Wage inequality and gender wage gap in Hungary,

Transcription

1 Wage inequaliy and gender wage gap in Hungary, By: Zsuzsanna Gulybán Submied o Cenral European Universiy Deparmen of Economics In parial fulfillmen of he requiremens for he degree of Masers Ars Supervisor: John E. Suherland Budapes, Hungary 2007

2 Absrac The aim of he paper is o invesigae how wage inequaliy evolved in Hungary beween 1992 and 1997 and wha effec he composiion of change in inequaliy may have on he esimaion of gender wage gap. The change in he composiion of he work force may lead o some bias in he esimaion of he overall residual variance (spurious growh) and he residual variance free of his bias measured wih Lemieux s mehod (2006) is lower for boh genders. According o my resuls his effec is sronger for women, which makes i probable ha some componens of gender wage gap decomposed wih he Juhn-Murphy and Pierce (1993) mehod have differen weighs as usually assumed. ii

3 Table of conens Absrac... ii Table of conens... iii Inroducion...1 Wage inequaliy...2 Tendencies in Hungary...4 Accouning for composiion effecs á la Lemieux...7 Daa and rends in wihin-group inequaliy by skill groups...11 Change in he gender wage gap...23 Juhn-Murphy-Pierce mehod...23 Resuls...27 Conclusion...29 Lieraure review...32 iii

4 Inroducion This paper has wo aims. Firs is o invesigae how wage inequaliy evolved afer ransiion in Hungary and which facors dominaed his process. Second is o esimae gender wage gap considering ha wha possible biases may emerge from he esimaion mehod used. In he mos recen lieraure (Lemieux, 2006) boh he effec of changes in he price of unobserved skills and he effec of he change in he composiion of he work force are considered when residual wage inequaliy is esimaed. The auhor claims ha a beer measure of inequaliy can be aained by omiing he composiion effec from he overall residual inequaliy. The imporance of finding a more precise esimaion mehod of residual inequaliy comes from is role in esimaing gender wage gap. Juhn, Murphy and Pierce (1993) conrol for he effecs of possible changes in residual inequaliy bu hey esimae i wih a less advanced mehod: hey do no conrol for he effecs of changes in he composiion of he work force; hey consider only he measured change in inequaliy. Using he residual variances obained by Lemieux (2006) may lead o differen measures of gender wage gap. In his paper he residual wage inequaliy is esimaed and hen he change in he gender wage gap in Hungary beween 1992 and 1997 wih a consideraion ha how residual variance obained by conrolling for composiion effec would change our resuls. The ouline of he paper is as follows: firs he inequaliy relaed endencies in Hungary are reviewed, and hen follows he examinaion of he heory of accouning for composiion effecs, afer comes he daa invesigaion. The second par of he paper focus on he gender wage differences, wih a shor review of endencies, he discussion of he decomposiion mehod of Juhn, Murphy and Pierce(1993) and finally he resuls. The las secion focuses on he common poins on he wo fields and on he possible effecs of incorporaing he inequaliy esimaing mehod ino he gender wage gap esimaing one. 1

5 Wage inequaliy Mos Cenral European counries experienced a sharp increase in boh income and wage inequaliy during and afer he ransiion from socialism o capialism (Newell, 2001). Wih marke liberalizaion, Hungary has gone hrough he same process (Tóh Isván György, 2003). However, here was some debae over is scale compared o oher ransiion counries. World Developmen Repor of World Bank (1996) claimed ha Hungary had he smalles income inequaliy increase in he region, bu local researchers did no agree (Andorka, Ferge, Tóh, 1997). Nevell (2001) also suppors Andorka e al. Explaining wage wih human capial relaed variables like educaion and experience has very developed radiions since Mincer (1974); consequenly i is sraighforward o base invesigaion of inequaliy in wages on hese facors. These variables are no able o explain all he variance in wages and variance of he residuals (inequaliy in he residuals) is he subjec of several sudies. According o Juhn, Murphy and Pierce (1993) and Kaz and Auor (1999) even wihin narrowly defined experience and educaion groups here was increasing inequaliy from he 70s ill he 90s in he US. This residual inequaliy is supposed o be caused by differen facors: Juhn, Murphy and Pierce (1993) inerpre i as he resul of increased reurns o he unobservable skill componens which is he resul of increase in he demand for skills. Ohers argue ha he role of minimum wage is considerable also (DiNardo, Forin, Lemieux (1996), Lee (1999) and Teuling (2002)). Lemieux (2006) emphasizes wo addiional facors. On he one hand he claims ha change in he composiion of work force had a major impac. Even Mincer (1974) discusses ha he condiional disribuion of he error erm in he mincerian equaion is no necessarily homoscedasic; residual wage dispersion generally increases boh in experience and in educaion. The reason is ha differen level of invesmens ino on-he-job raining of 2

6 individuals makes differen level of wages probable. Those who are willing o devoe more ime and effor o on-he job raining are used o accep lower earnings iniially and laer ge much higher earnings han he average. This leads o seeper experience-earnings profile han he average. Wih mincerian equaion he average is measured, so higher experience can lead o higher dispersion of residual wages (Mincer (1974), more recenly Chay and Lee (2000)). One oher reason for increasing inequaliy in experience can be he learning abiliy of marke: more experience means more available informaion for he marke on he produciviy of he worker (Farber and Gibbons, 1996). Moreover, increase in he educaion level causes higher dispersion because of he self selecion of hose who inves ino schooling: hey should have higher marginal reurns o educaion. Tha is why log-wage-schooling relaionship is generally convex (Mincer, 1974, 1997, Rosen 1977) which means ha he labor marke price of schooling will be higher a higher levels of educaion. This may lead o higher level of dispersion also (Lemieux, 2002). However Lemieux (2006) claims ha he increasing average age of employees and more years spen in school in average mus be he main reason of increasing residual inequaliy in he U.S. in he las 30 years. This is wha he calls composiion effec. The oher facor ha he emphasizes is he possible increase in measuremen error. In his paper I will invesigae how residual inequaliy evolved in Hungary afer ransiion, from 1992 o The analogy for he firs facor is more or less sraighforward: he quesion is wha kind of composiion effec can be idenified in Hungary during hese years. The variables of ineres changed in opposie direcion: average educaion of employees slighly increased while average age srongly decreased. Unforunaely here is no much possibiliy for esimaing he change in he measuremen error. Lemieux (2006) uses 2 differen daabases and makes he conclusion of increasing measuremen error by comparison. For carrying ou he same research work for 3

7 Hungary, a daabase wih hourly wages measured would be ineviable. Unforunaely such a daabase is no publicly available a he presen. Tendencies in Hungary This period is raher special compared o he US. Mos ransiion counries coped wih increasing unemploymen in he beginning of 90s, and mainly older and less educaed people los heir job. Following he mid-nineies job desrucion sagnaed and job creaion sared o increase very slowly. Meanwhile, reurns o educaion increased a lo and experience acquired in socialism became less worhy (Campos and Jolliffe, 2004a, Galasi and Varga, 2005). This increase in he demand for more educaed people induced an expansion of higher educaion, bu he effec of he jump in he number of more educaed persons is negligible for he whole work force. Alogeher, employers srongly preferred young and highly educaed employees (Galasi, Varga, 2005). Considering wages insead of employmen saus hese endencies are no so obvious because he wage of hose who los heir jobs canno be measured. Alhough focusing on he changes in he demographic characerisics of hose who are employed reflec hese processes. This is he case in my daa also. On Table 1A he average age of workers and average years spen in school can be seen in he saring and ending periods under invesigaion, and also he change beween hem. The average age of men employed decreased by 1.2 years during hese 7 years. For women he change is no so huge: a lile less han a year, 0.9 year. This can be due o he preference of younger employees by employers (he supply of workers did no become younger as in Hungary he sociey is ageing). Educaion increased for boh groups, bu only slighly. The possible reasons are ha he employers prefer more educaed fork force, or he increase of he 4

8 proporion of more educaed labor supply. For women he increase in he years spen in school is 3 imes he increase for men. This migh be due o he lower opporuniy cos of learning or o he sronger discriminaion for less educaed female work force. Table 1A. Average age and years spen in school for workers. men women change change age years in school On Table 1B he percenage disribuion of workers by educaion and experience groups can be seen. The educaion and experience caegories used here are described more horoughly laer. We can see ha he percenage of workers wih he lowes level of educaion (primary school or less) decreased by a quarer and all oher caegories above have exended for boh male and female. The only excepion is bachelor s or maser s degree owner male workers. The percenage share of his group dropped, which is a puzzle. For men, he percenage of hose increased he mos ha have already finished high school and for women, he mos educaed group exended he mos. 5

9 Table 1B. Percenage disribuion of workers by educaion and experience groups. men women A. educaion caegories primary school vocaional school high school ba and ma degree B. years of experience Experience shows similar paern: he share of mos experienced group decreased a lo in favor of hose wih less experience for boh genders. For men only he caegory wih less han 10 years of experience expanded, and all oher experience groups shrunk. Women a he edges of he experience range smooh in he endencies: more younger, much less older people employed, bu he share of women in beween also increased. These endencies are very differen from hose phenomena in he US. on which Lemieux (2006) focuses. In he US. he share of more experienced and more educaed workers increased from years o year. The fac ha boh variables changed in he same direcion and he residual wage inequaliy is posiively relaed o boh of hem makes he esimaion of composiion effec more sraighforward. In Hungary he changes in he characerisics happened in he opposie direcion, opposie o each oher. Presumably heir composiion effec on residual wage inequaliy is opposie also: lower average age should decrease while higher average educaion should increase he composiion effec. By Lemieux s approach which is shown in he following, only he overall composiion effec can 6

10 be esimaed, wihou any regard o he individual causal relaionship wih any of he 2 variables. Accouning for composiion effecs á la Lemieux In he following a here is a brief discussion of how o conrol for composiion effecs according o Lemieux (2006). He explains wo mehods of measuremen. Boh of hem focus on he change in he variance of he residual. The firs is abou dividing he sample ino a given number of cells and conrolling for boh he change in he wihin group variance and he change in he composiion of he work force along hese cells. The oher is abou esimaing an alernaive residual variance where he effec of change in he composiion of work force is omied by calculaing an appropriae weigh for each residual. A shor discussion of hese approaches will follow laer on. The basis of he esimaion is he Mincer-ype wage equaion: w i x b (1) i i where wi is he naural logarihm of he hourly wage rae, of individual i a ime, xi is a vecor of observed skills, b is he reurn o observed skills, i is he sandard residual. The inequaliy measured in his residual is wha Lemieux calls residual wage inequaliy. This residual is he produc of some unobserved skills, p e (2) i i ei and is price 1 : Variance is he main inequaliy measure used in he sudy because i is easy o decompose. The residual variance is: 2 Var( ) p Var( e ) (3) i i 1 And he measuremen error added which is no included here as i is no used in he res of he model. For he original model see Lemieux (2006). 7

11 From (3) i is obvious ha changes in he residual variance can be due o changes in he price of unobserved skills or change in unobserved skills hemselves. Composiion effecs can be accouned by he following way. Consider a case where observed skills xi are divided ino a finie number of cells, j. The uncondiional variance of unobserved skills Var e ) is linked o he condiional variance: ( i 2 Var( e i ) j j (4) j 2 Where j Var( ei xi j) and j is he share of workers in experience-educaion group j a ime. The condiional variance in wages V j is linked o he condiional variance of unobserved skills by he equaion (5): V (5) 2 j p 2 j To idenify he effecs of changes in skill prices Lemieux (2006) impose he following resricion: he disribuion of unobserved skills among workers wih he same level of experience and educaion is he same over ime. (6) 2 2 j j Subsiuing equaion (4) and (6) ino (3) leads o: 2 2 Var( ) (7) i p j j j From (7) i is sraighforward ha if he skill composiion of he work force is held consan a * some counerfacual j shares, an increase in he residual variance is due o an increase in skill prices. Plugging (5) ino (7) leads o: Var( ) V (8), i j j j Which shows how o compue counerfacual residual variance, from he sample): * V (as V j can be compued 8

12 * * V jv j (9) j This relaionship makes he decomposiion of he change in he residual variance possible beween 2 periods ino 2 erms in he following way: V V ( V V ) ( V V ) ( ) V (10) s j j j js js j js The firs erm on he righ hand side of (10) is a weighed average of changes in he wihin group variance. AsV 2 j p 2 j j js j, rising prices of unobserved skills can be checked by his erm. I can be also inerpreed as he change in he counerfacual variance, V if he j js j * * counerfacual weighs are se a base period s: j js The second erm is he composiion effec. Noe ha when changes in he weighs are posiively correlaed wih he wihin group variances, hen here is a spurious growh in he residual variance. In Table 2 some basic rends in residual and wihin group inequaliy is presened wih reference in noaions o equaion (10), and wih esimaion on he overall residual inequaliy, on he composiion effec and on he effec of changing in he price of unobserved skills for boh genders. Overall inequaliy proved o be negaive and prices mus have been decreasing also. The composiion effec is posiive, alhough is size is very small. Insead of using cells, anoher approach migh be esimaing a logi model o reweigh he daa such ha he disribuion of skills remains consan over ime (Lemieux, 2002, 2006, DiNardo e al. 1996). Residual variance can be compued direcly from he individual level daa: V i w r 2 i i (11) Where r i is esimaed wage residual and w i is he sample weigh, for worker i a ime (noe analogy wih eq. (8) for grouped daa). The counerfacual variance is (analogy wih eq. (9)): 9

13 V * i w r * 2 i i (12) The ask is o find he counerfacual weigh * wi ha makes he counerfacual disribuion of skills a ime he same as in a base year. This can be obained by esimaing a probabiliy, P i o be in year relaive o he base year by a logi model (on a pooled sample for he base year and year and wih he same regressors as he mincerian equaion) and calculaing he counerfacual weigh in his way: * i i i w i w (1 P ) / P (13) In case of Hungary his means ha younger and more educaed people are more likely o be observed in period, which means a larger value for P i, a lower value for ( 1 P i ) / Pi, so hey are down weighed by w. * i Unforunaely here was some confusion abou how o normalize he new weighs. In Lemieux (2002) he raio of esimaed probabiliy of being in year s / he esimaed probabiliy of being in year are muliplied by he uncondiional probabiliy ha an observaion is in period (he weighed share of he pooled sample ha is in period ). This gives he proporion of sample size of year divided by he overall sample size of he 2 years. In Lemieux (2006) he same approach can be found which in he heoreical review of his paper, suggesing a weigh of one over he sample size of only year. Lemieux (2002) also remarks in a foonoe ha he correcion facor is of lile imporance, since i changes he re-weighing facor only in a proporional way, bu here is much difference beween he esimaed counerfacual residual variance of he 2 approaches skeched above, because he proporion iself affecs he size of counerfacual variance. Tha is why I did no repor resuls of his mehod. 10

14 Daa and rends in wihin-group inequaliy by skill groups The daa used for he analysis is he Hungarian Household Panel Daabase from 1992 o 1997 of TÁRKI. I conains 8043 observaions for mos years, excep for 1996 wih 8211 and 1997 wih 8311 observaions. I can be regarded as a represenaive sample from he conemporaneous Hungarian populaion. I conains many observaions irrelevan o he paricular opic of his paper (children, unemployed, reired). The sample size decreases because of he separaion of he wo genders. Even hen he smalles sample size used for a regression hroughou he sudy included a leas 200 observaions, bu usually much above. In he paper only he wage of employees (who claim o be an employee) who are working age is analyzed, which is se o range from 16 years o 60 years. Defining working age is no sraighforward, as he reiremen age of men and women is differen and changed from year o year in his period. Besides many people have chosen early reiremen afer ransiion (insead of poenially facing unemploymen). Seing he upper bound a 60 seems plausible, as barely anyone claimed o be employed above his age. The daabase asks quesions abou he las monh wages of he main job and he average hours worked a week. Hourly wage is calculaed from here raw daa. Lemieux (2006) sresses he role of daabase where workers paid by he hour are asked direcly abou heir wages insead of using such a ransformed daa, because in his way measuremen errors and also biases coming from he changes of measuremen error can be diminished. Few employees repored very unlikely wage-hours worked combinaion; hey are omied (1 person in 1996 and 5 persons in1997). They migh seem o be of minor imporance because hey are few bu leaving hem in he sample leads o jumps in he variances. There is no reference in Lemieux (2006) wheher he used real or nominal wages. Following he pracice of Kaz and Auor (1999), who always use real wages, I did he same. 11

15 The high inflaion of his period also suggess preferring real wage. The CPI used in he calculaion is available in he Saisical Yearbook of Hungary 2004, he publicaion of he Hungarian Cenral Saisical Office. The TARKI household panel daabase asks quesions abou he highes degree acquired; he educaion relaed variables are consruced wih he help of his. Answers are given in 9 caegories by which approximaion is possible abou how many years he employee spen in school. During his approximaion he official minimum ime required o ge ha degree is considered. I should be noed ha here may be divergences from he real ime spen in school because eiher he caegories are no as flexible as he educaion sysem, or he meaning of he caegories could change over ime. Keresi and Varga (2005) shed ligh on he dimensions of he firs problem. Appendix repors he years relaed o he differen caegories by his sudy. The measures of residual wage inequaliy are compued from he residuals of a classical mincerian equaion. The log of hourly wages is regressed on age, years spen in school, age squared (and a consan) separaely for men and women. Lemieux (2006) uses a quie special regression in his analysis: a regression of log wages on an unresriced se of dummies for age, years of schooling and ineracions beween nine schooling dummies and a quadraic in age (p 469). He argues ha he advanage of his regression is is flexibiliy. There are some reasons for ignoring his regression form also. The fewer dummies are made, he more informaion is los. The more dummies are made, he harder i is o handle he regression during esimaion. There mus be some opimal choice in his rade-off, bu using he variables hemselves insead can be an alernaive soluion. Then he more informaion is kep on he expense of no allowing for break poins in he regression. An exension of his sudy can be esing for which funcional form is beer. 12

16 To increase he sample size I will follow Lemieux (2006) in pooling 2 years in he beginning ( ) and a he end ( ) of he reference period. To analyze he basic rends in wihin group variances, he work force is divided ino 20 educaion-experience skill groups. On he educaion dimension he caegories are: finished primary school or less, vocaional school, finished high school, and finished college or universiy (or even more). Each of he experience group caegories include en years, and calculaed as a poenial experience: age minus years spen in school minus seven, he age of compulsory school enrollmen. Since he group of workers wih more han 40 years of experience is empy or almos empy in many cases, I do no include hese ino he char. For bachelor s or maser s degree owners i is no a surprise considering ha he reiremen age is around 60 years. In i is empy for less educaed women also which may be due o large unemploymen and early reiremen among he older female populaion. The reason o include his group is he fac ha i provides some informaion abou less educaed men. Wihin-group variances of men can be seen on Table 2A. Lemieux could conclude for he US. and for 30 years ha variance increases in age and also in experience. Unforunaely we have a less obvious paern. Looking a a paricular schooling caegory i is no obvious ha residual variance increases in experience. I is rue for example for high school graduaes in , bu for mos of he schooling caegories variance shows concave shape wih a peak somewhere beween 10 and 40 or even 30 years of experience. Boh for and primary school and vocaional school finishers have concave variance wih a maximum a years of experience, in variance is also concave wih peak of years of experience. I would be a nice experimen o compare he endencies wih Lemieux s muliple-dummies regression o check for he effec of funcional form specificaion. 13

17 Looking a a paricular experience group a differen educaion levels behaves much nicer. There are some srong excepions, like he variance of workers wih years of experience for boh years, bu overall we can say ha he variance increases for mos of experience groups in educaion. Table 2A: Wihin group variance of wages by experience-educaion cell for men, and A. by educaion and wihin group variance work force share experience change change V js V j V j - V js js j j - js primary school ,0969 0,1096 0,0127 0,0260 0,0134-0, ,2657 0,1616-0,1040 0,0348 0,0372 0, vocaional school high school ba and ma degree B. weighed average acual shares period shares period shares

18 The change of wihin group variance can also be seen. The mos salien paern is he fac ha in mos groups wihin group variance decreased, which lead o overall decrease of variance as well. Resuls for women can be seen on Table 2B. Tendencies are harder o recognize (if here are any). Looking a paricular educaion groups only wo of hem show some paern: in he vocaional school finishers have concave shaped variance and he residual variance of college or universiy finishers is increasing in experience. All oher groups are random, no sysemaic rules can be observed in hem. Checking a paricular experience group across differen educaion groups gives shows some paern also. In only years of experience is slighly increasing in educaion, in boh years years of experience does he same and in he caegory of years is almos well-behaving. The changes in he variances are mainly negaive here also. 15

19 Table 2B: Wihin group variance of wages by experience-educaion cell for women, and A. by educaion wihin group variance work force share and experience change change V js V j V j - V js js j j - js primary school vocaional school high school ba and ma degree B. weighed average acual shares period shares period shares The share of differen skill groups can be seen on he lef hand side of he ables. The endencies menioned above can be raced. The share of leas educaed decreased for boh groups, while he share of more experienced decreased also. Difference of genders in he selecion can be noiced only a he mos educaed group: while he increase of he share of women wih college or universiy is independen of heir experience, he same if rue for men, bu in he oher direcion: heir share decreased (excep for hose who have more han 30 years of experience). 16

20 In he header of Table 2A and Table 2B we can see he counerpar parameers from equaion (10). Lemieux (2006) remarks ha composiion effec, which is capured by he second par of he righ hand side of equaion (10) resuls in a spurious growh in he residual variance when he wo facors are posiively correlaed. Tha is why he calculaes he correlaion coefficien beween he wihin group variance for he las period (V j ) and changes in he shares ( j - js ). In our case we have fairly differen resuls for he wo genders: for men i is very small, i is 0, and for women i is considerable, i is 0, This sugges ha for women bigger spurious growh can be expeced as higher is he correlaion, which seems a bi conradicional as in he overall endencies no much paern could be realized for men. (Panel B of Table 2Bconfirms ha for women composiion effec is higher). In he lower par of Table 2A and 2B he overall residual variances can be seen, calculaed for differen skill group shares also. In erms of equaion (10) he change in he acual shares can be also described by: j j ( V V ) (a). The difference in he weighed average using 1. period shares is j j js js ( V V ) (b), which is exacly he firs erm on he righ hand side of equaion (10), js j js js and which is he erm ha can separae he effec of changing skill prices. The difference in he weighed average using 2. period shares is ( jv j jv js ) (c). This sheds ligh on he j measure of he composiion effec we have o deal wih, as i is obvious ha he difference beween he change in he weighed average wih acual shares and he change in he weighed average wih 1. period shares (shorly: (a)-(b)) is exacly he composiion effec V V. j j js j For men he change of he overall residual variance is The second row shows us ha he change in he residual variance is no much smaller ( ) when he shares are hold a heir level. This shows us ha mos par of he change in he residual variance 17

21 is due o he decrease in he wihin group variances, due o he possible decrease in he price of unobserved skills. The composiion effec is responsible for only The resuls for women in able 2B seem raher differen: he change in he overall residual variance is only half of he men s, Keeping he shares of period gives residual variance change of , which shows ha he majoriy of he changes is due o he decrease in he wihin group variance, in price of unobserved skills. The difference beween he wo gives he composiion effec; i is , which is almos 5 imes he composiion effec of male workers. We can conclude ha he overall residual variance decreased for boh groups. The price of unobserved skills mus have decreased, as he effec of wihin group variance is negaive. The changes in he composiion of he work force had posiive effecs on he residual variance, which, assuming ha variance increases in boh educaion and experience, suggess ha he posiive effec of he increase in he schooling of workforce dominaed he negaive effec of decrease in age. Men had a sharper drop in he price of unobserved skills, while women had bigger variance because of he change of heir work force. As he scale of wihin-group variance came ino he foreground, in he following he deailed year by year evoluion of wihin group variance can be seen for each of he educaion groups for men (Figure 1A) and women (Figure 1B). As here are changes in he experience disribuion of he work force which mus be conrolled, he variance for each educaion group is defined as he simple averages of he wihin group variances over he experience groups. For example he wihin group variance for workers who finished primary school is he average of wihin group variance for primary school finishers wih 0-10, 11-20, 21-30, and more han 40 years of experience (wih 18

22 his he exac share of employees in he paricular experience group is ignored). In erms of equaion (10), we are dealing wih he evoluion of he componens of he firs erm on he righ hand side. On Figure 1A we can see ha variance is really higher for male workers wih more years of educaion: afer 1994 he variance is he smalles for primary school finishers and highes for high school graduaes and ba or ma degree owners. The college and universiy finishers have ousandingly high variance, bu i decreased by he ime. The variance for primary school finishers decreased also. Wihin group variance did no change much sysemaically for male workers during his period, i slighly decreased for all groups. Figure 1A. Wihin-group variance by educaion group for men 0,3 0,3 0,2 0,2 primary school vocaional school high school ba&ma 0, On Figure 1B he evoluion of wihin-group variance can be seen for each experience group, wih variances averaged over educaion groups. In his case his means ha for example he wihin group variance for workers who have 0-10 years for experience as he average of he variances of primary, vocaional and high school finishers and college and universiy graduaes. Four experience groups move ogeher, he wihin group variance evolved raher he same for hem; sysemaical paern can no be seen. For he group above 19

23 40 years of experience he variance dropped a lo, suggesing a fall in he price of he unobserved skills of his group. The variance of group and enrans behaves raher seady, while ha of group has dropped some. On Figure 1C he wihin-group variance can be seen for women by educaion groups. Women also show he classic feaures: he more educaed have he higher variance and less Figure 1B Wihin-group variance by experience for men 0,25 0,2 0,15 0,1 0, educaion means less variance. However here is some volailiy during his period: college and universiy finishers have survived a drop in heir unobserved-skill prices by he end of he period. Even hen no rend is obvious. 20

24 Figure 1C Wihin-group variance by educaion group for women 0,3 0,25 0,2 0,15 0,1 primary school vocaional school high school ba&ma 0, Figure 1D presens he wihin group variance graph of women for experience groups. The variaion of mos experience groups is seady, only sligh changes happened. Sligh decrease for enrans, and group and sligh increase for group The variance of mos experienced group (40+) for women has begun is drop from he same level as for men and had arrived a he same level also, bu have reached i much earlier. Figure 1D Wihin-group variance by experience group for women 0,25 0,2 0,15 0,1 0,

25 Taken Figure 1A, 1B, 1C and 1D sugges ha here is no much change in he wihin group variance for mos groups. The only clear endency in he drop in he unobserved skill prices of he mos experienced group, for workers of more han 40 years of educaion. Table 2A and 2B also showed ha he overall variance is negaive for boh groups and he composiion effec is even smaller han he unobserved price effec. For women, i is on one hird of he unobserved price effec, for men i is he 1/18 par. These numbers seem raher small; i is a valid quesion wheher composiion effec is really imporan? When does i maer afer all? Composiion effec maers when i is large enough o cause biases in esimaion of residual variance. In Lemieux (2006) ¾ of he overall residual variance was composiion effec which means ha ¾ of he growh in he residual variance is a spurious consequence of composiion effecs. According o he resuls of Table 2, we may hink ha he composiion effec has differen effec in Hungary for men and women. For men 6% of he overall residual variance in composiion effec (which is very small), for women he raio is much bigger, i is a lile more han 50%. This suggess ha for women omiing he possibiliy of he composiion effec may cause a much higher bias in he esimaion of he residual variance han for men. Figure 1 shown ha wihin-group variances are raher volaile, bu alogeher only few endencies can be discovered. This makes harder o separae he endencies in composiion effec also. In spie of he expecaions no much difference can be discovered beween men and women in wihin group variances. As for men only 6% of variance change is due o composiion effec, one may expec ha as he wihin group variances are responsible for he 94% of changes, some endencies may be discovered. Alhough for women wihin group variances are responsible only for he 50% of changes in he variance, here wihin-group variance graphs for men and women are raher similar. 22

26 Change in he gender wage gap There are several mehods o esimae gender wage gap. The Oaxaca s decomposiion is one approach; i is applied by an aricle of Campos and Jolliffe (2004b) for Hungary beween 1986 and Anoher mehod may be he Juhn-Murphy-Pierce decomposiion, which is an advanced form of he former, as i akes ino consideraion he effec changes in inequaliy also. My focus in on heir way of conrolling for changes in inequaliy and on incorporaing Lemieux s inequaliy-esimaion mehod. In Hungary he gender gap considerably decreased afer ransiion (Campos and Jolliffe (2004), which he auhors inerpre as he effec of an exraordinary improvemen of women s relaive siuaion. Elizabeh Brainerd (2000) found in 7 ransiion counries ha alhough increasing wage inequaliy depressed relaive wages of women, if he widening is no remendous (like in Russia or Ukraine), he losses may be offse by gains from reurns o observed skills, and an apparen decline in discriminaion. In erms of he key-equaion of he JMP decomposiion, equaion (4), losses from erm (D) can be offse by gains from (B) and (C). We have already seen ha residual inequaliy decreased beween 1992 and 1997 for Hungary. Juhn-Murphy-Pierce mehod To explore he reasons for he change in female-male relaive wages, one approach may be he framework given by Juhn, Murphy and Pierce (1993). Their mehod makes he decomposiion of differen effecs possible and conrols for inequaliy changes also. Firs, consider wage equaion for male individual M and period : W M X e (14) M M 23

27 where WM is he log of monhly wages, X M is he vecor of explanaory variables, is a vecor of coefficiens and em is he residual, he componen of wages accouned for by unobservables. According o Juhn, Murphy and Pierce (1993) his residual consiss of wo componens: an individual s percenile in he residual disribuion, M and he disribuion funcion of he wage equaion residuals, F (.) in he following way: e 1 M F ( M X M ), where F 1 (. ) is he inverse cumulaive residual disribuion for workers wih X M characerisics X M in year. Blau and Kahn (1997) and Brainerd (2000) defines differenly, hey sandardize he residual: M : em /, where is he residual sandard deviaion of male wages for ha year. I shows he unexplained level of male residual wage inequaliy, and has a mean 0 and variance 1. Brainerd (2000) remarks ha his shows he percenile he individual occupies in he residual disribuion which is a lile bi misleading 2. The value defined his way can be negaive also, so i is no he value of his sandardized residual ha shows he percenile, bu he accompanying cumulaive disribuion funcion values (which can be obained from he sample). By his simplificaion he male wage equaion becomes he following: W (15) M X M M The male-female wage gap for period is his: D W W X (16) M F where M and F refer o male and female averages, and is for he average male-female difference for he variable immediaely following (Blau and Kahn, 1997). I inerpre his explanaion phrasing as he difference of he average male and average female variable values (as hey did no menion paired sample requiremens). 2 In he aricle she menions he role of ranks given o individuals in he disribuion, bu no really connecs o he formulas. 24

28 For he las erm, / F ( WF X F ) is needed, where is he coefficien of he male regression (14). This reflecs he difference beween he wage a woman receives and she would receive if her skills were rewarded a he same rae a which men s skills are rewarded (Brainerd, 2000). According o he equaion (16), he gap in a given period consiss of he differences in observed skills weighed by he reurn received by men o hese skills and he differences in he sandardized residual, weighed by residual male inequaliy. The difference in he gender gap beween 2 periods is his: D D X X ) X ( ) ( ) ( ) (17) s ( s s s s s s (A) (B) (C) (D) The firs erm (A) is he observed X s effec, he changes in gender wage differenial ha comes from changes in male-female differences in observed labor marke skills. The nex erm (B), he observed prices effec is he change in he price ha he labor marke aaches o he observed skills of men. The hird erm (C), he gap effec is he effec of he change in he relaive posiion of women in he male residual wage disribuion when male wage disribuion is held consan. Women move upwards if heir unobserved labor marke skills improve relaive o men s or if labor marke discriminaion agains women decline. The fourh erm (D) is he unobserved prices effec ha measures he change in he gender gap due o he widening or he narrowing of he residual male wage inequaliy, holding he gap in male-female unmeasured skills consan (Brainerd, 2000). Assume ha deficis in unmeasured relaive skills or discriminaion lower women s posiion in he male wage residual disribuion. Then in case of wider disribuion, or wih oher words in higher 25

29 inequaliy women have o suffer from higher wage gap as his inequaliy imposes larger penaly on being below average in he disribuion. The calculaion of he hird and fourh componen of equaion (17) is he mos edious par of he model. According o Blau and Kahn (1997) i should be done in he following way considering year s and. Firs give each woman in year s a percenile number based on he ranking of her wage residual (from he male wage regression for year s) in he s year disribuion of male wage residuals. I shows her posiion in he year s male wage disribuion. Then mach her wih he residual in male disribuion of year which has he same percenile ha she had in he residual male disribuion in year s. The average of hese residuals (muliplied by -1 as he mean male residual is always 0) is he esimae for. For s he average female residual from male wage regression of should be considered. Alogeher we can say ha he effec of gender specific facors is refleced in he sum of he firs and hird erms: he effec of differen observable skills and gender differences in wage rankings a a given level of observables. The second and fourh erm reflecs he wage srucure, he effec of changing reurns o observed and unobserved characerisics (Blau and Kahn, 1997). The same daa is used as a Lemieux s decomposiion o make he resuls comparable. The log of real hourly wages is considered, and he sample consiss of employees. The pooled sample from he beginning and he end of he period ( and ) should be handled wih more care as in he JMP model he coefficiens are inerpreed also. 26

30 Resuls The paricular values for decomposed changes in gender wage differences can be seen in Table 3 for Hungary, beween 1992 and Observed change in he gender gap can be calculaed according o his: lnw ln W, he average male-female difference for he log s real wages, (which is he lef hand side of equaion (17)). This difference in differences is negaive which ells us ha he gender wage gap has closed from o Besides each componen of he equaion is negaive which shows ha he gender differences decreased in he componens separaely. Table 3. Decomposiion of he change in he gender wage differenial Observed change in he gender gap -0,05669 Observed X's (A) -0,02602 Observed prices (B) -4,3E-06 Gap (C) -0,01843 Unobserved Of which prices (D) -0,01363 We have seen in he firs chaper (Tendencies in Hungary) ha he observable characerisics of employees changed a lo. The erm denoed by (A) repors he wage effec of hese changes. This effec seems o he bigger and i is negaive, which shows ha he wo genders became more similar. The second erm conrols for he changes in he differences in he reurns o skills, i decreased also, bu only a lile bi. The hird erm conrols for he differences in he wage disribuions (keeping inequaliy consan), and according o he resuls his gap beween male and female wage-disribuion decreased also. The las erm checks for he change in unobserved prices, his is negaive and considerable also. 27

31 The aim of esimaing he gender gap was o show ha he residual variance is used o measure inequaliy, bu i is also essenial in measuring wage gaps. According o my resuls boh male and female variances change, boh became smaller. The effec is sronger for women, which makes i probable ha componens (C) and (D) would be smaller and bigger accordingly. I is no hard o see ha (D) should increase as he female residual sandard deviaion is in i wih negaive sign. Effec on (C) is less obvious, bu as he lef hand side of (17) mus remain he same, i mus decrease. 28

32 Conclusion I have found ha boh residual wage inequaliy and gender wage gap decreased beween 1992 and 1997 in Hungary. For men, wage inequaliy decreased by , wice as for women (0.0095) and he gender wage gap Afer conrolling for changes in he composiion of he work force we see ha residual wage inequaliy decreased by even more. This decrease is bigger for women, bu he change in he residual variance for women is smaller han for men even afer cleaning he composiion effec. Two facors are considered when checking for composiion effec, educaion and age; boh are posiively relaed o residual variance. The work force became more educaed and less old, he former is increasing he residual variance, and he laer is decreasing. The decrease in he cleaned residual variance, in he composie effec - free variance may be due o he dominance of he effec of lower average age. This alernaive residual variance esimaing mehod can affec esimaes for gender wage gap. I is common o conrol for changes in inequaliy when decomposing gender wage gap and variance in one of he main inequaliy measures. I would aler he esimaes of he gap effec in Juhn, Murphy and Pierce decomposiion (1993), which is he effec of he change in he relaive posiion of women in he male residual wage disribuion. I would also change he unobserved prices effec ha measures he change in he gender gap due o he widening or he narrowing of he residual male wage inequaliy, holding he gap in malefemale unmeasured skills consan. A possible exension of his paper would be o esimae he exac size of he changes of he gap and unobserved prices effec by using he alernaive residual inequaliy 29

33 measure proposed by Lemieux (2006). I is raher easy i do his in pracice in case of he unobserved price effec as sandard deviaion of he residuals is direcly in he formulas. In case of he gap effec he inerpreaion of composiion effec becomes much more complicaed. 30

34 Appendix The Quesionnaire is he same for each year. The following years spen in school can be relaed o he caegories used by he quesionnaire: Ca. Definiion in he quesionnaire Def. in English years 1. nem jár iskolába no aend o school oszály 1-3 classes oszáy 4-5 classes oszály 6-7 classes álalános primary schhol 8 6. szakmunkásképz vocaional school befejeze középiskola finished high school befejeze f iskola finished college befejeze egyeem finished universiy 17 31

35 Lieraure review Andorka Rudolf, Ferge Zsuzsa, Tóh I. György Valóban Magyarországon a legkisebbek az egyenlõlenségek? Közgazdasági Szemle, 2. sz o. Blau, Francine D. and Lawrence M. Kahn Swimming Upsream: Trends in he Gender Wage Differenial in he 1980s. Journal of Labor Economics, Vol. 15, No. 1, Par 1. (Jan), pp Blau, Francine D. and Lawrence M. Kahn The Gender Earnings Gap: Learning from Inernaional Comparisons. The American Economic Review, Vol. 82, No. 2, Papers and Proceedings of he Hundred and Fourh Annual Meeing of he American Economic Associaion. (May, 1992), pp Brainerd, Elizabeh Women in Transiion: Changes in Gender Wage Differenials in Easern Europe and he Former Sovie Union. Indusrial and Labor Relaions Review, Vol. 54(1), , Ocober Campos, Nauro, F. and Dean Jolliffe 2004.a. Afer, Before and During: Reurns o Educaion in Hungary ( ). Discussion Paper 4215, Cenre for Economic Policy Research, February Campos, Nauro and Dean Jolliffe b. Does Marke Liberalizaion Reduce Gender Discriminaion? Economeric Evidence from Hungary, WDI Working Papers Chay, Kenneh and David Lee Changes in Relaive Wages in he 1980s: Reurns o Observed and Unobserved Skills and Black-Whie Wage Differenials. Journal of Economeirics, 2000, 99(1), pp DiNardo, John, Nicole M. Forin, Thomas Lemieux Labor Marke Insiuions and he Disribuion of Wages, : A Semiparameric Approach Economerica, Vol. 64, No. 5. (Sep.), pp Farber, Henry and Rober Gibbons Learning and Wage Dynamics, Quarerly Journal of Economics, 1996, 111(4), pp Galasi Péer, Varga Júlia Munkaer piac és okaás, MTA Magyar Közgazdaságudományi Inéze 32

36 Juhn, Chinhui, Kevin M. Murphy, and Brooks Pierce Wage Inequaliy and he Rise in Reurns o Skill. Journal of Poliical Economy, Vol. 101(3), Kaz, Lawrence, David Auor Changes in he Wage Srucure and Earnings Inequaliy Handbook of Labor Economics, Vol3.A, Norh-Holland, Keresi Gábor, Varga Júlia Foglalkozaoság és iskolázoság Magyarországon. Közgazdasági Szemle, july-aug, pp KSH (Hungarian Cenral Saisical Office) Saisical Yearbook of Hungary Lee, David Wage Inequaliy in he U.S. during he 1980s: Rising Dispersion or falling minimum wage? Quarerly Journal of Economics 114, Lemieux, Thomas Decomposing Changes in wage Disribuions: A Unified Approach, The Canadian Journal of Economics, Vol 35, No 4. (Nov) pp Lemieux, Thomas Increasing Residual Wage Inequaliy: Composiion Effecs, Noisy daa or Rising Demand for Skill? American Economic Review, Vol. 96(3), , June Mincer, Jacob Schooling, experience and earnings. New York: Naional Bureau of Economic Research, Inc. Mincer, Jacob Changes in Wage Inequaliy Research in Labor Economics, 16, Newell, Andrew The Gender Pay Gap in he Transiion from Communism: Some Empirical Evidence. Discussion Paper No 267, March IZA Rosen, Sherwin Human capial, a survey of empirical research. Research in Labor Economics, vol.1., ed. R. Ehrenberg (Greenwich). Tóh Isván György Jövedelemegyenl lenségek: ényleg növekszenek, vagy csak úgy lájuk? Közgazdasági Szemle, L. évf. 3. sz p. World Bank (1996): From plan o marke. World Developmen Repor Published for he World Bank. Oxford Universiy Press, Oxford. 33