIGURE 2. FRACTION LEFTrFULL-TIME EDUCATION BY YEAR AGED 14 AND 15 (NorthernIreland) Note: The lower line shows the proportionof NorthernIrish adults aged 32 to 64 from the 1985 to 1998 GeneralHousehold Surveys who reportleaving full-time educationat or before age 14 from 1935 to 1965. The upper line shows the same, but for age 15. The minimum school-leaving age in NorthernIreland changed in 1957 from 14 to 15.

A third approach also uses changes to the market outcomes. The results provide evi- school-leaving age in the United Kingdom. dence that IV LATE estimates may often be Colm Harmon and Ian Walker (1995) were similar to ATE, and that the main reasons the first to adopt these school-leaving age why OLS results are weaker than IV are not changes to estimate returns to schooling, but likely due to differences in the populationof did not include birth cohort effects in their individualsaffected by the instrument. regressions to account for a rising trend in The next section outlines a theoretical education attainment and earnings. As a re- framework for interpretingreturns to compul- sult, their estimates do not allow for sys- sory schooling and provides a parametric ex- tematic inter-cohort changes in educational ample of how increasing the fraction affected attainment, and do not identify effects from by compulsory schooling affects the LATE cohorts who attended school just before and estimate relative to ATE. Section II provides just after the law changes. background to the school-leaving age in- The regression discontinuity method used creases in Britain and in Northern Ireland. in this paper offers more compelling evidence The regression discontinuity and instrumental on the average treatment effects of high variables analysis is also carried out in Sec- school. The main conclusion of the paper is tion II. Section III compares the RD-IV re- that the effects from compulsory schooling, sults from Britain and Northern Ireland to the are very large-ranging from an annual gain IV results for Canada and the United States. in earnings between 10 to 14 percent-- Section IV concludes with a discussion about whether a majority or minority of the popu- why compulsory school laws seem to gener- lation is affected. I also identify significant ate large gains for individuals who otherwise gains to health, employment, and other labor would have lefts school earlier. 156 THE AMERICANECONOMIC REVIEW MARCH2006

I. TheoreticalFramework the law, so that Si Soi. Imbens and Angrist (1994) show that this monotonicityassumption, A. Causal Inference and Compulsory together with independence,implies: Schooling E( YiZi = 1) - E(Y4iZi = 0) In this section, I discuss the theoreticalback- = (2) E(SilZi 1) - E(SilZi = 0) ground to my analysis, beginning with how laws facilitate compulsory-schooling making = - YoilSli> Soi). causal inferences about various effects of edu- E(Yi, cation. I illustrate the differences between the The left-handside of this expression is the pop- LATE and ATE using a parametricexample, ulation analog of the Wald Estimator. Since then discuss the within the optimal schooling Sli > Soi holds only for individuals who leave at context of the setup, if schooling is seen as an age 14 in the absence of the more restrictive investment. I follow the theoretical framework law, the LATE on the right-hand side is the used by Angrist and Krueger (1999) and by average effect of an additional year of school Angrist (2004) to link the LATE identified us- among those who otherwise would not have ing compulsory schooling as an instrumentwith taken that extra year. the population ATE. Let Si be an indicator for whether child i B. A Parametric Example attendsschool at age 15 (Si = 1) or leaves at age 14 (Si = 0). I define schooling, thus, as a binary Following Angrist (2004), I calculate a para- variable indicating only a measure of high metric model to show the relative differences school attainment because this approach best between LATE and ATE using the compulsory- represents the level of attainment affected by school-law instrument.First, I assume that the raising the minimum school-leaving age.4 Let distributionof - Yo,, mi)is bivariate nor- - (Yli o, Yli be child i's circumstances after age 15 if mal: (Y i 9mi) - p]. Si = 1, and let Yoibe her circumstancesafter age Thus, the ATEYoi, [E(Y1i - N2[,po,is px3,the 4' mean of 15 if = 0. one of these Yo/)] Si Although only poten- mqiis t.l, the correlationbetween Yli - Yoiand tial outcomes is ever observed, the average mriis p, and the respective variances for Y1i - treatmenteffect, - can be used to Yoiand ri are o and or2.If p is positive, the make predictive statementsE(Yli Yoi),about the impact of likelihood of dropping out at age 14 is corre- high school on a randomlychosen person. lated with higher gains from school (after age Let Zi be a binary variable with Zi = 1 if the 15). Since everyone must attend school at age school-leaving age equals 15, and Zi = 0 if it 15 when the school-leaving age is 15 (y1j-- o), equals 14. Suppose Si is determined by the the LATE is equal to the treatmenteffect on the latent-index assignment mechanism, nontreated-the average effect of attending school at age 15 for those who leave at age 14. It can be written as: (1) Si = + yZi > l(y0 r/i) where YT > 0 and ri is a random variable (3) independent of the instrument. The potential - > - = treatment are = > and E (Yli YoiISli Soi) = E(Yli YoiISoi 0) assignments Soi l(yo r7i) Sli = 1(yo + Y, > ni). The instrumenthas no effect on those already intending to attend = - > Yo) school at age 15, but has a nonnegativeeffect on E(Yli Yoiluri schooling for those leaving at age 14 without = E(Y11 - Yoi) + The focus here is on school. The or local 4 high average pooA(x,) average treatment effects at the college level may differ from those examined here. = L + po-Ao(x,) VOL. 96 NO. 1 OREOPOULOS:ESTIMATING ATE AND LATEWITH COMPULSORY SCHOOLING LAWS 157

.17.18

.05 =

ATE.12.13.14.15.16 .11 when .1 LATE.09 .08

.05.06.07 0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1 Pr(S= 0 lZ = 0)

FIGURE3. LATE AND ATE BY ALTERNATIVEFRACTIONS AFFECTED BY BINARY COMPULSORYSCHOOLING INSTRUMENT AND THEDEGREE OF SELECTIONON GAINS Note: Pr(S = 0IZ = 0) is the fraction of the population affected by the binary compulsory schooling instrumentZ. The figure assumes ATE = 0.05, op = .25, and p = 0.15. See text for details.

where A(x ) is the inverse Mill's ratio, qp(xn)/ The ratio of the difference between the LATE [1 - F(x)]; p(x,) and F(x ) are, respectively, and ATE is: the Normal density and distributionfunctions; and x. = (yo - This expression is the In)/rn. ) - . A special case to Imbens and Angrist's (1994) YoilSoi= ,0pL E(YIi- definitionof LATE when the instrumentaffects E(YJi - YoilSoi= 0, pH) - Ip =AH everyone with Soi = 0. The discrepancy be- tween the LATE and ATE decreases with Equation(4) indicates we can back out the value Pr(S = OIZ= 0) 1 - ((x ), the fraction of for xp from two LATE values that differ by the population affected by the compulsory- A(x,). The comparisonprovides much informa- school law, and increases with P, the correlation tion on the value of ATE, and also on the between treatment and gains. The interaction directionof p. Equal LATE values imply p = 0. between these parametersmatters as well. The If the ratio of the two LATE values, - LATE when the fraction affected the law is = 0, = E(Yliex- by YoiSoi pL)IE(Yli- YoilSoi 0, pH), large (for example, 0.5) is closer to the ATE ceeds one, p > 0 and vice versa. when p is small. To illustrate, Figure 3 plots the ATE and Even with p and op unknown, the ATE can LATE againstthe fractionof would-be-dropouts, be determined = from two LATE values that dif- Pr(S = 01Z = 0), when tLp 0.05, op = 0.25, fer only by the fraction of the population af- and p = 0.15. The figure shows the difference fected by the compulsory-schoollaw. Suppose, between ATE and LATE declining as the frac- for example, we have one LATE with Pr(S = tion affectedby compulsoryschooling increases.5 OIZ= 0) = PL, correspondingto A(x,) = AL and the another with Pr(S = 0Z = 0) = pH, to = AH.Assume the other corresponding A(x,) 5 This is generally not the case if the instrumentdoes not parametersare the same andpL H). fully constrainall individuals (see Angrist, 2004). 158 THE AMERICANECONOMIC REVIEW MARCH2006

When p is positive, a smaller fraction affected viduals wanting to leave sooner, even among by the instrumentalways leads to a larger dif- those who are credit constrained.6 ference between the LATE and ATE. The Expressions (1) and (5) imply LATE is 0.15, 0.13, and 0.08 when the instru- ment affects, respectively, 1, 5, and 50 percent (6) - Yo i - - of the population. The absolute difference be- Ti = (Y1 Yoi). tween the LATE and ATE when the instrument affects 5 percent of the populationis 2.6 times If individuals choose education attainmentby the difference when the instrumentaffects 50 weighing costs and benefits as in expression (6), percent of the population. and Pio is positive, then costs must be propor- The main point for the purposesof this paper tionately higher for those who drop out at age is that, with about half the students in mid- 14 than for those who continue on to age 15. centuryUnited Kingdomleaving school as soon Similar reasoninghas been used to explain why as possible, the LATE from raising the school- IV estimates of the returns to compulsory leaving age should come close to the ATE. In schooling are often higher than corresponding addition, comparingcompulsory school law ef- OLS estimates (see Card, 2001). If OLS esti- fects across countries helps verify how close mates of the ATE are upward biased because this estimate is to the ATE. A substantialdif- students with better cognitive and noncognitive ference between LATE estimates using North skills tend to obtain more schooling, IV esti- American compulsory-school laws (that affect mates that attemptto correctfor this bias should few) and those from the United Kingdom (that be lower. affect many) would suggest a high value for p. On the other hand, a small difference would suggest that the correlation between dropping II. MinimumSchooling Laws in Great Britain out and above-averagegains is small, and that a and Ireland large correlationis an unlikely explanation for why OLS and IV returnsto schooling estimates A. U.K. Data sometimes differ. The data used for the U.K. analysis are de- rived from combining 15 U.K. General House- C. ATE, LATE,and Optimal School hold Surveys(GHS) from 1983 to 1998 (the 1997 Attainment GHS was cancelled) with 14 NorthernIreland Continuous Household Surveys from 1985 to It is interesting to note the effect of com- 1998. (For simplicity's sake, I use the term GHS pulsory schooling when education is viewed to refer to both kinds of surveys, since the two as an investment. Suppose the total cost of questionnaireswere almost identical.) The ma- child i's schooling is ci, which may include jor difference was that earnings from the U.K. effort, psychological costs, forgone earnings, GHS were coded exactly, while earnings from and lowered immediate consumption caused the NorthernIreland GHS were coded by cate- by not being able to borrow. An investment gory. Average earnings in the Northern Irish model of education assumes an individual GHS were assigned for individuals within leaves school at age 14 (Si = 0) if costs grouped earnings categories. A fortuitouschar- exceed gains: acteristic of the U.K. data is that education is recorded as the age an individual completed full-time education. This measure corresponds (5) ci > Yli - Yoi.

In this example, the only individualsaffected by 6 While not advocating either for or against compulsory the instrumentare those for which costs from schooling, Barry R. Chiswick (1969) notes, "while those to over-invest an increase additional exceed circumstantial compelled [in school] experience schooling in their annual post-investment income, they experience a gains. In such a situation,compulsory schooling decrease in their marginal and average internal rates of restrictschoice and lowers welfare among indi- return." VOL.96 NO. 1 OREOPOULOS:ESTIMATING ATE AND IATE WITHCOMPULSORY SCHOOLING LAWS 159 exactly with the school-leaving-age laws. The The government's motivation for increasing combined dataset contains 66,185 individuals the school-leaving age was to "improve the who were age 14 between 1935 and 1965 and future efficiency of the labour force, increase 32 to 64 years of age at the time of the survey. physical and mental adaptability,and prevent (The data go back only to 1983, so we cannot the mental and physical cramping caused by use respondentsyounger than 32 for this anal- exposing children to monotonous occupations ysis.) I also examine unemployment outcomes at an especially impressionableage" (Halsey et and health status using the full sample of earn- al., 1980, p. 126). Public supportfor raising the ers and nonearners.The U.K. GHS sample in- school-leaving age was widespread for many cludes only British-born adults, while the years before the legislation was enacted. The Northern Ireland GHS includes all native and EducationAct of 1918, which raised the school- foreign born respondents, since the Northern leaving age from 12 to 14, also called for a Ireland surveys did not record place of birth. furtherincrease to age 15 "as soon as possible," The data were aggregated into cell groups by but for some time this proposal did not garner survey year, gender, birth cohort, and region much political support out of fear of the costs (Britain or Ireland). The remaining number of involved. Furtherattempts to raise the amount cells was 1,492, and half this for males. of compulsory schooling were made in 1926, 1929, 1933, 1934, and 1936, with no success, B. A Brief History of the 1947 and 1957 U.K. again mostly because of budgetary concerns. School-Leaving-AgeReforms7 But some officials opposed to additional age restrictionshad also arguedthat the majorityof There were two changes to the school-leaving the population did not perceive an advantage age in Britainand NorthernIreland between 1935 from extended education (Bernbaum,1967). In and 1965, both of which had a remarkableinflu- the years leading up to the 1944 legislation, ence on the educationattainment of Britishyoung however, public supportfor raising the school- people. Legislation from Great Britain's 1944 leaving age grew widespread. EducationAct raised the school-leaving age in Prior to 1947, those wanting to advance in England,Scotland, and Wales in 1947 from 14 to school beyond age 14 usually moved from ele- 15 years. Figure 1, previouslymentioned in the mentary to secondary school at age 12. Trans- introduction,shows the effect of this legislative fers were possible afterward,but not common. change:before 1947, a very high fractionof chil- Those planning to leave school and seek work dren in Britainleft full-time school at age 14 (or as soon as the law permittedgenerally remained before). Overjust threeyears, however (between in elementaryschool, which usually offered ed- 1945 and 1948), the portionof 14-year-oldsleav- ucation up to age 14. Pupils transferredto sec- ing schools fell from about57 percentto less than ondary school at no cost on the basis of 10 percent.8This massive rise in enrollmentwas competitive examinations. The proportion of made possible througha concertednational oper- mandatedfree places began in 1907 at 25 per- ation thatexpanded the supplyof teachers,build- cent of total attendanceand rose to more than 50 ings, and furniture.9 percentby 1931. Studentsat the secondarylevel who did not win free places paid fees that were subsidized by more than two-thirdsby the state. 7 For a more detailed discussion of the history of British The 1944 EducationAct removed these fees and and Irisheducation over the periodof analysis, good sources made the first year of secondary school com- include Albert H. Halsey et al. (1980), Gerald Bernbaum pulsory. The observations based on Figure (1967), Howard C. Barnard(1961), Harold C. Dent (1954, 1, that the removal of fees in 1944 had little 1957, 1970, 1971), P. H. J. H. Gosden (1969), and Thomas J. Durcan (1972). effect on educationattainment and that the rais- 8 The finding that some adults reportedfinishing school ing of the school-leaving age had little effect on at age 14, even after the school-leaving age had changed, education attainment beyond age 15, suggest may reflect measurementerror, noncompliance, or delayed enforcement. that fees were not the chief factor preventing 9 The governmentdubbed these operationsHORSA and early school-leavers from staying on. SFORSA: Hutting, Seating, and FurnitureOperations for Northern Ireland's 1947 Education Act was the Raising of the School-leaving Age. closely modeled on Britain's, similarly raising 160 THE AMERICANECONOMIC REVIEW MARCH2006

Local Averages and Parametric Fit

17

Education 16

Full-Time Left 15 Age

Avg. 14 9 1935 1940 1945 1950 1955 1960 1965 YearAged 14 LocalAverage PolynomialFit

FIGURE4. AVERAGEAGE LEvr FULL-TIME EDUCATION BY YEARAGED 14 (Great Britain) Note: Local averages are plotted for British-bornadults aged 32 to 64 from the 1983 to 1998 GeneralHousehold Surveys. The curved line shows the predictedfit from regressing average age left full-time education on a birth cohort quartic polynomial and an indicator for the school-leaving age faced at age 14. The school-leaving age increasedfrom 14 to 15 in 1947, indicated by the vertical line.

the school-leavingage from 14 to 15. In Northern C. A Regression Discontinuity and Ireland, however, the change was not imple- InstrumentalVariables (RD-IV)Analysis for mented until 1957 due to political stonewalling. the Returns to CompulsorySchooling in Figure 2 chartsthe proportionof NorthernIrish Britain and NorthernIreland youths dropping out at age 14 and the total proportiondropping out at age 15 or younger. A In order to estimate more familiar and com- clear break can be seen for portion of early parable returns to years of schooling, I also school-leavers in 1957. By this time, the frac- measured education changes by the age at tion of 14-year-old school-leavers had already which respondentsleft full-time school; the dis- gone down by 11.1 percentage points from its continuities observed in Figures 1 and 2 held 1946 level, but this was still a striking drop in true. The jump in education attainmentturned this variable, around39.8 percentagepoints, in out to be, not surprisingly,similar, since raising just two years.10 the school-leaving age to 15 had little effect on students who stayed on beyond that age. Figure 4 plots the mean age cohorts left full- 10 Bernbaum (1967) discusses the degree of disruption time school by the year they were age 14, using caused by World War II, especially to those evacuatedfrom native-born 32- to 64-year-olds in the 1983 to some urban areas in Britain. The regression discontinuity 1998 British GHS. The vertical line indicates design of this study avoids a general comparison between the after which cohorts faced a school- students in school before and after the war. Furthermore,I year While the education find similar results using an older group of cohorts from the leaving age of 15. average NorthernIreland data. attainmentrises for progressivelylater birth co- VOL. 96 NO. I OREOPOULOS:ESTIMATING ATE AND LATEWITH COMPULSORY SCHOOLING LAWS 161

TABLE 1-ESTIMATED EFFECT OF MINIMUM SCHOOL-LEAVING AGE ON AGE FINISHED FULL-TIME EDUCATION AND LOG ANNUAL EARNINGS (Great Britain and Northern Ireland, ages 25-64, 1935-1965)

(1) (2) (3) (4) (5) (6) (7) (First stage) dependentvariable: Age (Reduced form) dependent variable: Initial Sample population finished full-time school log annual earnings sample size Great Britain 0.440 0.436 0.453 0.065 0.064 0.042 57264 [0.065]*** [0.071]*** [0.076]*** [0.025]** [0.026]** [0.043] NorthernIreland 0.397 0.391 0.353 0.054 0.074 0.074 8921 [0.074]*** [0.073]*** [0.100]*** [0.27]* [0.025]*** [0.045] G. Britain and N. Irelandwith 0.418 0.397 0.401 0.073 0.058 0.059 66185 N. IrelandFixed Effect [0.040]***[0.043]*** [0.045]*** [0.016]*** [0.016]*** [0.018]*** Birth Cohort Polynomial Controls Quartic Quartic Quartic Quartic Quartic Quartic Age Polynomial Controls None Quartic None None Quartic None Age Dummies No No Yes No No Yes

Notes: The dependentvariables are age left full-time education and log annual earnings. Each coefficient is from a separate regression. Each regression includes controls for a birth cohort quartic polynomial and indicatorwhether a cohort faced a school leaving age of 15 at age 14. Columns 2, 3, 5, and 6 also include age controls: a quarticpolynomial and fixed effects where indicated.Each regression includes the sample of 25- to 64-year-olds from the 1983 through 1998 General Household Surveys, who were aged 14 between 1935 and 1965. Data are first aggregatedinto cell means and weighted by cell size. Regressions are clustered by birth cohort and region (Britain or N. Ireland). horts, there is a clear spike in mean attainment predictedbreak in educationattainment of 0.44, after 1947. Average schooling increases by ex- correspondingto Figure 2A. The t-statistic for actly half a year between the cohorts that were rejecting the discontinuityis 6.5. age 14 in 1946 and in 1948. The figure also Figure 5 shows the analogous graph for plots the fittedvalues from regressingthe means NorthernIreland, where the school-leaving age on a quarticpolynomial for year of birthand an increased from 14 to 15 in 1957. The plotted indicatorterm for whetheror not a cohort faced averages are somewhat less smooth than for a minimum school-leaving age of 15 (all 14- Britain because of the smaller sample size year-olds in 1947 and after). The fit predicts an (R2 = 0.989). The quartic polynomial fit, also increase in education attainmentbetween 1946 presented in Table 1, predicts an increase in = and 1947 of 0.44 years (R2 0.995)."1 average education attainmentof 0.397 years in This result, and the accompanying standard 1957, indicated by the vertical line. error (0.065), can also be seen in column 1 of Figures 6 and 7 plot the correspondingraw Table 1, which was produced from the same mean log earnings for the British and Northern GHS data as the figures. The data were first Irish samples for 32- to 64-year-olds who were aggregated into cell means by birth cohort, re- 14 years old between 1935 and 1965. Earnings gion, and age. All regressions are weighted by are measured in 1998 U.K. pounds using the cell size and clustered by cohort and region Retail Price Index.'13Earnings from the com- (Britain or Northern Ireland) using Huber- White standarderrors.12 Column 1 shows the 13 Note that the cross-section panel of the 1983 to 1998 panel includes fewer older cohorts at younger ages. For example, the GHS observes all those older than 51 who " I also tried fitting the grouped means in several other were 14-year-olds in 1945, but only those 14-year-olds of ways: with a quadratic,with a quadraticallowed to differ 1945 who are older than 61. This discrepancy does not before and after 1947, and by omitting 14-year-oldsin 1947, affect testing for a trend break in mean earnings following since not all faced a higher school-leaving age that year. the introductionof the more restrictive school-leaving age, These alternativespecifications generate similar results. but it does lead to an upwardtrend in earnings for younger 12 Card and David S. Lee (2004) underscorethe impor- cohorts. To account for the sensitivity of the results to the tance of avoiding using conventional standarderrors in a different age composition by birth cohorts, I also estimate discrete RD design, such as this one, which depends on a the discontinuitywith age polynomialcontrols and age fixed specific functional form to compute the cohort trend. effects. Age fixed effects are possible with cohort effects 162 THE AMERICANECONOMIC REVIEW MARCH2006

LocalAverages and ParametricFit

17

Education16

Full-Time

Left15 Age

Avg. 14 1935 1940 1945 1950 1955 1960 1965 YearAged 14

Local Average PolynomialFit

FIGURE5. AVERAGEAGE LEFTrFULL-TIME EDUCATION BY YEAR AGED 14 (NorthernIreland) Note: Local averagesare plotted for NorthernIrish adultsaged 32 to 64 from the 1985 to 1998 GeneralHousehold Surveys. The curved line shows the predictedfit from regressing average age left full-time education on a birth cohort quartic polynomial and an indicator for the school-leaving age faced at age 14. The school-leaving age increasedfrom 14 to 15 in 1957, indicated by the vertical line.

bined British GHS were 10.9 percenthigher for the inclusion of quartic age controls, shown in cohorts aged 14 in 1948 than for those aged 14 column 5 of Table 1. The confidence region in 1946. The ratio of reduced form coefficients widens somewhat with the inclusion of age for these two groupsis 0.279 (0.109/0.390). The fixed effects (shown in column 6), but generally polynomial fit in Figure 6, which includes a the results remain consistent with the trends quarticcohort trend, predicts that average earn- shown in the previous figures. ings increased by about 6.5 percent for the Table 2 calculates RD-IV estimates for both cohorts that come after the rise in the school- Britain and Northern Ireland by regressing leaving age. Column 4 in Table 1 shows this mean log earningson a fourth-orderpolynomial break is statistically significant, but the 95- controlfor birthcohort, the averageage a cohort percent confidence region around this value is left full-time school, with this education mea- considerably wide 0.016 to 0.114). The fitted sure instrumented by the minimum school- increase in log earnings for NorthernIreland in leaving age a cohort faced at age 14. All 1957, however, is similar: a quarticfit with no regressions use weighted cell means clustered age controls predictsan increase in log earnings by cohort. These results are shown in column 4: of 0.054 points from raising the school-leaving the estimated average increase in earnings in age to 15. These point estimates are robust to Britainfrom raisingthe school-leavingage to 15 is 14.7 percent. This figure correspondsto the Wald estimate from dividing the estimated av- from 6 by because the GHS contains multiple years of cross-section erage earnings discontinuity Figure data. The results are also robust to the inclusion of survey the estimated education attainmentdiscontinu- year controls. ity from Figure 4 (0.065/0.442). The compara- VOL. 96 NO. I OREOPOULOS:ESTIMATING ATE AND LATEWITH COMPULSORY SCHOOLING LAWS 163

LocalAverages and ParametricFit

9.4

Pounds) UK9.2

(1998 9

Earnings

8.8 Annual of

Log8.6 1935 1940 1945 1950 1955 1960 1965 Year Aged 14 LocalAverage PolynomialFit

FIGURE 6. AVERAGE ANNUAL LOG EARNINGS BY YEAR AGED 14 (Great Britain) Note: Local averages are plotted for British-bornadults aged 32 to 64 from the 1983 to 1998 General Household Surveys. The curved line shows the predictedfit from regressing average log annual earnings on a birth cohort quartic polynomial and an indicator for the school- leaving age faced at age 14. The school leaving age increasedfrom 14 to 15 in 1947, indicated by the vertical line. Earningsare measuredin 1998 U.K. pounds using the U.K. retail price index.

ble estimate for Northern Ireland is 13.5 ern Irish samples. Again I regressed average percent,and about 20 percentwith the inclusion education attainmenton a quartic birth cohort of age controls (see columns 5 and 6). These control, an indicator for the minimum school- estimated effects are similar to previous returns leaving age a cohortfaced, and now an indicator to compulsory schooling estimates, in particu- for Northern Ireland. The estimated increase lar those presented in Harmon and Walker's in years of schooling from the higher school- (1996) U.K. analysis. leaving age with the combined data is 0.42 The regression discontinuity approach leads years, compared to 0.44 using only the British to some imprecision, given that earnings are sample. The standarderror, however, falls con- taperingoff for successively older birth cohorts siderably, to 0.04 (t-statistic = 13.6), and the at the time the discontinuityoccurs. The analy- results are robust to including age controls sis is strengthened,however, by moving to a (shown in columns 2 and 3). difference-in-differences and instrumental- Figure 8, which shows the corresponding variables analysis by combining the two sets of combined plots of British and Northern Irish U.K. data. Doing so lowers the average fraction education attainment by cohort, clearly illus- affected by compulsory schooling a little, com- trates the differences in attainmentbefore and pared to using Britain alone, but the difference after the change in the school laws. Both re- is not great. The thirdrow in Table 1 shows the gions follow almost identical upward trends in estimated effects of raising the school-leaving schooling until 1947, when Britain's attainment age on the average age respondents left full- spikes. The average difference over the next ten time school for the combined British and North- years remains constant at about 0.5 years, and 164 THE AMERICANECONOMIC REVIEW MARCH2006

LocalAverages and ParametricFit

9.4

Pounds) UK9.2

(1998 9

Earnings

8.8 Annual of

Log8.6 1935 1940 1945 1950 1955 1960 1965 YearAged 14 LocalAverage PolynomialFit

FIGURE7. AVERAGEANNUAL LOG EARNINGSBY YEAR AGED 14 (NorthernIreland) Note: Local averagesare plotted for NorthernIrish adults aged 32 to 64 from the 1985 to 1998 General Household Surveys. The curved line shows the predictedfit from regressingaverage log annual earnings on a birth cohort quartic polynomial and an indicator for the school- leaving age faced at age 14. The school-leaving age increasedfrom 14 to 15 in 1957, indicated by the vertical line. U.K. pounds using the U.K. retail price index.

TABLE2-OLS AND IV RETURNSTO (COMPULSORY)SCHOOLING ESTIMATES FOR LOG ANNUALEARNINGS (Great Britain and NorthernIreland, ages 25-64, 1935-1965)

(1) (2) (3) (4) (5) (6) (7) Initial Returnsto schooling: OLS Returnsto compulsory schooling: IV sample size Great Britain 0.078 0.079 0.079 0.147 0.145 0.149 57264 [0.002]*** [0.002]*** [0.002]*** [0.061]** [0.063]** [0.064]** NorthernIreland 0.111 0.113 0.113 0.135 0.187 0.21 8921 [0.004]*** [0.004]*** [0.004]*** [0.071]* [0.070]** [0.135] G. Britain and N. Irelandwith 0.082 0.082 0.083 0.174 0.149 0.148 66185 N. Ireland fixed effect [0.001]*** [0.001]*** [0.001]*** [0.042]*** [0.044]*** [0.046]*** Birth cohort polynomial controls Quartic Quartic Quartic Quartic Quartic Quartic Age polynomial controls None Quartic None None Quartic None Age dummies No No Yes No No Yes

Notes: The dependentvariable is log annualearnings. Each regressionsincludes controls for a birthcohort quartic polynomial and age left full-time education (instrumentedby an indicatorwhether a cohort faced a school leaving age of 15 at age 14 in columns 4 through 6). Columns 2, 3, 5, and 6 also include age controls: a quartic polynomial and fixed effects where indicated.Each regressionincludes the sample of 25- to 64-year-oldsfrom the 1983 through1998 GeneralHousehold Surveys who were aged 14 between 1935 and 1965. Data are first aggregatedinto cell means and weighted by cell size. Regressions are clustered by birth cohort and region (Britain or N. Ireland). VOL. 96 NO. 1 OREOPOULOS:ESTIMATING ATE AND LATEWITH COMPULSORY SCHOOLING LAWS 165

Full Sample

17

School 16 Left

Age

15 Average

14 1935 1940 1945 1950 1955 1960 1965 Year Aged 14

Britain NorthernIreiand

FIGURE8. AVERAGEAGE LEFT FULL-TIME EDUCATION BY YEAR AGED 14 (Great Britain and Northern Ireland) Note: The upperdark line shows the average age left full-time education by year aged 14 for British-bornadults aged 32 to 64 from the 1983 to 1998 General Household Surveys. The lower light line shows the same, but for adults in NorthernIreland.

the gap quickly narrows again after 1957, the Table 2 shows IV estimates correspondingto year when Northern Ireland increased its the data displayed in Figures 8 and 9. Column 4 school-leaving age. of the third row shows that, without age con- Combining the two sets of U.K. data also trols, raising the school-leaving age is associ- helps increase the precision in estimating the ated with a 17.4-percent increase in earnings. reduced-formeffect on earnings. Figure 9 pre- Adding a quarticage control (column 5) or age sents the mean log earnings plots from Figures fixed effects (column 6) lowers this estimate to 6 and 7 on the same grid. While the trendbreaks 14.9 percent. for Britain in 1947 and for NorthernIreland in The OLS results shown in columns 1 to 3 are 1957 are apparent,comparing the two samples lower, consistent with many previous IV and reinforces these changes. The combined U.K. OLS comparisons. It may seem surprisingthat reducedform estimates for the average increase the OLS results differ from the IV results for in earnings using quartic cohort and age con- Britain, since the law change had an impact on trols are displayed in the third row of Ta- much of the same group used to estimate the ble 1, columns 4 and 5. Again, estimates based OLS results. But these results assume linear on the combined data are very similar to the returnsto all levels of schooling. If we restrict separate RD results: that raising the school- the OLS sample to only those who left school at leaving age to 15 increased earnings, on aver- age 16 or before, the resulting OLS estimates age, by about 5.5 or 7 percent,depending on the are more similar to the IV. The OLS estimates age controls used. This combined analysis al- correspondingto columns 1, 2, and 3 for this lows for more robustresults than the individual restricted sample of early school leavers are calculations,with a considerablylower standard 14.5, 14.1, and 14.0, respectively. Thus, while error. OLS and IV results for the high school dropout 166 THE AMERICANECONOMIC REVIEW MARCH2006

Full Sample

9.4

Pounds) UK9.2

(1998 9

Earnings

8.8 Annual of Log 8.6 1935 1940 1945 1950 1955 1960 1965 YearAged 14 Britain NorthernIreland

FIGURE9. AVERAGELOG ANNUAL EARNINGS BY YEAR AGED 14 (Great Britain and Northern Ireland) Note: The upper dark line shows the average log annual earnings by year aged 14 for British-bornadults aged 32 to 64 from the 1983 to 1998 General Household Surveys. The lower light line shows the same, but for adults in NorthernIreland.

sample are similar-which is not surprising A. North American Data given the large fraction in this sample affected by the school-leaving age-the OLS returnsfor Specific details of the U.S. and Canadiandata those older than the school-leaving age are still extracts are provided in the Data Appendix. smaller than the IV results. Wherever possible, I tried to maintain consis- tency in sample selection, school laws, and vari- III. A Cross-CountryComparison able definitions across countries. The samples include all 25- to 64-year-oldmales and females In this section, I move across the Atlantic to who were age 14 in the years that the school- consider the returnsto compulsory schooling in leaving ages were available (1915 to 1970 for North America and how they compare with the the United States, and 1925 to 1970 for Can- results for the United Kingdom. After a brief ada). The U.S. analysis uses all native-born discussion of my Canadian and U.S. data individuals age 25 to 64 from the six decennial sources, I show that the effects on education census microdata samples from 1950 through attainment from changes in the minimum 2000, and the Canadiandata use native-born25- school-leaving age in the United States and to 64-year-olds from the 33-percent sample of Canada were much smaller than for the United the 1971 Census, and the five 20-percent sam- Kingdom. I then look at how the LATE com- ples of the 1981 through 2001 Censuses. For pares across countries.The fact that my findings both countries, individuals are matched to the are reasonably similar suggests the LATE and minimum school-leaving age in their state or ATE for high school may also be reasonably province of birththe year that they were age 14. similar. I also matched to each individual a number of VOL. 96 NO. 1 OREOPOULOS:ESTIMATING ATE AND LATEWiTH COMPULSORY SCHOOLING LAWS 167 regional controls. For the United States, these compelled to stay in school an extra year who included average age, as well as the fractionsof end up staying beyond the new limit push the the population in each state that lived in an estimated effect in column 1 higher, so the urban city, lived on a farm, was black, was in fraction actually affected by compulsory the labor force, and worked in the manufactur- schooling in these countries may be smaller. ing industry.For Canada,I matchedaverage per (This situation differs from that in the United capita school and public expendituresand frac- Kingdom; as discussed in the last section, tions of the population in each province that Figures 1 and 2 show that raising the school- lived in urban areas and worked in the manu- leaving age from 14 to 15 had no noticeable facturingsector.14 1 collapsed both datasetsinto impact on students finishing beyond age 15.) cell means by state or province, birth cohort, The first-stageeffect for all countriesis consid- census year, and gender. erably powerful, and we easily reject that the coefficients are zero. B. The Effect of School-LeavingLaws on Comparingcolumns 2 and 3 of Table 3 pro- School Attainment vides a specification check for whether other region-specific policies or economic conditions Table 3 presents the first-stageeffects of the improved at the same time that minimum school-leaving age changes on educationattain- school-leaving ages increased. It is reassuring ment and the correspondingreduced form ef- that law changes have no positive effect on the fects of the school-leaving age on earnings.The fraction of individuals who attained at least first panel shows results for the United States, some post-secondary education or who left and the second for Canada; the third shows school beyond age 17 (column 3).15 The coef- comparableresults from the combined British- ficients for the samples of those with fewer than NorthernIrish sample. All data are aggregated 12 years of completed schooling and of those into cell means and weightedby populationsize. who finished school by age 16 are about the All regressionsinclude fixed effects for birthyear, same (column 2), as we would expect if those region, surveyyear, gender,race, and a quarticin compelledto takeadditional schooling by changes age-and additionalregional demographicand in these laws still droppedout, only later.16 economic controls according to when cohorts The last three columns show the reduced- were age 14. The fourthpanel repeatsthe regres- form estimates for the effects of these dropout sion discontinuityresults for Britain,discussed in ages on earnings and wages. The main purpose Section IIC. Since cohort fixed effects are not of showing these results is to demonstratethat identifiedwhile tryingto estimatethe compulsory changes in the dropout age do not affect earn- schoolingeffect, I use insteada quarticto control ings in the post-secondary sample. Just as we for cohorttrends and age fixed effects, as before. should not expect compulsoryschooling laws to Column 1 shows the estimated impact from affect post-secondary-schoolingattainment, we raising the school-leaving age on the total num- should not expect them to affect outcome vari- ber of years of completed schooling. Note that ables for the higher educated sample. If we did the impact is much smallerfor the United States observe either of these effects, we might be and Canadathan for the United Kingdom:rais- concernedthat other factors, ones affecting both ing the minimum school-leaving age by one dropouts and graduates, underlie the correla- year increased education attainment by only tions in Table 1. While the laws are strongly about 0.11 years. Furthermore,both Lochner and Moretti (2004) and I (Oreopoulos, 2003) find additionaleffects from school- compulsory 15 The fourth of Table on education attainment the mini- panel 3 shows that in the British ing beyond sample very few students stayed in school beyond age 16, mum requirementsfor North America. Students which makes it hard to draw any conclusions about the correspondingcoefficient in column 3. 16 The results also suggest that changes in U.S. school- 14 Results were not very sensitive to the inclusion of leaving laws influenced would-be dropouts to graduate.If alternative controls. Below I display the LATE estimates we restrictthe initial sample to those with 12 or fewer years with and withoutthe control variables,and with and without of completed schooling, the findings are very similar to cohort trends. those from using the full sample. 168 THE AMERICANECONOMIC REVIEW MARCH2006

TABLE3-FIRST-STAGE EFFECTSOF COMPULSORYSCHOOLING ON EDUCATIONATTAINMENT AND EARNINGSFOR THE UNITED STATES,CANADA, AND THEUNITED KINGDOM

(1) (2) (3) (4) (5) (6) First-stageeffects of dropout ages on schooling Reduced form coefficients on earnings Sample with Sample with Sample with Sample with Full sample < high school > high school Full sample < high school > high school United States [1901-1961 birth cohorts aged 25-64 in the 1950-2000 Censuses] Dependent variable Number of years of schooling Log weekly wage Minimum school-leaving age 0.110 0.100 0.003 0.016 0.010 0.003 at age 14 [0.0070]*** [0.0097]*** [0.0027] [0.0015]*** [0.0024]*** [0.0017]* Initial sample size 2,814,203 727,789 1,173,880 F-test: Schl.-leaving age coeff. is zero 243.5 Canada [1911-1961 birth cohorts aged 25-64 in the 1971-2001 Censuses] Dependent variable Number of years of schooling Log annual wage Minimum school-leaving age 0.130 0.130 -0.026 0.012 0.012 -0.003 at age 14 [0.0154]*** [0.0129]*** [0.0114]** [0.0037]*** [0.0047]** [0.0049] Initial sample size 854,243 355,299 298,342 F-test: Schl.-leaving age coeff. is zero 70.5 United Kingdom [1921-1951 birth cohorts aged 32-64 in the 1983-1998 GHHS] Dependent variable Age left full-time education Log annual wage Minimum school-leaving age 0.369 0.487 0.062 0.058 0.052 0.005 at age 14 [0.0305]*** [0.0309]*** [0.0785] [0.0198]*** [0.0242]** [0.0369] Initial sample size 66,185 47,584 13,760 F-test: Schl.-leaving age coeff. is zero 184.9 Britain [1921-1951 birth cohorts aged 32-64 in the 1983-1998 GHHS] Dependent variable Age left full-time education Log annual wage Minimum school-leaving age 0.453 0.483 0.351 0.042 0.045 -0.014 at age 14 [0.076]*** [0.0868]*** [0.2412] [0.043] [0.0387] [0.0542] Initial sample size 57,264 46,835 10,429 F-test: Schl.-leaving age coeff. is zero 36.0

Note: Regressions in the top three panels include fixed effects for birth year, region (state, province, Britain/N. Ireland), survey year, sex, and a quarticin age. The U.S. results also include a dummy variablefor race, and state controls for fractions living in urbanareas, black, in the labor force, in the manufacturingsector, female, and average age based on when a birth cohort was age 14. Provincial controls for Canadainclude fractions in urbanareas, in the manufacturingsector, and controls for per capital public and school expenditures.Data are groupedinto means by birth year, nation, sex, race (for the U.S.) and survey year and weighted by cell populationsize. Huber-Whitestandard errors are shown from clusteringby region and birth cohort. Single, double, and triple asterisksindicate significantcoefficients at the 10-percent,5-percent, and 1-percentlevels, respectively. The omitted variableindicates ability to drop out at age 13 or lower for the U.S. and Canada,and 14 or less for the U.K. Samples include all adults aged 25 to 64. Dependent variablein column 3 for Canadais 1 = some post-secondary schooling, 0 otherwise. The last panel shows results with only the British sample, using a quarticbirth cohort polynomial instead of cohort fixed effects. See text for more data specifics. related to earnings among dropouts, column 6 C. The LATEof CompulsorySchooling for shows no noticeable relationship between the the United States, Canada, and the United minimum schooling a cohort faced when young Kingdom and its average earningsfor the post-secondary- school sample. These results are also suggestive I estimate that dropoutscompelled to take an that raising high school attainmenthad no re- additionalyear of high school earn about 10 to gion-specific externalities on the birth cohorts 14 percent more than dropouts without the that attainedpost-secondary school.'7 additional year. The returns to compulsory- schooling estimates are similar across all countries, whether restrictingthe initial sample 17 For more specification checks to the robustness of by gender or by race. The effects generally these results, see Oreopoulos (2003). appearto be the largest for the United Kingdom VOL.96 NO. 1 OREOPOULOS:ESTIMATING ATE AND LATEWITH COMPULSORY SCHOOLING LAWS 169

TABLE4--OLS, IV-DD, ANDIV-RD ESTIMATESOF THE RETURNS TO (COMPULSORY) SCHOOLING FOR THE UNITED STATES, CANADA,AND THE UNITED KINGDOM

(4) (1) (2) (3) IV with OLS IV with IV with regional trends and full sample regional controls regional trends regional controls Dependent variable United States [1901-1961 birth cohorts aged 25-64 in the 1950-2000 censuses] Log weekly earnings (all workers) 0.078 0.142 0.175 0.405 [0.0005]*** [0.0119]*** [0.0426]*** [0.7380] Log weekly earnings (males) 0.070 0.127 0.074 0.235 [0.0004]*** [0.0145]*** [0.0384]* [0.1730] Log weekly earnings (black males) 0.074 0.172 0.119 0.264 [0.0004]*** [0.0137]*** [0.0306]*** [0.1295]** Canada [1911-1961 birth cohorts aged 25-64 in the 1971-2001 censuses] Log annualearnings (all workers) 0.099 0.096 0.095 0.142 [0.0007]*** [0.0254]*** [0.1201] [0.0652]** Log annualearnings (males) 0.087 0.124 -0.383 0.115 [0.0008]*** [0.0284]*** [1.1679] [0.0602]* United Kingdom [1921-1951 birth cohorts aged 32-64 in the 1983-1998GHHS] Log annual earnings (all workers) 0.079 0.158 0.195 NA [0.0024]*** [0.0491]*** [0.0446]*** Log annual earnings (males) 0.055 0.094 0.066 NA [0.0017]*** [0.0568] [0.0561] Britain [1921-1951 birth cohorts aged 32-64 in the 1983-1998 GHHS] OLS RD Log annual earnings (all workers) 0.078 0.147 NA NA [0.002]*** [0.061]** Log annual earnings (males) 0.055 0.150 NA NA [0.0017]*** [0.130]

Note: Regressions in the top three panels include fixed effects for birth year, region (state, province, Britain/N. Ireland), survey year, sex, and a quarticin age. The U.S. results also include a dummy variablefor race, and state controls for fractions living in urbanareas, black, in the labor force, in the manufacturingsector, female, and average age based on when a birth cohort was age 14. Provincial controls for Canadainclude fraction in urbanareas, in the manufacturingsector, and controls for per capita public and school expenditures.Data are groupedinto means by birthyear, nation, sex, race (for the U.S.) and survey year and weighted by cell populationsize. Huber-Whitestandard errors are shown from clusteringby region and birth cohort. Single, double, and triple asterisks indicate significantcoefficients at the 10-percent,5-percent, and 1-percentlevels, respectively. The omitted variableindicates ability to drop out at age 13 or lower for the U.S. and Canada,and 14 or less for the U.K. Samples include all adults aged 25 to 64. The last panel repeatsregression discontinuityresults from Table 2 using the British sample only and a quarticbirth cohort polynomial instead of cohort fixed effects. See text for more data specifics.

sample, though the associated standarderrors black, is in the labor force, works in the manu- are high. Overall, there is no evidence that the facturing sector, is female); and a variable for U.S. or Canadian effects are higher than the average age based on when the birthcohort was British ones, except perhaps for U.S. black age 14. Province controls were used for Canada, males. including the fraction of the province that lives The detailed IV estimates for the returns to in urban areas and works in the manufacturing compulsory schooling are shown in Table 4. sector, as well per capita public and school Column 2 includes the IV results corresponding expenditures.Data are grouped into means by to the first and second stages in columns 1 and birth year, region, gender, race (for the United 2 of Table 3. All regressions in the first three States), and survey year. Huber-Whitestandard panels include a quarticin age and fixed effects errorsare shown from clustering by region and for birth cohort, region, survey year, and gen- birth cohort. The IV-RD results for Britain are der. The U.S. results also include a dummy repeated in the fourth panel of Table 4 and variable for race; a number of state controls include a quartic cohort control and age fixed (fraction of state that lives in urban areas, is effects. 170 THE AMERICANECONOMIC REVIEW MARCH2006

The results are robust to including linear re- compulsory schooling lowers the likelihood of gion-specific cohorttrends (see columns 3 and 4 reporting such a disability by 1.7 percentage of Table 4). These were included to control for points, a figure that is similar to the OLS esti- relative changes in education attainment or mate. Another year of compulsory schooling earnings over time that differ by state or prov- also lowers the likelihood of reportinga disabil- ince, or between NorthernIreland and Britain, ity that limits one's daily activity by 2.5 per- and are not due to changes from compulsory centage points. In the United Kingdom, the school laws. The regressions,however, uninten- GHS questionnaire asks respondents to self- tionally absorb some of the effects of compul- report whether they are in good, fair, or poor sory schooling if schooling or earnings trend health. A one-year increase in schooling lowers over time in a nonlinear way, or if the effects the probabilitythat a respondentreports being from the minimumschool-leaving age take time in poor health by 3.2 percentage points, and to become fully enforced. Table 4, column 3, raises the chances he or she reports being in shows coefficient estimates after including lin- good health by 6 percentagepoints. ear region-cohorttrends, but drops the regional Schooling also affects many labor market control variables alreadyincluded in column 2. outcomes in addition to earnings. In all three Including these trendsproduces point estimates countries,I find that compulsoryschooling low- that are less precise-some smaller and some ers the likelihood of respondents being in the larger than in column 2-but not very different labor force and looking for work. The magni- from before. Column 4 includes both regional tude of the effect is similar across countries,and cohort trendsand the previousregional controls. also comparable to corresponding OLS esti- Including both controls leads to multicollinear- mates. Furthercompulsory schooling also low- ity, since regional changes in demographicsand ers the likelihood of receiving welfare and being economic conditions both try to captureoverall classified as poor. Dropouts who drop out one differences in regions over time. The range of year later are 6 percentagepoints less likely to possible true values for returns to schooling fall below the U.S. poverty line and 3 percent- shown here is so wide that we cannot draw any age points less likely to fall below Canada's meaningful conclusions from the results in this low-income cutoff.'8 column. The comparablefull sample OLS results are IV. Discussionand Conclusion shown in Table 4, column 1. I aggregated the country data also by level of schooling to cal- Because most students in the United King- culate these results (still weighted by cell sam- dom at mid-centurytended to leave school at ple size). For all countries,OLS point estimates the earliest legal age, studying the effects of are significantly lower than the IV results. raising this age from 14 to 15 allowed me to Across countries, however, the IV results are estimate local average treatmenteffects of edu- not very different, even though the proportion cation that come close to mirroring average affected by changes in the school-leaving age in treatmenteffects. The regression discontinuity the United Kingdomexceeded that in the United design of my U.K. analysis avoids having to States and Canada by 35 percentage points or assume unobservabletrends in regional charac- more. teristics that could also affect the outcomes. The results presented in Table 5 show other ComparingLATE estimates for North America, effects from compulsory schooling. Health out- where few students were affected by compul- comes are strongly associated with minimum sory school laws, to the U.K. estimates provides school-leavingage changes,corroborating Lleras- a test of whether IV returnsto schooling often Muney's (2002) finding that schooling lowers exceed OLS because gains are high only for mortality. The 1990 and 2000 U.S. Censuses small and peculiargroups among the more gen- ask questions about physical and mental health limitations. Over 9 percent of the individualsin the sample aged 25 to 84 claim a physical or 18 A household falls below the low-income cutoff if it mental health disability that limits their per- spends more than 20 percentage points above the average sonal care; I estimate that an additionalyear of comparativehousehold on food, clothing, and shelter. VOL.96 NO. 1 OREOPOULOS:ESTIMATING ATE AND LATEWITH COMPULSORY SCHOOLING LAWS 171

TABLE5-OLS AND IV ESTIMATESFOR EFFECTS OF (COMPULSORY)SCHOOLING ON SOCIALECONOMICOUTCOMES

(1) (3) Mean (2) IV < HS sample OLS full sample Country (schooling variable) Health outcomes (ages 25-84) United States (total years of schooling) Physical or mental health disability that limits personal care 0.092 -0.014 -0.025 [0.0003]*** [0.0058]*** Disability that limits mobility 0.128 -0.020 -0.043 [0.0004]*** [0.0070]*** United Kingdom (age left full-time education) Self reportedpoor health 0.150 -0.037 -0.032 [0.0016]*** [0.0113]*** Self reportedgood health 0.564 0.065 0.060 [0.0021]*** [0.0155]*** Other socialeconomic outcomes (ages 25-64) United States (schooling variable:total years of schooling) Unemployed 0.064 -0.004 -0.005 [0.0002]*** [0.0040] Receiving welfare 0.067 -0.013 -0.011 [0.0002]*** [0.0024]*** Below poverty line 0.220 -0.023 -0.064 [0.0002]*** [0.0085]*** Canada (total years of schooling) Unemployed: looking for work 0.062 -0.038 -0.010 [0.0044]*** [0.003]*** Below low-income cutoff 0.227 -0.038 -0.026 [0.0004]*** [0.0038]*** United Kingdom (age left full-time education) In labor force: looking for work 0.110 -0.030 -0.032 [0.0044]*** [0.0150]** Receiving income support 0.066 -0.025 -0.059 [0.0024]*** [0.0259]**

Note: All regressions include fixed effects for birth year, region (state, province, Britain/N.Ireland), survey year, sex, and a quarticin age. The U.S. results also include a dummy variablefor race, and state controls for fractions living in urbanareas, black, in the labor force, in the manufacturingsector, female, and average age based on when a birth cohort was age 14. Provincialcontrols for Canadainclude fractionin urbanareas, in the manufacturingsector, and controls for per capital public and school expenditures.Data are grouped into means by birth year, nation, sex, race (for the U.S.) and survey year and weighted by cell populationsize. Huber-Whitestandard errors are shown from clusteringby region and birth cohort. Single, double, and triple asterisksindicate significantcoefficients at the 10-percent,5-percent, and 1-percentlevels, respectively. See text for more data specifics.

eral population. I find, instead, that the gains OLS, is that individualsdropping out are credit- from compulsory schooling are very large-- constrained. Considering the similarity of IV between 10 and 14 percent-whether these laws results across countries, this explanation could affect a majorityor minority of those exposed. apply only if studentsfrom the United Kingdom This finding of high returns to compulsory tend to face greater financial constraints from schooling raises the question of why dropouts staying on than studentsfrom the United States drop out in the first place. Why did so many and Canada.As I discuss in Section II, however, leave school in the United Kingdom if staying while about half of secondary students in Brit- on would have led to substantialgains, on av- ain paid some fees to attendschool, the removal erage, to labor marketand health outcomes? of these fees in 1944 did not affect attainment One possibility, sometimes used to explain beyond age 15. Furthermore,many early school why IV returns to schooling estimates exceed leavers do not work. Among 15- and 16-year- 172 THE AMERICANECONOMIC REVIEW MARCH2006 olds recordedin the 1950 U.S. Census as not in ing dropout behaviour and, more generally, school, fewer than half (41 percent) were in the the overall education attainment decision- labor force and 89 percent lived with their making process. parents.19 Several alternative explanations for dropout behavior exist. First, dropouts may simply ab- DATA APPENDIX hor school. Poor classroom performance and condescending attitudes from students and A. The United States teachers may make students want to leave as soon as possible, even at the expense of forgo- Most of the U.S. analysis uses an extract of ing large monetary sums (Valerie E. Lee and native-bornindividuals aged 25 to 64 from the David T. Burkam, 2003). Second, the uncer- six decennial census microdata samples be- tainty of additional earnings from staying on tween 1950 and 2000.20 All censuses contained may be too high. If a student is risk-averse, individual wages, poverty status, and labor higher expected returnsfrom additionalschool- force participation,but only the 1990 and 2000 ing may not be enough to offset higher proba- datasetscontained disability outcome measures. bilities of earning particularly low wages The initial sample size among those with posi- (David Levhariand YoramWeiss, 1974; Stacey tive wages was 2,814,203. After collapsing H. Chen, 2001). A thirdalternative is that drop- these into cell means, there were 29,804 cells by outs may ignore or severely discount future state, birth cohort, census year, and gender, and consequences of their decisions (e.g., Ted 15,003 cells among males. Hawaiian-and Alas- O'Donoghue and Matthew Rabin, 1999). Cul- kan-bornrespondents were excluded. tural or peer pressures might also predominate I coded the schooling variablefor individuals adolescent decision-makingand lead to dropout in the 1950-1980 data as highest grade com- behavior;cultural norms that devalue schooling, pleted, capped at 17 to impose a uniform top- a lack of emotional support,and low acceptance code across censuses. Following Acemoglu and for higher education among peers may exacer- Angrist (2001), averageyears of schooling were bate students' distaste for school beyond the assigned to categorical values in the 1990 and minimum age (e.g., George A. Akerlof and 2000 Censuses using the imputationfor males Rachel E. Kranton, 2002; and James C. and females in Jin Huem Park (1999). The Coleman, 1961). A final consideration is that earnings variable, log weekly wage, was calcu- students may simply mispredict,making incor- lated by dividing annual wage and salary in- rect present-valuecalculations of future returns come by weeks worked, then taking logs. or else underestimatingthe real gains of in- The cell groups were assigned a minimum creased schooling. school-leaving age according to the year in We cannot determine with this paper's anal- which membersof a birth cohort were 14 years ysis which of these reasons might mattermost, old and the state in which they were born.21I since the effects of compulsory schooling measuredeach school-leaving age as the mini- examined here arise only after leaving school, and costs (pecuniary and nonpecuniary) are not examined. But each explanation carries 20 The specific datasets used were the 1950 General quite different implications about education 1/330 sample (limited to those with long-form responses), policy. Exploring these issues more directly the 1960 General 1-percentsample, the 1970 Form 2 State through innovative field experiments or by 1-percent sample, the 1980 Metro 1-percent sample, the data on school students' ex- 1990 1-percentunweighted sample, and the 2000 1-percent gathering high random on and costs from on unweighted sample. pectations gains staying 21 My analysis assumes that Americanswent to school in longer may shed further light on understand- their state of birth, Canadianswent to school in their prov- ince of birth, British-bornresidents went to school in Brit- ain, and NorthernIrish residentswent to school in Northern 19 Fifty years later, the patternhas not changed much. Ireland. Some individuals will be mismatched. If mobility Among 17-year-olds not in school, according to the 2000 across regions is unrelatedwith law changes, this measure- U.S. Census, for example, 90.4 percent lived with parents, ment errorwill not bias our estimates. Lleras-Muney(2005) and 45 percent were not in the labor force. concludes this seems to be the case for the United States. VOL.96 NO. 1 OREOPOULOS:ESTIMATING ATE AND LATEWITH COMPULSORY SCHOOLING LAWS 173 mum between a state's legislated dropout age The educationvariable used for the Canadian and the minimumage requiredto obtain a work- analysis was total years of schooling, which ing permit.22During this period, a few states refers to the total sum of the years (or grades) of had no laws in place. I grouped the 2.2 percent schooling at the elementary,secondary, univer- of the sample that faced school-leaving ages sity, and nonuniversityyears. I used the log of lower than 14 into one category (school-leaving annual wages and salaries as the earnings vari- age < 14). All others faced dropoutages of 14, able for the Canadiandata. I did not convert this 15, or 16. The laws changed frequentlyover this variable to weekly earnings because a consid- period, both across states and within states over erable number of full-time workers excluded time. About one-third of the variation in the their paid vacations or sick leave when report- school-leaving age is across states and two- ing number of weeks worked in the previous thirds is within. Not all changes were positive; year, contraryto census instructions. in some instances the minimum school-leaving The school-leaving laws were compiled di- age went down. rectly from provincial statutes and revised stat- I also generated control variables for state utes containing the acts of legislation and their economic and demographic conditions in the amendments since inception. In a previous year the laws were in place. For each census study, I documentedthe historyof these changes between 1910 and 1980, I calculated the aver- and other compulsory school laws extensively age age of the populationin each state, as well (Oreopoulos, forthcoming).A few provinces in as the fraction living in an urbancity, living on the first half of the century legislated different a farm, black, in the labor force, and working in dropout ages for urban and for rural areas. For the manufacturingindustry. Values between de- these cases, I recorded the dropout age as that cades were generatedby linear interpolation. for ruralareas, since for most of that period the majority of residents lived in rural areas. All B. Canada provinces except British Columbia experienced legislated increases in the school-leaving age The data extract for Canada comes from the during the period under study. Most provinces four public-use micro-datacensuses from 1981 allowed for working permit exceptions to the to 1996. The main extract contained 25- to age laws, but they were rarely applied. Fewer 64-year-olds born in a Canadianprovince who than 12 percent of the sample faced a school- were 14 years old between 1925 and 1975. leaving age of 16. I chose to group individuals While provincially legislated school-leaving facing a school-leaving age of either 15 or 16, ages were available for earlier years, I chose to since the effect on grade attainmentfrom raising begin with 1925 for two reasons: the cohorts the school-leaving age to 16 from 15 was not aged 14 before 1925 were older than 55 in the significantlydifferent from zero and was impre- 1971 Census, and compulsoryschool laws were cisely measured.Including an indicatorfor fac- often minimallyenforced at the beginningof the ing a school-leaving age equal to 16 did not century. The initial sample size among those alter the second-stage estimates. with positive wages was 854,243. After collaps- As with the U.S. extract, I generatedcontrol ing the data into province, birth cohort, gender, variables for provincial economic and demo- and census groups, the cell sample size was graphic conditions using historical tabulations 3,296 among males and females, and 1,648 and linear interpolation.Oreopoulos (forthcom- among males. ing) describes these control variables in more detail.

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