Ability Bias, Skewness and the College Wage Premium

Transcription

1 Ability Bis, Skewness nd the ollee We Preiu Robin A. Nylor nd Jerey Sith University of Wrwick My 009 Abstrct hnes in eductionl prticiption rtes cross cohorts re likely to iply chnes in the bility-eduction reltionship nd thereby to ipct on estited returns to eduction. We show tht skewness in the underlyin bility distribution is key deterinnt of the ipct of rdute expnsion on the collee we preiu. librtin the odel inst the incresed proportion of university students in Britin, we find tht chnes in the vere bility p between university students nd others re likely to hve itited dend-side forces. JEL lssifiction: Keywords: J31, J4, I1, D8 Ability Bis, ollee We Preiu, Grdute Returns, ohort Effects. Acknowledeents: We re rteful to Norn Irelnd for helpful coents. orrespondin Author: Professor Robin Nylor, Deprtent of Econoics, University of Wrwick, oventry, V4 7AL, Enlnd, UK. Eil: robin.nylor@wrwick.c.uk

2 1. Introduction hnes over cohorts in the proportions of youn people t iven levels of eductionl ttinent will ipct on vere bility ps by eductionl level, influencin the bis in estited returns to eduction ssocited with the oission of bility. If the nitude of bis is chnin over tie, it is correspondinly ore difficult to drw leitite inferences on the trends in returns to eduction fro series of cross-section snp-shots. onsider the cse of the collee we preiu, defined s the difference in we rtes between collee nd hih school rdutes. Suppose tht ll individuls re either collee rdutes ( c 1) or hih school rdutes ( c 0 ) nd tht we cn write wes, w, s function of bility,, nd c : w c, (1) 0 1 where is stochstic error ter. Ability is typiclly not observed in the dt nd hence the OLS estitor, ˆ 1, will be upwrd bised. Differentitin (1) with respect to c : dw d 1 dc dc. () The totl effect of collee on wes coprises the true effect plus n oitted vrible bis ter which depends on the nitude of both (i) the true effect of bility on wes,, nd (ii) the vere bility p between those with nd those without collee eduction, d / dc. The substntil literture on how the collee we preiu, in the US nd elsewhere, hs chned over tie focuses on chnes in 1 nd (see wley et l., 000, nd Tber, 001); insted, we focus on the role of chnes in d / dc. Blckburn 1

3 nd Neurk (1991, 1993) ddressed the issue of whether increses in collee tricultion in the US in the 1980s could explin risin collee we preiu throuh chnes in bility coposition by eductionl level. They found tht the likely effects were in the opposite direction to the epiricl evidence. In contrst, Rosenbu (003) finds evidence tht bility coposition chnes re cpble of explinin substntil proportion of the increse in the US collee we preiu between 1969 nd This pper ttepts to ke two contributions: first, we extend the existin theoreticl nlysis by identifyin the crucil role of the skewness of the underlyin bility distribution nd, second, we provide clibrtion of the odel to offer insihts into the behviour over tie of the collee we preiu in the UK.. Skewness in the bility distribution Blckburn nd Neurk (1991, 1993) hve shown tht n increse in the proportion of collee rdutes in the popultion will led to reduction in the collee we preiu under either norl distribution or syetric trinulr distribution of bility, so lon s collee rdutes re in inority in the popultion. In extendin the Blckburn- Neurk odel, we hihliht the iportnce of skewness in the bility distribution for the ipct on bility bis risin fro n increse in the nuber of collee rdutes. onsider the trinulr distribution, on the unit support, chrcterized by different derees of skewness,. As 1/, 1/ or 1/, the distribution is positivelyskewed, netively-skewed or syetric, respectively; see Fiure 1, for 1/, where: 1 / 1 f ( ) /. (3)

4 (i) se 1. First we consider the cse in which the distribution is positively skewed ( 1/ ) with 1 nd H. f / H ˆ 1 1 Fiure 1 se 1: Positive skewness with 1 nd H. ˆ denotes the bility of the rinl investor in collee eduction; ( H ) is the vere bility of collee (non-collee) rdutes; nd is the proportion of the cohort who rdute fro collee. By construction, denotes the proportion of the distribution below the ode. The difference between the vere bility of collee nd non-collee rdutes is iven by: d H dc. (4) The edin bility of collee rdutes,, is such tht: It follows tht: f d.. d 1. (5) 3

5 1 1 1, (6) nd hence: 1 1. (7) Siilrly, for H : H 1 f. d 1 H, (8) which iplies tht: H (9) Fro (7) nd (9), it follows tht: 1 1 d Hn, (10) dc in which cse: d d d dc. (11) 1 Hence, with reltively stron positive skewness such tht 1 nd H, rise in the proportion of collee rdutes within the cohort cuses fll in the preiu ttchin to deree. (ii) se onsider now the cse depicted in Fiure, where the bility distribution is sufficiently netively skewed tht 1 nd. In contrst to se 1, rise in will increse the vere bility p between collee nd hih school rdutes. 4

6 f 0 / 1 H ˆ 1 1 Fiure se : Netive skewness with 1 nd u. For se, we cn use siilr ethods to those outlined for se 1 in order to obtin: (1) nd H 1. (13) Fro (1) nd (13), it follows tht: d H 1 dc (14) nd hence tht: d d d dc. (15) 1 5

7 Thus, for this cse of sufficiently netively skewed distribution, rise in cuses n increse in the preiu for deree. (iii) se 3 We now consider the interedite cse in which nd re such tht H. In this cse, will is iven by eqution (7), while the vlue of H will be equl to tht shown in eqution (13). obinin these, it follows tht: nd hence: d 1 H 1 1 dc, (16) 1 1 d d 1 0 if 1 = d dc 1 0 if 1. (17) Toether with (11) nd (15) for ses 1 nd, respectively, (17) estblishes the result cptured in the followin proposition. Proposition 1 In the cse of the uni-odl trinulr distribution, the preiu for the possession of deree is decresin (incresin) in the proportion with deree if 1 ( 1 ). In other words, whether the deree preiu is fllin or risin in the proportion,, depends solely on the reltive size of nd 1. For iven, the preiu will fll (rise) s rises if is reltively sll (lre). For iven, the preiu is ore likely to be fllin in, t the rin, the sller is : tht is, the ore positively skewed is the bility distribution. Notice one corollry of the nlysis, which y hve prticulr epiricl relevnce; while sll increses in iht be ssocited with fllin collee we preiu consistent with the Becker Woytinsky lecture hypothesis 6

8 (Becker, 1975) this need not lwys hold s, if rises beyond criticl point, iven by 1, further increses in will led to risin preiu for deree. This is ore plusible the lrer is : tht is, the less positively skewed is the bility distribution. Our nlysis identifies the extent of the skewness of the underlyin bility distribution s key deterinnt of the behviour of the collee we preiu, showin the knife-ede sensitivity to the extent of skewness reltive to the size of. It is likely tht in ore enerl sinle-peked distributions, for which the uni-odl trinulr distribution is just liner pproxition, second nd hiher order derivtives will influence over the properties of the odel thouh these re likely to be of lower order iportnce copred to the sinificnce of the skewness property we hve isolted. 3. librtion Evidence for the UK suests tht despite increses in the reltive dend for ore hihly educted workers, the estited collee we preiu showed little, if ny, tendency to increse durin the lte 1980s nd 1990s (see Wlker nd Zhu, 008). Siilrly, Brtti et l. (008) find tht, for en, the collee we preiu for those born in Britin in 1970 (nd typiclly rdutin in the erly 1990s) is no different to tht for those born in 1958 (nd rdutin round 1980): for woen, the preiu fell considerbly. Over tie, the collee prticiption rte 1 ws risin drticlly: fro bout 15% for the 1958 cohort to 30% for the 1970 cohort (source: DfES, 003). An explntion for the bsence of cler skill-bised dend-side influence on the estited collee we preiu is the possibility tht the increse in the proportion of the cohort ttendin collee produced chnes in reltive bility coposition nd hence ffected the 1 More usully referred to s the hiher eduction prticiption rte in the UK 7

9 extent of bility bis. Our nlysis suests tht if 1, then rise in will led to reduction in bility bis, ceteris pribus, thus producin lower estite for the size of the collee we preiu nd hence offsettin ny positive dend-side forces. We now develop nuericl predictions for the chne in d / dc fro clibrted version of the odel, inputtin vlues of for the 1958 nd 1970 British birth cohorts nd considerin vrious vlues of. We set 0.15 for the 1958 birth cohort nd 0.30 for the 1970 birth cohort. In Tble 1, we clibrte d / dc for se 1 nd find tht, for ll vlues of which stisfy this cse, the vere bility p between those with nd those without collee eduction flls by bout 14%. This is not trivil chne, thouh the extent to which this iht ipct on estites of the collee we preiu will depend on the return to bility. In Tble, we consider clibrtion for se 3, the interedite cse. 3 In this cse, when the distribution is syetric the doublin in is ssocited with n 11% fll in the vere bility p siilr to tht in se 1. However, s the distribution becoes incresinly netively-skewed, the extent of the fll in the p diinishes until, for 0.8, the ipct of the increse in is (sll) rise in the p. As rows further s hs been the cse in the UK it becoes ore likely tht rise in iht led to n increse in the vere bility p. 3. onclusions We hve deonstrted the criticl role of skewness in the distribution of bility in deterinin the ipct of chnin eductionl prticiption on the reltionship between In further work, we ddress the issue of whether differentil levels nd chnes in university prticiption by ender iht explin observed differences in the collee we preiu by ender over tie. 3 Note tht, iven the vlues of, no vlues of stisfy the conditions under which se is fesible. 8

10 bility nd eduction nd hence on estited returns to eduction, focusin on the collee we preiu nd rdute expnsion. We hve lso exined clibrtion of the odel for the British birth cohorts of 1958 nd 1970 nd shown how the extent of chnes in the vere bility p between university students nd others vries under lterntive ssuptions rerdin skewness. We find tht unless the distribution is quite stronly netively-skewed, the observed increse in the proportion of the cohort rdutin is cpble of enertin reduction in the vere bility p of t lest ten percent, thereby potentilly ititin the effects of dend-side forces on the collee we preiu. 9

11 References Becker, G.S., 1975, Hun pitl, nd Edition, New York: Ntionl Bureu of Econoic Reserch. Blckburn, M. L. nd Neurk, D., 1991, Oitted-bility bis nd the increse in the return to schoolin, NBER Workin Pper Blckburn, M. L. nd Neurk, D., 1993, Oitted-bility bis nd the increse in the return to schoolin, Journl of Lbor Econoics, 11, Brtti, M., Nylor, R.A. nd Sith, J.P., 008, Heteroeneities in the returns to derees: evidence fro the British ohort Study 1970, ieo, University of Wrwick. wley, J., Heckn, J., Lochner, L. nd Vytlcil, E., 000, Understndin the role of conitive bility in ccountin for the recent rise in the econoic return to eduction, in Arrow, K., Bowles, S. nd Durluf, S. (eds), Meritocrcy nd Econoic Inequlity, Princeton University Press, New Jersey. DfES, 003, Widenin prticiption in hiher eduction. London: Deprtent for Eduction nd Skills. Tber,.R., 001, The risin collee preiu in the eihties: return to collee or return to unobserved bility? Review of Econoic Studies, 68, Wlker, I. nd Zhu, Y., 008, The collee we preiu, overeduction, nd the expnsion of hiher eduction in the UK, Scndinvin Journl of Econoics, 110,

12 Tble 1: librtion bsed on se 1, 1 nd H. se d / dc d / dc d / dc (%) Tble : librtion bsed on se 3, H. se d / dc d / dc d / dc (%)