Comparatve Advantage, Informaton and the Allocaton of Workers to asks: Evdence from an Agrcultural Labor Market Andrew D. Foster and Mark R. Rosenzweg Unversty of Pennsylvana February 1996 he research reported n ths paper was supported n part by NICHD grant No. HD-28687. We are grateful to two anonymous referees for helpful comments and to Howard Bous for makng the data used n ths paper avalable to us.
o understand the occupatonal dstrbuton of workers characterzed by any set of observed characterstcs such as sex, heght, or skn color requres attenton to a varety of mechansms that have been dentfed n the lterature as determnng who gets what jobs. Among these are the operaton of comparatve advantage, the nfluence of preferences over occupatons by workers and over worker characterstcs by employers, and the effects of partal employer gnorance about workers' productvtes and thus the relance on statstcal averages. Gven that observed worker characterstcs may be correlated wth both ther own productvtes and preferences, may be arguments n employers' preference functons, or may provde employers wth partal nformaton on worker productvty n a settng characterzed by ncomplete nformaton, t s not surprsng that the relatve mportance of these factors has not been dentfed. One salent example of a strong relatonshp between a measurable worker characterstc and the task dstrbuton that has generated much controversy s the well-known dsproportonate allocaton of women to weedng versus other agrcultural actvtes n Asan agrculture. able 1 presents the allocaton of tme to agrcultural tasks based on detaled survey data from three Asan socetes - the Phlppnes, Inda and Pakstan - that show how women are "overrepresented" n weedng actvtes compared to men. hese data also suggest that the dfferentals n tme allocaton may be partcularly strong when women are engaged n actvtes compensated usng tme wages, compared to when ther compensaton may more drectly be related to ther productvty (self-cultvaton and pece-rate work). he reasons for ths salent feature of Asan agrculture, where the technology of producton s well known and the labor market s much less complex than n developed socetes, stll have not been settled. For example, Boserup, n her mportant dstncton between "plow" agrcultural and "shftng" cultvaton, suggests that the observed dvson of labor n the plowng economes n Asa reflects a natural comparatve advantage; another observer of ths pattern, however, Kalpana Bardhan (1984), assumes that the predomnance of women n certan agrcultural actvtes reflects employer dscrmnaton and monopsony power. he noton that employer preferences mportantly nfluence the occupatonal dstrbuton 1
of workers n both developed and low-ncome countres has been the focus of a large lterature that s mostly nconclusve. In addton, some economsts have argued that t s not possble to test whether occupatonal allocatons are n part the result of preferences by workers that covary wth observed characterstcs (Zellner, 1975). ests of the roles of dfferental productvtes n occupatonal allocatons, n the absence of drect observatons on productvty, are also known to be dffcult. As ponted out n Heckman and Sedlacek (1988), the prncpal problem that arses n a attempts to test the dea that workers are allocated accordng to comparatve advantage s comparatve advantage tself - because workers undertakng a partcular task may be partcularly well-suted to that task (or unsuted to the alternatve), the sample of people for whch one observes a wage observaton n a partcular task s not a random sample of the populaton as a whole and thus the estmated wage equaton by task s subject to selectvty bas. he soluton proposed n Heckman and Sedlacek (HS) to dentfy the operaton of comparatve advantage and obtan consstent estmates of occupaton-or task-specfc wage equatons makes use of statstcal methods that correct for selectvty bas. he advantage of ths approach s that, as long as the dstrbutonal and other assumptons requred by the approach are met, t provdes consstent estmates of the parameters on measured varables n the wage and task allocaton equatons. A comparson of these equatons thus makes t possble to assess drectly whether ndvduals wth attrbutes that make them more lkely to do a partcular task are also lkely to be better remunerated n that task and to test for the possblty that worker preferences also nfluence the allocaton across tasks. Moreover, the selectvty correcton model provdes addtonal evdence on the ssue of comparatve advantage by ndcatng whether unmeasured aspects of productvty nfluence the allocaton decson. here are two dffcultes wth the selecton-correcton modellng approach. Frst, t requres the mposton of a sgnfcant amount of structure on the data. Whle flexble dstrbutonal assumptons can be used, as n HS, ths approach ncreases the computatonal burden and data requrements of the process. Moreover, the fact that consstent estmaton of the wage equaton requres use of nformaton from the allocaton equaton mples that any msspecfcaton n the latter wll also contamnate the estmates of the former. 2
Second, the approach does not permt an assessment of the role of mperfect nformaton n the allocaton of workers to tasks. Although the parameters of the wage and allocaton equatons under mperfect nformaton wll be estmated consstently usng the selecton model, the approach does not provde nsght nto the queston of whether or not employers have complete nformaton on worker productvty. hus, for example, t s not possble to dstngush between a world n whch most women perform a partcular task because they have comparatve advantage n t from one n whch many women have comparatve advantage n other tasks but are allocated to a partcular task because women on average have comparatve advantage n that task and employers cannot dfferentate women wth comparatve advantage n dfferent tasks (and smlarly for men);.e., statstcal dscrmnaton. In ths paper, we show that wth data from a labor market n whch (1) productvty estmates for workers are explctly avalable and (2) the same worker s observed earnng wages n dfferent actvtes, tests can be performed of the roles of comparatve advantage, nformaton problems and preferences n determnng the allocaton of workers across tasks wth mnmal mposton of structure not mpled by economc theory. he data we use to carry out the tests, from the Bukdnon area of the Phlppnes, s also characterzed by a marked dvson of agrcultural tasks by sex (able 1), and provdes nformaton on ndvdual worker's abltes based 1 on ther pece-rate wages. We thus apply the methods to explanng n partcular why women weed and men harvest. In secton 1, we set out the theoretcal and statstcal framework that establshes tests for the exstence of comparatve advantage and the role of preferences under perfect nformaton n determnng the sortng of workers among tasks based on task-specfc pece-rate wage data. Secton 2 expands the framework to ncorporate mperfect nformaton and to establsh tests of 1 In Foster and Rosenzweg (1993) we exploted these data by usng observatons on both tme wages and pece-rate wages for the same workers regardless of task to draw nferences about the roles of nformaton and preferences solely n wage determnaton. In that analyss, only one type of skll was assumed so that comparatve advantage was not present. hus, ndvdual workers were assumed to have dentcal productvty across tasks. Observatons on workers who work n multple tasks and under dfferent payment regmes are used here to test these assumptons (whch are rejected) and to dentfy the roles of task-specfc sklls, employer nformaton and preferences n task allocatons. 3
the role of employer perceptons n task allocaton when tme wages are pad. he estmaton method s brefly descrbed n secton 3, whch s followed n secton 4 by a descrpton of the data and a dscusson of sample selectvty and the determnants of payment regmes. he test results based on methods whch mpose no dstrbutonal assumptons are presented n secton 5, whch also ncludes a dscusson of estmates from the standard probt selecton model appled to the same data. he estmates ndcate that n the labor market that we study, whch s not atypcal of most rural labor markets of Asa, a one-factor productvty model adequately descrbes the data, that more productve workers have a comparatve advantage n harvestng relatve to weedng and that productvty dfferences sort workers across these tasks accordng to the theory of comparatve advantage. he tests also ndcate that the greater presence of female workers n weedng actvtes compared to men s not due to women preferrng such actvtes compared to men; n the pece-rate sector dfferental productvtes and comparatve advantage appear to explan the dvson of labor by sex. We also fnd, however, that more than half of the varance n the true productvty of workers s not known by employers and ths gnorance s manfested n the task allocatons by sex n the tme-wage market. In that sector, n whch employers appear to select workers for tasks, employers do not prefer men over women n harvestng among workers perceved to have the same productvty, but the dsproportonate presence of women n weedng among workers compensated by tme wages n part arses from statstcal dscrmnaton. Employer expectatons about worker productvty, gven worker-observed characterstcs, are, however, unbased. Fnally, the normal-dstrbuton verson of the selecton model provdes results that are broadly but not entrely consstent wth the fndngs that explot drect nformaton on the productvty of workers who engage n multple tasks. I. Perfect Informaton Labor Markets a. heory We begn the analyss by examnng a labor market envronment n whch there s perfect nformaton about worker productvty avalable to both employers and researchers. We show the crcumstances under whch t s possble, wth nformaton on actual worker productvty, 4
to dfferentate among and to test for the exstence of three determnants of the allocaton of workers among tasks: (1) dfferences n the productvty of workers at dfferent tasks (comparatve advantage); (2) preferences of ndvduals for dfferent types of work, and (3) preferences of employers for dfferent types of workers. he role of comparatve advantage n task allocaton under perfect nformaton s captured by the Roy model (1951), whch has been recently formalzed by Heckman and Sedlachek (1985). he basc features of the model are that each worker has endowments µ, j one for each possble task j, reflectng the productvty n each of the tasks. In the absence of preferences of workers and employers for partcular tasks or types of workers, respectvely, the allocaton of workers to tasks wll be the result of each worker choosng the occupaton n whch that worker s most hghly rewarded gven the task prces. ask prces reflect the relatve value of the two actvtes gven the demand for the two types of work on the part of employers as well as the avalablty of workers by type. Specfcally, f w s the log wage that would be receved by jt worker at tme t workng at task j and jt th s the log of the j task prce (.e., the prce per unt of output n task j) receved by worker at tme t then we may wrte w jt jt µ j (1) and the worker wll choose task j whenever w jt>w kt for all k j. Whle the above model ncorporates the possblty that worker heterogenety s characterzed by multple productvty factors, a sgnfcant smplfcaton arses f one factor s suffcent--that s f µ = µ where the j j j and µ are task and ndvdual-specfc effects, respectvely, and s normalzed to one so that µ=µ.hs smplfcaton assumes that workers who are more 1 1 2 productve n one task are also more productve n the other task but the percentage by whch 2 Although µ s by constructon equal to the log of productvty (as measured by output per unt tme n task 1), we wll n general refer to t smply as "productvty" except when t s mportant to dstngush between actual productvty and ts log. 5
3 one worker s more productve than another s dfferent n the two tasks. Under these condtons the wage equaton (1) may be wrtten w jt jt j µ (2) Equlbrum n ths context wth two tasks can be llustrated by a smple fgure that plots the log wage n each task as a functon of µ (see fgure 1). If both tasks are performed n the economy the task prces wll adjust (thus shftng the ntercepts of the lnes n fgure 1) to equate supply and demand n the two tasks. In equlbrum, for >1, there s some M such that the less 2 productve workers (those wth µ<m) wll receve a hgher wage n task 1 and thus wll choose that actvty whle more productve workers (those wth µ >M) wll choose task 2. 4 If the labor markets operate as a spot market n whch workers choose dfferent tasks n each perod, exogenous changes n the demand for the two tasks wll result n changes n the task prces (thus shftng the ntercepts of the two lnes) that equlbrate demand and supply for the two tasks. Fgure 1 llustrates the case where there s an ncrease n the demand for task 1, whch results n a shft n the allocaton of workers toward that sector and an ncrease n the average productvty of workers n that sector. Workers wth ntermedate levels of productvty (n ths case those wth M<µ<M') wll select dfferent tasks at dfferent ponts n tme, and thus the share of tme allocated by an ndvdual to task 1 and the probablty of workng at task 1 at all wll be decreasng n µ. If a denotes the share of tme spent by ndvdual n task 1 over a gven 5 nterval then we may wrte, n lnear form, the task allocaton equaton correspondng to (2), as a 0 µ µ (3) 3 If worker A earns 10 percent more than worker B n task 2 (.e., f µ 2A=µ 2B +.1) then A should earn 1 10 percent more n task 1. 4 hs assumpton s made prmarly for purposes of llustraton; however, as dscussed below, t provdes a reasonably approxmaton to agrcultural labor markets n many developng countres ncludng the area of the Phlppnes that s studed n ths paper. 5 In a two factor world, of course, a=a(µ 1,µ 2). We focus on the one-factor model for ease of presentaton; moreover, as shown below, a one-factor model adequately capture the structure of wages n the rural area of the Phlppnes that s the focus of our emprcal analyss. 6
where and are constants. Note that observed characterstcs, x, do not appear n ether (2) 0 µ or (3), as productvty, known by employers and employees, s the sole determnant of worker and employer choce. 6 Incorporaton of worker preferences nto the model s straghtforward. If worker utlty at tme t depends on the wage receved and the task performed then the share of tme spent n the dfferent actvtes wll depend on tastes for dfferent tasks. he basc structure of the model changes, however, dependng on how tastes are dstrbuted among workers. In the smplest case where there s no heterogenety n tastes (e.g., everyone prefers task 1 to task 2), relatve task prces wll adjust to reflect the relatve desrablty of the two tasks and the basc structure of the model wll be unchanged,.e., equatons (2) and (3) are suffcent to descrbe the wage economy. If tastes are correlated wth productvty but not wth observed characterstcs x net of productvty then f more productve workers prefer task 2, the relatonshp between productvty and the share of tme spent n the task 1 wll mmc or renforce the comparatve advantage result, whle f the opposte s true t s possble that more productve workers wll be observed to spend less tme dong the task n whch they have comparatve advantage. hs latter pont s mportant because t mples that t may be dffcult to dstngush the hypothess that more productve workers choose task 1 because they are more productve (and thus better compensated) n that sector from the hypothess that more productve workers smply prefer dong task 1 n the sense that they would undertake that task even f they were not more hghly rewarded for dong t. As we show below, ths dffculty can be addressed f there are nformaton asymmetres. If tastes for tasks on the part of workers are correlated, but not perfectly, wth a k-vector of observed characterstcs x, then the share of tme spent n the dfferent actvtes wll be related to x net of both productvty µ and task prces. hus 6 Note that the allocaton n any partcular perod wll also depend on the task prces n that perod. Equaton (3) should be thought of as the result of aggregatng perod-specfc allocaton decsons whch depend on task prces n the respectve perod. hus n a gven labor market for a specfed nterval the task-prce effects may be captured as a constant. 7
a 0 µ µ x x (4) where x s a k-dmensonal parameter vector. Competton among employers wll ensure, however, that wages reflect the preferences of workers only to the extent that relatve prces are affected. hus, wages and x do not covary, net of the productvty of workers and task prces, 7 even f preferences for tasks covary wth x. Employer preferences over the attrbutes of workers dong partcular types of tasks wll nfluence both the wages pad to workers net of task prces and the share of tme spent by workers n dfferent occupatons. If there s employer taste dscrmnaton wth respect to a partcular characterstc of workers x n the sense of Becker (1971) then wages wll covary wth x net of productvty and the task prces. Assumng a log-lnear effect and allowng for the possblty that taste dscrmnaton operates dfferentally n the two dfferent sectors, the wage equaton becomes w jt jt j µ j x (5) If worker characterstcs x are dfferentally rewarded n the two tasks ( 1 2 ) then these characterstcs wll also nfluence the allocaton of the workers to tasks, as n (4), even n the absence of dfferental worker preferences over tasks. Note that the key dstncton between the effects of employer and worker preferences s thus that observed worker characterstcs affect the allocaton of workers as well as wages net of productvty and task prces n the former case 7 hat s equally productve men and women dong the same task wll receve the same wage even f ceters parbus men prefer to do one task and women the other. hs mplcaton s also used by HS. If, however, there s mperfect competton, monopsonstc employers mght explot worker preferences. In that case worker characterstcs observed by employers and correlated wth worker preferences wll enter the wage equaton. 8
8 9 whle n the latter the x's only affect task allocatons. hese results wth respect to the correlaton of x wth wages and task allocatons, net of worker productvty and task prces, are summarzed n the frst two columns of able 2. b. Identfcaton of the roles of comparatve advantage and preferences n the complete nformaton settng usng pece-rate wages We have shown that by estmatng the approprate wage and allocaton equatons t s n prncple possble to test for and measure the roles of productvty and preferences n determnng the allocaton of workers to tasks n an economy. he prncpal problem s that, even n the case of complete nformaton among market actors, the equatons nclude a varable that s not generally measured - actual worker productvty. Wthout ths nformaton, tests of the hypothess that workers are allocated accordng to comparatve advantage have necessarly been based on methods that mpose substantal structure on the data. Moreover, because t s necessary to condton on worker productvty n order to determne whether employer or worker preferences mportantly nfluence wages or allocatons, test for these effects have generally been nconclusve. In ths secton, we show how tests of the number of unque productvty factors and of the sgnfcance of comparatve advantage and of preferences n determnng task allocaton under perfect nformaton can be carred out wth mnmal structure mposed by usng data characterzng an envronment, not uncommon n low-ncome labor markets, n whch (1) workers are pad on a pece-rate bass for some part of the year, so that productvty estmates for 8 Of course employee preferences wll affect wages through ther effect on the equlbrum task prces; the pont s that they do not lead to dfferental wages by characterstcs net of task, productvty, and the task prce. Note that, even f t s found that employer preferences are expressed n wage rates net of task prces, ths does not necessarly mply mperfect competton. It s possble that all employers share the same preferences, for example. 9 We gnore here the possblty that employers only exercse ther tastes by excludng ndvduals from partcular tasks, n whch case ths dstncton s of lttle value from an emprcal perspectve and of lttle relevance n the settng whch wll be the focus of our analyss, where most ndvduals are found to do both tasks. More problematcally, usng ths approach t does not seem possble to dstngush a model based on worker preferences from one n whch employers exercse ther tastes by excludng ndvduals from partcular tasks but are prohbted by legal or other means from payng dfferent wages to equally productve ndvduals wthn tasks. 9
workers are explctly avalable, and (2) the same worker s observed earnng wages n dfferent actvtes/occupatons. It s easly seen how pece-rate data may be used to conduct an analyss of the allocaton of workers to tasks n the presence of complete nformaton. Frst note that the pece-rate wage earned by a worker n a partcular task on a gven day s the product of the pece-rate prce for that task on that day and the amount produced n that day (productvty), where the latter conssts of a persstent component reflectng the amount of work done by the ndvdual and a resdual reflectng measurement error and dosyncratc varaton arsng from, for example, the fact that varaton n crop densty wll mply that the amount of crop pcked by a gven worker wll vary from day to day. akng logarthms yelds the wage equaton (1) plus an error term: w jt jt µ j e jt (6) In order to use pece-rate data to obtan productvty estmates from equaton (6), t s frst necessary to obtan estmates of the pece-rate prce terms. OLS cannot be used for ths purpose, however, for the reasons dscussed n HS. If two pece-rate observatons are observed for a sub-sample of the populaton, however, consstent estmates of jt may be obtaned (exclusve of a constant) by estmatng equaton (6) n frst dfferences (wthn ndvduals). he fact that a sub-sample of ndvduals wth two pece-rate observatons s not necessarly a random sample of the populaton presents no partcular problem for the estmaton of the jt because, by assumpton, all ndvduals face the same task prce. By subtractng task-prce effects from the pece rate wages one s left wth consstent estmates of worker productvty ˆµ jt µ j e jt If t s addtonally assumed that the measurement errors are uncorrelated, the covarance of two of the estmates of ˆµ jt for the same task, (ˆµ j1,ˆµ j2 ) 2 (µ j ), provdes a consstent estmate of the varance of task-specfc productvty n the populaton among those wth at least two pece-rate observatons n that task. Moreover, by further mposng the plausble restrcton that the varance of the measurement error term s the same across all workers, a comparson of the measured varance of µ among those workers wth only one pece-rate observaton to the j same measure taken from the populaton wth more than one pece-rate observaton provdes a 10
test of whether the varance n productvty wthn the two groups s the same because 2 (ˆµ jt ) 2 (µ) 2 (e jt ). It s also possble to test whether a one-factor model adequately descrbes the dstrbuton of productvty across workers. Consder a respecfcaton of (6) n whch we normalze accordng to one occupaton or task (and supress the task prces). Assume that the log pece-rate wage for ndvdual n occupaton 1 at tme t s gven by w 1t µ e 1t (7) hen for any other occupaton j the log pece-rate wage for the same ndvdual s gven by (8) f there s a unque productvty factor for that occupaton w jt j µ j e jt (8) where j s the occupaton-specfc productvty factor for ndvdual and j s an occupaton- specfc parameter. Wth two pece-rate observatons for each occupaton nclusve of the normalzed occupaton t s possble to dentfy the varances of the normalzed or common productvty factor µ and the task-specfc productvty factors as well as to dentfy the as long as the tme j j varyng productvty shocks e are orthogonal. In that case, the observed sample moments, for jt two pece-rate wage occupatons, are gven by: (w jt,w 1t ) j 2 (µ ) (9) (w 11,w 12 ) 2 (µ ) (10) (w j1,w j2 ) 2 j 2 (µ ) 2 ( j ) (11) here are three ndependent equatons derved from the four wage observatons relatng the three observed moments to the three model parameters. hus, the varances of the common and occupaton-specfc productvty factors are dentfed and t s possble to test whether a one- 11
2 factor model s adequate,.e, ( )=0. In the one-factor case, the parameter, whch s also j dentfed, characterzes the extent of comparatve advantage across the two tasks. Wth addtonal nformaton on worker allocatons n the pece-rate sector, t s also possble to test for the operaton of comparatve advantage and worker preferences n the allocaton of workers to tasks wthn a sector where problems of mperfect nformaton do not arse. In partcular, the allocaton equaton (equaton 4) parameters reflectng the operaton of comparatve advantage and of preferences n terms of the observed moments for the wages and task allocatons are: j µ (a,w j1 ) (x,x ) (a,x ) (w j1,x ) (w j1,w j2 ) (x,x ) (w j1,x ) 2 (12) and x (a,x ) (w j1,w j2 ) (a,w j1 ) (w j1,x ) (x,x ) (w j1,w j2 ) (w j1,x ) 2 (13) where t has been assumed for notatonal smplcty that x s a scalar. As dscussed, f comparatve advantage plays a role n occupatonal allocatons, then µ 0 and n the absence of worker preferences that are related to measured characterstcs of workers, occupatonal allocatons should not be nfluenced by any measured characterstc x net of actual productvty so that =0. estng for employer preferences s more dffcult because both wages and x allocaton are nfluenced under ths varant of the model; however, followng a suggeston of HS some nsght can be ganed by comparng separate estmates of pece-rate prces for ndvduals 10 wth dfferent characterstcs. 10 Because task prces estmated n ths way are only determned up to a constant, ths approach wll not dentfy employer dscrmnaton by sex f that dscrmnaton results n a constant sex-premum across tasks and tme perods. Unfortunately the data set we use does not contan nformaton on pece-rate prces that mght otherwse be used to address ths ssue drectly. In any case, t seems unlkely that employers would use dfferent pece-rate prces for dfferent ndvduals dong the same task n the same perod even f they pad dfferent wages when compensatng these ndvduals on a tme-rate bass. 12
2. Imperfect Informaton n the Labor Market a. heory he prncpal addtonal mplcaton for the allocaton of workers across occupatons n the absence of complete nformaton on worker productvty s that employers are unable ether to match perfectly workers to jobs or to attract the rght workers to the rght jobs by adjustng wages approprately and thus must use observable characterstcs to assgn wages and determne allocatons. o capture ths dea n the exstng framework let µ *=E(µ x) denote the expectaton of the log of productvty based on characterstcs known to the tme-wage employer and assume that the actual log of productvty may be wrtten as the sum of µ * and a resdual u wth dstrbuton F that does not depend on x: u 11 µ µ u (14) hen because competton among employers wll ensure that the wage receved by ndvdual s equal to the expected value of havng hm work at task j (.e., hs expected productvty gven observed characterstcs x), hs log tme wage w, may be wrtten jt w jt jt lne(e j µ x t ) jt jt j µ j µ ln e j u df u (u) j (15) where the superscrpt dentfes the log wages and prces as those assocated wth tme-rate employment. Note that equaton (15) dffers from equaton (2) by the presence of the constant j and by the fact that µ*, expected log productvty, appears n the wage equaton rather than µ. It s worth notng that the fact that j s a task-specfc constant mples that n a comparson of two 11 hs assumpton wll hold, for example, f log-productvty s a lnear functon of worker attrbutes only some of whch are observable to the employer and the vector of unobservable characterstcs can, n turn, be wrtten as a lnear functon of the observable characterstcs and an..d. (across ndvduals) error vector. Among other thngs, ths restrcton rules out the possblty that nformaton s more precse for ndvduals wth greater exposure to the labor market as shown by Foster and Rosenzweg (1993) n the context of Inda. hs assumpton s necessary n order for the log tme wage to be wrtten as a lnear functon of µ * and a task- specfc constant (see equaton (15)). 13
ndvduals, the one wth hgher expected log productvty wll also have hgher expected productvty and thus a hgher tme wage for the same task and tme perod. Allocatons under tme wages may be characterzed usng a fgure analogous to fgure (1) by replacng µ on the horzontal axs wth µ*; there wll now be some ntermedate level of expected productvty such that those workers wth characterstcs yeldng an expected productvty above that level wll receve hgher wages f they work at task 2, whle those wth an expected productvty below that level wll receve hgher wages f they work at task 1. hus n the absence of preferences over partcular tasks by the workers and over partcular types of workers by employers, the share of tme allocated by an ndvdual to task 1 wll depend, analogously to the perfect nformaton case, only on hs expected productvty and task prces; x wll not covary wth tasks net of µ*. However, agan analogously to the perfect nformaton case, when workers are heterogeneous n preferences for tasks that are correlated wth employer observable characterstcs of the worker x, the share of tme spent n task 2 (weedng) wll depend on expected productvty as well as x but wages wll not covary wth x net of µ* and task prces, as t n (4). In the mperfect nformaton envronment t s possble that worker task preferences are correlated wth characterstcs that are unobservable to the employers and also correlated wth productvty (ncludng productvty tself). hus the allocaton equaton under these crcumstances ncludes not only µ* and x but also u, so that: a 0 µ µ u u x x (16) hs equaton allows us to dstngush the comparatve advantage hypothess from the hypothess that more productve workers smply happen to prefer to undertake the task n whch they have comparatve advantage, a dstncton whch, as noted above, cannot be made n the perfect nformaton case. he dea s that workers wth smlar levels of expected productvty, µ *, wll receve smlar tme wages; thus f workers wth hgher u are found to be spendng more (or less) tme n the sector n whch they have comparatve advantage, then we may nfer that worker 14
preferences are mportantly nfluencng the allocaton of workers to tasks. 12 Fnally, nsghts drawn from the complete nformaton case are also applcable n the case of employer preferences: taste dscrmnaton by employers wll mply that workers wth partcular observed characterstcs wll receve hgher wages gven ther expected productvty, a fact that wll alter the share of tme that ndvduals spend n partcular tasks. hus, n the most general form the wage equaton can be wrtten w jt jt j µ j j x (17) An mplct assumpton of the analyss of the labor market n the mperfect nformaton settng s that employer expectatons are correct n the sense that the subjectve dstrbuton of worker productvty of the employer, condtonal on the observed characterstcs of the worker, s equal to the actual dstrbuton of productvty among all workers wth those characterstcs. It s possble, however, that employers msperceve the relatonshp between x and productvty. Because µ* s taken to be the true expected productvty gven x rather than the subjectve expectaton of the employer, ths possblty s easly captured by equatons (16) and (17): for example, f employers ncorrectly assume that males are better at task 2 than are females then, net of the true expected productvty, males are lkely to receve hgher wages and spend a greater share of ther tme n that actvty. hus t s not possble to dstngush between employers' bases n preferences and n nformaton. he thrd and fourth columns of able 2 present a summary of the relatonshps between observed worker characterstcs x and wages and task allocatons gven expected productvty and task prces n the mperfect nformaton envronment, based on equatons (16) and (17). Although all of the mplcatons about the covaraton of x wth wages and task allocatons under the dfferent scenaros of preferences (or gnorance) are dentcal between the perfect and mperfect nformaton settngs, there s an mportant dfference: n the former case one must have 12 Of course, f preferences are not correlated wth the unpreceved component of worker productvty, t s possble that u =0 whle preferences may stll play a role n the dstrbuton of workers across occupaton. 15
avalable a measure of actual worker productvty whle n the latter case one must dentfy that component of worker productvty that s known by employers. Inferences drawn from relatonshps (4) and (5) nvolvng actual productvty when employers are partally gnorant of true productvty can be ncorrect. It may be establshed, for example, that the coeffcent on an x varable n the allocaton equaton (16) n terms of the moments of the observed varables and perceved productvty µ* s x (a,x ) 2 (µ ) (a,µ ) (x,µ ) 2 (x ) 2 (µ ) (x,µ ) 2 (18) Consder, now an alternate verson of equaton (16) wth expected productvty replaced wth true * productvty, (µ replaced by µ), and droppng u for smplcty: a 0 µ µ x x (19) Now the analog to equaton (18) s x (a,x ) 2 (µ ) (a,µ ) (x,µ ) N 1 (a,x ) 2 (u ) 2 (x ) 2 (µ ) (x,µ ) 2 N 2 2 (x ) 2 (u ) (20) where N and N denote the numerator and denomnator of equaton (18), respectvely. 1 2 In the absence of worker preferences wth respect to tasks and employer taste dscrmnaton =0 and thus N =0. But under these crcumstances wll not be zero f both x 1 2 13 (u)>0 and (a,x)>0. he frst of these condtons s exactly the condton that some aspects of productvty are not known by tme-wage employers. he second says that x s correlated wth a as wll be the case f x s known by the employer and correlated wth productvty. hus, the fndng that dentcally-productve workers wth dfferent values of x have dfferent dstrbutons of tme n dfferent tasks does not necessarly mply ether that workers have preferences wth respect to tasks or employers exercse taste dscrmnaton n envronments where employers are x 13 Because actual productvty s, n effect, a nosy estmate of employer-perceved productvty (equaton 14), ths result s smply a manfestaton of measurement-error bas. 16
partally gnorant of worker productvtes and use x as a productvty sgnal. An analogous equaton holds for wages: f true productvty s used nstead of perceved productvty to estmate equaton (17) worker characterstcs that are known by the employer and predct productvty wll appear to affect wages even when structurally j =0. hs, along wth the dfferental allocaton across tasks reflect, of course, statstcal dscrmnaton (see, e.g., Agner and Can 1977): among workers wth the same true productvty, that worker wth the hgher employer-perceved productvty wll receve a hgher wage n both tasks, receve a hgher dfferental wage n the hgh-wage task (due to comparatve advantage), and work more n the hgh-wage task as a result. b. Estmaton under ncomplete nformaton usng pece-rate and tme wages As noted, n the presence of ncomplete nformaton the problem of dentfyng the determnants of task allocatons s more complex because, even when actual productvty s known, t s also necessary to obtan an estmate of that component of actual productvty that s perceved by employers. Whle drect observatons of expected productvty are not avalable, we now show that the key parameters of the allocaton and wage equatons (assumng a one factor model) can be estmated consstently usng nformaton for each worker on one pece-rate wage P 14 observaton (w ), one tme-wage observaton (w ), and at least one worker characterstc that j1t s correlated wth productvty and can be argued on a pror grounds to be () observed by the employer and () not tself subject to taste dscrmnaton by hm. hat s, we assume the exstence of a sgnalng equaton that relates a worker s actual productvty to a subset of the measured characterstcs y of the worker that are also known by the employer and to whch the employer s otherwse ndfferent, j1t µ y t (21) 14 Assumng a one factor model, t does not matter from whch task the pece and tmerate wages are taken as long as there s suffcent nformaton on both tasks to obtan a precse estmate of the parameter 2. hus, to smplfy subsequent dscusson t wll be assumed that, unless otherwse stated, all pece-rate wages are from task 1 and all tme wages from the same task (ether 1 or 2). 17
As n the perfect nformaton case, the sample moments may be used to construct estmates of the model parameters. In partcular, usng equatons (7), (14), (17), and (21) and allowng for measurement error wth respect to the tme wage, t may be shown that, when =0, the comparatve advantage coeffcent n the case of mperfect nformaton s: 15 j j (y,w 1t ) (y,w P jt ) (22) where we have assumed that the component of employer-preceved productvty that s not measured and the measurement errors n wages are orthogonal. hese same equatons also mply that the varance n perceved worker productvty s 2 (µ ) (w P 1t,w jt ) (y,w P jt ) (y,w 1t ) (23) from whch, as shown n Foster and Rosenzweg (1993), wth nformaton on the varance of true productvty obtaned from the covarance of two pece rate wages, as above, t s possble to dentfy the varance of the unobserved component of productvty, 2 (u). It s also possble to determne that component of the varance of expected productvty that s not drectly observed by 2 the econometrcan, ( ). he roles of both observed, and hence rewarded, and unobserved productvty n task allocatons can also be dentfed usng nformaton on two pece-rate and one tme-rate observatons for workers. For example, n the specal case n whch x s assumed to be zero the expressons and n terms of observed moments are smply µ* u 15 Analogous but more complcated expressons that allow for j 0,can also be derved. he estmates that we obtan, descrbed below, allow for the most general model. 18
µ (w p 11,a ) (w p 11,w 11 ) (24) and u (w p 11,a ) (x,w 11 ) (w p 11,w p 12 ) (x,w 11 ) (w 11,a ) (x,w p 11 ) (w p 11,w 11 ) (x,w p 11 ) (25) respectvely. Even when all measured worker characterstcs x are ncluded n the allocaton 16 equaton; excluson of at least one characterstc from the wage equaton (.e., the assumpton that there s at least one worker characterstc about whch employers do not care other than as a predctor of productvty ) s suffcent for dentfcaton of all of the parameters of the allocaton equaton. 3. Estmaton Method he estmaton method that we use to mplement the test of the two-factor model and to obtan the estmates of the task allocaton and wage equatons matches the theoretcal moments of the system of equatons, e.g., the rght-hand-sdes of equatons (9) through (11), denoted by, to the sample moments, e.g., the left-hand-sde varables n (9) through (11), denoted by M. he objectve functon Q=(m- ( ))' (m- ( )) s mnmzed wth respect to the parameter vector ; m s the vector of elements obtaned by strngng out the lower trangular elements of the matrx M, ( ) s the correspondng vector obtaned from whch depends on the set of model parameters, and s a weghtng matrx. he weghtng matrx s that whch corresponds to the "optmal mnmum dstance" estmator dscussed by Chamberlan (1982, 1984), also known as the optmal 16 Recall that f the preferences of the worker depend on productvty, expected productvty may vary by task f the wllngness of a worker to do a task n a partcular perod sgnals somethng addtonal about hs productvty to the employer. In ths case, expected productvty n a partcular perod (as measured from one tme-rate wage equaton) wll be a nosy estmate of average expected productvty, thus basng the coeffcent on expected productvty to zero. Even f ths s the case, however, ths specfcaton may be used to test for the effect of unobserved productvty on allocaton to task. 19
17 weghtng matrx (OWM) or arbtrary generalzed least squares estmator (AGLS) estmator hs estmator yelds consstent parameter estmates and standard errors wthout mposng any parametrc dstrbutonal assumptons. As noted, for all of our tests we need at least two measures of productvty (pece-rate wages) for the same task for each worker to dentfy the relevant parameters of each equaton. hs s because each task-specfc pece-rate wage s a nosy measure of productvty but each measure can be used, n effect, as an nstrument for the other. However, more effcent estmates can be acheved by ncludng groups of workers for whom we have only one productvty observaton under the assumpton that the parameters ncludng the varances n measurement errors and n all other unobserved constructs, such as productvty µ, are the same for all workers he generalzaton of the OWM method to multple groups, wth cross-group parameter constrants, s straghtforward. As noted, f t assumed only that measurement error varances are the same for workers regardless of ther partcpaton n task and payment regmes, then t s possble to perform dentfcaton tests nvolvng the assumpton of equalty for subsets of parameters across groups. In partcular, tests, reported below, of the equalty of the groupspecfc varances of productvty µ provde nformaton on whether subsamples of workers chosen on the bass of payment regme (whch determnes whether or not productvty s measured) or task are representatve of the entre populaton of workers. 4. he Data and Sample Selectvty he crtcal nformaton needed to dentfy the operaton of comparatve advantage and of preferences, f any, n determnng the allocaton of workers across occupatons or tasks that does not requre auxlary assumptons s the productvty of workers. As noted, one mportant 18 ndcator of worker productvty s a worker's performance under a pece-rate regme. he data 17 hs estmator was used by Abowd and Card (1989) to estmate an error components model of U.S. wage rates. 18 An mportant assumpton of the tests that we have dscussed s that productvty as measured n the pece-rate labor market s a relevant measure of productvty n the tme-wage labor market. here are a number of potental problems wth ths assumpton. It mght be argued, for example, that productvty dfferentals depend on dfferences n effort n addton to dfferences n fxed characterstcs lke strength or skll level. Because the returns to effort are 20
used n ths paper are well-suted to an analyss of these ssues. hey are from a stratfed random panel of 448 farmng households n Bukdnon n northern Mndanao, Phlppnes where, 19 as s typcal of agrculture n the Phlppnes, pece-rate and tme-wage work coexst. hese households were ntervewed n four rounds at four month ntervals n 1984-85 as part of an Internatonal Food Polcy Research Insttute study by Bous and Haddad (1990). In addton to detaled nformaton on agrcultural producton (prncpally of corn, rce and sugar cane) and basc anthropometrc and demographc nformaton for each household member that may be relevant to productvty and plausbly known by employers, the survey provdes extensve nformaton on labor market actvty n the study area. For every ndvdual n the sample households and n each round we observe days worked off the farm and average daly wages receved by crop, task and type of payment (pece- 20 rate versus tme-wage). Informaton on days worked by famly and hred laborers on the farm and supervsor-days by crop, task and type of payment s also avalable for each study household n each round. hus each round provdes averages of (t-specfc) daly spot-market prces and aggregates of the bnary task allocaton decsons made n each daly spot market. We use the totals across all four rounds of task-specfc days to construct measures of task allocatons by form of payment for each worker. Indvdual observatons on wages are based on the reported greater when an ndvdual s pad on a pece-rate bass than when he/she s pad tme wages, one would expect greater dfferences n productvty n the pece-rate and the tme wage sector. Whle ths argument has mert, t should be recognzed that because ndvduals wth more favorable endowments (e.g. those wth greater strength or sklls) wll need to provde less effort to produce the same output as those wth lower endowments, these workers are lkely to do more effectve work n a gven day than workers wth less favorable endowments n both sectors. hus whle dfferences n the return to effort n the two sectors wll affect productvty dfferentals, t wll not affect the rankng of workers by productvty. 19 Although we focus on the dstncton between pece-rates and tme-wage earnngs, there s some heterogenety n the form of payment wthn each type of work. Pece-rates ncludes cash payments on a unt bass as well as n-knd payments that are a share of the harvest. It should also be noted that the approprate unt to be used n the pece-rate payment for plowng or weedng may, for example, be the plot of land. 20 58.7 percent of men and 31.5 percent of women aged 18-59 n the sample households were observed to work at least once n the labor market. 21
average wages n each round by task so that a worker wth two task-specfc wage observatons under one payment regme s a worker who has worked at least one day n two dfferent rounds at that task under the specfed payment regme. he tasks performed by all workers are dvded nto four categores - plowng and sowng, weedng, harvestng and other. More than 93% of wage workers, totallng 657 workers, perform both weedng and harvestng actvtes over the course of the four-round sample perod, and weedng and harvestng account for 94% of all days spent by agrcultural wage workers n agrcultural actvtes. We thus focus on the allocaton of tme between these major task categores. he allocatons of work tme by men and women across these two tasks are smlar to those reported n able 1 wth respect to all tasks - among these workers, of whom 62% are men, of the days spent ether harvestng or weedng for tme wages across all four rounds, men and women spend 63.2% and 93.7% of ther days weedng, respectvely. he correspondng fgures for pece-rate days are 18.4% and 30.0%, respectvely. 21 Our strategy s to explot the pece-rate data provded for workers who work for pece rates to test frst whether a one-factor productvty model accurately characterzes the data and then, on the bass of that structure, to test the hypothess that comparatve advantage and/or worker preferences are reflected n the task allocatons, under the reasonable assumpton that nether nformaton problems nor wage dscrmnaton afflcts pece-rate payment regmes. For testng ssues of asymmetrc nformaton and dscrmnaton the tests requre that we have nformaton on tme-wage workers who also receve at least one pece-rate wage, to gauge ther productvty. It s mportant therefore to assess the selectvty of subsamples of such workers chosen on the bass of payment regmes. In partcular, t should not be the case, as was evdently true n the Unted States n the late nneteenth and early twenteth centures (Goldn (1986)), that women prmarly work n pece-rate jobs whle men work for tme-wages. 21 In order to carry out the varous stages of the analyss detaled n the prevous secton t s necessary to use samples of workers wth varyng numbers of harvestng and weedng observatons by form of payment. able A n the Appendx presents a breakdown of the sample of weedng or harvestng wage workers for varous combnatons of payment-method and tasks. 22
Employment under both payment regmes, however, s the norm for both men and women n the study area over the course of the study perod. hs s n part due to the fact that at certan tmes of the year only one or the other form of payment method s offered due to dfferng tme-sequences of agrcultural tasks across employers. Durng other parts of the year, both 22 pece-rate and tme-wage jobs are avalable. Of adult workers n the sample households who contrbute at least two observatons to the labor market data (.e., at the very least they performed the same job n two dfferent rounds or dfferent jobs n the same or dfferent rounds), 70.7 percent of men and 67.7 percent of women worked both for pece-rate and tme wages. Of workers wth at least four wage observatons durng the sample perod, 89 percent of women and 82 percent of men receved both tme and pece-rate wages. Moreover, although women are more lkely to be n the labor market durng the corn-harvest perod and are therefore more lkely to be pad pece rates (whch are typcally pad durng corn harvest operatons), net of ths partcular actvty we cannot reject the hypothess that men and women are equally lkely to do 23 pece work. hs s not surprsng, gven that nether men nor women are attached to partcular employers. Long-term contractual arrangements servng as dscplnary mechansms are absent and dfferentals n labor-force commtment, whch do vary by sex n ths settng, are rrelevant. 24 hus, those workers who are employed under both tme-wage and pece-rate regmes do not 22 hs gves rse to the possblty of adverse selecton, wth those workers havng hgher levels of u, that part of productvty unobserved by employers, beng more lkely to partcpate n pece-rate tasks when offered the choce. Evdence of ths tendency s provded n Foster and Rosenzweg (1993). 23 he followng logstc regresson was estmated usng the sample of wages by task and type of payment weghted by the number of days worked: logt PIECE = -.997 -.1043 MALE + 3.390 CORNHARV where PIECE s one f the task s pad usng pece-rates, MALE s one for males, and CORNHARV s one f the task was corn harvestng. he hypothess that coeffcent on MALE s not sgnfcantly dfferent from zero s not rejected at conventonal levels of sgnfcance (pvalue=.474). Note that the fact that women are not "crowded" nto pece-rate jobs suggests the absence of taste dscrmnaton, although t s not nconsstent wth statstcal dscrmnaton. 24 Although 34.1 percent of all those who work n the labor force are only observed to contrbute one observaton, these ndvduals contrbute relatvely few days to the labor market. Specfcally, those contrbutng observatons wth both forms of payment contrbute 0.5 percent of all days to the labor market. 23