NBER WORKING PAPER SERIES A REVIEW OF ESTIMATES OF THE SCHOOLING/EARNINGS RELATIONSHIP, WITH TESTS FOR PUBLICATION BIAS

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1 NBER WORKING PAPER SERIES A REVIEW OF ESTIMATES OF THE SCHOOLING/EARNINGS RELATIONSHIP, WITH TESTS FOR PUBLICATION BIAS Orley Ashenfelter Colm Harmon Hessel Oosterbeek Workng Paper NATIONAL BUREAU OF ECONOMIC RESEARCH 1050 Massachusetts Avenue Cambrdge, MA January 2000 There are a number of persons to thank for commentng on early drafts of ths paper ncludng Joshua Angrst, Kevn Denny, Henry Farber, Alan Krueger and Davd Madden, semnar partcpants at the Unversty of Essex and MIT, and Roope Uustalo, who frst suggested a meta-study. The work also draws on the research of many authors wth whom we have benefted from dscussons, especally Davd Card. Harmon acknowledged the support of a research award under the terms of the Presdent s Award Scheme n Unversty College Dubln and the hosptalty of the Industral relatons Secton at Prnceton, whch facltated ths collaboraton. Thanks to Emma Barron for assstance n preparng the data on rates of return for the meta-study n ths paper. The usual dsclamer apples. The computer code for the procedures used n ths paper can be obtaned on request from the authors. The vews expressed heren are those of the authors and not necessarly those of the Natonal Bureau of Economc Research by Orley Ashenfelter, Colm Harmon, and Hessel Oosterbeek. All rghts reserved. Short sectons of text, not to exceed two paragraphs, may be quoted wthout explct permsson provded that full credt, ncludng notce, s gven to the source.

2 A Revew of Estmates of the Schoolng/Earnngs Relatonshp, wth Test for Publcaton Bas Orley Ashenfelter, Colm Harmon, and Hessel Oosterbeek NBER Workng Paper No January 2000 JEL No. I2 ABSTRACT In ths paper we provde an analytcal revew of prevous estmates of the rate of return on schoolng nvestments and measure how these estmates vary by country, over tme, and by estmaton method. We fnd evdence reportng (or fle drawer ) bas n the estmates and, after due account s taken of ths bas, we fnd that dfferences due to estmaton method are much smaller than s sometmes reported, although some are statstcally sgnfcant. We also fnd that estmated returns are hgher n the U.S. and they have ncreased n the last two decades. Orley Ashenfelter Colm Harmon Industral Relatons Secton Unversty College Dubln Frestone Lbrary Belfeld Prnceton Unversty Dubln 4 Prnceton, NJ IRELAND and NBER and CEPR, London Hessel Oosterbeek Department of Economcs Unverstet van Amsterdam Roetersstraat WB Amsterdam NETHERLANDS and Tnbergen Insttute hessel@fee.uva.n1

3 1. Introducton In recent years there has been consderable nterest n whether measured correlatons between schoolng and earnngs reflect the causal mpact of schoolng on earnngs. Ths nterest has led to some nnovatve methods of estmaton that take advantage of ether exogenous determnants of schoolng decsons (nstrumental varables) or comparsons between genetcally dentcal workers (twns). In ths paper we provde an analytcal survey of estmates of the rate of return to schoolng that s desgned to determne the extent to whch rates of return dffer by country, over tme, and wth the method of estmaton. In provdng ths survey we have taken especal care to study the role that reportng or fle drawer bas may have played n the studes we observe. Reportng bas may arse because of the tendency n vrtually all scentfc felds to report statstcal results that tend to reject the hypothess of no effect. The result s that estmated effects of schoolng may be correlated wth samplng errors and, f these are n turn correlated wth other varables, conclusons about the determnants of rates of return may be serously based. The exstence of any such bas s no reflecton on any ndvdual scholar, but s nstead the natural workng of a scentfc process desgned to dscover mportant new results. We mplement a generalzed method for testng for reportng bas, and for adjustng reported estmates for reportng bas, that s due to Hedges (1992). The results of our study provde some evdence that estmated rates of return do suffer from reportng bas, especally those based on nstrumental varables or wthn-twn estmators. After adjustment for reportng bas we fnd strong evdence of a consderable payoff to schoolng that dffers less wth the estmaton method used to measure that payoff than s sometmes reported. 2

4 2. Smple Earnngs Functons & the Problems of OLS-Estmaton Ignorng other covarates, Mncer s (1974) specfcaton for the determnants of earnngs s y = α + βs + u (1) where y s the log of earnngs of ndvdual, S s a measure of ther schoolng, u s a statstcal error term and α and β are parameters to be estmated, wth the parameter β beng the return to schoolng. In the early lterature followng Mncer's approach, equaton (1) - extended wth lnear and quadratc experence terms to account for on-the-job tranng - was commonly estmated by means of ordnary least squares (OLS). Ths estmaton technque assumes that the explanatory varables are uncorrelated wth the unobserved dsturbance n the equaton, whch for varous reasons mght not be fulflled. The coeffcent β s based f an ndvdual s ablty or motvaton affects earnngs but s omtted from the earnngs equaton, wth the extent of the bas determned by the correlaton between educaton and ablty. The concern about the formulaton of an estmate of the return to schoolng β s that ablty may be assocated wth both wages and schoolng. Three approaches have been used to try to deal wth ths potental problem. One approach deals wth the ssue of ablty bas by ncludng explct measures that proxy for unobserved ablty. IQ and related tests are an example of such proxes (Grlches (1977), Grlches and Mason (1972)). The results of these studes have sometmes suggested that there s an upward bas n results that lack an ablty measure. The method of addng ablty proxes has been crtcsed, however, because t s extremely dffcult to develop ablty measures that are not themselves determned by schoolng. When the ablty measure s tself nfluenced by schoolng, the use of ablty proxes wll, n fact, bas estmated rates of return downward. 3

5 The sblngs or twns approach explots a belef that sblngs are more alke then a randomly selected par of ndvduals, gven that they share common heredty, fnancal support, peer nfluences, and geographc nfluences. The approach attempts to elmnate omtted ablty bas by estmatng the return to schoolng from dfferences between sblngs or twns n levels of schoolng and earnngs. If the omtted varable, say ablty (A), s such that sblngs have the same level of A, then any estmate of β from wthn famly data wll elmnate ths bas. Studes based on sblng or twn comparsons have suffered from two prmary crtcsms. Frst, f ablty has an ndvdual component as well as a famly component, whch s not ndependent of the schoolng varable, the wthn-famly approach may not yeld estmates that are less based than OLS estmates. Second, f schoolng s measured wth error, ths wll account for a larger fracton of the dfferences between the twns than across the populaton as a whole. Ths would mply that the bas from measurement error n schoolng s lkely to ncrease by formng dfferences between twns, whch means the wthn-twn estmates wll be based downwards. Recent contrbutons to the twns and sblngs lterature have attempted to deal wth the measurement error problem by collectng multple measures of schoolng by questonng the sblngs about each other or by usng ndependent measures of error varances to adjust the estmates. Many of the wthn-twn studes suggest that ablty bas s relatvely small, although ths s only the case when measurement error has been controlled. A thrd approach to the problem of ablty bas explots natural varaton n data caused by dfferent nfluences on the schoolng decson. The essence of ths 'natural experment' approach s to provde a sutable determnant (or nstrument) for schoolng that s not correlated wth the earnngs resdual. In prncple, natural experments provde the closest equvalent to a randomsed tral n a clncal study. In the context presented here the treatment group s chosen 4

6 (albet not randomly) ndependent of ndvdual characterstcs. The treatment and control groups should, n prncple, be dentcal n other observed and unobserved characterstcs that affect earnngs except for schoolng. By constructng nstruments for schoolng that are uncorrelated wth the earnngs resdual the nstrumental varables (IV) approach wll generate a consstent estmator of the return to schoolng. The basc dea of the IV estmator s to proceed n two stages. Frst, estmate the effect of the nstrumental varable on schoolng; then estmate the effect of the nstrumental varable on earnngs. Snce, by assumpton, the nstrument s correlated wth earnngs only because t nfluences schoolng, the rato of the effect of the nstrument on earnngs to ts effect on schoolng provdes an estmate of the causal effect of schoolng on earnngs. The prmary crtcsm of IV estmates revolves around the concern that the nstrument may not, n fact, be truly ndependent of the earnngs resdual. If, for example, the nstrument s postvely correlated wth earnngs, the IV estmator may be upward based. The results from IV studes are vared, but some pont towards the presence of a downward bas n OLS estmates. Card (1998) has proposed an explanaton for ths phenomenon that s based on the hypothess that the return to schoolng s heterogeneous and declnes at hgher levels of schoolng. IV estmates wll dffer from OLS estmates to the extent that the nstrument nfluences schoolng decsons at dfferent levels. If the nstrument nfluences decsons prmarly at lower levels of schoolng, the IV estmator may be hgher than the OLS estmator because t reflects the payoff to schoolng at lower rather than hgher schoolng levels. It s apparent from ths dscusson that the estmates of returns to schoolng may dffer because of the estmaton method. In what follows we systematcally nvestgate the role of the estmaton method - along wth regon and tme perod - as determnants of the payoff to schoolng. 5

7 3. Meta-Analyss of the Returns to Schoolng Lterature There already exst several extensve summares of the payoff to schoolng, ncludng Psacharopolous (1994) and Card (1998). Here we use methods common among statstcans, and sometmes called meta-analyss, to test whether estmated payoffs are senstve to estmaton perod or tme perod covered and to provde a framework to determne whether our nferences are senstve to reportng (or fle drawer ) bas. As noted n Huque (1988), Hunter et al.(1990) and Egger and Smth (1997) a meta-analyss combnes and ntegrates the results of several studes that share a common aspect so as to be 'combnable' n a statstcal manner. Although less common n economcs 1, there has been consderable concern n the medcal and statstcal lterature over whether the observed sample of publshed results was selected solely because they were "statstcally sgnfcant". If they were, then any survey of these results suffers from the sample selecton bas so well known n a dfferent context n econometrc analyses. In what follows we provde estmates of the extent of ths knd of selecton bas and also of ts effect on estmates of the factors assocated wth dfferences across tme, across econometrc methods, and across regons n the return to schoolng. We test for publcaton bas usng a method due to Hedges (1992) that we have generalzed to accommodate systematc heterogenety n the payoff to educaton. It s mportant to understand that reportng bas may exst even wthout the authors of ndvdual studes beng aware of t. The potental problem smply arses because of the desre to report useful fndngs. Except n unusual crcumstances, evdence aganst the null hypothess 1 Smlar ssues have been addressed extensvely by fnancal economsts; see Brown, Goetzmann, and Ross (1995) and Lo and MacKnlay (1990). Card and Krueger (1995) also comment on ths problem n ther survey of mnmum wage studes. 6

8 that s, favorable to the fndng of a treatment effect s more valuable and more lkely to be reported n any ratonal weghtng of the usefulness of emprcal evdence. Table 1 Sample Statstcs Rates of Return Data (27 studes, 9 countres) Varable ALL OLS IV TWINS Mean s.d. Mean s.d. Mean s.d. Mean s.d. Year Sample Sze/1000 Ablty Controls? (1=Yes) Estmated Rate Standard Error Publshed? Measurement Error? N For our analyss we created a data set of 96 dfferent returns to schoolng, obtaned from 27 studes. Table 1 reports some descrptve statstcs for ths sample of both publshed and unpublshed studes, broken down by estmaton method, wth the full lstng of the studes reported n Appendx Table A1. 2 The year of estmaton averages n the md-80's but ranges from 1974 to Sample sze s qute vared wth the smallest sample naturally beng observed n the twns studes. Ablty controls are qute common n the lterature, wth around 20% of the OLS estmated sample contanng ablty measures, and a somewhat hgher representaton n the IV estmated returns. Explct control for the presence of measurement error s ncreasngly a feature of the lterature and we see an average of 6% of the rates of return comng from models where ths s the case, although control for measurement error s far more common n the twns 7

9 studes. Wth respect to the returns and ther correspondng standard errors/t-statstcs we see the pattern emergng clearly - average returns of 6/7% wth correspondng IV and twns study estmated returns of 9%. Precson s lost when we move from OLS however, as seen n the far larger standard errors among the IV and twns studes. Table 2 Meta-Analyss OLS Regresson of Estmates of Returns to Schoolng ALL US Non-US Estmate Std.Err Estmate Std.Err Estmate Std.Err (A) Non-US Data Year of Sample Estmated by IV Estmated by Twns Sample Sze/1,000,000 Ablty Controls Publshed Measurement Error Constant Adjusted R (B) Non-US Data Year of Sample Estmated by IV Estmated by Twns Sample Sze /1,000,000 Ablty Controls Publshed Measurement Error Standard Error Constant Adjusted R N The crtera for study ncluson are not very strngent. The startng pont was the lst orgnally produced by Davd Card (1998), reported n Appendx Table A1 and the comprehensve revew of Cohn and Addson (1997) where the detals about the orgnal data were provded. The deadlne for entres n ths study s June

10 The top half of Table 2 provdes some regresson results whereby the estmated return s related to a range of other varables that may nfluence the estmated return. The omtted category s mportant to note - here we use an unpublshed return estmated va OLS wthout ablty or measurement error correctons as our specfcaton. The year varable s re-scaled so that 1974=0, so that the constant n the regresson measures the rate of return n For results pooled across countres the omtted category s the US. The dependent varable s the level of the estmated return. The pooled results suggest lttle dfference n the estmated returns by geographcal regon - countres n ths non-us groupng nclude Fnland, Honduras, Indonesa, Ireland, Netherlands, Portugal and the Unted Kngdom. Estmaton methods have sgnfcant effects throughout wth rates of return by IV and fxed effects/twns some 3% and 1.6% hgher than the OLS default category. Sample sze n tself has no effect on the estmated return but controllng for ablty lowers the OLS estmate for the US studes n lne wth conventonal wsdom, but rases the OLS estmate n the non-us studes. Controllng for measurement error has no sgnfcant effect on estmated rates of return, but publshed papers do tend to report hgher rates of return (although ths s only sgnfcant for the non-us studes). Lookng at the results for the US we see that the more recent estmates are hgher for the US studes n lne wth recent suggestons of a general shft upwards n the returns to schoolng n the US. However ths result s not apparent for the non-us studes, confrmng the fndngs of Harmon and Walker (1995) of a relatvely stable pattern of returns over tme n the UK, whch would be the largest groupng n the non-us block. The bottom half of Table 2 ncorporates all of the earler elements but n addton controls explctly for the standard error of the regresson coeffcent estmated for the rate of return n the model. The results here are rather startlng. Unlke the top half of the table we no longer fnd any evdence of dfferences n the returns estmated by dfferent estmaton procedures, nor do we 9

11 observe the pattern of hgher estmates n publshed studes (although the upward drft of returns over tme s stll observed). Ths s a very mportant result, for n the absence of any bas n the reportng of results the estmates should not be correlated wth the standard error. Ths leads us n the next secton to a more formal consderaton of the results n the context of reportng bas. 4. Model of Reportng Bas One straghtforward nterpretaton of the contrast between the result n panels A and B n Table 2 s that estmated payoffs that are sgnfcantly dfferent from zero are more lkely to be reported n journals and, snce the twns studes and IV studes tend to have larger samplng errors n general, a less representatve sample of these studes s typcally reported. The graphs n Fgure 1 examne ths ssue more closely and are related to the materal presented n Table 2 where we related the return to schoolng to the estmated standard error. These graphs show a plot of the estmated return aganst the standard error, together wth the estmated regresson lne. In the absence of any selectve reportng ths lne should be horzontal, as the return to schoolng should not vary n proporton to ts standard error. However f the tendency s to only report where the t-rato s greater than 2 the estmated return wll ncrease as the standard error ncrease n order to mantan the t-rato at or above 2. Over all of the estmates n our meta-analyss, shown n panel (a) we fnd a postve slope whch s sgnfcant (t = 7.11) but n the case of the OLS returns n panel (b) the slghtly postve slope s not statstcally sgnfcant. However the estmated returns n panel (c) and (d) for the IV and Twns estmates respectvely show far steeper slopes whch are statstcally sgnfcant (wth estmated t-ratos of 3.92 and 5.42 respectvely). 10

12 Fgure 1 Estmated Returns Plotted Aganst Estmated Standard Error (a) All Estmates Rate of Return Estmate Ftted values (b) OLS Estmates Rate of Return Estmate Ftted values Standard Error (Rate of Return) Standard Error (Rate of Return) (c) IV Estmates Rate of Return Estmate Ftted values (d) Twns Estmates Rate of Return Estmate Ftted values Standard Error (Rate of Return) Standard Error (Rate of Return)

13 Fgure 2 Predcted Interval Estmates of Returns Based on Random Effects Meta-Analyss (a) OLS Estmates Combned Rate of Return Estmate (b) IV Estmates (c) Twns Estmates Combned Rate of Return Estmate Combned Rate of Return Estmate

14 <nsert Fgures 1 and 2 about here> An alternatve way to consder ths problem s to estmate the study returns from the nformaton collected va a smple meta regresson. We mght expect some degree of heterogenety n the returns compared to some overall pooled 'average' return f what we are seeng n the reported studes s not exhbtng some degree of non-randomness. The graphs n Fgure 2 represent pooled meta-analyss estmates of the returns based on the relatonshp between the estmate and the standard error of the estmate. Note that n the case of the OLS estmates the pooled estmate (represented n the graph by the vertcal lne) bypasses many of the ndvdual nterval estmates. On the contrary the results for the IV and Twns estmates suggest a clusterng of the results around the pooled estmate n almost every nstance. Hedges (1992), n a revew of over seven hundred studes on the effectveness of apttude tests as a predctor of employment outcomes, proposes a formal model of publcaton bas based on the assumpton that there s a weght functon (based on outcome p-values) that determnes the probablty a study s observed. Full detals of ths weght functon are outlned n an appendx to ths paper but the estmaton procedure generates parameters that determne the ncreasng or decreasng probablty of observng a study. We have specfed dfferent probabltes of observaton of a study accordng to whether the p-value for that study s 0.01<p<0.05 (denoted ω 2 ) or p>0.05 (denoted ω 3 ), relatve to a default category of 0<p<0.01. Ths default category s weght ω 1 s normalzed to unty expressng the assumpton that results wth p-values n ths bracket are reported wth probablty one. In the absence of reportng bas ω 2 and ω 3 should equal unty as well, ndcatng the equalty of outcome probabltes when sgnfcance of results s 11

15 accounted for. In addton to these ω parameters the overall pooled estmate for the return to schoolng, denoted, s provded based on the observed studes. Fnally, the heterogenety (measured by the standard devaton) n rates of return s estmated, and denoted σ. Table 3 Hedges publcaton bas model; all studes All Studes Unrestrcted Restrcted (ω 2 = ω 3 = 1 ) Parameter Coeffcent Standard error Coeffcent Standard error ω ω ('true' rate of return) σ Log-Lkelhood N OLS Studes Unrestrcted Restrcted (ω 2 = ω 3 = 1 ) Parameter Coeffcent Standard error Coeffcent Standard error ω ω ('true' rate of return) σ Log-Lkelhood N IV Studes Unrestrcted Restrcted (ω 2 = ω 3 = 1 ) Parameter Coeffcent Standard error Coeffcent Standard error ω ω ('true' rate of return) σ Log-Lkelhood N Table 3 presents the results for all studes together, for the studes usng OLS and for the IV-studes, based on the modfed Hedges' procedure. The frst column gves the results of the full model, whle the results n the second column are based on the model assumng no publcaton bas. The presence of publcaton bas s determned by examnng the parameters ω 12

16 and testng the restrcton of ω 2 = ω 3 = 1. Rejecton of ths restrcton ndcates the presence of publcaton bas. The test statstc s the dfference of the log-lkelhood values of the two models tmes 2. Ths statstc has a ch-square dstrbuton wth 2 degrees of freedom. Hence for the OLS studes equalty of ω 2 and ω 3 to unty cannot be rejected, whle for the IV studes equalty of ω 2 and ω 3 to unty has to be rejected at the 1% level (test statstc equals 9.82 wth a crtcal value of 9.21). Thus the IV studes appear to exhbt publcaton bas. The parameter n ths context can be nterpreted as the true mean effect corrected for publcaton bas. Correctng for ths bas the IV estmated rate of return to a year of schoolng s equal to 0.081, hgher than the OLS rate of return of There s evdence of consderable heterogenety n estmated returns, wth an estmated standard devaton of around.03. Notce also that the corrected IV return s somewhat below the uncorrected IV return (0.081 vs ). The pont estmates for ω 2 exceed 1 so t s expected that studes wth p-values below 0.01 have a lower probablty to be observed than studes wth a p-values between 0.01 and 0.05, but these estmates are never sgnfcantly hgher than one. On the other hand, the probablty of observng a study wth a p-value numercally larger than 0.05 s much smaller than that of observng a p- value smaller than 0.01, and ths dfference s statstcally sgnfcant (Hedges found a smlar pattern). The nterpretaton of as the true mean effect corrected for publcaton bas (wth only random heterogenety) s a sensble nterpretaton n applcatons where t s ndeed reasonable to expect that there s one unform global effect. Wth medcal nterventons ths mght ndeed be the case. When returns to schoolng are consdered, however, we have presented evdence that the returns vary across, for nstance, countres and perods. A natural extenson of Hedges' lkelhood functon s to parameterze, thereby allowng the true return to schoolng to vary 13

17 wth some of these characterstcs. Thus the restrcton, present n Table 3, that the estmate of the true rate of return s a constant s removed whch allows us to show how the 'reportng-bascorrected' return to schoolng vares wth the studes' characterstcs. In Table 4 we supplement the parameter wth nteractons between t and the varous regressors n Table 2, thus combnng the OLS regressons n Table 2 wth the results n Table 3. 14

18 Table 4 Extended Publcaton Bas Model: All Studes All Studes Unrestrcted Restrcted (ω2 = ω3 = 1 ) Parameter Coeffcent Standard error Coeffcent Standard error ω ω (IV) (US) (Year) (Twns) (Ablty) σ Log-Lkelhood N OLS Studes Unrestrcted Restrcted (ω2 = ω3 = 1 ) Parameter Coeffcent Standard error Coeffcent Standard error ω ω (IV) (US) (Year) (Twns) (Ablty) σ Log-Lkelhood N IV Studes Unrestrcted Restrcted (ω2 = ω3 = 1 ) Parameter Coeffcent Standard error Coeffcent Standard error ω ω (IV) 2(US) (Year) (Twns) 5(Ablty) σ Log-Lkelhood N

19 Overall the results are farly smlar. Agan by a lkelhood rato test of restrcted versus unrestrcted models, the IV studes appear to suffer from reportng bas whereas the OLS studes do not. The results n the top panel of Table 4 provde perhaps the most general summary of our analyss. The results n ths panel reject the hypothess that there s no publcaton bas. The benchmark estmates of the overall average return to schoolng s 3.5% n 1974, but ncreasng at a rate of about 2 percentage ponts per decade. The estmated unexplaned heterogenety n rates of return, whch s reduced wth the use of the covarates n Table 4, has a standard devaton of around 2.6 percentage ponts. The IV and wthn-twns estmates of the return are 1.8 and 0.9 percentage ponts hgher than the OLS estmates, and the dfference between the IV and OLS estmates s statstcally sgnfcant whle the dfference between the wthn-twns and OLS estmates are not. However, these reportng-bas-corrected dfferences n returns due to estmaton method are much smaller than the uncorrected dfferences of 3.1 and 1.6 percentage ponts reported n Panel A of Table 2. Ablty control have no effect on the estmated rates of return, but there remans evdence that returns have ncreased over tme, at a rate of about 2 percentage ponts per decade. 5. Concluson There appears lttle controversy n the general prncple underpnnng the theory of schoolng and earnngs - schoolng adds consderably to the earnngs of ndvduals. What s at the centre of the debate s that n any context schoolng s a choce varable and may not be ndependent of other factors that affect earnngs. Ths rases the possblty that the observed correlaton between schoolng and earnngs s not a causal relatonshp, but merely masks a correlaton between other factors, such as ablty, and earnngs. 16

20 Studes of twns and other sblngs and studes that use nstrumental varables have been a major focus of research n the last decade n sophstcated attempts to measure the causal effect of schoolng on earnngs. Our survey of these studes suggests that, once the mpact of the lkelhood that a study result wll be reported s controlled, there are relatvely small dfferences among the estmates produced by the dfferent estmaton methods although some of these dfferences are statstcally sgnfcant. Estmated rates of return to schoolng appear to be hgher n the U.S. than elsewhere, n part because of ncreased returns n the U.S. n the last two decades. However apart from ths dfference the estmates of the returns are consderably closer to each other than a smple glance at the range of estmates would provde. The evdence that schoolng nvestments have a sgnfcant economc payoff s therefore very strong. A number of future drectons exst for ths research. For many purposes t s often more useful to know the returns to specfc types of schoolng (by level and feld) or the payoff to ncreased qualty of schoolng. It appears that the current methodology to estmate returns to years of schoolng should be appled to these other topcs as well. Lkewse, studes of the returns to work-related tranng (frm tranng) should be subject to smlar analyses. These, and related emprcal studes of human captal nvestments, are essental to makng wse publc and prvate choces. 17

21 References Angrst, J.D. and Krueger, A.B. (1991) "Does Compulsory Schoolng Attendance Affect Schoolng and Earnngs?" Quarterly Journal of Economcs, 106, pp (1995) "Splt Sample Instrumental Varable Estmates of the Returns to Schoolng." Journal of Busness and Economc Studes, 13(2) pp Angrst, J.D. and Newey, W.K. (1991). Over-Identfcaton Tests n Earnngs Functons wth Fxed Effects. Journal of Busness and Economc Statstcs, 9, pp Ashenfelter, O. and Rouse, C. (1998). Income, Schoolng, and Ablty: Evdence from a New Sample of Identcal Twns. Quarterly Journal of Economcs, 113, pp Bed, A. and Gaston, N. (1999). Usng Varaton n Schoolng Avalablty to Estmate Educatonal Returns for Honduras. Economcs of Educaton Revew, 18(1), pp Blackburn, M. and Neumark, D. (1993). "Omtted Ablty Bas and the Increase n the Return to Schoolng." Journal of Labor Economcs, 11, pp (1995). "Are OLS Estmates of the Return to Schoolng Based Downward? Another Look." Revew of Economcs and Statstcs, 77, pp Blanchflower, D. and Elas, P. (1993). "Ablty, Schoolng and Earnngs: Are Twns Dfferent?" Mmeo, Dartmouth College, New Hampshre. Butcher, K.F. and Case, A. (1994). The Effect of Sblng Composton on Women s Educaton and Earnngs. Quarterly Journal of Economcs, 109, pp Brown, S., Goetzmann, W. and Ross, S. (1995). Survval. Journal of Fnance, L, pp Card, D. (1993) "Usng Geographc Varaton n College Proxmty to Estmate the Return to Schoolng." Natonal Bureau of Economc Research (Cambrdge MA.) Paper No (1998) The Causal Effect of Educaton. Mmeo, Center for Labor Economcs, Unversty of Calforna at Berkeley. 18

22 Card, D., and Krueger, A. (1995). "Tme-Seres Mnmum-Wage Studes: A Meta-analyss, Amercan Economc Revew, 85, pp Cohn, E. and Addson, J.T. (1997), The Economc Returns to Lfelong Earnngs. Mmeo (College of Busness Admnstraton, Unversty of South Carolna, South Carolna, USA). Conneely, K. and Uustalo, R. (1998). "Estmatng Heterogeneous Treatment Effects n the Becker Schoolng Model. Mmeo, Prnceton Unversty. Dearden, L. (1995). The Returns to Educaton and Tranng for the Unted Kngdom. Unpublshed Ph.D. Dssertaton, Unversty College London.. (1997). Ablty Famles Educaton and Earnngs n Brtan. Mmeo. (Insttute for Fscal Studes, London, UK). Duflo, E. (1998). Evaluatng the Schoolng and Labor Market Consequences of a School Constructon Program. Mmeo, MIT. Egger and Smth, G.D. (1997). Meta-Analyss: Potentals and Problems. Brtsh Medcal Journal, Vol. 315, pp Grlches, Z. (1977) Estmatng the Return to Schoolng: Some Econometrc Problems. Econometrca, 45(1), pp Grlches, Z. and Mason, W. (1972) "Educaton, Income and Ablty." Journal of Poltcal Economy, 80(2), pp Hanson, J. and Wahlberg, R. (1998). Endogenous Schoolng and the Dstrbuton of the Gender Wage Gap. Mmeo, Concorda Unversty. Harmon, C. and Walker, I. (1995). "Estmates of the Economc Return to Schoolng for the UK, Amercan Economc Revew, 85, pp (1999). The Margnal and Average Effect of Schoolng. European Economc Revew, 43, pp (1999). The Returns to the Quantty and Qualty of Educaton Evdence for Men from England and Wales. Economca, forthcomng. 19

23 Hedges, Larry V. (1992). Modelng Publcaton Selecton Effects n Meta-Analyss. Statstcal Scence, Vol. 7, pp Hunter, John E. and Schmdt, Frank L. (1990). Methods of Meta-Analyss Correctng Error and Bas n Research Fndngs. London: Sage. Huque, M.F. (1988). Experences wth Meta-Analyss n NDA Submssons. Proceedngs of the Bopharmaceutcal Secton of the Amercan Statstcal Assocaton, vol. 2, pp Isaacson, G. (1997) "Estmates of the Return to Schoolng n Sweden from a Large Sample of Twns." Mmeo. (Centre for Research on Transportaton and Socety, Borlange, Sweden). Lo, A. and MacKnley, C. (1990). Data Snoopng Bases n Tests of Fnancal Asset Prcng Models. Revew of Fnancal Studes, 3, pp Meghr, C and Palme, M. (1999). Assessng the Effect of Schoolng on Earnngs Usng a Socal Experment. Mmeo, Insttute for Fscal Studes, London. Mller, P., Martn, N. and Mulvey, C. (1994) The Effects of Educaton on Income: Estmates from a Sample of Australan Twns. Mmeo, Unversty of Western Australa. Mncer, J. Schoolng, Experence and Earnngs. (1974) New York: Natonal Bureau of Economc Research. Plug, E. (1997). Season of Brth, Schoolng and Earnngs. Mmeo, Unversty of Amsterdam. Psacharopoulos, G. (1994). Returns to Investment n Educaton: A Global Update. World Development, 22, pp Rouse, C. (1999). Further Estmates of the Economc Return to Schoolng from a New Sample of Twns. Economcs of Educaton Revew;18(2), Aprl, pages Uustalo, R. (1997) Returns to Educaton n Fnland. Mmeo. (Unversty of Helsnk, Helsnk). Vera, J. (1997) Returns to Educaton n Portugal: OLS, IV and Selecton Model Estmates. Mmeo. (Unversty of the Azores, Azores). 20

24 APPENDIX A GENERALIZED PUBLICATION BIAS MODEL Hedges (1992) model of publcaton bas bulds on the assumpton that there s a weght functon that determnes the probablty that a study s observed. He posts that the weght functon depends on the p-value, whereby studes wth a lower p-value are more lkely to be observed. It s assumed that a random effects model generates the observed data. More precsely the observed data, X 1,.,X n are such that X ~ 2 N( δ, σ ), (A1) where σ 2 s known and δ s an unknown parameter dstrbuted as 2 δ ~ N (, σ ). (A2) Hence X ~ N(, η ) (A3) where σ + σ = 2 2 η. The observaton assocated wth each study forms part of the weght functon w(x ) whch determnes the probablty of beng observed, wth the relatonshp wth X comng va the p-value. In Hedges' formulaton the weght functon s a step functon wth the steps at ponts determned a pror. In our applcaton we dstngush three steps: 0<p<0.01, 0.01<p<

25 22 and p> Gven ths data generatng process and the weght functon, Hedges derves the jont log-lkelhood for the data X, whch has the followng form (Hedges 1992, p.250) for observatons over j steps n the weght functon, ( ) ( ) = = = = = σ ω η η ω + = n k j j j n n n B X X w c L , log ) log( 2 1, log, (A4) where B j (, σ) s the probablty that a normally dstrbuted random varable wth mean and varance η wll be assgned weght value ω. The parameter can be nterpreted as the true effect corrected for publcaton bas. Ths s a sensble nterpretaton n applcatons where t s ndeed reasonable to expect that there s one unform global effect. Wth medcal nterventons ths mght ndeed be the case. When returns to schoolng are consdered however, we have presented evdence that the returns vary between for nstance countres and perods. A natural extenson of Hedges' lkelhood functon s therefore to parameterze thereby allowng the true return to schoolng to vary wth some of these characterstcs. The extended lkelhood functon now reads: ( ) ( ) = = = = = + = n k j j j n n n Z B Z X X w c L , log ) log( 2 1, log σ ω η η ω, (A5) where Z s a vector of characterstcs of study and s (now) a vector of parameters to be estmated. In our applcaton the vector Z ncludes four dummes equal to 1 f the study uses IV, 3 Due to data lmtatons t s mpossble to dstngush the addtonal step of 0.05<p<0.10.

26 twns data, relates to the US and when an ablty measure s ncluded, as well as year to whch the study relates. 23

27 Appendx Table A1 Meta-Analyss Sources STUDY YEAR COUNTRY Angrst and Krueger 1991a USA Angrst and Krueger 1991b USA Angrst and Krueger 1995 USA Angrst and Newey 1991 USA Ashenfelter and Rouse 1997 USA Bed and Gaston 1998 HONDURAS Blanchflower and Elas 1993 UK Blackburn and Neumark 1993 USA Blackburn and Neumark 1995 USA Butcher and Case 1994 USA Card 1993 USA Card 1998 USA Conneely and Uustalo 1998 FINLAND Dearden 1995 UK Dearden 1997 UK Duflo 1998 INDONESIA Hansen and Wahlberg 1998 SWEDEN Harmon and Walker 1995 UK Harmon and Walker 1999 UK Harmon and Walker 1999 UK Isaacsson 1999 SWEDEN Meghr and Palme 1997 SWEDEN Mller, Martn & Mulvey 1995 AUSTRALIA Plug 1997 NETHERLANDS Rouse 1997 USA Uustalo 1997 FINLAND Vera 1997 PORTUGAL 24