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k "ln+$rA+!wOA+'Zd+n= NL

6.54181 I I

~9.0000 39.1333 59.6667 eo.aoon H - - - age

F - an AGE

Figure 3.5. Nonparametric conditional mean, agelimme relation (Chime data, male and female).

Looking at Fime 3.6, we see that the Canadian dataclearly exhibit variability in earnings that is a convex function of age; in particular, it appears to be inversely related to the mean earnings, that is, 3 ( y 11) ar (.&ylx))-l (his is dso me of the Chinese data). The result is consistent with Mincer's (1974, p. 101) finding based on 0,s. data. However, we should note that, although M i n e r calculates a variance based on an arbitray grouping of age, the nonparameaic analysis does not need such a p u p i n g . A useful implicationof the above finding is that, in practice, one can circurntzent the need for parametric specifications of (y I x), the conditional heteroskedasticitgr - see Chapter 5 for more on this point.

Another observation from Figure 3.6 is that, for the early ages, the income is high and the variability (uncertainty) is low, but for €he later ages the income is low and thevariability is high. This implies that the income inequality may be influenced by life cycle effects. To analyze this hyporhesis one can estimate several inequality measutes conditional on age. Usually, this is done by cal- culating interage p u p inequality, which is [hen interpreted as a meawe of inequality caused by life-cycle effects. The main criticism of this approach is thar the results may lx sensitive to the choice of the arbiwari t y chosen age groups and their widths. Alternatively, one can calculate various inequality measures mnditionaI on age. Some well-known inequality measures that satisfy the prin- ciple of transfers are Atkinson's (A) inequality measure. Theil'~ entropy (E)

Conditional Momcnt Estimation 157

-829051

NWRR- on AGE

Figure 3.6. Nonparamenic conditional variance for lncomdage relation (Canadian

measure, and the coefficient of variation (C.V.); see Kakwani (1980) for an ex- cellent description. The conditional versions of thesc measurer. can he written as 1

A ( x ) = 1 - [.E(yl-' ~X)] '~(~-* I ( ~ ( ~ \ x ) ) - ' , T E ( x ) = ( E ( ~ - l x ) ) - ' E[ylogylx] - log E ( y l x ) ,

~ . V ( X ) = J W / ~ ( y l x ) ,

where the pammeter c 2 0 controls the degree of inequality aversion or percep- I

tion. When E = 0 there is no ptrceived inequality and when E = w thee is con- cern for the poor only. In practice e is usually considered to be between 0 and 2.

Though we do not perfom such a calculalion here, the inequality measures R ( x ) and T E ( x ) can easily be calcula!ed by using theresults of Section 3.2.6.

I For exarnptt. the C. V . ( x ) foliows directly from the calculation of V ( y lx ) and E(y1.r). In fact, since in the above s!udy, c(y(r) cr ( l? ( ! l x ) ) - I . it rill be the case that c:v.(x) a ( d ( y ~ x ) ) - ~ ' !

I 3.34.3 Review of A p p W Work on Nonparome~n'c Rcgmsion

I There has been an increasing use of nonpararnedc methods in applied ccono- I metrics in recent years and an exhaustive treatmen! is impossible. Consequently. we limit ounelves to an inreresting selection of the papers that have made

ACADEMIC AND NONACADEMIC INFLUENCES ON THE COLLEGE DESTINATIONS OF 1981) HIGH SCHOOL GRADUATES

James C. Aearn

Social .srier~risrs atd poli~.~mnukers h a v ~ iorrg been irlfexested in ~grrrtli? of oppnrrtolin' m pirrsrct posrseconrlnry edrtcn~ior~. This research focrrsed otr otlc

nspecr of fhrrr rssrre, the relu~ioti~hips between high sc/lonl ~rndunres' per,~onnl chnmcrcrrsrrc.~ (ahilrn, nrl~~eveme~rrs, e.rpectariotu, socioeconomEc smnts, race- crlltticirs, arid ~errrlel-) und [he narurt- of ~ k e posfsecntidary i~irritrrnorts r h ~ y nrretlci. Bnsad ot! tlnrior~nl doto jor college anentiers porn the hi811 school clnss qf 1980, fhe jirlditr~t SlqgeSl rho[ nonaca&mic Jacrors, pnrrrcicinr/y socio~corrornic bcrck~rouncl, affecred grmilrares' posrsecmzdary de.rffnnrions. For e.mtnpie, srrrdertrs from lower-ir~carne families were partictrlnr!\. likely to nttertd lawer- s e l ~ c r i v i ~ i~lsrirurions, regardless of [heir levels ofncademic nhi l i~ , achi~v~merrr , arrd erpecrnrians. The possible reasons for rht persisretrce of s~rch ineqaaliriex, despire policy efom to iitnir or remow r k ~ m , nre disctrss~d.

The pursuit of equal opportunity to attend barriers tn atrendance appear to be greater in posrsecondary educar~onal institutions has regard to where the high school graduate can long been a focus of national attention {Aaron attend than in regard l o whether !he graduate 1978; Gladieux and WoEan~n 1976: Leslie can enter the system. 1977). One aspecr of this Issue, the college destinations of recent high school graduates, has become an ~ncreas~ngly significant re- search topic in recent years. Demographic, socioeconomic. and legislattve trends have lowered the barriers to access to college to such an extent that virtually any high school graduate can now obtain entry Into some pan of the postsecondary system (Camep~e Coun- cil 1980). That system is exrremely differen- tiated, however: While ently inro some sectors (such as the community colleges) IS granted easily under a relatively egalitarian. "open admissions" ethic, entry into other. more prestigious and better-funded secrors (the elite liberal ans colleges. for example). is highly restr~cted and granted ostensibly only on the basis of tight rncritocratic standards (Clark 1983; Trow 1984). Thus, today,

INSTITUTIONAL STRATIRCATION

Trow ( 1984) pointed out that these barriers reflect a definite stratification system in U.S. higher education: Institutions are dearly ordered by prestige and levels of resources, and an institution's place in this order lends to be rnversely related to i t s level of openness to the masses. What i q more, the strat~fication system is remarkably durable over time:

The advantages of elite institutions arc ~o overwheImin_r that they create what 1s for thcm (but perhapr no2 Tor thc rest of higher education or rhe larger sociery) a kind of "v~nuous circle" in which advanrase beper\ advanrage . . . [TJhe resources and activities that mark high-status institutions gravl tare toward those same irlsliiu- lions. which already have the mnqt nT thenr. lTlhe tendency nf like to beret like qeernq to be . - strong enough. with a few exccptrons. to suqtain

This research was ~upponed by a research grant ellw h~ehcr cducatlon apainst thc srrains of rapid from the Spencer Foundarjon and by computing pruwth, dernocratitatinr~, butraucra~lrar~on, and and Faculry rcrearch grants from the Universiiy of governmental repular~on. (Trow 1984, p. 149) Minnesota. The author would like to thank K . C. Green of rhe Htgher Education Research Institute Thus. as Trow noted. Menon's (I%&) ar UCL.4 for h j ~ help with selecliv~ly daza and concept of the "Matthew effect" may 10 Susan Urahn and Mary Peterson for Their help In hieher education, That i s , lnstituriona] ad- the dara analys~s. The author also appreciates the llelpful comnlenrs of Elaine El-Khawas. Richard - Richardson, and William H. Sewell. Address all ' Merton's concept (1968) i s drawn from fhe correspondence to Professor James C. Hcam. 300 stalemerit of Jesus In the Gospel of Matthew: "For Candler Hall. institute a[ Hrpher Education. unto every one that halh shall be given, and he University of Georgia. Athens. GA 30602. shall have in abundance: but from him that harh nor

166

Table 2. Regressions for Institutional Selecrivitya

HEARN

Background Rctors Only

Metric Standardized Coefficrent Cwffrc~ent

Full ModcZ

Mctric Standardized Cotfficicn~ Cwfficicnt

Black Hispanic Rrnale Father's cducarion Mother's education Parcn~al income Numkr 01 siblings Tcstcd ab~liry Hlgh-school gradcs Hipb-school rmck High-school siudenl government H~ph-schnol dcpmmcntal or

preprofc<sional club High-rchnol journalism H~gh-school drama or debate Mrlcal~onal cx~ctat ions Constant

- p c .04. + * p 5 .01.

*** p C ,001. ' Data are u,eightcd. Scc the text for definitions of indicatom.

scores, grades. and expecrat ions were positive academic club. All [old, the regression model influences on attendance at higher-spendin? exphined 13 percent of rhe variance in the ~nstitittrons, as were panicipation in the outcome. high-school sruden~ government and in an The full-model rcgreszion resuIts of Tnblcs

Tabfe 3. Repressions for Institutional Educational and General Expenditure5 Per Studenla

Background Faclon Only Full. Model

Merric Slandardtzcd Metric Sondardi7td Coefficient Cocffic~cnr CoefCicienf Cmificient

Black A~spanrc Female Father's education Mnthcr's education Parcnral income Nurnbcr of siblings Tertctl ahiliiy H~gh-school grades High-rchnol rrack Hlph-school siudenf povcrnmenl H~gh-school dcpartmcntal or

pwprofcsslonal cluh High-school joumallsrn Hiph-schml drama or dehaie Educar~onal expectations Conslanl

- - .-

* p c 05. *I p 5 .Ol.

* * * p 5 .OOI. " Dara arc wcifhfed. Scc the text for definitions of indicarm.

Melntr. Allred. Kathryn LangrveFl. Michael Kcanc. d Shcbly Nelson. Report on rhr Geqruphrc Dirlnhu~rm o j Vt'rrron Care Prouiders (Sliver Spring, Maryland: Appl~ed Managmcnt Sciences. rnc.. 1933).

Nelson, Phillbp, "Advcnrsing m Information," Journal OJ P d t - icol Econom.~ 81 (July/hug 1974), 729-754.

Nrwhousc, Joseph, Albert Williams, William Schwarh, and Brucc knntrt, "& Geographic Dirtributiort or Physi- cians: Is the Convtntional Wisdom Correct?" Rand (OCI. 1982).

Ofhcc of Technology Assessment, 'f7tr Conruct Lcnr rnllurry: S?nurure, Compe:iraon. and Plmtic Pdrcy, Health Tech- nology Case Study 31, Dcc. 1984,

Fauly. Mark, aud Mark Sattcrthwmtc, "Thc Pricing ol Primary Care Physicians' Srviccs: A Test of the Role of Con- sumer Znfonnation," Bell Journal oj Economics 12 (Aufurnn 19811, 4R8-506.

Pmner, Richard. Anrirnrrr Lmv-An Ecmomrc Pcrspecfiw (Chicago: Umvtrslty of Chicago Prcss. 2976).

Schmaltnsec. Richard, "Commodity Bundling by Slnglt-Prd- uct Uonopolic~." Journal a! h w ond Economics 25 (Apr. 19821, 61-71.

Stigler, Gcorge, "A Nore on Blmk Bmking," in The Orjpnrzu- rron 01 Industry ( H o m c w d : R. D. Irwln, 1968).

Waterson, Michael, Econonr~ Theory a! !he Indurrly (Cam- bridge: Cambridge Unlwrsiry Prcss, 1984).

SHEEPSKIN EFFECTS IN THE RETURNS TO EDUCATION

Thomas Hungerford and Gary Solon*

Absrmrt-%me p & m difcussianr have dismissed screening ~hcories cl ducation partly on h e ground that dkploma y e m at cducarion do not confcr especially l q c earnings gains. Similady, mast empirical restarch on earnings Iunctlons has arsumcd an ahcncc of "shrcpskin" effects. Wc report m- drncc. hnwmcr, of aubstant~al and statistically sipfrcmt shcepskin effects. Although lhs sugsests that lhe prcwous d~srnissds. of the scrcming hypotbrris were premature, our evidence of shccpshn eFT~rrs i s amenable to ~onscrttniog idtcrprelat~ons also.

According to screening theories of education, individ- uals with more schooling tend to c a m more not because (or, at ]cut, not solely because) scbmhng make,^ them more productive. but rather because i t credentmles 'them as more productive. A frequently cited article by Layard and Psacharopoulos (1974), however, dismissed the im- portance or the screening hypolhesis on the grounds that scvcrd of its rtfutablc predictions were not sup- ported by available evidence. One of thrse was the "sheepskin" prediction that "wages will rise faster with extra yews of cducahon when the extra year also con- veys a certificate." After surveying a number of studies, Layard and Psacharopoulous (henceforth LF) con- cluded that "rates of return to dropouts arc as high as to those who complete a course, which refutes the

hypothesis. A prominent proponent a1 the screerung hypothesis, Riley (19791, has acccptcd LP's summary 01 the empirical evidence, but resporded that m e wr- sions of the screening hypothesis da not imply sheep- skin cffccis. In the meantime, zhc ongoing flood of empirical research on earnings fueciions typically has continued to treat the natural logarithm of the wage rate as a hear (or ~ i o o a l l y quadratic) lwc[ba of years or education, with no allowance for disconrinui- ties in diploma yearsn2

The estimated rates of return used by LP were based an data h a t did not disaggregale dropouts' easnings by how many years of school rhcy had complcttd. LP acknowledged, " W c would have preferred to show thc camings gain associated with each yeat of Lhe course, including the year when i t was successfully completed." n i p note presents a reanalysis of sbccpskin cffccts based on the type of data LP wished they had. The results cantain very strong tvidcace of sheepskin effects after all. The next section describes our analysis, and the fnllowing section summarizts and discusses our results. -

h p i r i d Analysis

shccpskrn version of the screenhe, hypothesis,'" Since publication of the LP paper, an undagraduate

labor scmomics textbaakl has cited LP's analysis of sheepskin erects. as "telling critiasrn" of the screening

Rcccwcd for pthl~catim March 6. 1986. Rcvisim a c c q t d for puhl~cation July 8, 19R6.

The University ot Mxhigm. llc authors rhank Charltr Brown and the rclcrccs for their

comments. ' Addison and Siekrt (1979, p. 139)

Our analysis L based on May 1978 Current Popula- tion Survey data m white male nonagricultural wage and salary workers between the ages of 25 and 64. The uacommonly l a r ~ e sampIe size in this data set (16,498 observations) enables relatively precise estimation of nonlinear returns to education.

There have been occasional exceptions, however, such as G d m a n (1979). Mohan (1981). Olneck (1979). and Weiss (1 984).

Copyright b 1987 \

THE REVIEW OF ECONOMICS AND STATISTICS

The dependent variable in all our specifications is the natural logarithm of the ratio of usual weekly earnings to usual weekly hours.3 First, for comparimn purposes, we report least-squms estimates of the prototypical earnings Function popularized hy Mincer (1974). This specification treats the log wage as a linear function of education, work experience, and work experience squared. Out education variable (S) is the highest grade completed by the worker (except that, because of the design of the survey instrument, 18 denotes 18 or more years of schml), and experience is measured as age - S - 6 . The resulls, reported in the first column of table 1, are similar to those in previous studies.

The question we wish to address is whether, contrary to the prototypical specification, the returns to educa- tion increase discon~~nuously in diploma years. To allow for such a pattern, we generalize the specification by treating tbe relationship between the log wage and S as a discontinuous sphne function with discontinuities at S - 8, 22, and 16. Operationally, this involves regress- ing the log wage on S, a dummy variable equal to 1 if S 2 R, an interaction of this dummy with S - 8, another dummy equal to 1 if S 2 12, an interaction of this dummy with S - 12, a dummy equal to 1 if S 2 16, and two more dummies for S = 17 and S - 18. These last dummies and the interaction terms allow for slope changes in the retvrns to education. The dummies for S 2 8 , S 2 12, and S r 16 allow for sheepskin effects, which would be indicated by positive coeflicients for tbesc variables. Tbe results for this specification are q o r t e d in cob

umn 2 of table I . An F-test of the prototypical specifi- cation relative to this alternative rejects the prototypical specification at the 0.01 level. Most interestingly for present purposes, the estimated cefficients of the dummy variables for S 2 8, S 2 12, and S 16 sug- gest positive sheepskin eflects. For example, the cstl- mated effect on the log wage at an additional year of school is 0.058 for the 7th ycar, jumps to 0.082 (the sum of 0.058 and 0.024) for the 88t year, and recedes to 0.042 (0.058 minus O.OI6) tor the 9th year. Similarly, the estimated re'nurn is 0.042 for the 11th ycar, 0.077 for the 12th, and 0.044 for the 13th. Finally, the estimated return is 0.045 lor the 15th year, 0.134 for the lbtb, and 0.007 for the 17th. Substantial estimated diploma eRecls thus appear at every level. The F-statistic for resting the null hypothesis o l no sheepskin effects (~.e., the hy- pothcsw that the dummy variables for S 2 8, S r 12, and S 2 16 all have zero mefficlents) easily rejects: the null hypothesis at the 0.01 lewl. This is primarily due to the highly significant tstirnatd ooefficient of h e dummy

Note that mcasuremcrtt crror in eirher cornponcnt ot ihe ratio contnbutt~ to mcasurcmcfit error in our dependent van- able. This cumulation of mcawremnt error 1s probrbiy an Important facror behind the low ~ ~ ' s reported in rablcr 1 and 2.

TABLE 1.-ESTIMATED COFFFICIE~ (AND ~ ~ A N D A R D ERRORS) IN LOG WAGF ~ G R F S S I O P I S

1 2 1

Constant ,7499 .7654 ,7031 (.0234) (.0497) (.057%)

Expcricnr~ "0356 ,0361 ,0359 C.0012) (.Mk 3) (.0013)

~ x p m e n c ~ ' - 00060 -.(OM1 -.M306t (.om33 ( . r n 3 ) (.(Y3003)

S .05W .01'6 .OW6 (.MI 3) (.a)86) (.01K45

Dummy for S 2 U ,0242 ,0324 ( D8) 1.0318) {.0286) D8 X (S - 8) - ,0159

Dummy for 5 2 12 (012)

Dl2 x ( S - 12)

Dummy lor S 2 I6

Dummy tor S - 17

Dummy tor S - 18 nl A R )

- ,0042 (.00E9) ,om12

.1404 (.(XKx)6)

,1420 .1420

variable for S 2 16. By a one-sided test, the estimated coefficient for S 2 12 is significantly dilTermt from zero at the 0.10 level, but no1 quite at the 0.05 Iwtl. The estimated coefficient For S 2 R is not significantly diffcr- ent from zero at any conventional level.

The results from a different specification are shown in the third column of table 1. This specification allows tor slope changes in the returns to ducation by including a cubic In S rather than a spline function. Discontinuities in diploma years are still allowed lor by including the dummies for S r 8, S 2 12, and S 2 16. The estimated coefficients of these variables become slightly larger in this spec~fiaclation. The estimated coefficient of the dummy S 2 16 remains highly Isignifieant, and the one for S 2 12 becomes significant at the 0.05 levcl. Agan, the null hypothesis of no sheepskin effects is easily rejected at the 0.01 level.

Finally, table 2 provides a more direct look at the data by reporting the results of a regression o l the log wage on experience. experience squared, a d a set of dummy variables for S - 1,2,. . . , 1 R . This specification imposes no restrictions on the shape of ~ h c wage/ schooling profile. It treats the Iog wage as a step lunc- tion of years of education with a separate step for each year. Even given the l q e overall smplc size, he precision of estimation here is limited by the fact that most of the S categories contain very smdl fractions of the sample. I t is quite noticeable, though, that particu-

NOTES 137

TARLE 2.-ESTIMATSD C U E F F I C I E ~ ( A N D STANDARDERROM) of the screening hypothesis on the ground that shccp- IN ~ G R E S S I O N OF LOG WAGE AS STEP FWMCT~ON OF sfin do not ws prtmaturt,

Est~rnarcd ~ ~ ~ l i ~ d On the other hand, it should be noted that evidence CwTf~c~enis step: ~ l z c s

Constant ,5645 (.073E)

Evprrtrrrre .I1362 ( M 1 3 )

E rperrcnlu2 - M I ( m 3 1

S - l ,3022 ,3022 (.1672) (.1672)

2 .4351 1329 (.I 109) (.1726)

3 ,4498 ,0146 f.ngao) (. 1012)

4 ,7873 - 0665 ( OR91) / 01W)

5 rwj, .2of0 ( U t i Y ) (.0672)

6 ,561 8 - 02RS (.0796) (.0536)

3 ,5518 - , 0 1 0 (.0781) (.W! 7)

R .6830 1311 1.0741) (03ZR)

9 .TI SO .oJza ( 0750) (.02d2)

10 .JAHO .0'!0 ( 0145) (.024H)

I1 ,7953 .w73 (.0751) (.024S)

12 .XU10 .OH 5 H ( 0731) (.0197)

13 9713 ,0902 ( 0743) ( n i 3 )

14 9852 01 39 (.Of 40) (,0187)

I5 .9A03 - M 4 9 ( 0756) (.0233)

16 1.1561 ,175A (,0736) (.0220)

I7 1.1628 M 7 1.0157) (.0221)

1 R I ISSO ( 1 q 2 ( 0740) f.0274)

R? .1MO

lasly large upward steps in the predicted log wage appear for diploma years. It is also intemting that a large step appears lor the first year of college. This accords with Arrow's (1973) suggestion that admis~ron to college may serve a screening function.

of shccpslrin effects need not be intcrprrtcd as corrobo- ration of the screening hypothesis. For example, an alternative interpretation due to Chiswick (1973) is that dropouts arc disproportionately comprised a l incficlent learners who leave school when they realize bow httle their productivity i s augmented by education. Graduates are disproportionately comprised ol efficient learners who complete their diploma programs because their prodvetlv~ty is much enhanced by education. Statist~cal cornparions of wages of graduates and dropouts then appear to show large d~plorna effects because the graduates are much more productive. Under thrs inter- pretation, educat~on's rffect on wages ariqcs solely from 11s effect on productivity and not trom any screemng fuact~oa.

A related point Is that our regression analyses may be biased hy omission of abil~ty variables or other factors correlated with degree completion. Indeed, some of the studies highlighted by Layard and Psacharopoulos con- trolled for IQ or other ability measures, which are not avzulable in our data set. We doubt, howevcr, that this accounts for the discrepancy in results on sheepslun effects. Analyses of other data sets reported in table 6.3 of Olaeck (1979) estimated positive sheepskin effects from collegc graduation and found that these estimated effects were not generally reduced by contmlllng for such ability measures or for family background van- ables.

REFERENCES

Addison. John T.. and W, Stanlcy Sickrt. Thc Market lor Lab. An Analvrrcai Treoclrmmr (Santa Monica, Calif.: Goodycar Puhlirhng Company, IVQ)

Arrow, Kenncth J., " t fip,her Fducation a5 a Filter," Journal of Puhlrr Econom~cr 1 (July 11373), 193-216.

Chiswick, Rarry R., "Schooling. Scrccning. and Income," in Lew~s C. Solmon and Paul J. Tauhrnan ( c d ~ ), D m C O C R ~ Marrerq (Ncw York. Academic Press, 1973)

Goodman. Jcrry D.. "Thc Economic Reiurns or Education. An Assessment 01 Altcrnatlvt Models," Social Science Q w r f e r h 60 (SPpt. 197Q), 269-JA3

Layard, kchard. and (ieor~c Psacharopoulos. "The Screening Hypothesis and the Returns 10 Education." Joumol of Polrricul Ecmomv H2 (Stp~./Oct. 19741, 9R5-99R

Mincer, Jacob, Schooltw~, I'rperience, and Eurnrnpr (New York: National Rurcau of Economic Rr\cnrch, 14741.

Mohan, Rakcsh, "Thc Determinants or Labor Earnings In Dcvclop~ng Mctropoh. Estimares trom Uo~ota and Call, CoZornbia.'Ttaff Worlun~ Papcr No 498 (Wash in~ ion . D C. World nank, Oct. 19A1)

Summary Olneck. Mtchacl. "Thc Erects ol FAucation." in Chnstophcr Jenck~ t t al. (ed ), Who Gets Ahead? (Nw York. tlacic

All of our results paint to the existence of sheepskin Books. 1979). effects in the returns to education. This finding suggests, Riley, John G., "Testing the Educational Smcning Hypothe- first, that treating the log wage as a smmtb lunct~on of s~r," Journal oj Polrrrrol Ec:conom.v 83 (Uct. 1979).

years of education, z is conventionally done in the S227-S252. Weiss, Andrew, "Testing rht Soning Model of FAucation."

earnings function literature, gives an inierior fit to the Working Papcr Nq 1420 (Cambndpc, Mass.: National data. Ir implies. second, that previous authors' dismissal Bureau of Econom~c Research. AUR EPA4).

236 THE REVIEW OF ECONOMICS AND STATISTICS

TARIF. 1.-REGRESSION OF UXj WEEKLY EARNINOS, W!-t!TE hhU!!.& Oh' SCHOOL QUAW

Repression Number

Education ( E D )

Tmhcr-Pupil Ratio

Relatiw Teachcr Salary

Percent Teachers with Mas~er's

Teacher-Pupil Ratio ED

(ReI. TEBC her Salary) * ED

(Percent with Master's)* ED

Aditional Regressors Rcgion Dummies (Rcgion Durnmics) ED Year Dummies +

R ' Adjusrad R~ No. Ohsenrations LR Test of Model against Model 1, p-value IIcrtro-robust p-value

0.0475 (1.70) 1.3190

(0.49) 0.1430 (0.37)

-om25 I - 1.301 - 0.nPaer

( - 0.40) - 0.0 137 (- 0.50)

0.om (1.37) 0.W65

112.22) - 0.0152 ( - 4.42)

0.0166 (2.031 - 0.0061

( - 0.97)

Ycs Yes Yes 0.3151 0.3 128 11314

0.0480 (1.71) 0.9336

10.34) 0.1559

C0.W - 0 . W 6 ( - 1.31)

-0.0571 ( - 0.27) - 0.0 145

(- 0.53) 0.0002

(138) O.WI5R

(r ) . i n ) -fl.O119

(- 3.49) O O E 1 4

I1.40) - O.MI34

(- 0.54)

Ycs Yes No 0.3087 0.3070 11314 .m .m

0.MW 12.81) 1.4147

(0.53) 0.2 175 (0.63) -0.W19

(-1.02) - O.OY63

( -0.48) -0.0194

I - 0.81) 0.0001

(1 .US) 0.0065

(12.26) -0.0153

( - 4.45) 0.UlhS

(2.05) - U.0063

( - 0.99)

Yes No Yes 0.3143 0.3125 11314 0.1024 0 w5

0.0496 ( 1.761 1.3216

(0.48) 0.1 I43

(0.29) - 0.0025 (- 1.73)

-0.0869 (-11 41)

-U.UlM ( - 0.43)

0 . m (1.35) 0.0043

(27.011 - 0.W3

E-17U8)

Yes Yes Yes 0.3118 0.3096 11314 o.mo0o a m

N u n Orhcr r c p r c m na menlloncd in rhr lmblc arc dummyrariahles lor rnprllrl statvs and rmdmce in nn SMM. r ~ t n l h r l u arc hcterracedarllc- wnsistenl.

TMLE 2.-Tesrs OF R m r c n o ~ s ON SCHM)L Q U A L ~ YARIABW

Regression

Variable 1 2 3 4 5 6 7

FAumtion (ED) 0.0475 00420 0.0407 0.0409 0.0431 0.0362 0.0551 (1.70) (3.311 (3.50) (354) (1.64) (2.03) (1.99)

Teacher-mil Ratio 1.3190 0.2503 1.3544 1.4444 (fl.49) (0.57) (0.5U) 03.531

Relalive Teacher Salary 0.1430 - 0.03% 0.1400 0.1046 (0.37) ( - 0.62) (0.36) (0.27)

Pcrccnt Teachers with Master's -0.W25 0.000I -0.M26 -0.WS (- 1.30) ro.la) - 1 . 1 (-1.291

Teacher-Pupil Ratie- ED - 0.0848 0.0181 -0.0877 - 0.0965 (- 0.40) (0.53) (-0.41) (-0.45)

~ c l a t i v c Tcachcr S a t a ~ ) *ED - 0.01 37 - 0.034 - 0.0135 -0.0107 (-0.50) 1-0.751 (- 0.49) ( - 0.40)

(Percent with Masterg$)* ED O M m Q.OLW 0.0002 0 . m 1 . 3 (0.401 (1.37) 0.35)

R2 0.3151 0.3150 03150 0.3150 0.3151 0.3151 0.3150 Adjusted R' 0.3128 03128 0.3128 0.3130 0.3129 0.3129 0.3 t28 No. Observations 11314 11314 11314 11314 11314 11314 11314 LR Test of Model against Model 1, p-value 0.5173 0.4928 0.8054 0.7818 0.7733 0.3481 I Ictero-mbus~ D-valuc 0,5785 0.5485 0.7934 0.7815 0.E422 0 3734

-.

Nmu. Othtr rq- not s h m arc idcnllcnl 10 those m e n r c d In rtprrnicn I of trMt I. 1.slwtirtim are hettrorccdnslic~srcnl.

THE REVIEW OF ECONOMICS AND STATISTTCS

DOES SCHOOL QUALITY MATTER?

TABU 5.-REo~essrou OF LW WEEKLY EARNINUS, W m MALES. ON OTHER ~ H W L C H A R A C ~ P R I S ~ ~

Re~rcssion No.

(0.18) (3.83) (Enrollment) ih.uuo0n2 0 . m 3

(0.49) 13.891 Percent Students -0.005345 0.MWWIlI

Dtsadwnragcd (- 2.21) 10.03) (Percent D~sadvantaged) 0.000446 Q,R00012

ED (2.2:) (0 38) Percent Studtnia -0.009023 -0.001362

Urwp~ng Out (-5.43) (-4.21) (Percent Drmurs) 0.0006t2. - 0.OMXISS

ED (4.87) (-3.14) R Z 0319394 0.3193Wl 0339392 0.323226 0.322904 0322914 0.320047 0.318519 0.3 18021 Adjusted R~ 0 317443 0.317489 0.31 7501 0.321039 0.320779 0320789 0.31 8109 0.316632 0.316133 Nn. 0br;crvations 12273 12273 12273 I0868 10868 10868 12318 12318 12318

piotcs O!frct e * m m nM $hwn In thir lahlc srt Identlcal lo I h m ln rtfl?c$slan 4, labk 2 I - s ta l r r l~ fs arc hcrsmaeedarlic-fonai+lcnr.

set of seven additional school chatseterisrics was therefore selected. For each of these varia- bles three regressions were estimated. These con- sisted of the basic mode1 (regression 4, table 2) supplemented by, first, the new school character- isttc by itself, then by this characteristic rnter- acted with years of education, and then by these two variables together. For the followinpl whwl characteristics, none of the added variables was significant (with a p-va!uc below 0.135 in the 5-test) in any of thc regressions:

library lmks pet enrollee, a dummy variable set t~ 1 if any of 7 m a - tional curricula were avaijable at the schooI, the proportion of the student body which was bjack, the percentage of teachers who had left in the previous year for reasons other than death and retirement.

However, as shown in table 5, subsequent earn- ings of students do appear to be positively and significantly related to the number of students cnroltcd at the schwl, although the elasticity at the means is on ty 0.044. This suggests that rn~ldly increasing returns to scale may be at work.

Table 5 also presents evidence that a school with a higher percentage of disadvantaged stu- dents is likely to pmducc graduates with lower earnings, at least for those students who ach~eve less than 12 years of education. (The interaction term between this variable and education is actu-

ally positive, so that students with more than 11.98 yean of education are predicted to have higher wages as thc percentage of disadvantaged students rises.)

Similarly, the percentage of grade 10 students who drop out without completing grade '12 has a negative and significant effect on earnings, at least for thosc workcrs who obtain less than 13.4 years of educati~n.~' The reader should note the rather limited policy

significance of these findings. Legislators have some direct control over class sizes, teacher salaries and the level of education of teachers. But the percentages of students who are disad- vantaged or who drop out represent outcomes, not policy instruments. Indeed, one could argue that these variables reflect neighborhood effects rather than school quality.

Still, the size of the school, as measured 'by enrollment, is related to earnings, and is a varia- ble which policymakers can control. This 1s the sole measure of school "quality" which this study has found to be significantly related to students' subsequent earnings.

This r~sul t i s intriguing. Hanushek (1986) suggests that if education increases wases by prnvidinp, a signal of worker quality, then there should be h i~hcr returns to education for schools which hilvt higher dropout rates. The above result provides some evidence that such a relation may occur for those whu obtain more than one ycar of postsaondar)r educa- tion.

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