Generalists and Specialists, Ability and Earnings *

Transcription

1 Generalit and Specialit, Ability and Earnin * by San-Hyop Lee, Univerity of Hawaii-Manoa Workin Paper No February 2005 (revied) Abtract The comparative advantae model developed in thi paper predict eneralit enjoy a hiher rate of return to their overall abilitie than pecialit, but they mut alo bear a penalty due to any imbalance in abilitie. The prediction are teted uin tet core data from the NLSY. The reult how that individual with balanced tet core acro ubject are more likely to chooe job in manaerial, ale, and clerical occupation. In thee occupation, individual with more balanced tet core receive ubtantially hiher earnin than thoe with unbalanced tet core. In contrat, individual with hihly unbalanced tet core are more likely to chooe job in profeional, craft, and operator occupation, althouh the extent of imbalance doe not inificantly affect earnin in thee occupation. JEL Claification: J23, J24, J31 Keyword: heteroeneou ability, occupational choice, conitive kill, tet core. Correpondin Author:San-Hyop Lee, Department of Economic, Univerity of Hawaii-Manoa, 2424 Maile Way, Saunder Hall Room 542, Honolulu, Hawaii, U.S.A [phone] (808) [fax] (808) <leean@hawaii.edu> * I would like to thank workhop participant of the Univerity of Hawaii for their comment. The input from Edward Lazear i ratefully acknowleded. My pecial thank to Andrew Maon for hi helpful comment and uetion. Dolore Sanchez and Hui Huan provided able reearch aitance.

2 I. Introduction Althouh reearcher have identified ability or natural talent a the principal determinant of earnin, few conider the extent to which different apect of ability affect earnin. For example, the importance of analytical kill, oral kill, mechanical comprehenion, coordination, and manual dexterity hould matter to varyin deree acro occupation. There are job for pecialit which require a inle pecific talent. In thee job, natural ability ha a tron comparative advantae and earn individual hih return on their inle talent (Roen, 1981). Thu, the choice of pecialit job make other talent redundant. There are alo job for eneralit which require a comparative advantae in a wide rane of abilitie. When individual poe a broad rane of talent uch a intellience, enery, and other enerally valuable trait, they ain by chooin thee job (Lazear, 2002; Murphy et. al., 1991). Thu, the productivity of a eneralit i retricted by the peron limited poeion of variou abilitie, not by the peron inle talent. Conventional wae equation do not capture the difference between the two type of individual. Link between heteroeneou ability, earnin, and occupational choice have been addreed by two approache under the comparative advantae framework. One approach treat human capital a a variety of heteroeneou output produced by variou input, a in the cae where the comparative advantae of an individual talent determine the field of tudy (Groer and Eide, 1995; Montmarquette et. al. 2002; Palin and Rufolo, 1990; Berer, 1988). Another approach i a job choice model which decribe how people ort into ector or occupation that cater to their peronal trenth (Lazear, 2002; Gould, 2002; Heckman and Sedlacek, 1985). Both model, however, preume that the choice of the field of tudy or occupation i di- 1

3 rectly linked to their anticipated earnin. Surpriinly, little i known about how different abilitie tranlate into earnin difference. Thi i the motivation for further reearch. Thi paper provide a theoretical idea of how individual with heteroeneou endowment are paid differently and how thi lead to different occupational choice. The comparative advantae model developed in thi paper predict that balance of one abilitie ha a ditinct effect on the emerence of earnin inequality between and within occupation. Generalit enjoy a hiher rate of return to their overall abilitie than pecialit, but they mut alo bear a penalty due to any imbalance in abilitie. Specialit receive a lower rate of return to their overall ability than eneralit, but they alo receive a poitive return to any imbalance in abilitie. Thu, individual who have balanced ability are more likely to chooe certain occupation that require a comparative advantae in a number of different talent. The model i etimated uin the National Lonitudinal Survey of Youth (NSLY). The data et contain information on ten tet core which are ued to meaure everal dimenion of abilitie. Althouh thee tet core are error-ridden noiy meaure, they are till preferable to the rade of MBA tudent (Lazear, 2002) or GRE tet core (Palin and Rufolo, 1990) becaue the ASVAB tet are iven to individual when they are relatively youn. The youn are le likely to have firmed career plan; i.e., the ASVAB tet core are le likely to be endoenou variable. The main empirical findin i that the effect of imbalance in abilitie, a meaured by pread or tandard deviation of tet core, i different by job. The pread of tet core ha a inificant neative effect on earnin in manaerial, ale, and clerical occupation, uetin that individual with hiher imbalance of conitive kill receive lower earnin than thoe with balanced abilitie in thee eneralit occupation. Thu, an individual with lower variation in tet 2

4 core acro ubject i more likely to chooe thee occupation. In contrat, individual with hih variation in tet core are more likely to chooe job in profeional, craft, and operator occupation. The pread of tet core ha no inificant effect on earnin in thee pecialit occupation. In the remainder of thi paper, ection II decribe the model. Section III dicue data. Reult are preented in ection IV. Section V conclude the paper. II. Human Capital Model with Heteroeneou Ability Determinant of Earnin in Each Occupation The comparative advantae model developed in thi paper elaborate Lazear (2002) model of occupational choice by eneralit and pecialit. Lazear aume that there are two type of individual kill, denoted by µ 1 and µ 2. For eneralit job, both kill are eential and they are not ubtitutable for each other. For pecialit job, only one type of kill i required. An individual chooe a job for either pecialit or eneralit receivin earnin a follow: (1) w w = max( µ, µ ) 1 2 = θ min( µ, µ ) 1 2 where the ubcript repreent pecialit, eneralit, and the parameter θ i a market premium to eneralit. The parameter θ i aumed to be reater than one. Otherwie, the earnin of a pecialit alway exceed that of a eneralit and no one would chooe a eneralit job. Lazear applie the model to the job choice between entrepreneur and employee. The point of Lazear model i that entrepreneur are jack-of-all-trade ; they mut be killed in a number of different area. 3

5 The Lazear model i readily eneralized to n type of abilitie. 1,2 Earnin of pecialit and eneralit are iven by: (2) w w = max( µ, µ,..., µ ) 1 2 = θ min( µ, µ,..., µ ) 1 2 n n Aumin wae are tochatic, equation (2) can be rewritten a (3) w w = µ + δ + ε = θµ θ( δ + α) + ε where the averae level of ability µ = µ n n i and the diperion or pread of ability i= 1 δ = µ max µ = min µ µ α. The term α i the kewne of ability ( max min + ) where 2 µ ( µ µ ) max µ and min µ repectively repreent the maximum and the minimum talent of an individual. Term ε and ε denote diturbance term, both of which are aumed to be jointly normally di- 2 2 tributed with zero mean and variance of σ and σ, repectively. 3 Equation (3) conciely ummarize the economic content of our theory and ditinuihe it from the conventional human capital model. It predict that individual earnin depend on the firt, the econd, and the third moment of ability (it mean, variance, and kewne). With θ reater than one, eneralit enjoy hiher return to their overall ability ( µ ) than pecialit do, but they mut bear a cot due to any imbalance (δ ) of their abilitie. For pecialit, there will be 1 We alo aume that all n type of abilitie are eential and they are not ubtitutable for each other for eneralit job. For pecialit job only one type of ability i required. In practice, there i a pectrum of job between thee two extreme cae. The imple model can be eaily extended to the cae of n job, however, where each job require different number of abilitie; the firt job require only one type of ability, the econd job require two type of ability, and o on. 2 In thi paper, the term ability encompae both enetic difference and difference produced by early childhood experience. Althouh the concept of ability i ditinct from kill, for many purpoe, uch ditinction make little difference. 4

6 poitive return to both overall ability and pread. Specialit receive lower return to overall ability than eneralit but thee lower return are compenated by a poitive return for their pecialized ability. 4 Fiure 1 illutrate the wae determination for eneralit and pecialit. The iowae curve indicate combination of µ and δ alon which an employer offer ame wae rate for the eneralit job ( w ) and the pecialit job 0 0 ( w ). The iowae curve lope downward for pecialit job, and it lope upward for eneralit job. A peron with ability propertie at point E 0 will be offered the ame wae from both job. On the other hand, a peron with ability propertie in reion I i better off if he chooe a pecialit job, but he i wore off if he chooe a eneralit job. Likewie, a peron in ability reion II will earn hiher than 0 0 w w ( = ) no matter which job he chooe. <Fiure 1 about here> Occupational Choice A rational individual will elf-elect the occupation which yield the hihet earnin. From equation (3), the earnin of eneralit are reater than pecialit if and only if: (4) ε ε < [( θ 1) µ ( θ + 1) δ] Thu, the probability of an individual bein a eneralit i iven a (5) Pr[ I = ] = Pr[ ν < z] =Φ( z) 3 Althouh equation (3) doe not include meaured human capital a a predictor of earnin, the empirical pecification include human capital meaure uch a year of choolin and experience. 4 Our model doe not predict whether α will be poitive (riht-kewed) or neative (left-kewed). Thu for impler model we inore it and include it into the diturbance term. 5

7 where the denity function [( θ 1) µ ( θ + 1) δ] z =, σ v v ε ε =, v σ v σ repreent the tandard deviation of ε ε, and Φ i the cumulative tandard normal ditribution function with ( θ + 1) Φ (0) = 0.5. That i, when z equal zero ( µ = δ ), a peron i indifferent between takin a ( θ 1) eneralit or pecialit job. Fiure 2 illutrate the theory of job choice. The offer curve indicate combination of µ and δ that yield the ame level of earnin in both job. The fiure how three level of iowae curve. The hiher iowae curve, w 1 ( = w 1 ), indicate a hiher earnin level than 0 0 w w ( = ), and 2 2 w w ( = ) correpond to a hiher earnin level than 1 1 w w ( = ). E 0, E 1, and E 2 correpond to each iowae curve and the offer curve i a locu of E. <Fiure 2 about here> The probability of chooin between eneralit and pecialit job depend on µ and δ. ( θ + 1) A peron i more likely to chooe a eneralit job when z i poitive ( µ > δ ), in the reion which lie to the left and above the offer curve. Given θ, thi condition i more likely to be ( θ 1) met a µ increae and δ decreae. Likewie, a peron i more likely to chooe a pecialit job ( θ + 1) if z i neative ( µ < δ ), in the reion which lie to the riht and below the offer curve. ( θ 1) Given θ, thi condition i more likely to be met a µ decreae and δ increae. The probability of chooin a eneralit or pecialit job alo depend on the market premium to eneralit (θ) which can be individual-pecific. Even a peron with a pecific extraordinary talent and hih δ can become a eneralit if hi market premium a a eneralit i ufficiently hih. An example 6

8 miht be Bill Gate who i better off a a CEO than a technician. A ucceful collee dean miht be another example. Althouh both tarted a pecialit, their market premium a eneralit wa hih enouh to offet the neative effect of hih δ. Likewie, even with well-balanced ability (low δ), ome people till chooe pecialit job if their market value a ucceful eneralit i very low (θ bein cloe to one). If thi i the cae, their poitive return to pecialization till offet the market return a a eneralit. The parameter θ can be endoenouly determined by individual µ and δ. Two partial derivative are of interet to u. (6) Pr( I = ) φ = [ θ µ µ + ( θ 1)] µ σ Pr( I = ) φ = ( θµ δ 1) δ σ v v where φ i the tandard normal denity function, θ θ θµ = and θδ =. All the in in equa- µ δ tion (6) are unambiuouly determined if θ > 0 and θ < 0 ; i.e., accountin for endoeneity of µ δ θ doe not alter the baic implication of our model althouh the offer curve may be no loner a 1 θ traiht line. If, however, θµ < < 0 then the probability of chooin a eneralit decreae µ a µ increae. Likewie, if 1 < < θ, then the probability of bein eneralit increae a δ µ 0 δ increae. In thee cae, the offer curve will contain a backward-bendin (downward lopin) portion. The parameter θ can alo be determined by ocial factor uch a dicrimination. For example, if women face lower θ due to ender-biaed hirin, then the offer curve ( ) will be θ + 1 θ 1 7

9 teeper for women than for men. Becaue the area between vertical axi and the offer curve indicate the proportion of eneralit in the labor market, the ratio of women eneralit to women pecialit will be maller than that for men if thi i the cae. 5 Earnin Diperion and Self-Selection Occupation are not randomly ained acro the population; rather, individual make their own job choice. Given the variation in an individual productivity acro job, elfelection will influence oberved wae becaue a rational individual will elect the alternative which yield the hihet utility. In thi context, elf-election will caue the diturbance term in the wae equation to be correlated with the job deciion. Aume that would-be eneralit know θ before they commit themelve on whether they chooe a eneralit job. The expected income of a eneralit who chooe a pecialit job, Ew ( I= ), and the expected income of eneralit, Ew ( I= ), are repectively iven a: (7) σ σ 1 Ew ( I= ) = µ + δ + ( ρ ) λ σ k σσ Ew ( I= ) = θµ θδ + ( k ρ) λ σ v v 5 People have aked why there have been few women orchetra conductor while there have been many reat women pianit and violinit in orchetra. Our theory uet that women miht face lower θ than male a a conductor (eneralit) and thereby the offer curve for women i teeper than that for men. The lower θ may be a form of ex-biaed hirin. A blind-audition ueted by Goldin and Roue (2000) demontrate that there exit exbiaed hirin in orchetra and the blind-audition have helped eliminate the ender dicrimination. However, it will be difficult to demontrate and eliminate ex-biaed hirin of eneralit in orchetra in part due to it technical difficulty. 8

10 where ρ σ =, σ Cov( ε, ε) σ σ =, k σ =, and σ φ( z) σ σ λ =. Becaue and λ are both Φ ( z) σ v poitive, the earnin of the eneralit and the pecialit depend on value of ρ and k. For example, if the variance of earnin i hiher amon eneralit than amon pecialit, (i.e., 2 2 > > ), and if 1 ρ k k 1 or σ σ 1 < <, then the two election term ( ρ and k ρ ) are both k k poitive. In thi type of election, ome pecialit benefit by chooin a eneralit job and they outperform the oriinal eneralit. 6 A major concern in the literature on elf-election ha been with tetin for the electivity bia. Thee are tet for σ σ 1 σ ( ρ σ ) = 0and ( k ρ) = 0. However, an equally important σ k σ v v iue here miht be how electivity correction affect the etimated coefficient of µ and δ. Becaue [( θ 1) µ ( θ + 1) δ] φ( z) z = and λ =, the direction of bia for µ i oppoite to δ and it σ Φ ( z) v alo depend on the in of 1 ρ and k ρ. 7 For example, if the electivity term i poitive k and inificant, then the etimated coefficient under OLS etimation will be biaed downward for µ and biaed upward for δ. The followin ection dicue how the variable are contructed and how the model i teted. 6 Likewie, if k < 1 and k < ρ < 1/ k, then the two election term are both neative. In thi type of election, the eneralit job draw people from lower tail of income ditribution of pecialit and do not perform well a a eneralit. 7 We can how Cov( δ, λ ) >0 and Cov ( µ, λ ) <0. Proof i available upon requet. 9

11 III. Data Contruction The ource for etimation i the National Lonitudinal Survey of Youth Cohort (NLSY) data. The NLSY wa firt conducted in 1979 for individual aed 14 to 22, with 12,686 repondent. The cohort wa re-urveyed every year thereafter. The ample ued in thi analyi conit of male who were employed at leat once between 1979 and For etimation purpoe, all twenty-one year data et are pooled and year dummie are included to control for yearpecific macroeconomic effect. Member of the armed force, farmer, private houehold worker, and public ector worker are excluded. To avoid outlier problem, thoe who report wae that are le than one-half of the federal minimum wae each year, or reater than twenty time the minimum wae are alo excluded. For the purpoe of the paper, the NLSY data have very ueful feature. The advantae of the NLSY i that it contain variou tet core which can be ued a indicator of ability. The indicator of ability ued are Armed Service Vocational Aptitude Battery (ASVAB) tet core. Thee tet are reularly adminitered to ait in placement of U.S. military recruit. Thee tet conit of ten cateorie: pararaph comprehenion, eneral cience, arithmetic reaonin, mathematic knowlede, word knowlede, mechanical comprehenion, numerical operation, electronic information, auto and hop information, and codin peed. The tet core ued in thi tudy are obviouly error-ridden and noiy meaure of variou conitive kill. However, thee tet core may have an advantae over alternative. Lazear (2002) teted hi job choice model uin a data et of the MBA tudent at Stanford Univerity. The data election uet that individual have already inveted ubtantially in their choen career path. Thu, the key independent variable for job choice in the data et, uch a coure tudent have taken and the pread of rade between coure, may not be exoenouly iven. 10

12 The cauation miht be revered: it could be their future job plan which determine tudent trateie on curriculum choice and tet core. 8 In contrat, the ASVAB tet core are iven to repondent when the repondent are till youn, ae in Thu, the tet core are le likely to meaure achievement and more likely to meaure endowment, epecially for individual aed in 1980 or thoe who have never entered collee. 9 We will addre the related empirical iue in the next ection. In thi tudy, ASVAB tet core were converted to the 1980 tandard equivalent cale. Becaue thee caled core may differ acro ae roup becaue of ae (year) effect, ae effect are removed from the core by rerein each equivalent cale on a et of ae dummie. Then, the individual tandardized reidual i ued a the meaure. The variable of the pread of tet core for each individual contructed in thi way i not correlated with the averae tet core. The imple correlation coefficient i 0.011, indicatin that there i little linear correlation between thee two variable. Given the hih correlation amon ome tet core, it miht be more enible to cateorize them into a couple of imilar ability meaure. In particular, ome of the tet core miht reflect communicative and reaonin ability, while other reflect knowlede relevant to performin well on particular job. Thu, thi paper conider three type of abilitie: academic ability, non-academic ability, and operatin ability. The claification looely follow that ued by 8 Palin and Rufolo (1990) ue math and verbal core from the Scholatic Aptitude Tet (SAT) and the Graduate Record Exam (GRE) to examine the choice of the major, occupation, and earnin. Aain the GRE core could be a meaure of achievement the tudent acquired durin their education, rather than a meaure of initial endowment of a peron. In addition, Palin and Rufolo do not include any other independent variable in their choice of field of tudy model due to limited information of the data. Althouh they arue that it i not neceary to ditinuih between natural endowment and other variable in eneratin empirical tet of the model, it would be better to control for other factor uch a race, ender, and other characteritic a control variable. 9 A a reult, the NLSY enable u to conider youn worker with all level of choolin in the U.S wherea both Lazear and Palin and Rufolo conider job choice of only collee tudent or raduate tudent. 11

13 Blackburn and Neumark (1995). 10 Thi paper calculate the mean core of each cateory firt, then ue the rand-mean of the three mean core a the proxy for the level of conitive kill. The difference between maximum and minimum mean value i then ued a the meaure of individual imbalance of conitive abilitie. The reult may depend on how we define academic ability, non-academic ability, and operatin ability. Therefore, thi tudy alo employ other meaure, uch a the tandard deviation of the ten tet core to check the robutne of the reult. Thi paper ue occupation a a meaure of job requirin different talent and kill. The ainment of worker to different occupation i baed on direct repone in the urvey to the occupation of worker cateorie. Unfortunately, the wae model contructed in ection II doe not tell u which occupation are for eneralit and which are for pecialit, per e. One miht arue that manaerial job are more likely to be for eneralit than, for example, profeional or craft occupation. One could alo arue that manaerial reponibility i more or le cloe to that for entrepreneur althouh manaer differ from entrepreneur in term of ownin the aet they produce. 11 Table 1 preent the mean and tandard deviation of variable for each occupation. The imbalance of ability, meaured by the pread between maximum and minimum tet core (Max- 10 The academic tet are aumed to be pararaph comprehenion, word knowlede, mathematic, arithmetic, and eneral cience; the nonacademic tet are mechanical knowlede, numerical operation, electronic, and auto hop knowlede; operatin ability i codin peed. 11 One could ue an indicator of entrepreneurhip a a meaure of eneralit job a Lazear (2002) did. However, there i no information about entrepreneurhip in the NLSY. One miht arue that elf-employment could be an alternative variable. But the definition of elf-employed, both at the theoretical and empirical level, i quite different from entrepreneur. A Lazear (2002) arue, a elf-employed peron need not have any other employee and the kind and broader rane of ability that are neceary for real entrepreneurhip may not be important at all for, ay, a elf-employed handyman who work alone. In addition, the earnin of elf-employed are not alway well-defined in the NLSY. The elf-employed peron miht run an incorporated buine. In that cae, ome or all of the reported elf-employed buine income could be earnin. Furthermore, to ome extent optin for elf-employed depend on other economic factor, uch a tax evaion, overall buine condition, or employee-protection reulation (Hamermeh, 1990; Blau, 1987; Fairlie and Meyer, 1994). There i other evidence that liquidity contraint play the mot important role for bein elf-employed (Evan and Jovanovic, 1989). Unfortunately, the NLSY contain little information on any of thee variable. 12

14 Min), i hih for craft, operatin, and profeional job, and low for manaerial, ervice, and clerical job. Furthermore, there i no apparent relationhip between Max-Min and the mean of tet core or the year of choolin. Worker in profeional and manaerial job both have hiher tet core than other worker, but the pread (Max-Min) for manaerial worker i lower than averae while the pread for profeional worker i hiher than averae. <Table 1 about here> Fiure 3 how the mean and pread (Max-Min) of tet core averaed by occupation. The mean of lo hourly wae appear in parenthee. Occupation are broken into four cateorie by mean and pread of tet core. Profeional job are in Group I, where both the mean and the pread of tet core are hiher than averae. Worker in manaerial, ale, and clerical job have a mean that i hiher than averae, but a pread that i lower than averae. Worker in craft and operatin job have the hihet pread, but their mean are below averae. The fiure demontrate that both the mean and the pread are critical to roupin occupation. The craft occupation i cloet to ervice and clerical job if we only conider averae tet core, but the craft occupation i cloet to operator if we conider both the mean and the pread of tet core. <Fiure 3 about here> The earnin pattern i alo an interetin feature of Fiure 3. Within roup or controllin for pread, occupation with hiher averae tet core have hiher earnin. Acro roup, however, the relationhip i much weaker a i evident from the comparion acro Group II and Group IV. The averae tet core i much hiher amon ale occupation than amon craft occupation, but craft job pay more than ale occupation. Likewie, the averae tet core i hiher amon clerical job than amon operator occupation, but the operator occupation pay more than clerical job. Comparion acro Group III and Group IV yield imilar anomalie. 13

15 Operator job pay much more than ervice job, on averae, even thouh ervice worker have hiher tet core. The difference in year of choolin and averae tet core cannot entirely explain why ale and craft occupation pay imilar wae on averae. A can be een from Table 1, the averae year of choolin are much hiher amon worker in the ale occupation than amon worker in the craft occupation and it i alo hiher for clerk than for operator, on averae. Union memberhip doe not explain everythin either. For example, the percentae of clerk (17%) covered by collective barainin i only lihtly lower than that of operator (20%). One traditional approach to explainin earnin differential acro occupation i to explain it a a form of equalizin difference baed on job characteritic. Another approach i to explain them a a form of return to heteroeneou human capital, which i the earnin model developed in thi paper under the comparative advantae framework. Accordin to the latter model, worker in ervice and craft job are imilar to each other in term of their averae required ability, but they are very different from each other in term of the ditribution of their poeed abilitie. The job deciion and earnin determination, however, will depend on many other factor in addition to the level and the rane of abilitie meaured by the mean and the pread of tet core. Therefore, to ain better iniht we turn to the rereion reult. IV. Reult Rereion Reult for Job Choice Model Becaue there i a pectrum of occupation requirin different level and cope of abilitie, we aume that the election of worker into each occupation ha the tructure of a multi- 14

16 nomial loit model, rather than a binary dependent model. The probability that each alternative job will be choen can be calculated by: (8) Pr( I = ) = i exp(z γ ) (1 exp(z γ )) + S where I i i an indicator of each individual choice of occupation, and Z i the et of variable in the multinomial loit equation which include both the pread (Max-Min) and the mean of tet core. Specifically, the independent variable include year of choolin, actual experience at the beinnin of the job and it quared term, dummie for individual demoraphic characteritic (married, and non-white), reional dummy variable (urban, North Central, Wet, South, and SMSA dummie), and year-dummie. All etimate in thi paper were obtained uin the conitent variance-covariance matrix etimator of White (1980). The tandard error are thu robut to heterocedaticity. Table 2 preent the coefficient of the firt-tae multinomial loit etimate. The bae cateory i laborer which i cloet to median pread of tet core. The coefficient are reported in the relative rik form. For example, the etimated coefficient of the black worker dummy in the profeional occupation i 1.023, implyin that the probability of chooin a profeional job over a laborer job i 2.3 percent hiher for black relative to white. The point etimate of the pread of tet core i tatitically inificant at the one percent level in all occupation cateorie, uetin that the balance amon conitive kill doe matter in the choice of job. The Max-Min i poitive in profeional, craft, and operatin job. It i neative in manaerial, ale, clerical, and ervice job. Thu, compared to laborer, thoe who have a hiher pread of tet core are more likely to chooe profeional, craft, and operatin job. Thoe who have 15

17 lower pread of tet core are more likely to chooe job in manaerial, ale, clerical, and ervice occupation. <Table 2 about here> The pread of tet core affect job choice in a way that i ditinct from the effect of year of choolin and the averae tet core. Thoe with more year of choolin and hih averae tet core are more likely to chooe profeional and manaerial job for example; but thoe with divere tet core are more likely to chooe a profeional and le likely to chooe a manaerial job. OLS Etimate of Wae Equation In the next, the paper explore how the pread of tet core affect earnin in each occupation. Panel A of Table 3 preent the OLS rereion reult of wae equation by occupation. The dependent variable i lo hourly wae of an employee. The independent variable are ame a in the occupational choice model. 12 <Table 3 about here> The imbalance amon conitive kill, meaured by the pread of the variou tet core, ha a inificant neative effect on earnin in manaerial (-0.023), ale (-0.065), and clerical ( ) job. Of coure, the empirical reult preented here hould be interpreted with caution iven that potentially noiy meaure of the proxy variable. Nonethele, let take the etimate 12 Althouh everal pecification iue have been raied with repect to the wae equation, thi tudy ue a parimoniou pecification. For example, one may include tenure and it quare term. However, incluion of tenure variable in the wae equation i controverial ince they are potentially endoenou. Another variable for conideration i etablihment ize. We do not have any prediction how incluion of thi variable miht affect the etimated coefficient. However, it i far from clear whether it i appropriate to include the etablihment ize variable in the equation, ince etablihment ize i alo an outcome variable of worker job choice. 16

18 eriouly and ue them to evaluate the impact of the imbalance of ability on earnin. When evaluated at the mean of the variable, the pread of the variou tet core explain about 2 percent of earnin for manaerial job and 1.5 percent for clerical job. The neative impact i biet for ale job, about 6 percent of earnin. The etimated coefficient i mall and tatitically ininificant for all other occupation. For example, the coefficient of the pread of tet core in the profeional and the operator occupation are poitive, but they are tatitically ininificant and very mall a well. Thi reult may not be urpriin accordin to the model in thi tudy, becaue the compenation for pecialit (δ) due to imbalance of the ability hould be much maller than the penalty for eneralit (θδ). Thu, the reult are conitent with the theoretical prediction a well a the reult from the multinomial loit model. Senitivity analye are ued to check the robutne of the wae rereion reult. Firt, we ue the tandard deviation of the ten tet core to ae the enitivity of the reult to the method by which pread i meaured. The reult are reported in Panel B of Table 3. Second, we ae the exoeneity of the tet core variable. A we arued, the ASVAB tet core are le likely to be an outcome of their collee education becaue the tet i iven to individual when they are till youn. However, the tet core, in part, reflect the collee experience of thoe enrolled in collee in To control for the potential endoeneity problem, the wae equation i re-etimated uin individual aed in 1980 and thoe who did not ubequently enroll in collee. Thee reult are reported in Panel C of Table 3. The reult chane lihtly. Uin the alternative meaure, the tandard deviation of tet core, chane the in for thoe in the labor occupation (Panel B). Retrictin the data et chane the in for ervice worker (Panel C). The variable i till ininificant in thee occupa- 17

19 tion, makin the reult qualitatively unchaned. However, the coefficient of the Max-Min variable in the manaerial occupation turn ininificant for the retricted ample, uetin that our meaure may not be entirely free from the exoeneity iue. Selectivity Correction Given variation in an individual productivity acro type of job, elf-election influence the oberved wae a well a the etimated coefficient. An important iue here i how job election affect the etimated coefficient of µ and δ. To addre thi iue, the wae equation i re-etimated uin the two-tae electioncorrection etimation procedure, known a the polychotomou choice model with electivity correction. The approach hould be viewed a jut illutratin the problem with the OLS etimation iven the potential problem of the approach (uch a the difficulty of findin compellin identifyin variable). Statitical aumption are baed on Lee (1982), in which the error in the lo wae rereion i normally ditributed, and i alo jointly normally ditributed with an appropriate tranformation of the error underlyin the multinomial loit model. The approach ued here involve etimatin eparate earnin rereion, allowin different election in each occupation. That i, a wae equation of the form in occupation j (9) ln( w ) = X β + ( σ ρ ) λ + ε j j j j j j j i etimated uin the two-tae election-correction etimation procedure, where σ i tandard deviation of the diturbance in the wae equation, ρ i correlation coefficient of the two diturbance in the two equation (the ector choice and wae equation), and λ i a electivity parameter. 18

20 In the firt tae, etimate of the electivity parameter are obtained from the multinomial loit model. Thi enable u to predict the electivity variable in each occupation which alo involve the appropriate tranformation of the error. In the econd, we can conitently etimate the wae equation by OLS after ubtitutin the etimated electivity variable into wae equation. 13 What i required to provide identification in the model i a et of variable that explain variation in the probability of bein in a pecific occupation, but doe not directly affect the current wae. Family backround could be uch a variable. Thi paper ue the primary occupation of father and mother in 1978 a intrument variable. Table 4 preent the coefficient of the econd-tae etimate of the wae equation. 14 The electivity term (invere Mill ratio) are only inificant for profeional, manaerial, ale, and labor occupation. The pread of the variou tet core i till only inificant in manaerial, ale, and clerical job and the electivity term are all poitive for thee occupation. The etimated coefficient i for manaerial, uetin that the previou OLS etimate without electivity correction (-0.023) i ubtantially biaed upward. The Hauman tet p- value i inificant at one percent level. The etimate for ale and clerical occupation uet that the OLS etimate of wae equation without electivity correction alo bia the coefficient upward althouh the bia i tatitically ininificant. The direction of bia for the mean of tet core ( µ ) under OLS etimation without electivity correction i oppoite to that for the pread 13 Thi ubtitution implie that the aymptotic variance-covariance matrix reported by OLS will be biaed downward ince it doe not account for the amplin variability in the firt tae rereion. The aymptotic variancecovariance matrix i corrected by uin the method in Murphy and Topel (1985). 14 The etimated coefficient of the fit tae are imilar to the multinomial loit reult in Table 3 and they are not reported here. Chi-quare tatitic how the father and mother occupation are hihly inificant in the multinomial loit model, indicatin that mall ample biae may not be an iue (Bound, et al., 1995). The etimated effect of the father and mother occupation on the child ame occupation i poitive and jointly inificant in all occupation, uetin that there i a poitive correlation between thee variable and worker probability of current employment. 19

21 of tet core (δ ) for all three occupation, which i conitent with the theoretical prediction. However, for occupation with ininificant δ, no inificant pattern of bia i found. <Table 4 about here> V. Concluion In hi influential tudy, Jutu von Liebi, enerally credited with bein the Father of Fertilizer Indutry, propounded The Law of the Minimum. It tate that The yield potential of a crop i like a barrel with tave of unequal lenth. The capacity i retricted by the lack of a inle element, even thouh there may be ufficient quantitie of all other nutrient. (Jutu von Liebi The Law of the Minimum) Thi iniht may be equally applicable to human capital: the productivity of an individual in a certain job may be retricted by hi or her minimum innate ability, even thouh there may be ufficient quantitie of all other talent. Thi i epecially true for eneralit who hould be veratile in many thin. Varyin rane of ability may have a ditinct effect on earnin dependin on whether the job i for a eneralit or pecialit. Thi poibility i nelected by the conventional human capital model. Thi paper contruct a model and tet whether individual with balanced conitive kill earn more in ome occupation. Uin an individual pread of tet core a a meaure of the balanced conitive kill, we find ditinct and ubtantial effect on earnin and job choice, independent of the effect of year of choolin and averae tet core. Individual with balanced tet core are more likely to chooe job in manaerial, ale, and clerical occupation. For thee occupation, individual with more balanced tet core receive ubtantially hiher earnin than thoe with unbalanced tet core. In contrat, individual with a hih pread of tet core 20

22 are more likely to chooe job in profeional, craft, and operator occupation. For thee occupation, the pread of tet core doe not inificantly affect earnin. The ample ued in thi analyi conit only of male. Althouh it i not a topic of thi paper, an interetin quetion i whether the reult are robut acro ender. The anwer i no. Women with more balanced tet core receive uually lower earnin than thoe with unbalanced tet core even for eneralit job, uetin that mot women are pecialit. It i unclear exactly what mechanim would lead to the reult. One poible explanation i that the market premium to eneralit (θ) i much lower for women than men. Thi i an iue that warrant further attention in future reearch. Given the error-ridden and noiy meaure of tet core a proxy variable of variou abilitie, the reader hould reard the etimated parameter in thi paper a uetive. Thi tudy i not immune to the widely noted hortcomin of uin proxy variable. One may even attribute everythin we have oberved to the ue of proxy variable. However, a more natural and impler way to interpret the reult i that the imbalance of conitive kill, a meaured by the pread of tet core, doe have ditinct effect on earnin and job choice. Reference Berer, M.C Predicted future earnin and choice of collee major, Indutrial and Labor Relation Review, 41: Blackburn, M.L. and D. Neumark "Are OLS etimate of the return to choolin biaed downward? Another look," Review of Economic and Statitic, 77: Blau, D A time-erie analyi of elf-employment in the United State, Journal of Political Economy, 95: Bound, J., D.A. Jaeer, and R.M. Baker Problem with intrumental variable etimation when the correlation between the intrument and the endoenou explanatory variable i weak, Journal of American Statitical Aociation 90, pp

23 Evan, D.S. and B. Jovanovic An etimated model of entrepreneurial choice under liquidity contraint, Journal of Political Economy, 97: Farlie, R. and B. Meyer The ethnic and racial character of elf-employment, NBER Workin Paper No, 4791 (Cambride: National Bureau of Economic Reearch) Goldin, C. and C. Roue Orchetratin impartiality: The impact of "blind" audition on female muician, American Economic Review, 90: Gould, E Riin wae inequality, comparative advantae, and the rowin importance of eneral kill in the United State, Journal of Labor Economic, 20: Groer, J. and E. Eide Chane in collee kill and the rie in the collee premium, Journal of Human Reource, 30; Hamermeh, D Shirkin or productivity chmoozin: wae and the allocation of time at work, Indutrial and Labor Relation Review, 43:S121-S133. Heckman J. and G. Sedlacek Heteroeneity, areation, and market wae function: An empirical model of elf-election in the labor market, Journal of Political Economy, 93: Lazear, E.P Entrepreneurhip, NBER Workin Paper No.9109 (Cambride: National Bureau of Economic Reearch). Lee, L-F Some approache to the correction of electivity bia, Review of Economic Studie 49:3, pp Montmarquette, C How do youn people chooe collee major? Economic of Education Review, 21: Murphy, K.M., A. Shleifer, and R.W. Vihny The allocation of talent: Implication for rowth, Quarterly Journal of Economic, 106: Murphy, K.M. and R.H. Topel Etimation and inference in two-tep econometric model, Journal of Buine and Economic Statitic 3:4, pp Palin, M., and A.M. Rufolo Heteroeneou human capital, occupational choice, and male-female earnin difference, Journal of Labor Economic, 8: Roen, S The economic of upertar, American Economic Review, 71: White, H.J A heterocedaticity-conitent covariance matrix etimator and direct tet for heterocedaticity, Econometrica, 48:

24 µ II 0 w = θµ θδ w w III 0 w w E I w w IV w w 0 w = µ + δ Fiure 1. Iowae Curve: the comparative role of the mean and the pread of abilitie alon which an employer offer ame wae rate for the eneralit job and the pecialit job. δ µ ( θ + 1) µ = δ ( θ 1) 2 w E 2 2 w 1 w E 1 1 w 0 w E 0 0 w Fiure 2. Offer Curve: the combination of the mean and the pread of abilitie that yield the ame level of earnin in both job δ

25 Group II Manaer (2.156) Mean Profeional (2.260) Group I Clerical Sale 0.4 (1.750) (1.927) Spread (Max-Min) Service (1.535) Group III Labor (1.657) Operator (1.794) Craft (1.944) Fiure 3. Mean and pread of tet core by occupation Group IV

26 Table 1. Decriptive Analyi Profeional Manaerial Sale Clerk Craft Operator Labor Service Lo (Wae) (0.529) (0.594) (0.594) (0.436) (0.438) (0.415) (0.424) (0.400) Mean(ASVAB) (0.653) (0.702) (0.702) (0.794) (0.797) (0.809) (0.835) (0.903) Max-Min(ASVAB) (0.620) (0.596) (0.596) (0.565) (0.623) (0.580) (0.571) (0.561) Year of choolin (2.368) (2.231) (2.231) (1.979) (1.757) (1.719) (1.819) (1.913) Experience (5.107) (5.263) (5.263) (4.844) (5.209) (5.108) (4.880) (4.597) Married Union Black Urban SMSA North Eat North Central South Number of ob. 5,582 5,341 2,814 4,894 11,569 12,371 7,271 7,272 Standard deviation in parenthei.

27 Table 2. Multinomial Loit Etimate for Occupation Choice Profeional Manaerial Sale Clerk Craft Operator Service Mean(ASVAB) (28.13) (21.02) (15.28) (13.86) (15.83) (3.01) (0.93) Max-Min(ASVAB) (1.37) (4.80) (2.08) (3.96) (6.27) (2.00) (4.85) Year of choolin (53.15) (36.73) (32.11) (26.42) (1.25) (0.41) (12.10) Experience (9.76) (17.33) (5.92) (6.09) (15.80) (12.39) (0.27) Experience quared (4.76) (7.52) (0.78) (2.38) (9.21) (8.10) (0.39) Married (10.05) (12.48) (7.24) (2.98) (12.67) (13.21) (6.37) Union (15.32) (22.41) (18.10) (9.43) (5.67) (2.62) (12.79) Black (0.38) (5.55) (4.02) (3.82) (8.54) (1.91) (4.68) Urban (2.96) (3.06) (6.70) (4.80) (0.74) (2.53) (4.97) SMSA (11.71) (7.97) (7.14) (9.80) (3.96) (0.05) (8.39) North Eat (2.70) (1.87) (3.56) (4.26) (0.10) (0.12) (0.43) North Central (4.06) (5.40) (1.45) (2.37) (3.60) (2.26) (1.12) South (2.72) (2.54) (1.15) (4.96) (0.90) (1.10) (7.80) Reported a relative rik form. t-value are in parenthee. Other variable include year dummie. Total number of obervation i 57,114.

28 Table 3. Wae Rereion Reult by Occupation Profeional Manaerial Sale Clerk Craft Operator Labor Service Panel A. OLS Rereion Mean(ASVAB) (0.011) (0.011) (0.017) (0.008) (0.006) (0.005) (0.007) (0.006) Max-Min(ASVAB) (0.011) (0.010) (0.015) (0.009) (0.006) (0.006) (0.007) (0.008) Year of choolin (0.003) (0.003) (0.005) (0.003) (0.002) (0.002) (0.003) (0.003) Experience (0.006) (0.006) (0.009) (0.005) (0.003) (0.003) (0.004) (0.004) Experience quared (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) Married (0.013) (0.013) (0.021) (0.012) (0.007) (0.007) (0.010) (0.012) Union (0.022) (0.023) (0.033) (0.014) (0.008) (0.007) (0.011) (0.012) Black (0.019) (0.019) (0.028) (0.013) (0.010) (0.009) (0.011) (0.010) Urban (0.019) (0.016) (0.026) (0.018) (0.009) (0.008) (0.011) (0.013) SMSA (0.023) (0.018) (0.027) (0.018) (0.009) (0.009) (0.011) (0.013) North Eat (0.018) (0.018) (0.029) (0.015) (0.011) (0.011) (0.015) (0.014) North Central (0.017) (0.016) (0.028) (0.015) (0.010) (0.010) (0.014) (0.012) South (0.017) (0.016) (0.026) (0.015) (0.010) (0.010) (0.013) (0.013) Number of ob. 5,582 5,341 2,814 4,894 11,569 12,371 7,271 7,272 R-quared Panel B. Alternative meaure (Standard Deviation; S.D.) of ASVAB Mean(ASVAB) (0.011) (0.011) (0.017) (0.008) (0.006) (0.005) (0.007) (0.006) S.D.(ASVAB) (0.035) (0.033) (0.050) (0.031) (0.018) (0.018) (0.024) (0.025) Panel C. No-Collee Education in 1980 or Never Attended Collee Mean(ASVAB) (0.015) (0.014) (0.019) (0.009) (0.006) (0.006) (0.007) (0.006) Max-Min(ASVAB) (0.031) (0.027) (0.037) (0.021) (0.012) (0.012) (0.016) (0.017) Number of ob. 2,415 2,878 1,599 3,339 9,802 10,784 6,283 5,807 Standard error in parenthei. Total number of obervation i 57,114 for Panel A and B and 42,907 for Panel C. Other variable include year dummie.

29 Table 4. Selectivity Correction Etimate and Senitivity Analyi Profeional Manaerial Sale Clerk Craft Operator Labor Service OLS Reult Mean(ASVAB) (0.011) (0.011) (0.017) (0.008) (0.006) (0.005) (0.007) (0.006) Max-Min(ASVAB) (0.011) (0.010) (0.015) (0.009) (0.006) (0.006) (0.007) (0.008) Selectivity Correction Reult Mean(ASVAB) (0.015) (0.013) (0.015) (0.009) (0.006) (0.006) (0.009) (0.007) Max-Min (ASVAB) (0.011) (0.011) (0.007) (0.010) (0.007) (0.006) (0.007) (0.008) Invere Mill' Ratio (0.218) (0.308) (0.579) (0.409) (0.172) (0.170) (0.406) (0.213) Hauman Tet P-value for Mean Max-Min Standard error in parenthei. Total number of obervation i 57,114. Other variable include year dummie.