Unobserved Heterogeneity and Risk in Wage Variance: Does Schooling Provide Earnings Insurance?

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1 TI /3 Tinbergen Intitute Dicuion Paper Unoberved Heterogeneity and Rik in Wage Variance: Doe Schooling Provide Earning Inurance? Jacopo Mazza Han van Ophem Joop Hartog * Univerity of Amterdam; * Tinbergen Intitute.

2 Tinbergen Intitute i the graduate chool and reearch intitute in economic of Eramu Univerity Rotterdam, the Univerity of Amterdam and VU Univerity Amterdam. More TI dicuion paper can be downloaded at Tinbergen Intitute ha two location: Tinbergen Intitute Amterdam Gutav Mahlerplein MS Amterdam The Netherland Tel.: +31(0) Tinbergen Intitute Rotterdam Burg. Oudlaan PA Rotterdam The Netherland Tel.: +31(0) Fax: +31(0) Duienberg chool of finance i a collaboration of the Dutch financial ector and univeritie, with the ambition to upport innovative reearch and offer top quality academic education in core area of finance. DSF reearch paper can be downloaded at: Duienberg chool of finance Gutav Mahlerplein MS Amterdam The Netherland Tel.: +31(0)

3 Unoberved Heterogeneity and Rik in Wage Variance: Doe Schooling Provide Earning Inurance? Jacopo Mazza 1 Han van Ophem Joop Hartog February 011 Abtract We apply a recently propoed method to dientangle unoberved heterogeneity from rik in return to education. We replicate the original tudy on US men and extend to US women, UK men and German men. Mot original reult are not robut. A college education cannot univerally be conidered an inurance againt unpredictability of wage. One concluion i unequivocally confirmed: uncertainty trongly dominate unoberved heterogeneity. JEL claification: C01, C33, C34, J31 Keyword: wage inequality, wage uncertainty, unoberved heterogeneity, electivity, education, replication 1 Correponding author. Univeriteit van Amterdam, Addre: Univeriteit van Amterdam, Roetertraat 11, 1018 WB Amterdam, The Netherland, Univeriteit van Amterdam. All data and computer program are available on requet.

4 I. Introduction Benefit from chooling are uncertain. Going to chool may either increae or decreae earning rik. Realied earning variance for individual with given level of chooling are well documented, but uch data are not informative on rik a they alo include unoberved heterogeneity that may govern potential tudent choice. Empirical information on the extent of rik in chooling choice i very important. With uncertain chooling benefit a fact of life, we need to know the extent of rik a an input for realitically modeling chooling choice a a choice under rik (Levhari and Wei, 1974). Knowing the extent of rik i particularly relevant for policy iue. Education i often promoted a an inurance againt the vagarie of the labour market (or even life) but the argument only hold if indeed continued education reduce rik; we have no olid evidence that it doe. A recent paper by Chen (008) recognize the potential bia in ex pot earning data and ugget a method to correct for it. She claim two major contribution. The firt i the identification of the caual relation between education and inequality. The econd i the decompoition of wage inequality between uncertainty and unoberved heterogeneity 3. We conidered Chen method a ufficiently promiing approach to learn about the relationhip between chooling and rik and we decided to apply it to data from different countrie, in earch of reliable and robut empirical information. A a natural check on reliability of Chen reult and on correct application of her method, we will replicate her etimation on the original population. Economit often praie the virtue of replication, but rarely attempt it. We trongly believe that putting empirical reult under careful crutiny i an important if not eential tak per e. Hamermeh (007) define pure replication a examining the ame quetion and model uing the underlying original data et and cientific replication a the ame type of reearch on different ample and different population. The preent work cover both apect. Our reult undercore the value of both type of replication. Chen report two main concluion. Firt, rik doe not increae with educational level a previou reearch on the topic uggeted. Second, he find evidence of pervaive underetimation of potential wage difference by oberved wage inequalitie. Our etimation on the ame ample and population do not confirm thee finding. On one hand, Realied earning variance ha no robut relationhip with length of education: depending on time and country, it may increae, decreae or tay contant. See Hartog, Van Ophem and Bajdechi (004) and Raita (005). 3 A different method to reach the ame goal ha been propoed by Cunha, Heckman and Navarro (005). Alo Belzil and Leonardi (007) take endogeneity into account to etablih how rik averion i affecting educational choice.

5 we find that rik doe increae, for every level after high chool. On the other hand, we obtain a theoretically unexpected underetimation of potential inequality by oberved inequality. We cannot locate the exact caue for thee deviation, a exact replication wa prohibited by US data dicloure regulation and by obcuritie in Chen report 4. Britih data do not confirm our reult and are neither in conformity with Chen original reult. In fact, rik decreae by chooling level while for only three out of ix educational categorie we encounter the expected poitive ratio of potential/oberved wage variability. With German data, we find correlation coefficient outide the permitted interval: the model imply doe not apply to thee data. We mut conclude that the relationhip between level of chooling and rik i far from ettled. We proceed a follow. In ection II we et forth Chen model, in Section III we dicu the data and in Section IV we preent the replication reult. In Section V we apply the model to American women, in Section VI to men in the UK and in Section VII to men in Germany. Section VIII conclude. II. Chen model A. The theoretical model The model in Chen (008) ha been contructed to exploit the data in the NLSY79. Conider a panel dataet of N worker oberved over T time period indexed by ubcript i and t repectively. In the firt period worker i chooling level i determined; it will not change over the following period. The chooling level choen by the individual will be indicated with. The poible choice in the NLSY79 are four: no high chool diploma ( i =0), high chool graduate ( i =1), ome college ( i =) and four year college or beyond ( i =3). yit indicate the oberved log wage in period t for peron i. The worker potential wage i obviouly oberved only in one educational level, therefore, the worker oberved wage i: y y I { 0} y I { 1} y I { } y I { 3}, (1) it 0it i 1it i it i 3it i 4 All our doubt and querie raied in the replication have been ubmitted to Chen. Unfortunately, we have not received any clarification for any of the unclear paage, not even after the editor of REStat upported our requet. 3

6 where I{ } i the indicator function taking value 1 if the ubject belong to that pecific chooling category and 0 otherwie. The link between chooling level i and potential wage ( y it ) i given by the following regreion model: yit xit ei t it if i =. () i the intercept for chooling level, the vector of coefficient of the obervable characteritic x it, e i and it are unit root random variable uncorrelated with each other. The time invariant individual fixed effect are incorporated in e i. Thi term meaure the unoberved earning potential at chooling level which i allowed to be correlated with obervable characteritic x it. t it denote the tranitory hock, aumed to be uncorrelated with obervable. The potential wage variation i for ubject chooling choice and covariate at time t. The permanent component t i created by variation in the individual pecific effect which are uppoed to vary acro education, but to be contant in time. The temporary hock emerging from macroeconomic condition or intitutional change are incorporated in t which can vary with both time and chooling level. The variable of interet in thi model are the variance of both component in potential wage. The election problem i formalized in a latent-index chooling aignment rule: i if i Afor =0,1, or 3, (3) where the unoberved chooling factor i ummarize the private information uch a tate for education, ability and o on, which influence the ubject educational choice. A { i : ai i a 1, i} i the group of individual who choe educational level. a z i the minimal level of the unoberved chooling factor in A. The vector i i zi contain both covariate x it and an intrument for education whoe coefficient are contained in. 0 and 4. The tructure of error term i known to all agent and ummarized by: 4

7 ei it ~ N 0, 1 0. (4) 0 1 i A aumed, the unoberved chooling factor i correlated with the individual fixed effect, but not with the tranitory hock t. The correlation coefficient ( ) can aume either poitive or negative value. In cae of poitive value we have poitive election, the oppoite in cae of negative value. The parameter i clarifie why it i important to ditinguih between wage variability and rik. In fact, the private information, by definition unobervable to the econometrician, can be ued to predict the ditribution of potential wage acceible to the ubject for each chooling level. The expected value of potential wage at time t and chooling level, from a peronal point of view i given by: Ey [ x,, ] x, (5) it i it i it i where i repreent the unoberved heterogeneity component at chooling level. Equation (5) follow from the ditributional aumption in (4) and and Ee [ x,, ]. i i it i i Since the agent know hi own ability and tate and ue the information to elect the appropriate level of chooling, the degree of wage uncertainty can not exceed the degree of potential wage inequality. The wage uncertainty at chooling level i meaured by 5 : Var[ e, x, ] (1 ). (6) i t it i it i t t The econd equality follow from the ditributional aumption decribed in (4): Var e x Thi equation make explicit that potential wage variability ( i i, it, i ) 1. ( t ) i formed by two component: inequality created by wage uncertainty t and inequality from unoberved heterogeneity. In fact, if we rewrite equation (6) we obtain: t and remembering we ee that t. 5 We copy thi equation from Chen; it i clear that hould be ubcripted for time, but Chen ignore thi. See alo ection 3C. 5

8 Thi equation alo how the three ource of uncertainty that each individual ha to face: the earning potential of the individual fixed effect ( e i ); correlation between potential wage and private information ( ); tranitory hock due to intitutional change ( t ). Equation (4) and (5) imply that potential wage are compoed of oberved heterogeneity ( xit ), unoberved heterogeneity ( i ) and an unforeeeable component ( t ) plu an error term ( u it ) y x u, (7) it it i t it where u it i a normalized random variable, uncorrelated with obervable and unobervable characteritic. t u it i called the unforeeeable component of wage reidual, that i to ay rik. The firt three term of equation (7) are a direct conequence of the value of potential wage expected (by the individual) a explained in equation (5). The lat term i decribing uncertainty a modeled in equation (6) corrected by a normally ditributed error term. From thi dicuion it hould be clear that the target of identification are: wage uncertainty ( t ) and the permanent and tranitory component of potential wage inequality ( and t ). B. Model etimation and parameter identification Equation (5) and (6) can not be ued for regreion analyi ince i i unoberved; what i oberved i the educational choice of an agent. The mean and variance of oberved wage are derived by the following equation: Ey [ x ;, z] Ey [ A; x, z] x (8) it i it i it i it i it i, Var[ y ; x, z ] Var[ e A ; x, z ] (1 ) (9) it i it i i t it i it i i t t Thee equation pecify the requirement for the contruction of adjutment for truncation ( ) and election ( ), explained below. Equation (8) how that oberved wage overtate or 6

9 undertate the mean potential wage depending on the ign of the correlation term. The electivity adjutment i i an invere Mill ratio: i E[ i i A ] [ ( ai ) ( a 1, i ) / ( a 1, i ) ( a i )]. (10) Equation (9) how how regardle of the ign of election bia, the oberved wage undertate the degree of potential wage inequality for each educational level. The degree of undertatement i called by Chen truncation adjutment ( i ): 1 Var[ A ] [ a ( a ) a ( a )] / [ ( a ) ( a )], (11) i i i i i i 1, i 1, i 1, i i where and denote tandard normal denity and ditribution function, repectively. The incluion of invere Mill ratio i not enough if the target of identification i the untruncated variance of wage. For thi purpoe, a multi-tep proce i propoed. The firt tep i to obtain the truncation and electivity adjutment in the firt tage of a Heckman election model. Then, a fixed-effect model baed on equation (8) i etimated and the tranitory component t identified 6. The fixed effect model i expreed a: ( y y ) ( x x ) ( ) if i =, (1) it i it i it i where y i, xi and i denote the average over time of the correponding variable over the urvey year. Next, a between-individual model identifie the chooling coefficient: y x w (13) i i i i The error term wi ui i i atifie by contruction Ew [ x ;, z] 0 and i i i i Var w x z T. Thu, the [ i i ; i, i ] i t / t i conitent etimator for the permanent component of potential wage inequality i: 6 The complete proce leading to the identification of the tranitory component i dicued in Chen (008) note 9 p

10 Var ˆ w x z ˆ ˆ ˆ T (14) ˆ ( i i ; i, i) t / t The firt term of thi ummation i the mean quared error of the between-individual model, whoe etimate will be preented in table 4a in ection III; the econd i the interaction between the conitent etimate of the unoberved heterogeneity term ( ) and the ample average of the truncation adjutment ( ˆ ); the third the ratio between the tranitory 1 1 component of wage inequality ( ) andt ( T / N). ˆt Let recollect the concept that have been introduced o far: Oberved wage ( y ; x, z ): wage oberved in the data. it i it i i i Potential wage ( y it ): wage obtained by individual i if he had choen chooling level. Potential wage i the um of oberved heterogeneity ( xit - known to individual and econometrician); unoberved heterogeneity ( i - known only to the individual); unforeeeable component ( t u it - unknown to everyone). Oberved wage inequality ( Var[ y ; x, z ]): within educational category it i it i variation in wage. It i decompoed a the um of tranitory volatility ( - etimate hown in panel B and B of table 4a below) and the mean quared error of the between individual-model (etimate hown in Panel A of table 4a below). Potential wage inequality ( + t ): wage inequality that would have been experienced for each educational category if education wa not choen, but randomly aigned. It i the um of the tranitory volatility a defined above ( ) and the permanent component ( ). The permanent component here account for election and truncation biae (Panel C and D in table 4b). Unoberved heterogeneity ( i ): include all the characteritic known to the t t individual, but unknown to the econometrician that influence the chooling deciion and bia the OLS wage etimate (Panel H and I of Table 4c). Wage uncertainty ( ): proper meaure of rik in educational category, equal to the um of tranitory component a defined above and a permanent component (etimate in Panel G table 4c) accounting for the unoberved chooling factor i. Etimate of wage uncertainty (rik) can be found in Panel H and I in table 4c. 8

11 III. Data Chen etimate are baed on the NLSY: merged with retricted geocode data. The geocode give acce to detailed information on the reidence of repondent; it allow to control for the population denity in the county of reidence and to contruct an intrument: average tuition fee in the county of reidence for a public four-year college in the year when the repondent wa 17. We do not have acce to the geocode data ince their ue i limited to reearcher at American intitution. We will have to ue a different intrument for chooling and we will not be able to control for population denity in the area of reidence. However, thi hould have no conequence a long a our intrument erve the ame purpoe a Chen intrument. At wort we will experience ome lo of efficiency. Both our and Chen original ample conit of 1,686 repondent aged 14- in Chen focue only on male between urvey year , which correpond to calendar year , o that all the repondent hould have already terminated their tudie. Sampling weight are ued to calculate all etimate. Since he doe not pecify which ampling weight were ued, we will apply the tandard ampling weight 7 provided with the NLSY79. She exclude repondent that do not provide any information about parental education or the particular ability index that he utilize. Following her line of conduct 4930 individual remain in our ample 8. We alo have to drop 11 individual who do not have any information on highet grade completed. An additional 8 obervation were deleted ince it wa impoible to retrieve the exact work experience accumulated over the period in conideration. Finally, for a many a 1318 individual no information on the hourly rate of pay i available. Since thi i one of the outcome variable, we had to erae them from our ample. Thu, at thi point, our balanced panel ample contitute of 3373 individual. Chen (008) i not explicit about the exact ize of her ample. Her time invariant variable, elected with the above mentioned procedure, have 430 repondent, 68 individual le than what we obtained. She alo ha an unbalanced ample for time variant regreor. For the firt year he ha 86 obervation. The ize contantly diminihe with time, until only 5 individual remain in the 1999 ample 9. It i not clear to u how he obtained thoe number ince all the variable he claim to elect her ample on are time invariant and the original NLSY79 databae ha no attrition. She doe not provide any 7 The ampling weight ued are coded a R , R , R , R , R , R , R in the NLSY79 for the urvey year 1991, 199, 1993, 1994, 1996, 1998, 000 repectively female, 45 individual with no information about ability index, 414 individual with no information about mother and 607 about father education were deleted. 9 Chen (008) p.80 table 1. 9

12 information about ample ize ued in her firt tage regreion. Her wage regreion are baed on 3184 repondent and 1845 obervation. Thu, apparently, 1118 individual included in Chen decriptive tatitic that we will preent in table 1a have no information about wage. We follow Chen data choice a much a we can. Schooling i defined by the highet grade completed according to the 1990 urvey when all repondent were at leat 5 year old, and meaured with four dummy variable: no high chool (YOS<1); high chool (YOS=1); ome college (1<YOS<16); college (YOS 16). The ability index i the Armed Force Qualifying Tet (AFQT). It wa conducted in 1980 for all repondent of all age and chooling level; original core are regreed on age dummie and quarter of birth and reidual are included in the choice and wage regreion. Quarter of birth capture chooling effect through compulory chooling law (Angrit and Krueger (1991). We ue hourly pretax earning, from wage, alary, commiion or tip from all job in the calendar year preceding the urvey 10. The family income meaure conider family income at age 17, or a cloe to 17 a poible. If family income at 17 i unavailable then the meaure i taken at 16 or 18. For nearly half of the repondent the family income meaure at age 17 i unavailable 11. The work experience meaure i contructed from the longitudinal work hitory in the NLSY79. Number of week worked in pat calendar year are converted in number of full working year by dividing by 49. We have to deviate from Chen becaue we have no acce to the geocode data. Chen add two geographical control to choice and wage equation: an urban dummy at age 14 and the county of reidence population denity in 1980, but population denity i not available to u. The intrument for chooling in the original paper i the potential college tuition cot at county level defined a the average tuition fee at the local public four-year college in the year when the repondent wa 17. Thi meaure alo exploit the retricted information on the repondent county of reidence that i not available to u. We intrumented chooling choice with the average unemployment rate differentiated by ex, age group and ethnic origin for the year pent in chool after the mandatory chooling age. The intuition behind thi intrument 10 Chen (008) p. 79 claim to ue annual earning. Thi claim doe not correpond with the earning meaure preented in table 1 which i the logarithm of hourly earning in 199 dollar. We tried both outcome variable and choe the latter. In fact, if annual earning were ued a dependent variable in the betweenindividual model, the magnitude of the reidual a preented in table 4 panel I would eem to be too mall. Thi i not the cae if hourly earning are the explained variable ued. 11 A i evident from table a and b, it eem that Chen included four dummie to characterize the entire quartile ditribution of family income at age 17. Since it i evident that four dummie plu the contant would create a dummy trap, we upect that, even if he doe not exprely tate it in her paper, he created a dummy variable for non repone to the family income quetion. Thi i the way we proceed. 10

13 i that the facility to find a job in the market might influence the outide option of each tudent. A poible concern uing thi variable i that unemployment rate during youth might correlate with current unemployment rate and thu wage. We will therefore alo include the unemployment rate for the year in which the wage i meaured in the wage regreion. The aumption i then that conditional on current unemployment rate in the country, pat unemployment rate are uncorrelated with wage earned 1. The lack of precie geographical location force u to ue the national rate of unemployment for young worker. Data about unemployment rate are taken from the Current Population Survey (CPS) 13. The rik of taking uch a crude meaure of unemployment a the national rate i a weak correlation between the intrument and chooling choice. We will how in the choice equation preented in table a and b that thi concern i miplaced. 195 individual dropped out of chool before the legal mandatory age. Unemployment figure from the CPS are only available for people aged 16 and older. If a repondent dropped out of chool before that age no unemployment rate i imputable. Our final ample thu count 3,178 repondent and 1,573 obervation. In table 1a and 1b we report ummary tatitic. Our ample differ from the original one 14 in ome apect. Firt, it how a higher number of individual without a high chool education, which reflect in a lower number of high chool graduate and college (or more) graduate. Second, the average AFQT core i lower. Lat, the hare of ethnic minoritie, black and Hipanic, i coniderably higher in our ample. Alo, family income i coniderably lower. In table 1b we can ee how our work experience meaure i almot contantly one year higher, while the log of hourly earning i lightly lower. The difference in hourly earning might be explained by the larger hare of high chool drop out and high chool graduate that our ample ha. Overall, our ample appear to repreent a le educated, more ethnically diverified and poorer hare of the population than the one Chen ue for her analyi. Thi i an unintended difference for which there i no clear explanation. It can influence the reult of our etimation a we will ee later on. 1 Arke (010) and Hauman and Taylor (1981) are two of the very few tudie that ue unemployment during chooling year a intrument for chooling. 13 The URL addre i: (Acceed 15/06/010) 14 Chen (008) p

14 Table 1a. Mean and tandard deviation time invariant variable NLSY79 Our ample Chen' ample (a)schooling variable Year of chooling (.57) (.50) Categorical education No high chool.0.10 (.40) (.30) High chool (.48) (.50) Some college.1.1 (.41) (.41) Four-year college or beyond..6 (.41) (.44) (b) Ability and family background Armed force qualifying tet core (adjuted) (9.1) (8.50) Highet grade mother (3.0) (.61) Highet grade father (3.93) (3.53) Number of ibling (.5) (.17) Family income 3,30* 50,31* (16,941) (34,544) Black.5.11 (.4) (.31) Hipanic (.35) (.) (c)geographic control at age 14 Urban (.41) (.4) Northeat.19.1 (.39) (.41) South.33.9 (.47) (.45) Wet (.39) (.36) (d) Intrument for chooling Average unemployment during chooling year 5.33 (5.6) *1999 dollar. Average unemployment rate calculated on CPS data. 1

15 Table 1b. Mean and tandard deviation time variant variable NLSY79 Our Sample Calendar year Labor market variable Actual work experience (3,58) (4.05) (4.35) (4.68) (5.04) Log Hourly earning (.98) (1.06) (1.06) (1.14) (1.5) Unemployment rate (.13) (.51) (1.74) (1.87) (1.05) Chen ample Calendar year Labor market variable Actual work experience (3.37) (3.87) (4.11) (4.34) (4.67) Log Hourly earning* (.68) (.69) (.70) (.84) (.85) Note: *in 199 dollar. Standard deviation in parenthei. Unemployment rate are taken from CPS. IV. Replication We will preent our reult in three tep: firt tage etimate to intrument chooling level, GLS and IV wage equation, and decompoition of variance of oberved wage, potential wage and uncertainty. In each of thee table, column in bold report the reult of our etimate, while the normal print reproduce Chen original reult. We have crupulouly teted our etimation routine through a Monte-Carlo imulation (reult available on requet). Our routine wa able to retrieve all the parameter of the imulated dataet with good preciion. Therefore, we exclude that dicrepancie reported below are the reult of a miundertanding of the etimation procedure. A. Firt Stage: uing national unemployment rate a intrument Table report the reult of the ordered probit taking chooling level a the explained variable. Given that we have to ue a different intrument, it i important to point to the ignificant effect that our intrument ha for every level of education even after controlling for ability, family background, racial and geographical origin and age. Overall our fit i imilar to Chen. All covariate how the ame ign and roughly the ame magnitude. The only appreciable difference between the two etimation i the magnitude of the two et of cutoff point. Our cutoff point are negative and the interval are wider. It perhap remarkable that the effect of the unemployment rate i negative. One uually reaon that the opportunity cot of chooling fall when unemployment i high. But of coure the benefit from extended chooling may fall even more during a receion, thu making the invetment le profitable. 13

16 Table. Firt tage etimate ordered probit and marginal effect. Coefficient Marginal effect at mean Le than high chool High chool Some college 4 year college or beyond Covariate (1) () (3) (4) (5) (6) (7) (8) (9) (10) Tuition cot in county/1, ***.010***.01*** -007** -.015** (.01) (.00) (.003) (.00) (.003) Average unemployment rate during chooling year -.063***.009***.016*** -.009*** -.016*** (.005) (.001) (.001) (.001) (.001) Interact unemp. Rate with/ Mother attended college.071*** -.010*** -.018***.010***.018*** (.009) (.001) (.00) (.001) (.00) Father attended college.055*** -.008*** -.014***.007***.014*** (.008) (.001) (.00) (.001) (.00) Highet grade mother.040***.033** -.006*** -.006** -.010*** -.007*.005***.004*.010***.009** (.005) (.011) (.001) (.00) (.001) (.003) (.001) (.00) (.001) (.003) Highet grade father.048***.09** -.007*** -.005* -.01*** -.006**.007***.004***.013***.008*** (.004) (.009) (.001) (.00) (.001) (.00) (.001) (.001) (.001) (.00) Family income bottom quartile (.035) (.154) (.005) (.033) (.009) (.05) (.005) (.04) (.009) (.34) Family income econd quartile * * * * (.031) (.153) (.005) (.07) (.008) (.033) (.005) (.00) (.008) (.040) Family income third quartile (.08) (.15) (.004) (.05) (.007) (.035) (.004) (.018) (.007) (.041) Family income top quartile.38*** *** *** *** ***.045 (.08) (.151) (.004) (.03) (.008) (.037) (.003) (.016) (.008) (.044) AFQT core (adjuted).08***.04*** -.004*** -.004*** -.007*** -.005***.004***.003***.007***.006*** (.000) (.001) (.000) (.000) (.000) (.0003) (.000) (.000) (.000) (.0003) Black.713***.653*** -.069*** -.08*** -.06*** -.173***.045***.047***.30***.08*** (.06) (.056) (.00) (.006) (.008) (.017) (.00) (.004) (.009) (.00) Hipanic.587***.435*** -.057*** -.059*** -.171*** -.113***.039***.038***.189***.134*** (.037) (.070) (.003) (.008) (.011) (.00) (.00) (.004) (.013) (.04) Geographic control Ye Ye Ye Ye Ye Ye Ye Ye Ye Ye Cohort and age control Ye Ye Ye Ye Ye Ye Ye Ye Ye Ye Contant(K0) ***.711* (.54) (.315) Cut point (K1) ***.148*** (.41) (0.316) Cut point(k) -8.35***.905*** (.9) (.317) Wald chi-quared 9, ,

17 B. Caual effect of chooling on average wage The etimate of the caual effect of chooling on wage are preented in table 3. Our GLS etimation how the expected poitive effect of education, experience and ability on wage. In our cae, return to education increae while in Chen cae both high chool graduate and college graduate have higher benefit from chooling after intrumenting. In our cae, Hipanic alo appear to earn more after intrumenting. In tark contrat to Chen reult, we find no ignificant effect of the electivity correction term. The different effect of the four invere Mill ratio will have a trong impact on the calculation of the correlation coefficient and, in turn, on the etimate of potential wage inequality. 15

18 Table 3. Wage equation: etimate of GLS and Heckman election model Between-individual model(gls) Heckman Covariate (1) () (3) (4) High chool graduate.085***.088** ** (.01) (.030) (.039) (.148) Some college.13***.4***.106*.4*** (.014) (.081) (.045) (.081) Four-year college or beyond.397***.41***.48***.599*** (.016) (.08) (.057) (.116) Experience.130***.076***.184***.074*** (.005) (.014) (.011) (.014) Experience -.001*** *** (.000) (.001) (.000) (.001) AFQT core (adjuted).005***.004***.004***.0005 (.000) (.000) (.001) (.00) Mother year of chooling * (.00) (.004) (.004) (.005) Father year of chooling (.001) (.003) (.003) (.004) Family income bottom quartile.005** (.00) (.056) (.035) (.057) Family income econd quartile (.015) (.055) (.03) (.055) Family income third quartile -.030* (.013) (.054) (.030) (.055) Family income top quartile **.053 (.01) (.054) (.030) (.057) Number of ibling.005** (.00) (.004) (.004) (.004) Black.064*** -.053**.331** -.158*** (.013) (.06) (.18) (.053) Hipanic.039*.00.55** -.06 (.015) (.09) (.087) (.045) Unemployment rate ** (.00) (.06) Contant.39*** 1.118***.89*** 1.077*** (.046) (.103) (.17) (.117) Geographic control Ye Ye Ye Ye Cohort and age control Ye Ye Ye Ye Selectivity adjutment No High chool ** (.05) (.113) High chool graduate ** (.08) (.089) Some college (.0) (.079) Four-year college or more *** (.047) (.106) R-quared Note: Column (1) and (3) are our etimate, column () and (4) are from Chen (008) and alo control for local population denity. Our geographic control include the urban dummy and three regional dummie for reidence at 14. Cohort control include a full et of birth cohort dummie and age in the initial urvey year. */**/*** indicate confidence level of 10/5/1 percent repectively. Standard error in parenthee. 16

19 C. Main reult In table 4a panel A we report oberved wage inequality and it two component. The firt i the permanent component, identified by the mean quared reidual in the between-individual model 15 (equation 10). The econd i the tranitory component t identified by exploiting the mean-quared error of the fixed-effect model a decribed in note 9 p. 78 in Chen (008) 16. Tranitory volatility i conitently etimated by 17 : t ˆ ˆ, (15) 1 1 ˆ V N T t t i /( T i ) N i /( T i ( T i )) i i where V ˆt i the mean quared error of the fixed-effect model and ˆ ˆ Vt /(1 1/ Ti). Our etimate of the permanent component are larger than Chen but the ranking i the ame and even the difference between chooling level are very cloe. Our etimate of the tranitory component are maller than Chen ; our profile acro level of chooling i fairly flat, wherea in Chen cae, there i a ubtantial dip after high chool drop-out and tability thereafter. The reult for total oberved inequality alo differ. In Chen reult, the group with ome college tand out with low variance, while in our reult, college graduate tand out with the highet variance. Remarkably, in both etimate the oldet age group ha the highet tranitory variance. 15 Chen affirm on page 83 that the permanent component i defined a the variance in the individual fixed effect model. Thi would conflict with the definition given on page 78 and with equation 1. For thi reaon, we will adhere to the definition provided on page 78 and ue the mean quared error of the between-individual model. 16 In a footnote to table 4 Chen (008 p. 84) affirm that: The etimate of tranitory volatility are derived by regreing quared reidual on age dummie and categorical education variable. Thi eem to contrat with the pecification of the tranitory volatility parameter provided in note 9 p.78 that we adopted for our etimate. We have etimated the tranitory parameter alo with thi alternative pecification and reult are very imilar. Etimate available on requet. 17 A mentioned in footnote, Chen doe not add a time ubcript to the parameter t and when he preent the parameter etimate, he doe not make it dependent on time either but only report difference by age group (poibly for brevity of expoition). While we do have eparate etimate of thi parameter for each year, we will follow Chen methodology and ditinguih only within age group. Meaurement of the tranitory component i not clear. The note to Chen table 4 tate that: the etimate of tranitory volatility are derived by regreing quared reidual on age dummie and categorical education variable. (Chen, 008 p. 84). Thi procedure eem to contrat with the one highlighted in note 9 p.78. The quared reidual mentioned in Chen note are mot likely thoe obtained from the fixed-effect model. Since we could not undertand whether the outcome variable he regree the categorical education and age dummie on i the variance of reidual of the fixed effect model or we have applied both method. The difference are negligible. ˆt 17

20 Thi reult contradict pat reult (Chen, 008) that pointed toward a decreae in wage variance with age. A hown in Panel A, for every educational category, we ytematically obtain a larger permanent component than Chen. The difference varie between 3% for high chool drop out and 5% for college dropout. Remember that the permanent component here i defined imply a the mean quared reidual of the GLS model preented in table 3b column 1 and. Thi mean that our reidual hould be larger than Chen. Thi i contradicted by our R-quared which i ubtantially higher than the one in Chen (008). Table 4a. Etimate of variance of oberved wage inequality. Le than high chool High chool Some college College graduate (1) () (3) (4) (5) (6) (7) (8) A. Permanent component (.019) (0.6) (.016) (0.14) (.03) (0.8) (.06) (.0) B. ( )-Tranitory component ˆt Age Age Age Oberved inequality (A+B) C. ( )-Permanent component -Adjuted for election and truncation biae E. Tranitory component (ame a B) Potential wage inequality (C+E) F. Correlation coefficient G. Permanent component (C-C*F) Accounted for unoberved Schooling Factor I. Tranitory component (ame a B) Degree of wage uncertainty (G+I) Unoberved heterogeneity(c+e G-I) Note: Column (1), (3), (5) and (7) are our etimate, column (), (4), (6) and (8) are taken from Chen (008). In Table 4b we preent etimate of potential wage inequality, the um of the permanent component after taking out the effect of election and truncation and the tranitory component ( + ). Chen ha analytically hown how oberved wage t inequality ytematically undertate potential inequality if education were randomly 18

21 aigned (Chen, 008, p 78). She correct thi by incorporating a truncation adjutment term and a heterogeneity term (equation (11) above). Comparing row A in table 4a with row C in table 4b, how that the prediction i not confirmed in our data: potential inequality i maller than oberved inequality. The reult would ugget that pupil elect themelve into the wrong educational category or that their chooling factor doe not influence their choice. Since thee reult are quite urpriing we conducted ome robutne check with Monte-Carlo imulation. We tried different intrument uch a number of ibling and being raied in a Jewih family, but both elaboration led to the ame urpriing reult. The reult i theoretically impoible if normality in the error term i aumed, but there are no retriction in Chen etimation method impeding it. The permanent component i defined in equation (14). The firt term of the um i the oberved wage inequality preented in row A and it enter alo in the calculation of the potential wage inequality in row C. The difference between the two row i due to the two remaining term in (14). The only retriction on thee two term regard the truncation adjutment ( i ): it hould range between 0 and 1. Thi retriction i repected in our etimation. If the econd term of the addition ( ) dominate the third term ( t / T ), potential wage inequality i higher than oberved wage t inequality. In our cae the third term dominate the econd and thu the unexpected reult emerge. The low value of the econd term i related to the low value of the correlation coefficient, a reported in Table 4c: the correlation coefficient determine the magnitude of the correction for electivity, and in our cae, thi correction i very mall. Conceivably, the reult i due to inability of our intrument to create an adequate correction to the biaed GLS etimator. But our intrument i urely relevant, a hown in the firt tage reported. Since we have a jut identified model, we cannot tet it validity with a Sargan tet, but we have no reaon to believe that the country unemployment rate in youth year would have any effect on thi group of repondent wage once we control for current unemployment rate. Furthermore, our intrument perform well in the IV etimation preented in table 3. Our reult and Chen both point to a permanent component in potential wage inequality that i more or le table acro the lowet three education level and then jump for college graduate. But the outcome differ for total potential inequality: in 19

22 our cae it i markedly higher for college graduate than for the other education level, wherea in Chen cae the pattern i U-haped and inequality for college graduate i not higher than for high chool drop-out. The key reult of the analyi i the breakdown of oberved wage inequality into uncertainty (pure rik) and heterogeneity (table 4c). We find dramatically lower correlation between the unoberved chooling factor and the unoberved permanent component in wage. By conequence, accounting for unoberved chooling factor, a done in row H, ha minimal effect on the etimated magnitude of the permanent component of wage inequality. Only for college graduate we ee a minor reduction of about 5%. Chen core concluion urvive: unoberved heterogeneity i negligible; wage inequality i completely dominated by uncertainty. But in our etimate, uncertainty i clearly highet for college graduate, while in Chen etimate it i highet for high chool graduate. D. Concluion on the replication We have been unable to replicate Chen (008) exactly. Data availability regulation prevented u from uing the ame intrument. Chen intrument for chooling, local tuition cot, may be particularly relevant for tudent from poor familie and with relatively low ability. Number of ibling, our intrument in the Britih and German cae, may have imilar relevance. Our intrument for the US data, the national unemployment rate, ha a negative effect on the inclination to continue into higher education. Thi i compatible with tandard human capital theory if benefit from extended education decline more than the cot of education with riing unemployment, a cae that may well hold for low ability tudent from poor familie. Chen decription of her procedure wa not alway unequivocal. Following the intruction in Chen original paper did not bring u to the ame ample of individual. In our ample, we have a larger hare of lower educated individual, from poorer family background. Thi may lead to difference in etimated coefficient. If le advantaged people are more prone to loe their job we would oberve a higher tranitory volatility. In reality what we oberve i a lower tranitory volatility in our replication. Le advantaged individual might alo poe le private information or they might not be able to ue it correctly and that would reflect in higher hare of pure rik and poibly in higher oberved than potential permanent variance. In effect that 0

23 i what we oberve in our elaboration. The enitivity of our reult to modet change in ample compoition i reaon for concern. We do feel confident though, that our etimation procedure faithfully reflect Chen model. In our etimate, the tranitory component in oberved wage inequality i about 1/ to 1/3 of the permanent component, while in Chen etimate they are about equal. Chen find that potential wage inequality i larger than oberved inequality, while we find the revere (at a larger gap). In our cae, oberved wage inequality i virtually identical to uncertainty, leaving no room for unoberved heterogeneity, and thi concluion i imilar to what Chen find (her heterogeneity i marginally bigger). We find that uncertainty i cloe to 40% higher for college graduate than for high chool drop-out, while Chen find that high chool drop-out have ome 30 % higher uncertainty than college graduate. V. Applying the analyi to American women We extend the analyi to women in the NLSY ample, but to avoid complication due to labor market participation behavior, we retrict the analyi to full time female worker only. We define full time worker a thoe women who worked at leat 5 hour per week in each urvey year. Applying the ame election criteria adopted in the previou ection we obtain a ample with 535 obervation. The full time working women are more educated, by almot one year, than the male ample. They are alo more able a meaured by the AFQT adjuted tet core. Thi i not urpriing given the particular condition we impoed. It i indeed probable that highly educated women are more likely to participate in the labor market (Connelly, 199) and thu be included in our analyi. A for the time variant variable, full time working women how a better performance in the labor market. They have a ubtantially higher working experience and earn more than their male counterpart. The firt tage etimate are not hown here. No appreciable difference emerge between the previou firt tage baed on men only and thee new one. The intrument i till relevant and ha the ame impact on further education. The cut-off point are modified. The interval between the three point i lightly larger than before. 1

24 Alo, the between-individual model, intrumental variable etimation and Heckman econd tage do not preent appreciable difference between the female and male ample. Full time working female belonging to ethnical minoritie earn more than their white counterpart. Thi i probably reflecting that ethnic minority female that decide or ucceed to work full time are particularly talented or dedicated. The other covariate do not how ignificant difference with the etimate preented earlier for men only. Table 6a. Etimate of variance of oberved wage inequality Full time female worker. Le than high chool High chool Some college College F M F M F M F M A. Permanent component (.007) (.019) (.005) (.016) (.007) (.03) (.009) (.06) B. Tranitory component ( ) ˆt Age Age Age Oberved inequality (A+B ) C. ( )-Permanent component -Adjuted for election and truncation biae E. Tranitory component (ame a B) Potential wage inequality (C+E) F. Correlation coefficient G. Permanent component (C-C*F) -Accounted for unob. Schooling Factor I. Tranitory component (ame a B) Degree of wage uncertainty (G+I) Unoberved heterogeneity(c+e- G-I) A the reult in table 6 how, eentially all inequality meaure are maller for women than for men, in mot cae quite ubtantially o. The women that we now included are working full time over the entire period of analyi and therefore, by contruction, the variability of their wage mut be lower than thoe of male who are allowed to experience unemployment pell with the conequent udden fall of income and till be part of the ample. Thi i alo reflected in the very low value of tranitory volatility. A for men, potential wage inequality i lower than oberved

25 wage inequality. Both oberved and potential wage inequality are increaing with education level, jut a for men. The correlation coefficient hown in table 6c are bigger than before, but till much maller than thoe calculated by Chen and truncation and election adjutment have minimal impact on permanent component. The mot affected category i college drop out whoe permanent component ha a 8% decreae. Potential wage inequality i completely dominated by uncertainty, even tronger than for men; unoberved heterogeneity i virtually abent. Uncertainty, jut a for men in our etimate, i increaing in level of education. VI. Etimation on Britih data The Britih Houehold Panel Survey (BHPS) i an annually collected urvey that begun in Every year a repreentative ample of 5,500 houehold, containing approximately 10,000 individual, i interviewed. If a member of the original ample plit-off from hi original family, he i followed in the new houehold and all adult member of the new family are interviewed a well. Alo new member joining a elected family are added to the ample and children are interviewed once they reach age 16. Further extenion to Welh, Scottih and Northern Irih familie increaed the ample ize to 10,000 houehold acro the UK. We could acce the urvey until 008; therefore 18 wave are included in our analyi. A the required unemployment data are not available to u, we ued number of ibling in the family a intrument for chooling. An additional brother/iter will limit the hare of family income dedicated to a particular child education. Familie might decide to pay only for the education of thoe children who how a better inclination for tudie. Then, number of ibling will be negatively correlated with chooling year and probability to acce higher educational level. We recontruct the number of ibling for thoe young individual who were till living with their parent in the firt year of the urvey. Our ample i limited to thoe individual that were claified a on in the firt wave (we focued on men for the uual reaon). Our ample i, for thi reaon, reduced to 16,359 individual. From the original ample, 7,795 female were deleted. Additionally, we had to drop 1,674 individual that have 3

26 no information on income and 1,3 obervation lacking information on work experience. Our final ample count 1,403 time-individual combination. The BHPS doe not provide any meaure comparable to the AFQT core collected in the NLSY nor any other proxy plauibly related to ability. An additional difference between BHPS and NLSY i how earning are recorded: monthly intead of hourly earning. Thi will change the cale of tranitory and permanent component that will be preented later on. A. Britih educational ytem Compulory education in the UK lat for 11 year, from age five until age ixteen. It i divided in four key tage. The firt two year (age five to even) compoe the firt tage; the following four year (from even to ten) the econd and along with the firt tage it contitute primary education. The third (3 year from eleven to thirteen) and fourth ( year from fourteen to fifteen) key tage form, altogether, the econdary education. At the end of econdary education the GSCE (General Certificate for Secondary Education) i awarded in pecific ubject. Often, a good core in the GSCE i a requirement for acce to further education. A-level (Advanced Level of General Education) are the firt degree of noncompulory education and are a prerequiite for acce to academic coure in UK intitution. They take two year for completion, from age 16 to age 17. Univerity education i divided in two cycle. The firt award a Bachelor degree and generally lat three year, while the econd lead to a Mater degree and take in mot cae one year. Along with the tandard tertiary education, a number of other profeional higher education uch a the Pot Graduate Certificate in Education (PGCE) or the Bachelor of Education (BEd) or nuring degree exit. B. Wage variance in Britih data In table 7 we only preent a ummary of the reult 18. Education i divided in ix categorie: no qualification, vocational econdary education, high chool education, A-level qualification, vocational tertiary education and college education or above. Secondary vocational education i a reidual category where we placed all repondent who declared to have accomplihed econdary education, but have not 18 Decriptive tatitic along with etimate of firt-tage and wage regreion are available from the author. 4

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