Estimating Average and Local Average Treatment …econ.ucsb.edu/~jon/Econ230C/Oreopoulos.pdfEstimating Average and Local Average Treatment Effects of Education when Compulsory Schooling

Estimating Average and Local Average Treatment Effects ofEducation when Compulsory Schooling Laws Really Matter

By PHILIP OREOPOULOS

The change to the minimum school-leaving age in the United Kingdom from 14 to15 had a powerful and immediate effect that redirected almost half the populationof 14-year-olds in the mid-twentieth century to stay in school for one more year Themagnitude of this impact provides a rare opportunity to (a) estimate local averagetreatment effects (LATE) of high school that come close to population averagetreatment effects (ATE) and (b) estimate returns to education using a regressiondiscontinuity design instead of previous estimates that rely on difference-in-differencesmethodology or relatively weak instruments Comparing LATE estimates for theUnited States and Canada where very few students were affected by compulsoryschool laws to the United Kingdom estimates provides a test as to whetherinstrumental variables (IV) returns to schooling often exceed ordinary least squares(OLS) because gains are high only for small and peculiar groups among the moregeneral population I find instead that the benefits from compulsory schooling arevery large whether these laws have an impact on a majority or minority of thoseexposed (JEL I20 I21 I28)

Researchers routinely use the IV method toevaluate programs and estimate consistent treat-ment effects A valid instrumental variablewhich helps determine whether an individual istreated but does not determine other factors thataffect the outcomes of interest can overcomeestimation biases that often arise when using theOLS method Recent work in this field clarifies

how to interpret estimated treatment effects us-ing IV When the treatment being evaluated hasthe same effect for everyone any valid instru-ment will identify this unique parameter Butwhen responses to treatment vary different in-struments measure different effects Guido WImbens and Joshua D Angrist (1994) point outthat in this more realistic environment the onlyeffect we can be sure that this method estimatesis the average treatment effect among those whoalter their treatment status because they react tothe instrument they call this parameter theLATE In some cases the LATE also equals theaverage treatment effect among those exposedto the treatment but only when persons do notmake decisions to react to the instrument basedon factors that also determine treatment gains(James J Heckman 1997)

In the return to schooling literature research-ers frequently use IV Some often-cited exam-ples include studies that measure the LATEamong persons who attend college because theylive close to college (David Card 1995) per-sons who attend college because tuition is low(Thomas J Kane and Cecilia Elena Rouse1995) and persons obliged to stay in schoollonger because they face more restrictive com-

Department of Economics University of Toronto 140St George Street Toronto M55 3G6 Canada and NationalBureau of Economic Research (e-mail oreoeconomicsutorontoca) I am very grateful to Joshua Angrist EnricoMoretti and staff members from the UK Data Archive forproviding me with necessary data for this project Seminarand conference participants at UC-Berkeley the LondonSchool of Economics the Chicago Federal Reserve RoyalHolloway Duke University McGill University QueensUniversity NBER Summer Institute IZASOLE Transat-lantic Meetings and the universities of Toronto BritishColumbia and Guelph provided helpful discussion I amespecially thankful to George Akerlof Joshua Angrist AlanAuerbach David Autor Michael Baker Gregory BesharovDavid Card Liz Cascio Stacey Chen Botond KoszegiJohn Quigley Marco Manacorda Rob McMillan JustinMcCrary Costas Meghir Mathew Rabin Jesse RothsteinEmmanuel Saez Aloysius Siow Alois Stutzer Jo VanBiesebroeck Ian Walker and three anonymous referees formany helpful comments and discussions I am solely re-sponsible for this paperrsquos contents

152

pulsory school laws (Angrist and Alan BKrueger 1991 Daron Acemoglu and Angrist2001) These instruments typically affect fewerthan 10 percent of the population exposed to theinstrument and often generate treatment effectsthat exceed those generated from OLS Card(2001) and Lang (1993) suggest that the higherIV results could occur because they approxi-mate average effects among a small and pecu-liar group whereas OLS estimates in theabsence of omitted variables and measurementerror biases approximate average effectsamong everyone In a model where individualsweigh costs and benefits from attaining addi-tional school LATE estimates from IV couldexceed OLS estimates for a variety of reasonsfor example because individuals affected by theinstruments are more credit constrained havegreater immediate need to work or have greaterdistaste for school1

Previous LATE estimates have provided littleinkling about what the gains to schooling are fora more general population An alternative pa-rameter that captures this is the ATE theexpected gain from schooling among all indi-viduals (or all individuals with a given set ofcovariates) Unlike the LATE it does not de-pend on a particular instrument or on who getstreated The ATE offers a theoretically morestable parameter when considering potential gainsfor anyone receiving an extra year of schooling orcollege study A comparison between ATE andprevious LATE estimates would help determinewhether the earlier LATE results are anomalies orwhether the effects of education are by and largesimilar across a wider population

In this paper I exploit historically high drop-out rates in the United Kingdom to estimate theLATE for secondary schooling The result is anIV estimate that is probably closer to the ATEthan any previously reported I focus on a pe-riod when legislative changes had a remarkableeffect on overall education attainment Fig-ure 1 shows this effect on the fraction of British-born adults that left full-time education at ages14 or less and 15 or less It is not difficult to

realize at a glance of the figure that the mini-mum school-leaving age in Britain increasedfrom 14 to 15 in 1947 Within two years of thispolicy change the portion of 14-year-olds leav-ing school fell from 57 percent to less than 10percent The trend for the fraction of childrendropping out at age 15 or less however re-mained intactmdashit appears virtually everyonewho would have left school at age 14 left at age15 after the change I found an equally dramaticresponse to an increase in the minimum legalschool-leaving age in Northern Ireland (see Figure2) where the law change occurred ten years later

I use these two UK experiences to make twocontributions to the returns-to-schooling litera-ture First I estimate average returns to highschool from instrumental variables that affectalmost half the population The magnitude ofthe response from these policies provides a testto whether previous IV estimates often match orexceed OLS estimates because they identifyaverage returns to schooling for a select groupin the population I demonstrate this test bycomparing the results with LATE estimatesfrom compulsory schooling laws in the UnitedStates and Canada where very few students leftearly to the UK estimates If high school drop-outs have more to gain than high school grad-uates from staying on an extra year the localaverage treatment effect of compulsory educa-tion will be higher than the average treatmenteffect for the total population2 As the fractionaffected by compulsory education increases how-ever the LATE and ATE converge since the ATEincludes the population of would-be dropoutsWhen the fraction affected by compulsory school-ing increases we can use the gradient of theseestimates to determine the ATE population Thisapproach is similar in spirit to one proposed byHeckman and Edward Vytlacil (2001)

My second contribution is to adopt a regres-sion discontinuity (RD) design to estimate av-erage returns to schooling The RD approachdiffers from previous studies by comparing ed-ucation attainment and adult earnings for stu-dents just prior to and just after the policy

1 Alternatively IV results might exceed OLS if the in-struments are invalid Pedro Carneiro and James J Heck-man (2002) criticize the validity of some earlier studies bydemonstrating that some often-used instruments correlatewith proxies for innate ability

2 The term ldquodropoutrdquo is something of a misnomer in theUnited Kingdom since those who failed to advance tosecondary school were expected to leave at the earliestopportunity I shall occasionally refer to UK school leaversas dropouts for convenience

153VOL 96 NO 1 OREOPOULOS ESTIMATING ATE AND LATE WITH COMPULSORY SCHOOLING LAWS

change The break in education attainment is sostark in both Britain and Northern Ireland thatwe can show graphically the correspondingbreak in earnings and the source of the LATEidentification

My analysis addresses some previous con-cerns that have been expressed in the literatureabout the validity of earlier approaches to esti-mate returns to compulsory schooling One ap-proach introduced by Angrist and Krueger(1991) uses quarter of birth to identify studentsallowed to drop out with less education thanothers because they were born after the school-entry cutoff date and waited a full year beforeentering school compared to those born prior tothe cutoff date John Bound et al (1995) showthat if education attainment and quarter of birthare only weakly correlated estimates can bebiased in the same direction as OLS results arebiased3 A second concern is that timing of birth

may be related to other factors affecting earn-ings Carneiro and Heckman (2002) providesome evidence that day of birth also relates toproxies for early childhood development

Another approach takes advantage of differ-ences in the timing of compulsory schoolinglaw changes across regions (eg Acemoglu andAngrist 2001 Lance Lochner and Enrico Mor-etti 2004 Adriana Lleras-Muney 2005) Thistechnique uses the same identification strategyas a differences-in-differences research designTo estimate consistently the LATE of compul-sory schooling the timing of the law changesmust not be correlated with any other policychanges or regional characteristics that also re-late to the outcome variables These studiesassume in the absence of law changes thatrelative trends in the outcome variables are thesame across regions

3 Douglas Staiger and James H Stock (1997) and LuizM Cruz and Marcelo J Moreira (2005) address concernsabout this source of bias Both attempt to correct for the

weak instrument bias that may result from using quarter ofbirth to estimate returns to compulsory schooling and arriveat generally similar estimates to Angrist and Kuregerrsquosoriginal study

FIGURE 1 FRACTION LEFT FULL-TIME EDUCATION BY YEAR AGED 14 AND 15(Great Britain)

Note The lower line shows the proportion of British-born adults aged 32 to 64 from the 1983to 1998 General Household Surveys who report leaving full-time education at or before age14 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

154 THE AMERICAN ECONOMIC REVIEW MARCH 2006

A third approach also uses changes to theschool-leaving age in the United KingdomColm Harmon and Ian Walker (1995) werethe first to adopt these school-leaving agechanges to estimate returns to schooling butdid not include birth cohort effects in theirregressions to account for a rising trend ineducation attainment and earnings As a re-sult their estimates do not allow for sys-tematic inter-cohort changes in educationalattainment and do not identify effects fromcohorts who attended school just before andjust after the law changes

The regression discontinuity method usedin this paper offers more compelling evidenceon the average treatment effects of highschool The main conclusion of the paper isthat the effects from compulsory schoolingare very largemdashranging from an annual gainin earnings between 10 to 14 percentmdashwhether a majority or minority of the popu-lation is affected I also identify significantgains to health employment and other labor

market outcomes The results provide evi-dence that IV LATE estimates may often besimilar to ATE and that the main reasonswhy OLS results are weaker than IV are notlikely due to differences in the population ofindividuals affected by the instrument

The next section outlines a theoreticalframework for interpreting returns to compul-sory schooling and provides a parametric ex-ample of how increasing the fraction affectedby compulsory schooling affects the LATEestimate relative to ATE Section II providesbackground to the school-leaving age in-creases in Britain and in Northern IrelandThe regression discontinuity and instrumentalvariables analysis is also carried out in Sec-tion II Section III compares the RD-IV re-sults from Britain and Northern Ireland to theIV results for Canada and the United StatesSection IV concludes with a discussion aboutwhy compulsory school laws seem to gener-ate large gains for individuals who otherwisewould have lefts school earlier

FIGURE 2 FRACTION LEFT FULL-TIME EDUCATION BY YEAR AGED 14 AND 15(Northern Ireland)

Note The lower line shows the proportion of Northern Irish adults aged 32 to 64 from the1985 to 1998 General Household Surveys who report leaving full-time education at or beforeage 14 from 1935 to 1965 The upper line shows the same but for age 15 The minimumschool-leaving age in Northern Ireland changed in 1957 from 14 to 15


I Theoretical Framework

A Causal Inference and CompulsorySchooling

In this section I discuss the theoretical back-ground to my analysis beginning with howcompulsory-schooling laws facilitate makingcausal inferences about various effects of edu-cation I illustrate the differences between theLATE and ATE using a parametric examplethen discuss the optimal schooling within thecontext of the setup if schooling is seen as aninvestment I follow the theoretical frameworkused by Angrist and Krueger (1999) and byAngrist (2004) to link the LATE identified us-ing compulsory schooling as an instrument withthe population ATE

Let Si be an indicator for whether child iattends school at age 15 (Si 1) or leaves at age14 (Si 0) I define schooling thus as a binaryvariable indicating only a measure of highschool attainment because this approach bestrepresents the level of attainment affected byraising the minimum school-leaving age4 LetY1i be child irsquos circumstances after age 15 ifSi 1 and let Y0i be her circumstances after age15 if Si 0 Although only one of these poten-tial outcomes is ever observed the averagetreatment effect E(Y1i Y0i) can be used tomake predictive statements about the impact ofhigh school on a randomly chosen person

Let Zi be a binary variable with Zi 1 if theschool-leaving age equals 15 and Zi 0 if itequals 14 Suppose Si is determined by thelatent-index assignment mechanism

(1) Si 10 1 Zi i

where 1 0 and i is a random variableindependent of the instrument The potentialtreatment assignments are S0i 1(0 i) andS1i 1(0 1 i) The instrument has noeffect on those already intending to attendschool at age 15 but has a nonnegative effect onschooling for those leaving at age 14 without

the law so that S1i S0i Imbens and Angrist(1994) show that this monotonicity assumptiontogether with independence implies

(2)EYiZi 1 EYiZi 0

ESiZi 1 ESiZi 0

EY1i Y0iS1i S0i

The left-hand side of this expression is the pop-ulation analog of the Wald Estimator SinceS1i S0i holds only for individuals who leave atage 14 in the absence of the more restrictivelaw the LATE on the right-hand side is theaverage effect of an additional year of schoolamong those who otherwise would not havetaken that extra year

B A Parametric Example

Following Angrist (2004) I calculate a para-metric model to show the relative differencesbetween LATE and ATE using the compulsory-school-law instrument First I assume that thedistribution of (Y1i Y0i i) is bivariate nor-mal (Y1i Y0i i) N2[

2 2 ]

Thus the ATE [E(Y1i Y0i)] is the mean ofi is the correlation between Y1i Y0i andi is and the respective variances for Y1i Y0i and i are

2 and 2 If is positive the

likelihood of dropping out at age 14 is corre-lated with higher gains from school (after age15) Since everyone must attend school at age15 when the school-leaving age is 15 (13 )the LATE is equal to the treatment effect on thenontreatedmdashthe average effect of attendingschool at age 15 for those who leave at age 14It can be written as

(3)

E13

Y1i Y0iS1i S0i EY1i Y0iS0i 0

EY1i Y0ii 0

EY1i Y0i

x

x

4 The focus here is on high school The average or localaverage treatment effects at the college level may differfrom those examined here


where (x) is the inverse Millrsquos ratio 13(x)[1 (x)] 13(x) and (x) are respectivelythe Normal density and distribution functionsand x (0 ) This expression is thespecial case to Imbens and Angristrsquos (1994)definition of LATE when the instrument affectseveryone with S0i 0 The discrepancy be-tween the LATE and ATE decreases withPr(S 0Z 0) 1 (x) the fraction ofthe population affected by the compulsory-school law and increases with the correlationbetween treatment and gains The interactionbetween these parameters matters as well TheLATE when the fraction affected by the law islarge (for example 05) is closer to the ATEwhen is small

Even with and unknown the ATE canbe determined from two LATE values that dif-fer only by the fraction of the population af-fected by the compulsory-school law Supposefor example we have one LATE with Pr(S 0Z 0) pL corresponding to (x) Land the another with Pr(S 0Z 0) pHcorresponding to (x) H Assume the otherparameters are the same and pL pH (L H)

The ratio of the difference between the LATEand ATE is

(4)EY1i Y0iS0i 0 pL

EY1i Y0iS0i 0 pH

L

H

Equation (4) indicates we can back out the valuefor from two LATE values that differ by(x) The comparison provides much informa-tion on the value of ATE and also on thedirection of Equal LATE values imply 0If the ratio of the two LATE values E(Y1i Y0iS0i 0 pL)E(Y1i Y0iS0i 0 pH) ex-ceeds one 0 and vice versa

To illustrate Figure 3 plots the ATE andLATE against the fraction of would-be-dropoutsPr(S 0Z 0) when 005 025and 015 The figure shows the differencebetween ATE and LATE declining as the frac-tion affected by compulsory schooling increases5

5 This is generally not the case if the instrument does notfully constrain all individuals (see Angrist 2004)

FIGURE 3 LATE AND ATE BY ALTERNATIVE FRACTIONS AFFECTED BY BINARY

COMPULSORY SCHOOLING INSTRUMENT AND THE DEGREE OF SELECTION ON GAINS

Note Pr(S 0Z 0) is the fraction of the population affected by the binary compulsoryschooling instrument Z The figure assumes ATE 005 25 and 015 See textfor details


When is positive a smaller fraction affectedby the instrument always leads to a larger dif-ference between the LATE and ATE TheLATE is 015 013 and 008 when the instru-ment affects respectively 1 5 and 50 percentof the population The absolute difference be-tween the LATE and ATE when the instrumentaffects 5 percent of the population is 26 timesthe difference when the instrument affects 50percent of the population

The main point for the purposes of this paperis that with about half the students in mid-century United Kingdom leaving school as soonas possible the LATE from raising the school-leaving age should come close to the ATE Inaddition comparing compulsory school law ef-fects across countries helps verify how closethis estimate is to the ATE A substantial dif-ference between LATE estimates using NorthAmerican compulsory-school laws (that affectfew) and those from the United Kingdom (thataffect many) would suggest a high value for On the other hand a small difference wouldsuggest that the correlation between droppingout and above-average gains is small and that alarge correlation is an unlikely explanation forwhy OLS and IV returns to schooling estimatessometimes differ

C ATE LATE and Optimal SchoolAttainment

It is interesting to note the effect of com-pulsory schooling when education is viewedas an investment Suppose the total cost ofchild irsquos schooling is ci which may includeeffort psychological costs forgone earningsand lowered immediate consumption causedby not being able to borrow An investmentmodel of education assumes an individualleaves school at age 14 (Si 0) if costsexceed gains

(5) ci Y1i Y0i

In this example the only individuals affected bythe instrument are those for which costs fromadditional schooling exceed circumstantialgains In such a situation compulsory schoolingrestricts choice and lowers welfare among indi-

viduals wanting to leave sooner even amongthose who are credit constrained6

Expressions (1) and (5) imply

(6) i 0 ci Y1i Y0i

If individuals choose education attainment byweighing costs and benefits as in expression (6)and 10 is positive then costs must be propor-tionately higher for those who drop out at age14 than for those who continue on to age 15Similar reasoning has been used to explain whyIV estimates of the returns to compulsoryschooling are often higher than correspondingOLS estimates (see Card 2001) If OLS esti-mates of the ATE are upward biased becausestudents with better cognitive and noncognitiveskills tend to obtain more schooling IV esti-mates that attempt to correct for this bias shouldbe lower

II Minimum Schooling Laws in Great Britainand Ireland

A UK Data

The data used for the UK analysis are de-rived from combining 15 UK General House-hold Surveys (GHS) from 1983 to 1998 (the 1997GHS was cancelled) with 14 Northern IrelandContinuous Household Surveys from 1985 to1998 (For simplicityrsquos sake I use the term GHSto refer to both kinds of surveys since the twoquestionnaires were almost identical) The ma-jor difference was that earnings from the UKGHS were coded exactly while earnings fromthe Northern Ireland GHS were coded by cate-gory Average earnings in the Northern IrishGHS were assigned for individuals withingrouped earnings categories A fortuitous char-acteristic of the UK data is that education isrecorded as the age an individual completedfull-time education This measure corresponds

6 While not advocating either for or against compulsoryschooling Barry R Chiswick (1969) notes ldquowhile thosecompelled to over-invest [in school] experience an increasein their annual post-investment income they experience adecrease in their marginal and average internal rates ofreturnrdquo


exactly with the school-leaving-age laws Thecombined dataset contains 66185 individualswho were age 14 between 1935 and 1965 and32 to 64 years of age at the time of the survey(The data go back only to 1983 so we cannotuse respondents younger than 32 for this anal-ysis) I also examine unemployment outcomesand health status using the full sample of earn-ers and nonearners The UK GHS sample in-cludes only British-born adults while theNorthern Ireland GHS includes all native andforeign born respondents since the NorthernIreland surveys did not record place of birthThe data were aggregated into cell groups bysurvey year gender birth cohort and region(Britain or Ireland) The remaining number ofcells was 1492 and half this for males

B A Brief History of the 1947 and 1957 UKSchool-Leaving-Age Reforms7

There were two changes to the school-leavingage in Britain and Northern Ireland between 1935and 1965 both of which had a remarkable influ-ence on the education attainment of British youngpeople Legislation from Great Britainrsquos 1944Education Act raised the school-leaving age inEngland Scotland and Wales in 1947 from 14 to15 years Figure 1 previously mentioned in theintroduction shows the effect of this legislativechange before 1947 a very high fraction of chil-dren in Britain left full-time school at age 14 (orbefore) Over just three years however (between1945 and 1948) the portion of 14-year-olds leav-ing schools fell from about 57 percent to less than10 percent8 This massive rise in enrollment wasmade possible through a concerted national oper-ation that expanded the supply of teachers build-ings and furniture9

The governmentrsquos motivation for increasingthe school-leaving age was to ldquoimprove thefuture efficiency of the labour force increasephysical and mental adaptability and preventthe mental and physical cramping caused byexposing children to monotonous occupationsat an especially impressionable agerdquo (Halsey etal 1980 p 126) Public support for raising theschool-leaving age was widespread for manyyears before the legislation was enacted TheEducation Act of 1918 which raised the school-leaving age from 12 to 14 also called for afurther increase to age 15 ldquoas soon as possiblerdquobut for some time this proposal did not garnermuch political support out of fear of the costsinvolved Further attempts to raise the amountof compulsory schooling were made in 19261929 1933 1934 and 1936 with no successagain mostly because of budgetary concernsBut some officials opposed to additional agerestrictions had also argued that the majority ofthe population did not perceive an advantagefrom extended education (Bernbaum 1967) Inthe years leading up to the 1944 legislationhowever public support for raising the school-leaving age grew widespread

Prior to 1947 those wanting to advance inschool beyond age 14 usually moved from ele-mentary to secondary school at age 12 Trans-fers were possible afterward but not commonThose planning to leave school and seek workas soon as the law permitted generally remainedin elementary school which usually offered ed-ucation up to age 14 Pupils transferred to sec-ondary school at no cost on the basis ofcompetitive examinations The proportion ofmandated free places began in 1907 at 25 per-cent of total attendance and rose to more than 50percent by 1931 Students at the secondary levelwho did not win free places paid fees that weresubsidized by more than two-thirds by the stateThe 1944 Education Act removed these fees andmade the first year of secondary school com-pulsory The observations based on Figure1 that the removal of fees in 1944 had littleeffect on education attainment and that the rais-ing of the school-leaving age had little effect oneducation attainment beyond age 15 suggestthat fees were not the chief factor preventingearly school-leavers from staying on

Northern Irelandrsquos 1947 Education Act wasclosely modeled on Britainrsquos similarly raising

7 For a more detailed discussion of the history of Britishand Irish education over the period of analysis good sourcesinclude Albert H Halsey et al (1980) Gerald Bernbaum(1967) Howard C Barnard (1961) Harold C Dent (19541957 1970 1971) P H J H Gosden (1969) and ThomasJ Durcan (1972)

8 The finding that some adults reported finishing schoolat age 14 even after the school-leaving age had changedmay reflect measurement error noncompliance or delayedenforcement

9 The government dubbed these operations HORSA andSFORSA Hutting Seating and Furniture Operations forthe Raising of the School-leaving Age


the school-leaving age from 14 to 15 In NorthernIreland however the change was not imple-mented until 1957 due to political stonewallingFigure 2 charts the proportion of Northern Irishyouths dropping out at age 14 and the totalproportion dropping out at age 15 or younger Aclear break can be seen for portion of earlyschool-leavers in 1957 By this time the frac-tion of 14-year-old school-leavers had alreadygone down by 111 percentage points from its1946 level but this was still a striking drop inthis variable around 398 percentage points injust two years10

C A Regression Discontinuity andInstrumental Variables (RD-IV) Analysis for

the Returns to Compulsory Schooling inBritain and Northern Ireland

In order to estimate more familiar and com-parable returns to years of schooling I alsomeasured education changes by the age atwhich respondents left full-time school the dis-continuities observed in Figures 1 and 2 heldtrue The jump in education attainment turnedout to be not surprisingly similar since raisingthe school-leaving age to 15 had little effect onstudents who stayed on beyond that age

Figure 4 plots the mean age cohorts left full-time school by the year they were age 14 usingnative-born 32- to 64-year-olds in the 1983 to1998 British GHS The vertical line indicatesthe year after which cohorts faced a school-leaving age of 15 While the average educationattainment rises for progressively later birth co-

10 Bernbaum (1967) discusses the degree of disruptioncaused by World War II especially to those evacuated fromsome urban areas in Britain The regression discontinuitydesign of this study avoids a general comparison betweenstudents in school before and after the war Furthermore Ifind similar results using an older group of cohorts from theNorthern Ireland data

FIGURE 4 AVERAGE AGE LEFT FULL-TIME EDUCATION BY YEAR AGED 14(Great Britain)

Note Local averages are plotted for British-born adults aged 32 to 64 from the 1983 to 1998General Household Surveys The curved line shows the predicted fit from regressing averageage left full-time education on a birth cohort quartic polynomial and an indicator for theschool-leaving age faced at age 14 The school-leaving age increased from 14 to 15 in 1947indicated by the vertical line


horts there is a clear spike in mean attainmentafter 1947 Average schooling increases by ex-actly half a year between the cohorts that wereage 14 in 1946 and in 1948 The figure alsoplots the fitted values from regressing the meanson a quartic polynomial for year of birth and anindicator term for whether or not a cohort faceda minimum school-leaving age of 15 (all 14-year-olds in 1947 and after) The fit predicts anincrease in education attainment between 1946and 1947 of 044 years (R2 0995)11

This result and the accompanying standarderror (0065) can also be seen in column 1 ofTable 1 which was produced from the sameGHS data as the figures The data were firstaggregated into cell means by birth cohort re-gion and age All regressions are weighted bycell size and clustered by cohort and region(Britain or Northern Ireland) using Huber-White standard errors12 Column 1 shows the

predicted break in education attainment of 044corresponding to Figure 2A The t-statistic forrejecting the discontinuity is 65

Figure 5 shows the analogous graph forNorthern Ireland where the school-leaving ageincreased from 14 to 15 in 1957 The plottedaverages are somewhat less smooth than forBritain because of the smaller sample size(R2 0989) The quartic polynomial fit alsopresented in Table 1 predicts an increase inaverage education attainment of 0397 years in1957 indicated by the vertical line

Figures 6 and 7 plot the corresponding rawmean log earnings for the British and NorthernIrish samples for 32- to 64-year-olds who were14 years old between 1935 and 1965 Earningsare measured in 1998 UK pounds using theRetail Price Index13 Earnings from the com-

11 I also tried fitting the grouped means in several otherways with a quadratic with a quadratic allowed to differbefore and after 1947 and by omitting 14-year-olds in 1947since not all faced a higher school-leaving age that yearThese alternative specifications generate similar results

12 Card and David S Lee (2004) underscore the impor-tance of avoiding using conventional standard errors in adiscrete RD design such as this one which depends on aspecific functional form to compute the cohort trend

13 Note that the cross-section panel of the 1983 to 1998panel includes fewer older cohorts at younger ages Forexample the GHS observes all those older than 51 whowere 14-year-olds in 1945 but only those 14-year-olds of1945 who are older than 61 This discrepancy does notaffect testing for a trend break in mean earnings followingthe introduction of the more restrictive school-leaving agebut it does lead to an upward trend in earnings for youngercohorts To account for the sensitivity of the results to thedifferent age composition by birth cohorts I also estimatethe discontinuity with age polynomial controls and age fixedeffects Age fixed effects are possible with cohort effects

TABLE 1mdashESTIMATED EFFECT OF MINIMUM SCHOOL-LEAVING AGE ON AGE FINISHED FULL-TIME EDUCATION AND LOG

ANNUAL EARNINGS

(Great Britain and Northern Ireland ages 25ndash64 1935ndash1965)

Sample population

(1) (2) (3) (4) (5) (6) (7)(First stage) dependent variable Age

finished full-time school(Reduced form) dependent variable

log annual earningsInitial

sample size

Great Britain 0440 0436 0453 0065 0064 0042 57264[0065] [0071] [0076] [0025] [0026] [0043]

Northern Ireland 0397 0391 0353 0054 0074 0074 8921[0074] [0073] [0100] [027] [0025] [0045]

G Britain and N Ireland withN Ireland Fixed Effect

0418 0397 0401 0073 0058 0059 66185[0040] [0043] [0045] [0016] [0016] [0018]

Birth Cohort PolynomialControls Quartic Quartic Quartic Quartic Quartic Quartic

Age Polynomial Controls None Quartic None None Quartic NoneAge Dummies No No Yes No No Yes

Notes The dependent variables are age left full-time education and log annual earnings Each coefficient is from a separateregression Each regression includes controls for a birth cohort quartic polynomial and indicator whether a cohort faced aschool leaving age of 15 at age 14 Columns 2 3 5 and 6 also include age controls a quartic polynomial and fixed effectswhere indicated Each regression includes the sample of 25- to 64-year-olds from the 1983 through 1998 General HouseholdSurveys who were aged 14 between 1935 and 1965 Data are first aggregated into cell means and weighted by cell sizeRegressions are clustered by birth cohort and region (Britain or N Ireland)


bined British GHS were 109 percent higher forcohorts aged 14 in 1948 than for those aged 14in 1946 The ratio of reduced form coefficientsfor these two groups is 0279 (01090390) Thepolynomial fit in Figure 6 which includes aquartic cohort trend predicts that average earn-ings increased by about 65 percent for thecohorts that come after the rise in the school-leaving age Column 4 in Table 1 shows thisbreak is statistically significant but the 95-percent confidence region around this value isconsiderably wide 0016 to 0114) The fittedincrease in log earnings for Northern Ireland in1957 however is similar a quartic fit with noage controls predicts an increase in log earningsof 0054 points from raising the school-leavingage to 15 These point estimates are robust to

the inclusion of quartic age controls shown incolumn 5 of Table 1 The confidence regionwidens somewhat with the inclusion of agefixed effects (shown in column 6) but generallythe results remain consistent with the trendsshown in the previous figures

Table 2 calculates RD-IV estimates for bothBritain and Northern Ireland by regressingmean log earnings on a fourth-order polynomialcontrol for birth cohort the average age a cohortleft full-time school with this education mea-sure instrumented by the minimum school-leaving age a cohort faced at age 14 Allregressions use weighted cell means clusteredby cohort These results are shown in column 4the estimated average increase in earnings inBritain from raising the school-leaving age to 15is 147 percent This figure corresponds to theWald estimate from dividing the estimated av-erage earnings discontinuity from Figure 6 bythe estimated education attainment discontinu-ity from Figure 4 (00650442) The compara-

because the GHS contains multiple years of cross-sectiondata The results are also robust to the inclusion of surveyyear controls

FIGURE 5 AVERAGE AGE LEFT FULL-TIME EDUCATION BY YEAR AGED 14(Northern Ireland)

Note Local averages are plotted for Northern Irish adults aged 32 to 64 from the 1985 to 1998General Household Surveys The curved line shows the predicted fit from regressing averageage left full-time education on a birth cohort quartic polynomial and an indicator for theschool-leaving age faced at age 14 The school-leaving age increased from 14 to 15 in 1957indicated by the vertical line


ble estimate for Northern Ireland is 135percent and about 20 percent with the inclusionof age controls (see columns 5 and 6) Theseestimated effects are similar to previous returnsto compulsory schooling estimates in particu-lar those presented in Harmon and Walkerrsquos(1996) UK analysis

The regression discontinuity approach leadsto some imprecision given that earnings aretapering off for successively older birth cohortsat the time the discontinuity occurs The analy-sis is strengthened however by moving to adifference-in-differences and instrumental-variables analysis by combining the two sets ofUK data Doing so lowers the average fractionaffected by compulsory schooling a little com-pared to using Britain alone but the differenceis not great The third row in Table 1 shows theestimated effects of raising the school-leavingage on the average age respondents left full-time school for the combined British and North-

ern Irish samples Again I regressed averageeducation attainment on a quartic birth cohortcontrol an indicator for the minimum school-leaving age a cohort faced and now an indicatorfor Northern Ireland The estimated increasein years of schooling from the higher school-leaving age with the combined data is 042years compared to 044 using only the Britishsample The standard error however falls con-siderably to 004 (t-statistic 136) and theresults are robust to including age controls(shown in columns 2 and 3)

Figure 8 which shows the correspondingcombined plots of British and Northern Irisheducation attainment by cohort clearly illus-trates the differences in attainment before andafter the change in the school laws Both re-gions follow almost identical upward trends inschooling until 1947 when Britainrsquos attainmentspikes The average difference over the next tenyears remains constant at about 05 years and

FIGURE 6 AVERAGE ANNUAL LOG EARNINGS BY YEAR AGED 14(Great Britain)

Note Local averages are plotted for British-born adults aged 32 to 64 from the 1983 to 1998General Household Surveys The curved line shows the predicted fit from regressing averagelog annual earnings on a birth cohort quartic polynomial and an indicator for the school-leaving age faced at age 14 The school leaving age increased from 14 to 15 in 1947 indicatedby the vertical line Earnings are measured in 1998 UK pounds using the UK retail priceindex


TABLE 2mdashOLS AND IV RETURNS TO (COMPULSORY) SCHOOLING ESTIMATES FOR LOG ANNUAL EARNINGS


(1) (2) (3) (4) (5) (6) (7)

Returns to schooling OLS Returns to compulsory schooling IVInitial

sample size

Great Britain 0078 0079 0079 0147 0145 0149 57264[0002] [0002] [0002] [0061] [0063] [0064]


G Britain and N Ireland withN Ireland fixed effect

0082 0082 0083 0174 0149 0148 66185[0001] [0001] [0001] [0042] [0044] [0046]

Birth cohort polynomialcontrols Quartic Quartic Quartic Quartic Quartic Quartic

Age polynomial controls None Quartic None None Quartic NoneAge dummies No No Yes No No Yes

Notes The dependent variable is log annual earnings Each regressions includes controls for a birth cohort quartic polynomialand age left full-time education (instrumented by an indicator whether a cohort faced a school leaving age of 15 at age 14in columns 4 through 6) Columns 2 3 5 and 6 also include age controls a quartic polynomial and fixed effects whereindicated Each regression includes the sample of 25- to 64-year-olds from the 1983 through 1998 General Household Surveyswho were aged 14 between 1935 and 1965 Data are first aggregated into cell means and weighted by cell size Regressionsare clustered by birth cohort and region (Britain or N Ireland)

FIGURE 7 AVERAGE ANNUAL LOG EARNINGS BY YEAR AGED 14(Northern Ireland)

Note Local averages are plotted for Northern Irish adults aged 32 to 64 from the 1985 to 1998General Household Surveys The curved line shows the predicted fit from regressing averagelog annual earnings on a birth cohort quartic polynomial and an indicator for the school-leaving age faced at age 14 The school-leaving age increased from 14 to 15 in 1957 indicatedby the vertical line UK pounds using the UK retail price index


the gap quickly narrows again after 1957 theyear when Northern Ireland increased itsschool-leaving age

Combining the two sets of UK data alsohelps increase the precision in estimating thereduced-form effect on earnings Figure 9 pre-sents the mean log earnings plots from Figures6 and 7 on the same grid While the trend breaksfor Britain in 1947 and for Northern Ireland in1957 are apparent comparing the two samplesreinforces these changes The combined UKreduced form estimates for the average increasein earnings using quartic cohort and age con-trols are displayed in the third row of Ta-ble 1 columns 4 and 5 Again estimates basedon the combined data are very similar to theseparate RD results that raising the school-leaving age to 15 increased earnings on aver-age by about 55 or 7 percent depending on theage controls used This combined analysis al-lows for more robust results than the individualcalculations with a considerably lower standarderror

Table 2 shows IV estimates corresponding tothe data displayed in Figures 8 and 9 Column 4of the third row shows that without age con-trols raising the school-leaving age is associ-ated with a 174-percent increase in earningsAdding a quartic age control (column 5) or agefixed effects (column 6) lowers this estimate to149 percent

The OLS results shown in columns 1 to 3 arelower consistent with many previous IV andOLS comparisons It may seem surprising thatthe OLS results differ from the IV results forBritain since the law change had an impact onmuch of the same group used to estimate theOLS results But these results assume linearreturns to all levels of schooling If we restrictthe OLS sample to only those who left school atage 16 or before the resulting OLS estimatesare more similar to the IV The OLS estimatescorresponding to columns 1 2 and 3 for thisrestricted sample of early school leavers are145 141 and 140 respectively Thus whileOLS and IV results for the high school dropout

FIGURE 8 AVERAGE AGE LEFT FULL-TIME EDUCATION BY YEAR AGED 14(Great Britain and Northern Ireland)

Note The upper dark line shows the average age left full-time education by year aged 14 forBritish-born adults aged 32 to 64 from the 1983 to 1998 General Household Surveys Thelower light line shows the same but for adults in Northern Ireland


sample are similarmdashwhich is not surprisinggiven the large fraction in this sample affectedby the school-leaving agemdashthe OLS returns forthose older than the school-leaving age are stillsmaller than the IV results

III A Cross-Country Comparison

In this section I move across the Atlantic toconsider the returns to compulsory schooling inNorth America and how they compare with theresults for the United Kingdom After a briefdiscussion of my Canadian and US datasources I show that the effects on educationattainment from changes in the minimumschool-leaving age in the United States andCanada were much smaller than for the UnitedKingdom I then look at how the LATE com-pares across countries The fact that my findingsare reasonably similar suggests the LATE andATE for high school may also be reasonablysimilar

A North American Data

Specific details of the US and Canadian dataextracts are provided in the Data AppendixWherever possible I tried to maintain consis-tency in sample selection school laws and vari-able definitions across countries The samplesinclude all 25- to 64-year-old males and femaleswho were age 14 in the years that the school-leaving ages were available (1915 to 1970 forthe United States and 1925 to 1970 for Can-ada) The US analysis uses all native-bornindividuals age 25 to 64 from the six decennialcensus microdata samples from 1950 through2000 and the Canadian data use native-born 25-to 64-year-olds from the 33-percent sample ofthe 1971 Census and the five 20-percent sam-ples of the 1981 through 2001 Censuses Forboth countries individuals are matched to theminimum school-leaving age in their state orprovince of birth the year that they were age 14I also matched to each individual a number of

FIGURE 9 AVERAGE LOG 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 forBritish-born adults aged 32 to 64 from the 1983 to 1998 General Household Surveys Thelower light line shows the same but for adults in Northern Ireland


regional controls For the United States theseincluded average age as well as the fractions ofthe population in each state that lived in anurban city lived on a farm was black was inthe labor force and worked in the manufactur-ing industry For Canada I matched average percapita school and public expenditures and frac-tions of the population in each province thatlived in urban areas and worked in the manu-facturing sector14 I collapsed both datasets intocell means by state or province birth cohortcensus year and gender

B The Effect of School-Leaving Laws onSchool Attainment

Table 3 presents the first-stage effects of theschool-leaving age changes on education attain-ment and the corresponding reduced form ef-fects of the school-leaving age on earnings Thefirst panel shows results for the United Statesand the second for Canada the third showscomparable results from the combined BritishndashNorthern Irish sample All data are aggregatedinto cell means and weighted by population sizeAll regressions include fixed effects for birth yearregion survey year gender race and a quartic inagemdashand additional regional demographic andeconomic controls according to when cohortswere age 14 The fourth panel repeats the regres-sion discontinuity results for Britain discussed inSection IIC Since cohort fixed effects are notidentified while trying to estimate the compulsoryschooling effect I use instead a quartic to controlfor cohort trends and age fixed effects as before

Column 1 shows the estimated impact fromraising the school-leaving age on the total num-ber of years of completed schooling Note thatthe impact is much smaller for the United Statesand Canada than for the United Kingdom rais-ing the minimum school-leaving age by oneyear increased education attainment by onlyabout 011 years Furthermore both Lochnerand Moretti (2004) and I (Oreopoulos 2003)find additional effects from compulsory school-ing on education attainment beyond the mini-mum requirements for North America Students

compelled to stay in school an extra year whoend up staying beyond the new limit push theestimated effect in column 1 higher so thefraction actually affected by compulsoryschooling in these countries may be smaller(This situation differs from that in the UnitedKingdom as discussed in the last sectionFigures 1 and 2 show that raising the school-leaving age from 14 to 15 had no noticeableimpact on students finishing beyond age 15)The first-stage effect for all countries is consid-erably powerful and we easily reject that thecoefficients are zero

Comparing columns 2 and 3 of Table 3 pro-vides a specification check for whether otherregion-specific policies or economic conditionsimproved at the same time that minimumschool-leaving ages increased It is reassuringthat law changes have no positive effect on thefraction of individuals who attained at leastsome post-secondary education or who leftschool beyond age 17 (column 3)15 The coef-ficients for the samples of those with fewer than12 years of completed schooling and of thosewho finished school by age 16 are about thesame (column 2) as we would expect if thosecompelled to take additional schooling by changesin these laws still dropped out only later16

The last three columns show the reduced-form estimates for the effects of these dropoutages on earnings and wages The main purposeof showing these results is to demonstrate thatchanges in the dropout age do not affect earn-ings in the post-secondary sample Just as weshould not expect compulsory schooling laws toaffect post-secondary-schooling attainment weshould not expect them to affect outcome vari-ables for the higher educated sample If we didobserve either of these effects we might beconcerned that other factors ones affecting bothdropouts and graduates underlie the correla-tions in Table 1 While the laws are strongly

14 Results were not very sensitive to the inclusion ofalternative controls Below I display the LATE estimateswith and without the control variables and with and withoutcohort trends

15 The fourth panel of Table 3 shows that in the Britishsample very few students stayed in school beyond age 16which makes it hard to draw any conclusions about thecorresponding coefficient in column 3

16 The results also suggest that changes in US school-leaving laws influenced would-be dropouts to graduate Ifwe restrict the initial sample to those with 12 or fewer yearsof completed schooling the findings are very similar tothose from using the full sample


related to earnings among dropouts column 6shows no noticeable relationship between theminimum schooling a cohort faced when youngand its average earnings for the post-secondary-school sample These results are also suggestivethat raising high school attainment had no re-gion-specific externalities on the birth cohortsthat attained post-secondary school17

C The LATE of Compulsory Schooling forthe United States Canada and the United

Kingdom

I estimate that dropouts compelled to take anadditional year of high school earn about 10 to14 percent more than dropouts without theadditional year The returns to compulsory-schooling estimates are similar across allcountries whether restricting the initial sampleby gender or by race The effects generallyappear to be the largest for the United Kingdom

17 For more specification checks to the robustness ofthese results see Oreopoulos (2003)

TABLE 3mdashFIRST-STAGE EFFECTS OF COMPULSORY SCHOOLING ON EDUCATION ATTAINMENT AND EARNINGS FOR THE UNITED

STATES CANADA AND THE UNITED KINGDOM

(1) (2) (3) (4) (5) (6)First-stage effects of dropout ages on schooling Reduced form coefficients on earnings

Full sampleSample with

high schoolSample with

high school Full sampleSample with


high school

United States [1901ndash1961 birth cohorts aged 25ndash64 in the 1950ndash2000 Censuses]Dependent variable

Number of years of schooling Log weekly wageMinimum school-leaving age

at age 140110 0100 0003 0016 0010 0003

[00070] [00097] [00027] [00015] [00024] [00017]Initial sample size 2814203 727789 1173880F-test Schl-leaving age coeff

is zero 2435Canada [1911ndash1961 birth cohorts aged 25ndash64 in the 1971ndash2001 Censuses]

Dependent variableNumber of years of schooling Log annual wage

Minimum school-leaving ageat age 14

0130 0130 0026 0012 0012 0003[00154] [00129] [00114] [00037] [00047] [00049]

Initial sample size 854243 355299 298342F-test Schl-leaving age coeff

is zero 705United Kingdom [1921ndash1951 birth cohorts aged 32ndash64 in the 1983ndash1998 GHHS]

Dependent variableAge left full-time education Log annual wage


0369 0487 0062 0058 0052 0005[00305] [00309] [00785] [00198] [00242] [00369]


is zero 1849Britain [1921ndash1951 birth cohorts aged 32ndash64 in the 1983ndash1998 GHHS]



0453 0483 0351 0042 0045 0014[0076] [00868] [02412] [0043] [00387] [00542]


is zero 360

Note Regressions in the top three panels include fixed effects for birth year region (state province BritainN Ireland)survey year sex and a quartic in age The US results also include a dummy variable for race and state controls for fractionsliving in urban areas black in the labor force in the manufacturing sector female and average age based on when a birthcohort was age 14 Provincial controls for Canada include fractions in urban areas in the manufacturing sector and controlsfor per capital public and school expenditures Data are grouped into means by birth year nation sex race (for the US) andsurvey year and weighted by cell population size Huber-White standard errors are shown from clustering by region and birthcohort Single double and triple asterisks indicate significant coefficients at the 10-percent 5-percent and 1-percent levelsrespectively The omitted variable indicates ability to drop out at age 13 or lower for the US and Canada and 14 or less forthe UK Samples include all adults aged 25 to 64 Dependent variable in column 3 for Canada is 1 some post-secondaryschooling 0 otherwise The last panel shows results with only the British sample using a quartic birth cohort polynomialinstead of cohort fixed effects See text for more data specifics


sample though the associated standard errorsare high Overall there is no evidence that theUS or Canadian effects are higher than theBritish ones except perhaps for US blackmales

The detailed IV estimates for the returns tocompulsory schooling are shown in Table 4Column 2 includes the IV results correspondingto the first and second stages in columns 1 and2 of Table 3 All regressions in the first threepanels include a quartic in age and fixed effectsfor birth cohort region survey year and gen-der The US results also include a dummyvariable for race a number of state controls(fraction of state that lives in urban areas is

black is in the labor force works in the manu-facturing sector is female) and a variable foraverage age based on when the birth cohort wasage 14 Province controls were used for Canadaincluding the fraction of the province that livesin urban areas and works in the manufacturingsector as well per capita public and schoolexpenditures Data are grouped into means bybirth year region gender race (for the UnitedStates) and survey year Huber-White standarderrors are shown from clustering by region andbirth cohort The IV-RD results for Britain arerepeated in the fourth panel of Table 4 andinclude a quartic cohort control and age fixedeffects

TABLE 4mdashOLS IV-DD AND IV-RD ESTIMATES OF THE RETURNS TO (COMPULSORY) SCHOOLING FOR THE UNITED STATESCANADA AND THE UNITED KINGDOM

(1)OLS

full sample

(2)IV with

regional controls

(3)IV with

regional trends

(4)IV with

regional trends andregional controls

Dependent variable United States [1901ndash1961 birth cohorts aged 25ndash64 in the 1950ndash2000 censuses]Log weekly earnings (all workers) 0078 0142 0175 0405

[00005] [00119] [00426] [07380]Log weekly earnings (males) 0070 0127 0074 0235

[00004] [00145] [00384] [01730]Log weekly earnings (black males) 0074 0172 0119 0264

[00004] [00137] [00306] [01295]Canada [1911ndash1961 birth cohorts aged 25ndash64 in the 1971ndash2001 censuses]

Log annual earnings (all workers) 0099 0096 0095 0142[00007] [00254] [01201] [00652]

Log annual earnings (males) 0087 0124 0383 0115[00008] [00284] [11679] [00602]

United Kingdom [1921ndash1951 birth cohorts aged 32ndash64 in the1983ndash1998 GHHS]

Log annual earnings (all workers) 0079 0158 0195 NA[00024] [00491] [00446]

Log annual earnings (males) 0055 0094 0066 NA[00017] [00568] [00561]

Britain [1921ndash1951 birth cohorts aged 32ndash64 in the 1983ndash1998 GHHS]OLS RD

Log annual earnings (all workers) 0078 0147 NA NA[0002] [0061]

Log annual earnings (males) 0055 0150 NA NA[00017] [0130]

Note Regressions in the top three panels include fixed effects for birth year region (state province BritainN Ireland)survey year sex and a quartic in age The US results also include a dummy variable for race and state controls for fractionsliving in urban areas black in the labor force in the manufacturing sector female and average age based on when a birthcohort was age 14 Provincial controls for Canada include fraction in urban areas in the manufacturing sector and controlsfor per capita public and school expenditures Data are grouped into means by birth year nation sex race (for the US) andsurvey year and weighted by cell population size Huber-White standard errors are shown from clustering by region and birthcohort Single double and triple asterisks indicate significant coefficients at the 10-percent 5-percent and 1-percent levelsrespectively The omitted variable indicates ability to drop out at age 13 or lower for the US and Canada and 14 or less forthe UK Samples include all adults aged 25 to 64 The last panel repeats regression discontinuity results from Table 2 usingthe British sample only and a quartic birth cohort polynomial instead of cohort fixed effects See text for more data specifics


The results are robust to including linear re-gion-specific cohort trends (see columns 3 and 4of Table 4) These were included to control forrelative changes in education attainment orearnings over time that differ by state or prov-ince or between Northern Ireland and Britainand are not due to changes from compulsoryschool laws The regressions however uninten-tionally absorb some of the effects of compul-sory schooling if schooling or earnings trendover time in a nonlinear way or if the effectsfrom the minimum school-leaving age take timeto become fully enforced Table 4 column 3shows coefficient estimates after including lin-ear region-cohort trends but drops the regionalcontrol variables already included in column 2Including these trends produces point estimatesthat are less precisemdashsome smaller and somelarger than in column 2mdashbut not very differentfrom before Column 4 includes both regionalcohort trends and the previous regional controlsIncluding both controls leads to multicollinear-ity since regional changes in demographics andeconomic conditions both try to capture overalldifferences in regions over time The range ofpossible true values for returns to schoolingshown here is so wide that we cannot draw anymeaningful conclusions from the results in thiscolumn

The comparable full sample OLS results areshown in Table 4 column 1 I aggregated thecountry data also by level of schooling to cal-culate these results (still weighted by cell sam-ple size) For all countries OLS point estimatesare significantly lower than the IV resultsAcross countries however the IV results arenot very different even though the proportionaffected by changes in the school-leaving age inthe United Kingdom exceeded that in the UnitedStates and Canada by 35 percentage points ormore

The results presented in Table 5 show othereffects from compulsory schooling Health out-comes are strongly associated with minimumschool-leaving age changes corroborating Lleras-Muneyrsquos (2002) finding that schooling lowersmortality The 1990 and 2000 US Censusesask questions about physical and mental healthlimitations Over 9 percent of the individuals inthe sample aged 25 to 84 claim a physical ormental health disability that limits their per-sonal care I estimate that an additional year of

compulsory schooling lowers the likelihood ofreporting such a disability by 17 percentagepoints a figure that is similar to the OLS esti-mate Another year of compulsory schoolingalso lowers the likelihood of reporting a disabil-ity that limits onersquos daily activity by 25 per-centage points In the United Kingdom theGHS questionnaire asks respondents to self-report whether they are in good fair or poorhealth A one-year increase in schooling lowersthe probability that a respondent reports beingin poor health by 32 percentage points andraises the chances he or she reports being ingood health by 6 percentage points

Schooling also affects many labor marketoutcomes in addition to earnings In all threecountries I find that compulsory schooling low-ers the likelihood of respondents being in thelabor force and looking for work The magni-tude of the effect is similar across countries andalso comparable to corresponding OLS esti-mates Further compulsory schooling also low-ers the likelihood of receiving welfare and beingclassified as poor Dropouts who drop out oneyear later are 6 percentage points less likely tofall below the US poverty line and 3 percent-age points less likely to fall below Canadarsquoslow-income cutoff18

IV Discussion and Conclusion

Because most students in the United King-dom at mid-century tended to leave school atthe earliest legal age studying the effects ofraising this age from 14 to 15 allowed me toestimate local average treatment effects of edu-cation that come close to mirroring averagetreatment effects The regression discontinuitydesign of my UK analysis avoids having toassume unobservable trends in regional charac-teristics that could also affect the outcomesComparing LATE estimates for North Americawhere few students were affected by compul-sory school laws to the UK estimates providesa test of whether IV returns to schooling oftenexceed OLS because gains are high only forsmall and peculiar groups among the more gen-

18 A household falls below the low-income cutoff if itspends more than 20 percentage points above the averagecomparative household on food clothing and shelter


eral population I find instead that the gainsfrom compulsory schooling are very largemdashbetween 10 and 14 percentmdashwhether these lawsaffect a majority or minority of those exposed

This finding of high returns to compulsoryschooling raises the question of why dropoutsdrop out in the first place Why did so manyleave school in the United Kingdom if stayingon would have led to substantial gains on av-erage to labor market and health outcomes

One possibility sometimes used to explainwhy IV returns to schooling estimates exceed

OLS is that individuals dropping out are credit-constrained Considering the similarity of IVresults across countries this explanation couldapply only if students from the United Kingdomtend to face greater financial constraints fromstaying on than students from the United Statesand Canada As I discuss in Section II howeverwhile about half of secondary students in Brit-ain paid some fees to attend school the removalof these fees in 1944 did not affect attainmentbeyond age 15 Furthermore many early schoolleavers do not work Among 15- and 16-year-

TABLE 5mdashOLS AND IV ESTIMATES FOR EFFECTS OF (COMPULSORY) SCHOOLING ON SOCIALECONOMIC OUTCOMES

(1)Mean

HS sample(2)

OLS

(3)IV

full sample

Country (schooling variable)Health outcomes (ages 25ndash84)

United States (total years of schooling)Physical or mental health disability that limits personal care 0092 0014 0025

[00003] [00058]Disability that limits mobility 0128 0020 0043

[00004] [00070]United Kingdom (age left full-time education)

Self reported poor health 0150 0037 0032[00016] [00113]

Self reported good health 0564 0065 0060[00021] [00155]

Other socialeconomic outcomes (ages 25ndash64)United States (schooling variable total years of schooling)

Unemployed 0064 0004 0005[00002] [00040]

Receiving welfare 0067 0013 0011[00002] [00024]

Below poverty line 0220 0023 0064[00002] [00085]

Canada (total years of schooling)Unemployed looking for work 0062 0038 0010

[00044] [0003]Below low-income cutoff 0227 0038 0026


In labor force looking for work 0110 0030 0032[00044] [00150]

Receiving income support 0066 0025 0059[00024] [00259]

Note All regressions include fixed effects for birth year region (state province BritainN Ireland) survey year sex and aquartic in age The US results also include a dummy variable for race and state controls for fractions living in urban areasblack in the labor force in the manufacturing sector female and average age based on when a birth cohort was age 14Provincial controls for Canada include fraction in urban areas in the manufacturing sector and controls for per capital publicand school expenditures Data are grouped into means by birth year nation sex race (for the US) and survey year andweighted by cell population size Huber-White standard errors are shown from clustering by region and birth cohort Singledouble and triple asterisks indicate significant coefficients at the 10-percent 5-percent and 1-percent levels respectively Seetext for more data specifics


olds recorded in the 1950 US Census as not inschool fewer than half (41 percent) were in thelabor force and 89 percent lived with theirparents19

Several alternative explanations for dropoutbehavior exist First dropouts may simply ab-hor school Poor classroom performance andcondescending attitudes from students andteachers may make students want to leave assoon as possible even at the expense of forgo-ing large monetary sums (Valerie E Lee andDavid T Burkam 2003) Second the uncer-tainty of additional earnings from staying onmay be too high If a student is risk-aversehigher expected returns from additional school-ing may not be enough to offset higher proba-bilities of earning particularly low wages(David Levhari and Yoram Weiss 1974 StaceyH Chen 2001) A third alternative is that drop-outs may ignore or severely discount futureconsequences of their decisions (eg TedOrsquoDonoghue and Matthew Rabin 1999) Cul-tural or peer pressures might also predominateadolescent decision-making and lead to dropoutbehavior cultural norms that devalue schoolinga lack of emotional support and low acceptancefor higher education among peers may exacer-bate studentsrsquo distaste for school beyond theminimum age (eg George A Akerlof andRachel E Kranton 2002 and James CColeman 1961) A final consideration is thatstudents may simply mispredict making incor-rect present-value calculations of future returnsor else underestimating the real gains of in-creased schooling

We cannot determine with this paperrsquos anal-ysis which of these reasons might matter mostsince the effects of compulsory schoolingexamined here arise only after leaving schooland costs (pecuniary and nonpecuniary) arenot examined But each explanation carriesquite different implications about educationpolicy Exploring these issues more directlythrough innovative field experiments or bygathering data on high school studentsrsquo ex-pectations on gains and costs from staying onlonger may shed further light on understand-

ing dropout behaviour and more generallythe overall education attainment decision-making process

DATA APPENDIX

A The United States

Most of the US analysis uses an extract ofnative-born individuals aged 25 to 64 from thesix decennial census microdata samples be-tween 1950 and 200020 All censuses containedindividual wages poverty status and laborforce participation but only the 1990 and 2000datasets contained disability outcome measuresThe initial sample size among those with posi-tive wages was 2814203 After collapsingthese into cell means there were 29804 cells bystate birth cohort census year and gender and15003 cells among males Hawaiian- and Alas-kan-born respondents were excluded

I coded the schooling variable for individualsin the 1950ndash1980 data as highest grade com-pleted capped at 17 to impose a uniform top-code across censuses Following Acemoglu andAngrist (2001) average years of schooling wereassigned to categorical values in the 1990 and2000 Censuses using the imputation for malesand females in Jin Huem Park (1999) Theearnings variable log weekly wage was calcu-lated by dividing annual wage and salary in-come by weeks worked then taking logs

The cell groups were assigned a minimumschool-leaving age according to the year inwhich members of a birth cohort were 14 yearsold and the state in which they were born21 Imeasured each school-leaving age as the mini-

19 Fifty years later the pattern has not changed muchAmong 17-year-olds not in school according to the 2000US Census for example 904 percent lived with parentsand 45 percent were not in the labor force

20 The specific datasets used were the 1950 General1330 sample (limited to those with long-form responses)the 1960 General 1-percent sample the 1970 Form 2 State1-percent sample the 1980 Metro 1-percent sample the1990 1-percent unweighted sample and the 2000 1-percentunweighted random sample

21 My analysis assumes that Americans went to school intheir state of birth Canadians went to school in their prov-ince of birth British-born residents went to school in Brit-ain and Northern Irish residents went to school in NorthernIreland Some individuals will be mismatched If mobilityacross regions is unrelated with law changes this measure-ment error will not bias our estimates Lleras-Muney (2005)concludes this seems to be the case for the United States


mum between a statersquos legislated dropout ageand the minimum age required to obtain a work-ing permit22 During this period a few stateshad no laws in place I grouped the 22 percentof the sample that faced school-leaving ageslower than 14 into one category (school-leavingage 14) All others faced dropout ages of 1415 or 16 The laws changed frequently over thisperiod both across states and within states overtime About one-third of the variation in theschool-leaving age is across states and two-thirds is within Not all changes were positivein some instances the minimum school-leavingage went down

I also generated control variables for stateeconomic and demographic conditions in theyear the laws were in place For each censusbetween 1910 and 1980 I calculated the aver-age age of the population in each state as wellas the fraction living in an urban city living ona farm black in the labor force and working inthe manufacturing industry Values between de-cades were generated by linear interpolation

B Canada

The data extract for Canada comes from thefour public-use micro-data censuses from 1981to 1996 The main extract contained 25- to64-year-olds born in a Canadian province whowere 14 years old between 1925 and 1975While provincially legislated school-leavingages were available for earlier years I chose tobegin with 1925 for two reasons the cohortsaged 14 before 1925 were older than 55 in the1971 Census and compulsory school laws wereoften minimally enforced at the beginning of thecentury The initial sample size among thosewith positive wages was 854243 After collaps-ing the data into province birth cohort genderand census groups the cell sample size was3296 among males and females and 1648among males

The education variable used for the Canadiananalysis was total years of schooling whichrefers to the total sum of the years (or grades) ofschooling at the elementary secondary univer-sity and nonuniversity years I used the log ofannual wages and salaries as the earnings vari-able for the Canadian data I did not convert thisvariable to weekly earnings because a consid-erable number of full-time workers excludedtheir paid vacations or sick leave when report-ing number of weeks worked in the previousyear contrary to census instructions

The school-leaving laws were compiled di-rectly from provincial statutes and revised stat-utes containing the acts of legislation and theiramendments since inception In a previousstudy I documented the history of these changesand other compulsory school laws extensively(Oreopoulos forthcoming) A few provinces inthe first half of the century legislated differentdropout ages for urban and for rural areas Forthese cases I recorded the dropout age as thatfor rural areas since for most of that period themajority of residents lived in rural areas Allprovinces except British Columbia experiencedlegislated increases in the school-leaving ageduring the period under study Most provincesallowed for working permit exceptions to theage laws but they were rarely applied Fewerthan 12 percent of the sample faced a school-leaving age of 16 I chose to group individualsfacing a school-leaving age of either 15 or 16since the effect on grade attainment from raisingthe school-leaving age to 16 from 15 was notsignificantly different from zero and was impre-cisely measured Including an indicator for fac-ing a school-leaving age equal to 16 did notalter the second-stage estimates

As with the US extract I generated controlvariables for provincial economic and demo-graphic conditions using historical tabulationsand linear interpolation Oreopoulos (forthcom-ing) describes these control variables in moredetail

REFERENCES

Acemoglu Daron and Angrist Joshua D ldquoHowLarge Are Human-Capital Externalities Ev-idence from Compulsory Schooling Lawsrdquoin Ben S Bernanke and Kenneth eds Ro-goff NBER macroeconomics annual 2000

22 Acemoglu and Angrist (2001) Lleras-Muney (2005)and Claudia Goldin and Lawrence Katz (2003) find workingpermit restrictions were often more binding than school-leaving age restrictions The results are not sensitive tousing just the dropout age as the compulsory school lawvariable or the predicted mandatory number of schoolyears used by Acemoglu and Angrist (2001) and Lochnerand Moretti (2004)


Cambridge MA MIT Press 2001 pp 9ndash59Akerlof George A and Kranton Rachel E

ldquoIdentity and Schooling Some Lessons forthe Economics of Educationrdquo Journal of Eco-nomic Literature 2002 40(4) pp 1167ndash1201

Angrist Joshua D ldquoTreatment Effect Heteroge-neity in Theory and Practicerdquo EconomicJournal 2004 114(494) pp C52ndash83

Angrist Joshua D and Krueger Alan B ldquoDoesCompulsory School Attendance AffectSchooling and Earningsrdquo Quarterly Journalof Economics 1991 106(4) pp 979ndash1014

Angrist Joshua D and Krueger Alan B ldquoEmpir-ical Strategies in Labor Economicsrdquo in OrleyAshenfelter and David Card eds Handbookof labor economics Vol 3A AmsterdamElsevier Science North-Holland 1999 pp1277ndash366

Barnard Howard C A history of English edu-cation from 1760 2nd ed London Univer-sity of London Press 1961

Bernbaum Gerald Social change and theschools 1918ndash1944 London Routledge andK Paul 1967

Bound John Jaeger David A and Baker ReginaM ldquoProblems with Instrumental VariablesEstimation when the Correlation between theInstruments and the Endogenous ExplanatoryVariable Is Weakrdquo Journal of the AmericanStatistical Association 1995 90(430) pp443ndash50

Cameron Stephen V and Taber ChristopherldquoEstimation of Educational Borrowing Con-straints Using Returns to Schoolingrdquo Journalof Political Economy 2004 112(1) pp 132ndash82

Card David ldquoUsing Geographic Variation inCollege Proximity to Estimate the Return toSchoolingrdquo in Louis N Christofides E Ken-neth Grant and Robert Swidinsky eds As-pects of labour market behaviour Essays inhonour of John Vanderkamp Toronto Uni-versity of Toronto Press 1995 pp 201ndash22

Card David ldquoEstimating the Return to School-ing Progress on Some Persistent Economet-ric Problemsrdquo Econometrica 2001 69(5)pp 1127ndash60

Card David and Lee David S ldquoRegression Dis-continuity Inference with Specification Er-rorrdquo University of California BerkeleyCenter for Labor Economics Working PaperNo 74 2004

Carneiro Pedro and Heckman James J ldquoTheEvidence on Credit Constraints in Post-Secondary Schoolingrdquo Economic Journal2002 112(482) pp 705ndash34

Chen Stacey H ldquoIs Investing in College Educa-tion Riskyrdquo State University of New York atAlbany Department of Education DiscussionPapers No 01-09 2001

Chiswick Barry R ldquoMinimum Schooling Leg-islation and the Cross-Sectional Distributionof Incomerdquo Economic Journal 196979(315) pp 495ndash507

Coleman James S The adolescent society NewYork The Free Press 1961

Cruz Luiz M and Moreira Marcelo J ldquoOn theValidity of Econometric Techniques withWeak Instruments Inference on Returns toEducation Using Compulsory School Atten-dance Lawsrdquo Journal of Human Resources2005 40(2) pp 393ndash410

Cusick Philip Inside high school The studentrsquosworld New York Holt Rinehart and Winston1972

Dent Harold C Growth in English education1946ndash1952 London Routledge and KeganPaul 1954

Dent Harold C The Education Act 1944 Lon-don University of London Press 1957

Dent Harold C 1870ndash1970 Century of growthin English education London LongmanGroup Limited 1970

Dent Harold C The educational system ofEngland and Wales London University ofLondon Press 1971

Dominitz Jeff and Manski Charles F ldquoUsingExpectations Data to Study Subjective In-come Expectationsrdquo Journal of the AmericanStatistical Association 1997 92(439) pp855ndash67

Durcan Thomas J History of Irish educationfrom 1800 Bala Wales UK Dragon Books1972

Godsen P H J H How they were taught Ananthology of contemporary accounts of learn-ing and teaching in England 1800ndash1950 Ox-ford Basil Blackwell 1969

Goldin Claudia and Katz Lawrence ldquoMass Sec-ondary Schooling and the Staterdquo NationalBureau of Economic Research Inc NBERWorking Papers No 10075 2003

Halsey Albert H Heath Anthony F and RidgeJohn M Origins and destinations Family


class and education in modern Britain Ox-ford Clarendon Press 1980

Harmon Colm and Walker Ian ldquoEstimates ofthe Economic Return to Schooling for theUnited Kingdomrdquo American Economic Re-view 1995 85(5) pp 1278ndash86

Heckman James J ldquoInstrumental Variables AStudy of Implicit Behavioral AssumptionsUsed in Making Program Evaluationsrdquo Jour-nal of Human Resources 1997 32(3) pp441ndash62

Heckman James and Vytlacil Edward ldquoCausalParameters Structural Equations TreatmentEffects and Randomized Evaluation of SocialProgramsrdquo Unpublished Paper 2001

Imbens Guido W and Angrist Joshua D ldquoIden-tification and Estimation of Local AverageTreatment Effectsrdquo Econometrica 199462(2) pp 467ndash75

Kane Thomas J and Rouse Cecilia Elena ldquoLa-bor-Market Returns to Two- and Four-YearCollegerdquo American Economic Review 199585(3) pp 600ndash14

Lang Kevin ldquoAbility Bias Discount Rate Biasand the Return to Educationrdquo UnpublishedPaper 1993

Lee Valerie E and Burkam David T ldquoDroppingOut of High School The Role of SchoolOrganization and Structurerdquo American Edu-cational Research Journal 2003 40(2) pp353ndash93

Levhari David and Weiss Yoram ldquoThe Effect ofRisk on the Investment in Human CapitalrdquoAmerican Economic Review 1974 64(6) pp950ndash63

Lleras-Muney Adriana ldquoWere Compulsory At-tendance and Child Labor Laws Effective

An Analysis from 1915 to 1939rdquo Journal ofLaw and Economics 2002 45(2) pp 401ndash35

Lleras-Muney Adriana ldquoThe Relationship be-tween Education and Adult Mortality in theUnited Statesrdquo Review of Economic Studies2005 72(1) pp 189ndash221

Lochner Lance and Moretti Enrico ldquoThe Effectof Education on Crime Evidence fromPrison Inmates Arrests and Self-ReportsrdquoAmerican Economic Review 2004 94(1) pp155ndash89

OrsquoDonoghue Ted and Rabin Matthew ldquoDoing ItNow or Laterrdquo American Economic Review1999 89(1) pp 103ndash24

OrsquoKeeffe Dennis J ldquoSome Economic Aspects ofRaising the School Leaving Age in Englandand Wales in 1947rdquo Economic History Re-view Second Series 1975 28(3) pp 500ndash16

Oreopoulos Philip ldquoDo Dropouts Drop Out TooSoon International Evidence from Changesin School-Leaving Lawsrdquo National Bureauof Economic Research Inc NBER WorkingPapers No 10155 2003

Oreopoulos Philip ldquoThe Compelling Effects ofCompulsory Schooling Evidence from Can-adardquo Canadian Journal of Economics 200639(1) (forthcoming)

Park Jin Huem ldquoEstimation of Sheepskin Ef-fects Using the Old and New Measures ofEducational Attainment in the Current Popu-lation Surveyrdquo Economics Letters 199962(2) pp 237ndash40

Staiger Douglas and Stock James H ldquoInstru-mental Variables Regression with Weak In-strumentsrdquo Econometrica 1997 65(3) pp557ndash86


pulsory school laws (Angrist and Alan BKrueger 1991 Daron Acemoglu and Angrist2001) These instruments typically affect fewerthan 10 percent of the population exposed to theinstrument and often generate treatment effectsthat exceed those generated from OLS Card(2001) and Lang (1993) suggest that the higherIV results could occur because they approxi-mate average effects among a small and pecu-liar group whereas OLS estimates in theabsence of omitted variables and measurementerror biases approximate average effectsamong everyone In a model where individualsweigh costs and benefits from attaining addi-tional school LATE estimates from IV couldexceed OLS estimates for a variety of reasonsfor example because individuals affected by theinstruments are more credit constrained havegreater immediate need to work or have greaterdistaste for school1

Previous LATE estimates have provided littleinkling about what the gains to schooling are fora more general population An alternative pa-rameter that captures this is the ATE theexpected gain from schooling among all indi-viduals (or all individuals with a given set ofcovariates) Unlike the LATE it does not de-pend on a particular instrument or on who getstreated The ATE offers a theoretically morestable parameter when considering potential gainsfor anyone receiving an extra year of schooling orcollege study A comparison between ATE andprevious LATE estimates would help determinewhether the earlier LATE results are anomalies orwhether the effects of education are by and largesimilar across a wider population

In this paper I exploit historically high drop-out rates in the United Kingdom to estimate theLATE for secondary schooling The result is anIV estimate that is probably closer to the ATEthan any previously reported I focus on a pe-riod when legislative changes had a remarkableeffect on overall education attainment Fig-ure 1 shows this effect on the fraction of British-born adults that left full-time education at ages14 or less and 15 or less It is not difficult to

realize at a glance of the figure that the mini-mum school-leaving age in Britain increasedfrom 14 to 15 in 1947 Within two years of thispolicy change the portion of 14-year-olds leav-ing school fell from 57 percent to less than 10percent The trend for the fraction of childrendropping out at age 15 or less however re-mained intactmdashit appears virtually everyonewho would have left school at age 14 left at age15 after the change I found an equally dramaticresponse to an increase in the minimum legalschool-leaving age in Northern Ireland (see Figure2) where the law change occurred ten years later

I use these two UK experiences to make twocontributions to the returns-to-schooling litera-ture First I estimate average returns to highschool from instrumental variables that affectalmost half the population The magnitude ofthe response from these policies provides a testto whether previous IV estimates often match orexceed OLS estimates because they identifyaverage returns to schooling for a select groupin the population I demonstrate this test bycomparing the results with LATE estimatesfrom compulsory schooling laws in the UnitedStates and Canada where very few students leftearly to the UK estimates If high school drop-outs have more to gain than high school grad-uates from staying on an extra year the localaverage treatment effect of compulsory educa-tion will be higher than the average treatmenteffect for the total population2 As the fractionaffected by compulsory education increases how-ever the LATE and ATE converge since the ATEincludes the population of would-be dropoutsWhen the fraction affected by compulsory school-ing increases we can use the gradient of theseestimates to determine the ATE population Thisapproach is similar in spirit to one proposed byHeckman and Edward Vytlacil (2001)

My second contribution is to adopt a regres-sion discontinuity (RD) design to estimate av-erage returns to schooling The RD approachdiffers from previous studies by comparing ed-ucation attainment and adult earnings for stu-dents just prior to and just after the policy

1 Alternatively IV results might exceed OLS if the in-struments are invalid Pedro Carneiro and James J Heck-man (2002) criticize the validity of some earlier studies bydemonstrating that some often-used instruments correlatewith proxies for innate ability

2 The term ldquodropoutrdquo is something of a misnomer in theUnited Kingdom since those who failed to advance tosecondary school were expected to leave at the earliestopportunity I shall occasionally refer to UK school leaversas dropouts for convenience























(1) Si 10 1 Zi i



(2)EYiZi 1 EYiZi 0

ESiZi 1 ESiZi 0

EY1i Y0iS1i S0i




2 2 ]




(3)

E13


EY1i Y0ii 0

EY1i Y0i

x

x






(4)EY1i Y0iS0i 0 pL

EY1i Y0iS0i 0 pH

L

H












(5) ci Y1i Y0i




(6) i 0 ci Y1i Y0i



A UK Data
































ANNUAL EARNINGS


Sample population




sample size

Great Britain 0440 0436 0453 0065 0064 0042 57264[0065] [0071] [0076] [0025] [0026] [0043]



0418 0397 0401 0073 0058 0059 66185[0040] [0043] [0045] [0016] [0016] [0018]





















(1) (2) (3) (4) (5) (6) (7)


sample size

Great Britain 0078 0079 0079 0147 0145 0149 57264[0002] [0002] [0002] [0061] [0063] [0064]



0082 0082 0083 0174 0149 0148 66185[0001] [0001] [0001] [0042] [0044] [0046]



































Kingdom










high school



at age 140110 0100 0003 0016 0010 0003





0130 0130 0026 0012 0012 0003[00154] [00129] [00114] [00037] [00047] [00049]





0369 0487 0062 0058 0052 0005[00305] [00309] [00785] [00198] [00242] [00369]





0453 0483 0351 0042 0045 0014[0076] [00868] [02412] [0043] [00387] [00542]


is zero 360







(1)OLS

full sample

(2)IV with

regional controls

(3)IV with

regional trends

(4)IV with






























(1)Mean

HS sample(2)

OLS

(3)IV

full sample








Unemployed 0064 0004 0005[00002] [00040]














DATA APPENDIX

A The United States










B Canada





REFERENCES









































































(1) Si 10 1 Zi i



(2)EYiZi 1 EYiZi 0

ESiZi 1 ESiZi 0

EY1i Y0iS1i S0i




2 2 ]




(3)

E13


EY1i Y0ii 0

EY1i Y0i

x

x






(4)EY1i Y0iS0i 0 pL

EY1i Y0iS0i 0 pH

L

H












(5) ci Y1i Y0i




(6) i 0 ci Y1i Y0i



A UK Data
































ANNUAL EARNINGS


Sample population




sample size

Great Britain 0440 0436 0453 0065 0064 0042 57264[0065] [0071] [0076] [0025] [0026] [0043]



0418 0397 0401 0073 0058 0059 66185[0040] [0043] [0045] [0016] [0016] [0018]





















(1) (2) (3) (4) (5) (6) (7)


sample size

Great Britain 0078 0079 0079 0147 0145 0149 57264[0002] [0002] [0002] [0061] [0063] [0064]



0082 0082 0083 0174 0149 0148 66185[0001] [0001] [0001] [0042] [0044] [0046]



































Kingdom










high school



at age 140110 0100 0003 0016 0010 0003





0130 0130 0026 0012 0012 0003[00154] [00129] [00114] [00037] [00047] [00049]





0369 0487 0062 0058 0052 0005[00305] [00309] [00785] [00198] [00242] [00369]





0453 0483 0351 0042 0045 0014[0076] [00868] [02412] [0043] [00387] [00542]


is zero 360







(1)OLS

full sample

(2)IV with

regional controls

(3)IV with

regional trends

(4)IV with






























(1)Mean

HS sample(2)

OLS

(3)IV

full sample








Unemployed 0064 0004 0005[00002] [00040]














DATA APPENDIX

A The United States










B Canada





REFERENCES
































































(1) Si 10 1 Zi i



(2)EYiZi 1 EYiZi 0

ESiZi 1 ESiZi 0

EY1i Y0iS1i S0i




2 2 ]




(3)

E13


EY1i Y0ii 0

EY1i Y0i

x

x






(4)EY1i Y0iS0i 0 pL

EY1i Y0iS0i 0 pH

L

H












(5) ci Y1i Y0i




(6) i 0 ci Y1i Y0i



A UK Data
































ANNUAL EARNINGS


Sample population




sample size

Great Britain 0440 0436 0453 0065 0064 0042 57264[0065] [0071] [0076] [0025] [0026] [0043]



0418 0397 0401 0073 0058 0059 66185[0040] [0043] [0045] [0016] [0016] [0018]





















(1) (2) (3) (4) (5) (6) (7)


sample size

Great Britain 0078 0079 0079 0147 0145 0149 57264[0002] [0002] [0002] [0061] [0063] [0064]



0082 0082 0083 0174 0149 0148 66185[0001] [0001] [0001] [0042] [0044] [0046]



































Kingdom










high school



at age 140110 0100 0003 0016 0010 0003





0130 0130 0026 0012 0012 0003[00154] [00129] [00114] [00037] [00047] [00049]





0369 0487 0062 0058 0052 0005[00305] [00309] [00785] [00198] [00242] [00369]





0453 0483 0351 0042 0045 0014[0076] [00868] [02412] [0043] [00387] [00542]


is zero 360







(1)OLS

full sample

(2)IV with

regional controls

(3)IV with

regional trends

(4)IV with






























(1)Mean

HS sample(2)

OLS

(3)IV

full sample








Unemployed 0064 0004 0005[00002] [00040]














DATA APPENDIX

A The United States










B Canada





REFERENCES

























































(1) Si 10 1 Zi i



(2)EYiZi 1 EYiZi 0

ESiZi 1 ESiZi 0

EY1i Y0iS1i S0i




2 2 ]




(3)

E13


EY1i Y0ii 0

EY1i Y0i

x

x






(4)EY1i Y0iS0i 0 pL

EY1i Y0iS0i 0 pH

L

H












(5) ci Y1i Y0i




(6) i 0 ci Y1i Y0i



A UK Data
































ANNUAL EARNINGS


Sample population




sample size

Great Britain 0440 0436 0453 0065 0064 0042 57264[0065] [0071] [0076] [0025] [0026] [0043]



0418 0397 0401 0073 0058 0059 66185[0040] [0043] [0045] [0016] [0016] [0018]





















(1) (2) (3) (4) (5) (6) (7)


sample size

Great Britain 0078 0079 0079 0147 0145 0149 57264[0002] [0002] [0002] [0061] [0063] [0064]



0082 0082 0083 0174 0149 0148 66185[0001] [0001] [0001] [0042] [0044] [0046]



































Kingdom










high school



at age 140110 0100 0003 0016 0010 0003





0130 0130 0026 0012 0012 0003[00154] [00129] [00114] [00037] [00047] [00049]





0369 0487 0062 0058 0052 0005[00305] [00309] [00785] [00198] [00242] [00369]





0453 0483 0351 0042 0045 0014[0076] [00868] [02412] [0043] [00387] [00542]


is zero 360







(1)OLS

full sample

(2)IV with

regional controls

(3)IV with

regional trends

(4)IV with






























(1)Mean

HS sample(2)

OLS

(3)IV

full sample








Unemployed 0064 0004 0005[00002] [00040]














DATA APPENDIX

A The United States










B Canada





REFERENCES























































(4)EY1i Y0iS0i 0 pL

EY1i Y0iS0i 0 pH

L

H












(5) ci Y1i Y0i




(6) i 0 ci Y1i Y0i



A UK Data
































ANNUAL EARNINGS


Sample population




sample size

Great Britain 0440 0436 0453 0065 0064 0042 57264[0065] [0071] [0076] [0025] [0026] [0043]



0418 0397 0401 0073 0058 0059 66185[0040] [0043] [0045] [0016] [0016] [0018]





















(1) (2) (3) (4) (5) (6) (7)


sample size

Great Britain 0078 0079 0079 0147 0145 0149 57264[0002] [0002] [0002] [0061] [0063] [0064]



0082 0082 0083 0174 0149 0148 66185[0001] [0001] [0001] [0042] [0044] [0046]



































Kingdom










high school



at age 140110 0100 0003 0016 0010 0003





0130 0130 0026 0012 0012 0003[00154] [00129] [00114] [00037] [00047] [00049]





0369 0487 0062 0058 0052 0005[00305] [00309] [00785] [00198] [00242] [00369]





0453 0483 0351 0042 0045 0014[0076] [00868] [02412] [0043] [00387] [00542]


is zero 360







(1)OLS

full sample

(2)IV with

regional controls

(3)IV with

regional trends

(4)IV with






























(1)Mean

HS sample(2)

OLS

(3)IV

full sample








Unemployed 0064 0004 0005[00002] [00040]














DATA APPENDIX

A The United States










B Canada





REFERENCES
























































(5) ci Y1i Y0i




(6) i 0 ci Y1i Y0i



A UK Data
































ANNUAL EARNINGS


Sample population




sample size

Great Britain 0440 0436 0453 0065 0064 0042 57264[0065] [0071] [0076] [0025] [0026] [0043]



0418 0397 0401 0073 0058 0059 66185[0040] [0043] [0045] [0016] [0016] [0018]





















(1) (2) (3) (4) (5) (6) (7)


sample size

Great Britain 0078 0079 0079 0147 0145 0149 57264[0002] [0002] [0002] [0061] [0063] [0064]



0082 0082 0083 0174 0149 0148 66185[0001] [0001] [0001] [0042] [0044] [0046]



































Kingdom










high school



at age 140110 0100 0003 0016 0010 0003





0130 0130 0026 0012 0012 0003[00154] [00129] [00114] [00037] [00047] [00049]





0369 0487 0062 0058 0052 0005[00305] [00309] [00785] [00198] [00242] [00369]





0453 0483 0351 0042 0045 0014[0076] [00868] [02412] [0043] [00387] [00542]


is zero 360







(1)OLS

full sample

(2)IV with

regional controls

(3)IV with

regional trends

(4)IV with






























(1)Mean

HS sample(2)

OLS

(3)IV

full sample








Unemployed 0064 0004 0005[00002] [00040]














DATA APPENDIX

A The United States










B Canada





REFERENCES
















































































ANNUAL EARNINGS


Sample population




sample size

Great Britain 0440 0436 0453 0065 0064 0042 57264[0065] [0071] [0076] [0025] [0026] [0043]



0418 0397 0401 0073 0058 0059 66185[0040] [0043] [0045] [0016] [0016] [0018]





















(1) (2) (3) (4) (5) (6) (7)


sample size

Great Britain 0078 0079 0079 0147 0145 0149 57264[0002] [0002] [0002] [0061] [0063] [0064]



0082 0082 0083 0174 0149 0148 66185[0001] [0001] [0001] [0042] [0044] [0046]



































Kingdom










high school



at age 140110 0100 0003 0016 0010 0003





0130 0130 0026 0012 0012 0003[00154] [00129] [00114] [00037] [00047] [00049]





0369 0487 0062 0058 0052 0005[00305] [00309] [00785] [00198] [00242] [00369]





0453 0483 0351 0042 0045 0014[0076] [00868] [02412] [0043] [00387] [00542]


is zero 360







(1)OLS

full sample

(2)IV with

regional controls

(3)IV with

regional trends

(4)IV with






























(1)Mean

HS sample(2)

OLS

(3)IV

full sample








Unemployed 0064 0004 0005[00002] [00040]














DATA APPENDIX

A The United States










B Canada





REFERENCES






































































ANNUAL EARNINGS


Sample population




sample size

Great Britain 0440 0436 0453 0065 0064 0042 57264[0065] [0071] [0076] [0025] [0026] [0043]



0418 0397 0401 0073 0058 0059 66185[0040] [0043] [0045] [0016] [0016] [0018]





















(1) (2) (3) (4) (5) (6) (7)


sample size

Great Britain 0078 0079 0079 0147 0145 0149 57264[0002] [0002] [0002] [0061] [0063] [0064]



0082 0082 0083 0174 0149 0148 66185[0001] [0001] [0001] [0042] [0044] [0046]



































Kingdom










high school



at age 140110 0100 0003 0016 0010 0003





0130 0130 0026 0012 0012 0003[00154] [00129] [00114] [00037] [00047] [00049]





0369 0487 0062 0058 0052 0005[00305] [00309] [00785] [00198] [00242] [00369]





0453 0483 0351 0042 0045 0014[0076] [00868] [02412] [0043] [00387] [00542]


is zero 360







(1)OLS

full sample

(2)IV with

regional controls

(3)IV with

regional trends

(4)IV with






























(1)Mean

HS sample(2)

OLS

(3)IV

full sample








Unemployed 0064 0004 0005[00002] [00040]














DATA APPENDIX

A The United States










B Canada





REFERENCES





























































ANNUAL EARNINGS


Sample population




sample size

Great Britain 0440 0436 0453 0065 0064 0042 57264[0065] [0071] [0076] [0025] [0026] [0043]



0418 0397 0401 0073 0058 0059 66185[0040] [0043] [0045] [0016] [0016] [0018]





















(1) (2) (3) (4) (5) (6) (7)


sample size

Great Britain 0078 0079 0079 0147 0145 0149 57264[0002] [0002] [0002] [0061] [0063] [0064]



0082 0082 0083 0174 0149 0148 66185[0001] [0001] [0001] [0042] [0044] [0046]



































Kingdom










high school



at age 140110 0100 0003 0016 0010 0003





0130 0130 0026 0012 0012 0003[00154] [00129] [00114] [00037] [00047] [00049]





0369 0487 0062 0058 0052 0005[00305] [00309] [00785] [00198] [00242] [00369]





0453 0483 0351 0042 0045 0014[0076] [00868] [02412] [0043] [00387] [00542]


is zero 360







(1)OLS

full sample

(2)IV with

regional controls

(3)IV with

regional trends

(4)IV with






























(1)Mean

HS sample(2)

OLS

(3)IV

full sample








Unemployed 0064 0004 0005[00002] [00040]














DATA APPENDIX

A The United States










B Canada





REFERENCES




































































(1) (2) (3) (4) (5) (6) (7)


sample size

Great Britain 0078 0079 0079 0147 0145 0149 57264[0002] [0002] [0002] [0061] [0063] [0064]



0082 0082 0083 0174 0149 0148 66185[0001] [0001] [0001] [0042] [0044] [0046]



































Kingdom










high school



at age 140110 0100 0003 0016 0010 0003





0130 0130 0026 0012 0012 0003[00154] [00129] [00114] [00037] [00047] [00049]





0369 0487 0062 0058 0052 0005[00305] [00309] [00785] [00198] [00242] [00369]





0453 0483 0351 0042 0045 0014[0076] [00868] [02412] [0043] [00387] [00542]


is zero 360







(1)OLS

full sample

(2)IV with

regional controls

(3)IV with

regional trends

(4)IV with






























(1)Mean

HS sample(2)

OLS

(3)IV

full sample








Unemployed 0064 0004 0005[00002] [00040]














DATA APPENDIX

A The United States










B Canada





REFERENCES





























































(1) (2) (3) (4) (5) (6) (7)


sample size

Great Britain 0078 0079 0079 0147 0145 0149 57264[0002] [0002] [0002] [0061] [0063] [0064]



0082 0082 0083 0174 0149 0148 66185[0001] [0001] [0001] [0042] [0044] [0046]



































Kingdom










high school



at age 140110 0100 0003 0016 0010 0003





0130 0130 0026 0012 0012 0003[00154] [00129] [00114] [00037] [00047] [00049]





0369 0487 0062 0058 0052 0005[00305] [00309] [00785] [00198] [00242] [00369]





0453 0483 0351 0042 0045 0014[0076] [00868] [02412] [0043] [00387] [00542]


is zero 360







(1)OLS

full sample

(2)IV with

regional controls

(3)IV with

regional trends

(4)IV with






























(1)Mean

HS sample(2)

OLS

(3)IV

full sample








Unemployed 0064 0004 0005[00002] [00040]














DATA APPENDIX

A The United States










B Canada





REFERENCES






















































(1) (2) (3) (4) (5) (6) (7)


sample size

Great Britain 0078 0079 0079 0147 0145 0149 57264[0002] [0002] [0002] [0061] [0063] [0064]



0082 0082 0083 0174 0149 0148 66185[0001] [0001] [0001] [0042] [0044] [0046]



































Kingdom










high school



at age 140110 0100 0003 0016 0010 0003





0130 0130 0026 0012 0012 0003[00154] [00129] [00114] [00037] [00047] [00049]





0369 0487 0062 0058 0052 0005[00305] [00309] [00785] [00198] [00242] [00369]





0453 0483 0351 0042 0045 0014[0076] [00868] [02412] [0043] [00387] [00542]


is zero 360







(1)OLS

full sample

(2)IV with

regional controls

(3)IV with

regional trends

(4)IV with






























(1)Mean

HS sample(2)

OLS

(3)IV

full sample








Unemployed 0064 0004 0005[00002] [00040]














DATA APPENDIX

A The United States










B Canada





REFERENCES
















































































Kingdom










high school



at age 140110 0100 0003 0016 0010 0003





0130 0130 0026 0012 0012 0003[00154] [00129] [00114] [00037] [00047] [00049]





0369 0487 0062 0058 0052 0005[00305] [00309] [00785] [00198] [00242] [00369]





0453 0483 0351 0042 0045 0014[0076] [00868] [02412] [0043] [00387] [00542]


is zero 360







(1)OLS

full sample

(2)IV with

regional controls

(3)IV with

regional trends

(4)IV with






























(1)Mean

HS sample(2)

OLS

(3)IV

full sample








Unemployed 0064 0004 0005[00002] [00040]














DATA APPENDIX

A The United States










B Canada





REFERENCES









































































Kingdom










high school



at age 140110 0100 0003 0016 0010 0003





0130 0130 0026 0012 0012 0003[00154] [00129] [00114] [00037] [00047] [00049]





0369 0487 0062 0058 0052 0005[00305] [00309] [00785] [00198] [00242] [00369]





0453 0483 0351 0042 0045 0014[0076] [00868] [02412] [0043] [00387] [00542]


is zero 360







(1)OLS

full sample

(2)IV with

regional controls

(3)IV with

regional trends

(4)IV with






























(1)Mean

HS sample(2)

OLS

(3)IV

full sample








Unemployed 0064 0004 0005[00002] [00040]














DATA APPENDIX

A The United States










B Canada





REFERENCES

































































Kingdom










high school



at age 140110 0100 0003 0016 0010 0003





0130 0130 0026 0012 0012 0003[00154] [00129] [00114] [00037] [00047] [00049]





0369 0487 0062 0058 0052 0005[00305] [00309] [00785] [00198] [00242] [00369]





0453 0483 0351 0042 0045 0014[0076] [00868] [02412] [0043] [00387] [00542]


is zero 360







(1)OLS

full sample

(2)IV with

regional controls

(3)IV with

regional trends

(4)IV with






























(1)Mean

HS sample(2)

OLS

(3)IV

full sample








Unemployed 0064 0004 0005[00002] [00040]














DATA APPENDIX

A The United States










B Canada





REFERENCES






















































Kingdom










high school



at age 140110 0100 0003 0016 0010 0003





0130 0130 0026 0012 0012 0003[00154] [00129] [00114] [00037] [00047] [00049]





0369 0487 0062 0058 0052 0005[00305] [00309] [00785] [00198] [00242] [00369]





0453 0483 0351 0042 0045 0014[0076] [00868] [02412] [0043] [00387] [00542]


is zero 360







(1)OLS

full sample

(2)IV with

regional controls

(3)IV with

regional trends

(4)IV with






























(1)Mean

HS sample(2)

OLS

(3)IV

full sample








Unemployed 0064 0004 0005[00002] [00040]














DATA APPENDIX

A The United States










B Canada





REFERENCES
























































(1)OLS

full sample

(2)IV with

regional controls

(3)IV with

regional trends

(4)IV with






























(1)Mean

HS sample(2)

OLS

(3)IV

full sample








Unemployed 0064 0004 0005[00002] [00040]














DATA APPENDIX

A The United States










B Canada





REFERENCES


































































(1)Mean

HS sample(2)

OLS

(3)IV

full sample








Unemployed 0064 0004 0005[00002] [00040]














DATA APPENDIX

A The United States










B Canada





REFERENCES

























































(1)Mean

HS sample(2)

OLS

(3)IV

full sample








Unemployed 0064 0004 0005[00002] [00040]














DATA APPENDIX

A The United States










B Canada





REFERENCES
























































DATA APPENDIX

A The United States










B Canada





REFERENCES






















































B Canada





REFERENCES
























































































































Documents

Estimating Average and Local Average Treatment …econ.ucsb.edu/~jon/Econ230C/Oreopoulos.pdfEstimating Average and Local Average Treatment Effects of Education when Compulsory Schooling