Wage Inequality and The Effort Incentive Effects of Technological Progress

Transcription

1 Wage Inequalty and The Effort Incentve Effects of Technologcal Progress Cecla García-Peñalosa GREQAM and CNRS, Marselle Campbell Leth Department of Economcs Unversty of Glasgow November 30, 2001 Chol-Won L Department of Economcs Unversty of Glasgow Abstract Ths paper ntroduces technologcal progress nto an effcency wage model, and argues that changes n the rate of techncal change affect not only the demand for but also the effectve supply of labour. Ths creates a new mechansm through whch technologcal progress mpacts on the wage of sklled workers relatve to that of the unsklled. Prevous work has argued that an ncrease n the relatve wage would only come about f there were an acceleraton n the rate of skll-based technologcal change. In contrast, we fnd that techncal change affects the skll premum even when t s neutral. Moreover, the paper shows that slower techncal change may also ncrease the relatve wage, allowng us to reconcle the change n the skll premum wth the productvty slowdown experenced by OECD countres. The man problem of demand-based explanatons of the ncrease n the skll premum s that they cannot account for the smultaneous ncrease n the unemployment rates for both sklled and unsklled workers. Our framework emphasses the jont determnaton of wages and employment, and generates wage and employment patterns that are consstent wth the evdence. We would lke to thank partcpants at the CES-fo conference on Growth and Inequalty for helpful comments on an earler draft of ths paper, whch was orgnally publshed n dscusson paper form as Leth and L (2001). We would also lke to thank partcpants at the semnar at the Unversty of Strlng for ther comments. All errors reman our own. Cecla García-Peñalosa, GREQAM, Centre de la Velle Charte, 2 rue de la Charte, Marselle, France. e-mal penalosa@ehess.cnrs-mrs.fr. García-Peñalosa would lke to thank the Unversty of Geneva for ts hosptalty. Campbell Leth, Department of Economcs, Unversty of Glasgow, Adam Smth Buldng, Glasgow G12 8RT, UK; (Tel.) ++44-(0) ; (Fax) ++44-(0) ; (E-mal) c.b.leth@socsc.gla.ac.uk; (Web) Deppartment of Economcs, Unversty of Glasgow, Adam Smth Buldng, Glasgow G12 8RT, UK; (Tel.) ++44-(0) ; (Fax) ++44-(0) ; (E-mal) cw.l@socsc.gla.ac.uk; (Web)

2 1 Introducton The recent ncrease n earnngs nequalty n a number of ndustralsed countres s by now a well-documented event. Countres have dffered n ther experences, wth the most pronounced ncreases takng place n the UK and the USA. The rato of the 90th to the 10th percentle of the male wage dstrbuton rose from 2.51 to 3.11 n the UK and from 3.26 to 4.35 n the US over the perod An mportant component of ths ncrease n nequalty has been the rse n the educatonal wage dfferental. Between 1980 and 1988, the wage rato of unversty graduates to workers wth no qualfcaton ncreased by almost 8 per cent n the UK, and the wage rato of college to hgh school graduates rose by some 25 per cent n the US over the perod (Acemoglu, 2000). For half a decade the man explanaton for the upsurge n wage nequalty has been the hypothess of an acceleraton n skll-based technologcal change. The argument that has been put forward s that the development of new nformaton technologes has resulted n a shft n relatve demand for labour n favour of those wth greater sklls (see Berman, Bound and Grlches, 1994). An extensve lterature has subsequently tred to understand the relatonshp between technology and the relatve demand for sklled labour. 2 Recent emprcal work has, however, documented the mportance of both nternatonal trade and changes n the supply of sklls. Feenstra and Hanson (1999) show that when we measure trade by the degree of outsourcng, ncreased competton n the market for low-skll manufactures from newly-ndustralsng countres can account for a large fracton of the change n the relatve wage n the US. Supply effects have been documented by Card and Lemeux (2001). Usng data for the US, the UK, and Canada, they decompose the US labour force nto cohorts and fnd that, startng wth the cohorts born n 1 See OECD Employment Outlook (1996). 2 Ths hypothess has been theoretcally explored by Echer (1996), Galor and Tsddon (1997), Greenwood and Yorukoglu (1997), Acemoglu (1998), and Casell (1999), among others. 1

3 the 1950s, there has been a sgnfcantslowdownntherateofgrowthofeducatonalattanment that can explan the sharp ncrease n the premum to educaton for these cohorts. Stll, they fnd that there has been an ncrease n the returns to educaton for all cohorts that cannot be explaned by aggregate supply changes, and whch may well be due to technologcal change. The am of ths paper s two-fold. Frst, t contrbutes to the theoretcal lterature on the relatonshp between technologcal progress and relatve wages by examnng how, n the presence of mperfect nformaton n the labour market, techncal change can affect not only demand but also the effectve supply of sklls. Second, mperfect nformaton wll generate equlbrum unemployment, and wll allow us to account for a fact that has largely been gnored by prevous explanatons of the rse n the skll premum, namely, that the ncrease n the relatve wage has been accompaned by an ncrease n unemployment rates for both sklled and unsklled workers (see the dscusson n secton 2). Our argument s based on the effcency wage model of Shapro and Stgltz (1985), whereby mperfect nformaton on the part of frms about whether or not employees are shrkng forces the former to pay wages above the market clearng level, whch n turn leads to unemployment. The combnaton of hgh wages and the rsk of remanng unemployed f found shrkng and fred, nduces optmal effort on the part of workers. We ntroduce technologcal progress nto ths framework. We stress that an mportant feature of new technologes s that they not only create new jobs, they also destroy old ones. When an nnovaton arrves, some workers retan ther jobs but others are reallocated between jobs or made redundant. 3 Ths process affects the effort ncentves of workers, and hence the effectve labour supply. That s, changes n the rate of techncal change alter the trade-off between pay and unemployment that frms face, and wll affect equlbrum wages and employment. 3 The mportance of ths process has been documented by Davs and Haltwanger (1992). They fnd that n the US, between one thrd and one half of total worker reallocaton (between employers or from employment to joblessness) s due to shfts n employment opportuntes across frms. 2

4 In general, the net mpact of techncal change on wages s ambguous. Faster techncal change ncreases the dscounted wage flow but, snce t also rases turnover, t reduces the probablty of remanng wth the current employer, and hence t may ncrease or decrease the present value of beng employed. Dependng on parameter values, one or the other effect wll domnate. Moreover, f some of these parameters dffer across types of workers, changes n the rate of techncal change wll affect relatve effectve supples. We consder two types of workers, sklled and unsklled, and mantan that certan characterstcs of the labour markets n whch they operate dffer. In partcular, we assume that t s easer to montor the effort levels of the unsklled and that t s easer for a sklled worker that has lost her job to mmedately fnd a new one, as her transferable sklls make her more adaptable to the new technology than an unsklled worker. These dfferences mply that the ncentves of the two types of workers wll not be affected n the same way by a change n the rate of techncal progress, and that consequently therelatve(effectve) supply of workers wll shft. A number of results emerge. Frst, f techncal change s based, n the sense that t ncreases the demand for sklled workers relatve to that for unsklled, then the ncentve mechansm may strengthen or partally offset the effect of demand on relatve wages. A more surprsng fndng s that f techncal change s neutral, n the sense that t leaves the relatve demand for labour unchanged, an ncrease or fall n the rate of techncal change wll stll change the relatve wage. In other words, technologcal progress affects the skll premum even when t s skll-neutral. Thrd, we fnd that a reducton n the rate of techncal change can generate an ncrease n the skll premum. Fourth, the model generates patterns of unemployment that are consstent wth the data. As we wll see n detal n the next secton, demand-based explanatons have problems explanng the productvty slowdown and the ncrease n both the sklled and the unsklled unemployment rates that have been contemporaneous wth the ncrease n relatve wages. The 3

5 effcency wage model allows us to reconcle these three facts. Ths paper contrbutes to two recent strands n the growth lterature, both of whch have not receved as much attenton as they mert. The frst one s the lterature on unemployment and technologcal progress, poneered by Aghon and Howtt (1994). Aghon and Howtt ntroduce technologcal progress nto a search model of the labour market to examne the nteracton between growth and long-term unemployment. The adopton of new technologes requres the reallocaton of labour across frms, and hence determnes the rate of job destructon. They show that faster technologcal progress has two effects on the demand for labour. By ncreasng the dscounted flow of profts from a new job, t ncreases frms ncentves to post a new vacancy, and tends to rase the demand for labour. There s also a negatve creatve destructon effect, as faster nnovaton tends to reduce the expected duraton of a job match, reducng the demand for labour. Parameter values then determne whch of these two effects domnates. Our approach also explots the dea that technologcal progress makes hrng and frng endogenous. However, nstead on concentratng on the demand for labour, we focus on the supply of labour when mperfect nformaton forces frms to pay effcency wages n order to dscplne workers. The second related area of research s the lterature on growth and mperfect nformaton. The analyss of nformaton asymmetres n growth models has almost exclusvely focused on the role of captal market mperfectons. 4 Although labour economsts have long emphaszed the mportance of mperfect nformaton n understandng the workngs of the labour market, ts mplcatons for macroeconomc outcomes have seldom been explored. An excepton s the work of Echer and Kalatzdaks (1997) and Echer (1999) (see also Kalatzdaks, 1996). These papers examne a setup n whch workers need to be traned to use a partcular technology. The tranng costs to frms are decreasng n the worker s ablty, but frms have mperfect nformaton about 4 See, for example, Zera (1991) and Tsddon (1992). 4

6 an applcant s ablty. As a result there s an adverse selecton problem whereby a reducton n the wage reduces the qualty of the applcant pool. The mplcatons of ntroducng adverse selecton n the labour market for an open-economy growth model are strkng: there wll be nformatonal effcency gans from trade that can lead to a reducton n the ncome gap between tradng partners. We explore a very dfferent type of nformatonal asymmetry, yet our approach also emphases that the fact that frms need to pay effcency wages has mportant mplcatons at the aggregate level. The paper proceeds as follows. Secton 2 dscusses the exstng lterature on techncal change and the skll premum, and argues that there are a number of emprcal regulartes that they have dffculty n explanng. Secton 3 outlnes the model and consders the ncentve effects of technologcal progress. We show that there are two effects workng n opposte drectons, and examne the mpact of a change n the rate of technologcal progress on wages and employment n a partcular labour market. Secton 4 then uses the model to analyse the mpact of techncal progress on the skll-premum. We fnd that both skll-based and skll-neutral technologcal progress affect the relatve wage. We then show how our framework can generate a smultaneous ncrease n the relatve wage and n the unemployment rates of both types of workers. Polcy mplcatons are dscussed n secton 6, whle secton 7 concludes. 2 Based Techncal Change, Demand, and the Increase n Relatve Wages The early emprcal lterature on the ncrease n relatve wages found lttle support for the role of supply or nternatonal trade as potental explanatons. 5 Theoretcal work has consequently concentrated on modellng the way n whch new technologes shft the relatve demand for 5 See Murphy and Welch (1992) and Berman, Bound, and Grlches (1994). 5

7 labour. Ths lterature has, however, encountered three problems when tryng to ft the evdence. The frst one s the productvty slowdown. The 1970s and 1980s wtnessed a sharp reducton n rates of total factor productvty growth, wth TFP growth n the US fallng from 3% n the md-1960s to around 1% by the late 1980s. The UK, France, and Germany experenced even sharper declnes over the perod. 6 Yet most work on wages and techncal change reles on an ncrease n the rate of technologcal progress. The reason s that ths approach s based on the hypothess, frst put forward by Nelson and Phelps (1966), that the man dfference between educated and non-educated workers s the greater capacty of the former to absorb and mplement new technologes. The relatve demand for sklled labour wll then only ncrease f there s faster techncal change that forces frms to employ more educated ndvduals needed to mplement the new technologes. Crtcs of the skll-based techncal change explanaton have argued that t s not consstent wth the productvty slowdown observed durng the 1970s and 1980s. Several counterarguments have been put forward to reconcle faster techncal change wth slower productvty growth. For example, Howtt (1998) hghlghts the measurement problems assocated wth standard measures of total factor productvty based on resdual calculatons from aggregate output data. The most common approach has, however, been the argument that the mplementaton of a new technology nduces a temporary productvty slowdown. The reasons may be that t takes tme to learn to use the new technology, that mplementaton nvolves dvertng resources nto the rsky expermentaton of the new technology, or that durng the phase of mplementaton there s a reducton n the concentraton of hgh-ablty workers n the technologcally advanced sectors, whch dmnshes the lkelhood of further technologcal breakthroughs (see Greenwood and Yorukogklu, 1997; Aghon and Howtt, 1998, chapter 8; and Galor and Tsddon, 1997, 6 See OECD Economc Outlook (2001) 6

8 respectvely). Yet, productvty has fallen over a 20 year perod, whch seems a rather long expermentaton perod. A major concern of our paper s hence whether t s possble for the skll premum to ncrease when the rate of techncal change tself falls. One of the few explanatons of the ncrease n the relatve demand for sklled workers that does not requre faster technologcal change has been put forward by Acemoglu (1998). He argues that researchers can target ther effort to nnovatons that complement ether sklled or unsklled labour. Because of the ncrease n the supply of educated workers n the 1960s, techncal change became skll-based, and the wage rato started to ncrease even though there was no change n the aggregate rate of productvty growth. We buld on the dea that nnovatons are targeted to one or other type of workers. More specfcally, we assume that some goods are produced only wth sklled labour and others wth only unsklled labour. The number of goods produced by each type of worker ncreases over tme, but they may ncrease at dfferent rates. Ths means that the rate of technologcal change n the two sectors can dffer. In ths scenaro, a slowdown n unsklled-orented techncal change would make techncal change more based towards the skll, whle reducng the average rate of productvty growth n the economy. We could then wtness a smultaneous ncrease n the skll premum and a reducton n TFP. Moreover, n our framework a slowdown can ncrease the relatve wage even f techncal change s neutral (.e. f the number of goods n both sectors grows at the same rate). As we have argued before, dfferences n the sklled and unsklled labour markets mply that they are not equally affected by changes n the speed of techncal change. It s then possble for an overall slowdown to reduce both wages, but reduce those of the unsklled by more, leadng to a hgher skll premum. The second problem of the skll-based techncal change hypothess s the evdence of a sharp reducton n the real wage of low-skll workers n the US over the 1980s. Between 1980 and 1989, the real wage of the lowest decle of the earnng dstrbuton fell by 11% n the US (OECD 7

9 Employment Outlook, 1993). Ths can be easly reconcled wth the hypothess that ncreased tradehascausedthechangenrelatvewages,yettsdffcult to explan how faster techncal change -even f skll-based- would reduce the margnal product of unsklled workers. 7 Two recent papers have provded possble explanatons. Casell (1999) consders a set up n whch, followng a technologcal breakthrough, new and old machnes are smultaneously n use. Workers wth hgh (low) sklls use the new (old) machnes. Snce the rate of return on captal has to be equalsed across all types of machnes, there s an ncrease (reducton) n the captal-labour rato for new (old) machnes. Low-sklled workers are now operatng wth less captal, and hence ther margnal product falls. Galor and Moav (2000) explore the dea that f the lowly educated have technology specfc sklls, whle the hghly educated have general sklls, faster techncal change makes some of the sklls of former obsolete, and consequently reduces ther level productvty (see also Echer and García-Peñalosa, 2001). The effcency wage model examned n ths paper provdes an alternatve explanaton for the reducton n real wages, namely that because the rate of growth affects the ncentves of workers to shrk, t mpacts on the level of wages that frms have to pay n order to extract optmal effort from ther labour force. Lastly, the demand-based explanatons have dffcultes accountng for the shfts n employment experenced by OECD countres. As we can see n table 1, the ncrease n the skll-premum has ndeed been greatest n the US and the UK, wth rather modest changes n Italy, Germany and Sweden. Ths rases the queston of why s t that changes that should have affected all ndustral economes n roughly the same way, have not had smlar effects on relatve wages. The standard explanaton has been the followng. Technologcal change and/or trade, have shfted the relatve demand for sklled workers n OECD countres. In the US and the UK, flexble labour markets permtted an adjustment of wages and resulted n the observed ncrease n the 7 See Acemoglu (2000) on ths crtque. 8

10 relatve wage. In Europe, wage rgdtes mantaned the skll premum constant; employment had to adjust, leadng to an ncrease n unsklled unemployment. Table 1 around here However, as t was frst ponted out by Nckell and Bell (1995, 1996), the above argument does not ft the data. Frst, as we can see n table 2, unemployment rates were much hgher n the 1980s than n the 1970s for both sklled and unsklled workers. Ths ncrease n unemployment took place n both the North Amercan and the European economes. Second, the relatve wages of the unsklled have fallen n the UK and the US, whle they have stayed constant n Germany. Yet, unsklled unemployment rates are smlar n Germany and the US, and much hgher n the UK. The demand-based explanatons are ncapable of accountng for the smultaneous shft n relatve wages and the ncrease n unemployment for both types of workers. Our framework provdes a possble explanaton. The effcency wage model mples that there s equlbrum unemployment n all labour markets. Moreover, changes n the rate of techncal change wll affect both wages and employment. In ths context t s possble that a declne n the rate of technologcal progress ncreases both the sklled and unsklled wage, and reduces the level of employment for both types of workers. If the sklled wage ncreases by more, we can smultaneously observe a hgher skll premum and greater rates of unemployment for both types of workers. Table 2 around here To sum up, the hypothess that the ncrease n the skll premum has been due to faster skllbased technologcal progress fnds t dffcult to account for the contemporaneous productvty slowdown, the fall n the unsklled real wage n the US, and the ncrease n unemployment rates 9

11 for both hgh-educaton and low-educaton workers. Usng a supply-sde approach based on the effcency-wage model we are capable of provdng a framework n whch all these varables can move n a way consstent wth the evdence. 3 The Model 3.1 Features of the Economy Workers Tme s contnuous and denoted by t. There are H sklled and L unsklled workers, and E (t) and U (t), = H, L denote the number of workers employed and unemployed, respectvely. Ths means H = E H (t)+u H (t) and L = E L (t)+u L (t). We assume that H and L are fxed and do not allow for ther endogenous determnaton. As regards preferences, all workers are dentcal n that they are rsk-neutral and the ntertemporal utlty functon s tme-addtve. Ths mples thattherealrateofnterestsgvenbytherateoftmepreference,ρ, whchscommontoall consumers. We assume that agents consume all ther labour ncome, w (t), = H, L, as they receve t. They also decde whether or not to exert effort when employed. The nstantaneous utlty functon when employed s w (t) εt (t),= H, L, where εt (t) s the dsutlty of effort and ε can take values ether 0 or 1. T (t) s an ndex of the level of technology whch s specfc to each type of worker snce, as we wll see below, sklled and unsklled workers operate dfferent technologes. Ths means that the cost of effort dffersacrossthetwotypesofworkers. Jobs can be termnated due to technologcal progress. For smplcty, we assume that technologcal progress s the only way n whch workers are separated from frms n equlbrum. There s a probablty η,= H, L that a worker mmedately fnds a job elsewhere followng a technologcal nnovaton whch destroys her job. Ths assumpton captures, n a smple way, the observaton of Davs and Haltwanger (1992) that job-to-job reallocaton of workers n the US 10

12 represents a substantal fracton of worker turnover. In what follows we assume η H η L,that s, that the rate of job-to-job reallocaton s at least as large for sklled as for unsklled workers, reflectng the dea that the former have more transferable sklls that make them more able to deal wth new technologes. The return to a worker from beng employed and not shrkng, denoted by V N by the followng asset equaton: (t), s defned ρv N (t) =w (t) εt (t)+b (t) V U (t) V N (t) + V N (t), = H, L (1) where V U asset value V N (t) s the value of beng unemployed. Ths equaton says that the nterest rate ρ tmes (t) equals the flow benefts of beng an employed non-shrker. The flow benefts consst of the real wage w (t), the dsutlty cost of effort, εt (t), and captal gans/losses. The rate of worker dslocaton, b (t), s endogenous and as we wll see below results from the fact that technologcal progress destroys jobs. Ths then determnes whether or not the worker suffers the captal loss assocated wth movng from a state of employment to unemployment, V U (t) V N (t). Thefnal term, V N (t), captures the captal gans/losses arsng from changes n wages due to the productvty effects of techncal progress and the dynamcs of employment adjustment. (t), follows a smlar recursve equaton, The value of beng an employed shrker, denoted by V S ρv S (t) =w (t)+[b (t)+s ] V U (t) V S (t) + V S (t), = H, L, (2) where the probablty of enterng the state of unemployment s ncreased by s, the probablty of beng found shrkng. Ths probablty s specfc to each category of worker and, n lne wth the lterature on worker montorng, we assume that s L >s H. 11

13 The value of beng unemployed s gven by the followng recursve equaton ρv U (t) =zt (t)+a (t) V N (t) V U (t) + V U (t), = H, L. (3) zt (t) denotes the opportunty cost of employment, ncludng unemployment beneft. Snce n equlbrum no worker shrks, the only way the worker can re-enter employment s f an nnovaton creates new jobs. The rate at whch workers of type are selected from the pool of unemployed to enter employment s gven by a (t). Snce the effort s costly, frms need to ensure that workers do not shrk, whch requres V N = V S. Equatng (1) and (2) gves v N v U = ε s (4) where v U V U /T and v N V N /T are the productvty-adjusted values of beng unemployed andemployedrespectvely.equaton(4)nturnmples v N = v U, = H, L. (5) Producton There s a contnuum of frms wth measure one. The economy produces N varetes of fnal goods, ndexed by j. Aggregate output s then gven by Y = Z N 0 P (j)q(j)dj, (6) where Q(j) s the amount of good j produced, and P (j) ts prce. We assume that we are n a small open economy. All goods are nternatonally traded, ther prces beng determned n world markets and hence exogenously gven. A partcular varety s produced by one type of labour only. Let n H be the number of varetes produced by sklled workers and n L the number produced by unsklled workers, wth 12

14 N = n L + n H. Supposng that all unsklled-produced goods have the same prce, P L, and that all skll-produced varetes have prce P H, we can wrte aggregate output as Y = Z nl 0 Z nh P L Q L (j) dj + Q H (n L + j) dj, (7) 0 where the prce of sklled-produced goods has been normalsed to 1. The producton of fnal goods takes place accordng to a Cobb-Douglas technology n whch only labour s used, Q L (j) = x α L (j) =xα L, (8) Q H (j) = x α H (j) =x α H, (9) where 0 < α < 1, and x(j) s employment n the producton of good j. Frms maxmze profts by equatng the margnal product of labour to the real wage, whch mples the nverse labour demand functons w = αp. (10) x 1 α We defne our ndex of techncal progress as T = n 1 α, and let ω w /T denote the productvty-adjusted wage. We can then express the demand functons as αp ω = (n x ) 1 α (11) = αp. (12) E 1 α where E = n x s total employment of type workers. Techncal Change Techncal change s exogenous, and takes the form of expandng varety. The rate of growth of unsklled-produced and sklled-produced varetes are, respectvely, g L =. n L n L and g H =. n H n H. (13) 13

15 In what follows we are gong to examne how technologcal progress affects relatve wages and employment. Snce most of the lterature on the ncrease of relatve wages has been concerned wth the shft n demand due to skll-based techncal change, we make the followng defntons: Techncal change s neutral whenever g H = g L = g. Techncal change s skll-based whenever g H >g L. Techncal change s de-skllng whenever g H <g L. To understand these defntons, consder for a moment the relatve demand for labour. From equaton (12) we have E Ht E Lt = = µ wlt /P 1 α Lt n Ht w Ht µ wlt /P Lt w Ht n Lt 1 α n H0 n L0 e (g H g L )t, (14) where n 0 s the ntal number of type varetes.whentherateofgrowthofthetwotypesof varetes s the same, the two labour demand functons shft proportonally, leavng the relatve demand for sklls unchanged. Ths s what we term neutral techncal change. A faster rate of growth of skll-produced varetes mples that the relatve demand for sklls ncreases over tme,.e. results n skll-based techncal change, whle for g H <g L the relatve demand falls as technology mproves. 3.2 The Incentve Effects of Technologcal Progress Labour Reallocaton A salent feature of technologcal progress s that new jobs are created as old jobs are destroyed. To understand how these effects work n our model, consder the labour demand functons (11). The number of workers used to produce a gven varety depends on the number 14

16 of varetes of ntermedate goods and on the equlbrum wage. Log-dfferentatng equaton (11) and usng (13) we obtan µ ẋ = x g α ω ω. (15) The left-hand sde s the number of jobs lost n a gven varety n a unt tme nterval. The rght-hand sde shows that the number of jobs lost s proportonal to the number of jobs that exsted wth a coeffcent determned by the rate of ncrease n real wages and by the rate of technologcal progress. If all workers who are separated from frms could not fnd jobs elsewhere, ẋ would be equvalent to the number of ndvduals becomng unemployed n a gven varety. However, recall that we have assumed that a fracton η of workers who are separated from frms are mmedately recruted by a new frm. Therefore, the number of workers jonng the unemployment pool from a gven varety s (1 η ) ẋ, and the probablty of a gven worker becomng unemployed s b = (1 η ) ẋ /x.wethenhave µ b = (1 η ) g + 1 ω 1 α ω Ã! = (1 η ) g Ė. (16) E When employment E s constant, the probablty of becomng unemployed s smply b = (1 η ) g. The number of workers becomng unemployed n a gven varety durng tme nterval dt s gven by x b dt, hence n b x dt s the total number of workers of type becomng unemployed n an economy as a whole. The number of unemployed workers who fnd jobs s a U dt. Therefore, changes n employment durng tme nterval dt are Ė dt =(a U n x b ) dt, whch gves, upon rearrangement, Incentve Effects a = η Ė +(1 η ) g E U. (17) 15

17 We can now examne the mpact of technologcal progress on workers effort ncentves and ts effect on the wage-employment trade-off. Frms ensure that workers do no shrk by settng V N = V S, whch usng equatons (1) and (2) can be solved for productvty adjusted wages ω. The resultng ndvdual no-shrkng condton (NSC )s () ω =[ρ (1 α) g ] µv U + εs + ε +(1 η ) () g Ė /E s ε v N, (18) where v U s to be determned. In fact, equatons (1) to (5) mply v U = z + ε s ηė +(1 η ) U ρ (1 α) g () (v) g E + v U. (19) These two equatons together determne the combnatons of wages and unemployment that ensure that workers do not shrk. Before obtanng the equlbrum NSC t s worth examnng n detal the ncentve effects of techncal change. Equaton (18) gves the combnatons of ω and E that ensure no shrkng (for gven v U ), and shows that ths trade-off s affected by the rate of techncal change. Frst, consder the term ndcated by (). Technologcal progress results n ncreased returns to employment, mplyng that workers lose more f they are found to be shrkng. It therefore tends to strengthen the dscplnary effect of unemployment, allowng frms to reduce the wage for a gven level of employment. We call ths the employment captalzaton effect of productvty growth. It s analogous to what Aghon and Howtt (1994) call the captalzaton effect of growth on labour demand, whch ncreases the return of creatng a new job and makes t proftable for frms to hre more workers. The second effect, ndcated by (), s what we call the job destructon effect. Recallthatb = (1 η ) ³g Ė /E s the probablty of a worker becomng unemployed, and ts nverse, 1/b, s the average duraton of employment. As g ncreases, employment duraton falls, weakenng 16

18 the dscplnary effect of unemployment. Frms are consequently requred to rase ω n order to extract effort from workers. Note that the strength of the job destructon effect depends on the extent of job-to-job reallocaton. If the latter s hgh, the expected duraton of employment s long, and the mpact of job destructon weakens. Techncal change also affects the employment-wage trade-off through v U, as the greater the value of beng unemployed, the hgher the wage needed to nduce no shrkng s. From equaton (19), a hgher g reduces the effectve dscount rate at whch consumers captalze future benefts as unemployed, and makes unemployment a more attractve opton. We call ths the unemployment captalzaton effect of productvty growth. Because ths effect ncreases v U, t tends to rase ω. The last effect s ndcated by (v) n (19). It operates through the job-acquston rate a, whch as we saw n equaton (17) s a functon of the rate of techncal change. Its nverse 1/a s the average duraton of unemployment. As g rses, duraton falls and the dscplnary effect of unemployment weakens. Ths s termed the job creaton effect of technologcal progress. Note that as more jobs are created, real wages rse. Ths predcton sharply contrasts wth studes of technologcal unemployment arsng from the demand sde, n whch more job creaton results n greater employment and lower wages (see, for example, Aghon and Howtt, 1994). Our assumpton that the rate of detecton of shrkers s less than nfnty mples that frms need to use a combnaton of hgher wages and unemployment to provde workers wth suffcent ncentves not to shrk. Usng (5), equatons (18) and (19) can be rearranged nto (ω z) s ε + (1 α) (1 η ) g ρ s E Ė = E 1+ η. (20) E In steady state, where Ė =0, ths condton reduces to ω = z + ε + ε ρ (1 α) g + (1 η ) s 1 E / g. (21) 17

19 The steady state NSC mples an upward-slopng relatonshp between the wage and the level of employment. The wage s equal to the unemployment beneft plus the cost of effort plus a term that captures the ncentve effects. The four effects we dscussed above are n fact combned nto two effects. The term (ρ (1 α) g ) s the effectve dscount rate, and captures the employment and unemployment captalzaton effects. These two effects move n opposte drectons. Yet snce the steady-state flow benefts from unemployment are necessarly less than the flow benefts from employment, 8 the unemployment captalzaton effect wll be less than the employment captalzaton effect, and the overall effect on wages s negatve. The job destructon and job creaton effects are also combned n a sngle term capturng the probabltes of enterng and extng unemployment, snce a + b =(1 η ) g /(1 E /). Botheffects mply that faster techncal change tends to reduce the value of not shrkng, and hence tend to ncrease the wage. Clearly, η plays a crucal role n determnng the strength of the job creaton-destructon effect. A very hgh value, would make t mpossble for frms to use unemployment as a dscplnary mechansm, as when workers get fred they would hardly ever become unemployed. Equaton (21) reveals that there are two basc competng tendences determnng the mpact of growth on effort ncentves. On the one hand, a hgher g reduces the effectve dscount rate, as the growth n real wages caused by technologcal progress rases the value of employment relatve to unemployment and reduces the ncentves to shrk. On the other, the reallocaton of workers nduced by techncal progress ncreases job turnover, mplyng that workers have less ncentve to avod shrkng as they are more lkely to lose ther jobs for other causes. Ether of these two effects may domnate. 8 If the flow benefts of employment were not greater than the flow benefts when unemployed, then there would be no dscplnng effect from unemployment, and t would be mpossble to prevent shrkng. 18

20 3.3 Equlbrum and Comparatve Statcs The equlbrum wage and employment level are then gven by the ntersecton of the demand functon wth the steady state NSC, gven, respectvely, by the followng expressons: ω = αp E 1 α ω = z + ε + ε ρ + ε 1 η (1 α) s s 1 E /, (DD) g. (NSC ) As depcted n Fgure 1, the demand functon s monotoncally decreasng and the NSC monotoncally ncreasng, mplyng a unque equlbrum, (E, ω ). Note from equaton (20) that whenever the wage s greater than ω,thenė > 0, whle for ω < ω,. E < 0. Ths mples that the equlbrum s stable, wth frms movng along the demand functon untl the equlbrum s reached. 9 We can now examne the effect of a number of parameters on the equlbrum. Consder frst the mpact of technologcal change. Dfferentatng the steady state NSC wth respect to g yelds dω dg > 0 for E > be =0 for E = be < 0 for E < be where be = η α <. (22) 1 α Whether a change n g ncreases or decreases the productvty-adjusted wage depends on the equlbrum level of employment relatve to a crtcal value, be. Fgure 2 llustrates the case of a reducton n the rate of technologcal change. A lower value of g pvots the NSC curve around be, from the sold to the dotted curve. If employment s ntally above be, thenthewagefalls and employment rses followng a slowdown n the rate of techncal change, whle f employment s ntally below be alowerg decreases ω and ncreases E. The ntuton for ths results s 9 See Georges (1994) for a proof that ths gradual employment adjustment s the unque equlbrum of the Shapro-Stgltz model. 19

21 smple. We have seen that technologcal progress creates two types of effort ncentve effects, the captalzaton effect and the job creaton-destructon effect. For hgh levels of employment, the latter effect s strong as t mples a short duraton of unemployment. Therefore any slowdown n productvty growth reduces job turnover, reduces the ncentves to shrk and allows frms to reduce the non-shrkng real wage. When employment s low, the captalzaton effect domnates, and the wage rses after a decrease n g. Note that the job-to-job reallocaton rate plays a crucal role n shapng the relatonshp between technologcal progress and wages, as t determnes the threshold level of employment be. For a gven level of employment, the larger η s, the weaker the job creaton-destructon effect s, and hence the more lkely t s that an ncrease n the rate of techncal change reduces the equlbrum wage (.e. the more lkely t s that E s below be ). The rest of the comparatve statcs are straght-forward. A hgher cost of effort shfts upwards the NSC, ncreasng the wage and reducng employment; whle an ncrease n ether the probablty of beng caught shrkng, the rate or job-to-job reallocaton, or the supply of labour tends to reduce the wage and rase employment. Lastly, consder a shft n the demand functon caused by an decrease n the prce of the good produced by type- workers. A lower P shfts the demand functon leftward, resultng n a lower equlbrum wage and level of employment, as see n fgure 3. The long-run equlbrum moves from B 1 to B 3. However, n the short-run the economy moves to B 2 wth ω 2 undershootng ts equlbrum value, ω. Proft maxmzng behavour on the part of frms mples that they wll reman on ther labour demand curves at all ponts n tme, whle n the short-run they can le off the steady-state no-shrkng condton. The reason for ths s that as frms attempt to reduce the sze of ther workforce, the ncreased hre rate has a postve effect on the effort ncentves of ther employees. Ths means that frms can reduce the wages they offer and stll mantan 20

22 effortlevels. Asthehreratereturnstothesteady-statelevel,wagesmustberased,andthe economy moves along the new demand curve untl t reaches the new steady-state equlbrum. That s, the NSC mples that there wll undershootng of wages n response to an decrease n the demand for labour (and correspondngly overshootng n response to an ncrease n demand). 4 Relatve Wages Havng obtaned the equlbrum n each of the two labour markets, we are now n a poston to examne the effect of techncal change on the skll premum. Let Ω t w Ht /w Lt be the relatve wage at tme t. Fromourproductonfunctonwecanexpresstas Ω t = ω Ht.nHt 1 α ω Lt.n 1 α = ω Ht ω Lt or usng the demand functons (12), as Ω t = µ nh0 n L0 Lt µ nh0 n L0 1 α µ ELt E Ht 1 α e (1 α)(g H g L )t, (23) 1 α 1 P Lt e (1 α)(g H g L )t. (24) In the absence of ncentve effects, the levels of employment are smply equal to the supples of the two types of labour, that s, E Lt = L and E Ht = H. 10 Equaton (24) then encompasses the three hypotheses that have been put forward to explan the recent ncrease n the skll premum: the relatve supply of sklls, H t /L t ;theeffect of nternatonal trade, captured by a change n the relatve prce of unsklled-produced goods P Lt ; and skll-based techncal change, as reflected by the dfference n the rate of nnovaton of the two types of goods, g H g L. Introducng ncentve consderatons mples that wages wll depart from ther market-clearng levels, and adds an alternatve mechansm through whch technologcal progress can affect relatve wages. There are two mportant ways n whch the supply-sde effect dffers from the 10 We are mplctly assumng that the unemployment beneft s below the wage that would clear the market. Otherwse, E t =(αp /z) 1 α andtherewouldbeunemployment. 21

23 above demand-drven mpact of techncal change. Frst, n contrast to the exstng lterature, an ncrease n the skll premum can be consstent wth a reducton n the rate of technologcal change. Second, as we wll see below, techncal change may ncrease the skll premum even f t s neutral. 4.1 Based Techncal Change and the Productvty Slowdown That skll-based techncal change ncreases the relatve wage n our model wll come as no surprse. Stll, t s worth examnng how the supply-sde effects nteract wth the standard demand-sde mpact. Because of the mportance of the productvty slowdown durng the 1980s, let us consder the effect of a fall n the rate of technologcal change. Suppose, more precsely, that we start n a stuaton of neutral techncal change, wth g L = g H,andthattheresa reducton n g L to gl 0,whleg H remans constant. That s, technologcal progress becomes skll-based. The economy experences a productvty slowdown. To see ths, dfferentate the producton functon and use the fact that, n steady state, ẋ /x = g to express the rate of output growth as. Y Y =(1 α)(θg H +(1 θ)g L ), where θ s the share of output produced by sklled workers, θ = n H Q H /(n L P L Q L + n H Q H ). In steady state, snce employment does not change, output growth s equvalent to productvty growth, and the change n g L lowers the rate of productvty growth from (1 α)g H to (1 α)(θg H +(1 θ)gl 0 ). Consder now what happens to wages. The sklled labour market remans unchanged, employment remans constant and the real wages of sklled workers keep growng at rate (1 α)g H. In the unsklled labour market, the NSC pvots. As we saw before, two stuatons are possble. 22

24 If the ntal level of employment s above the threshold be L, then the productvty adjusted wage ω L falls n response to the change n g L. Both the rato ω H /ω L and the extent of skll-bas n demand, as measured by (g H g L ), ncrease and by equaton (23) so does the relatve wage. In ths case, the supply-sde effect magnfes the ncrease n relatve wages stemmng from the demand for labour. If the ntal level of employment s below the threshold be L,thenω L wll rse. The rato ω H /ω L wll fall, mplyng that the presence of ncentve effects partly offsets the demand-led ncrease n the relatve wage. Note that for E L > be L, the real unsklled wage, w Lt = ω L (n L0 ) 1 α e (1 α)glt, may actually fall when g L falls. If the fall n g L s large enough, then the reducton n the productvty adjusted wage could, for a perod of tme, offset the effect of mprovng productvty. 11 Under ths scenaro, we would smultaneously have an ncrease n the skll premum, a productvty slowdown, and a reducton n the real unsklled wage. 4.2 Neutral Techncal Change Suppose now that the two types of varetes ncrease at the same rate, g H = g L = g, and that there s a reducton n the rate of techncal change. What would be the mpact on the relatve wage? We can see from equaton (23) that there s no demand effect as the demand for both types of workers shfts proportonally. The only mpact stems from the mpact of a lower g on the productvty-adjusted wages. Consder the rato of the productvty-adjusted wages, ω H /ω L.Dfferentatng we have d(ω H /ω L ) dg = 1 dωh ω L dg ω H dω L. (25) ω L dg where dω (1 α) ³E be dg = s ( E ) g ε + 1 η 1 α ω. E E 11 For example, the unsklled wage would defntely fall f g L dropped to zero. 23

25 The frst thng to note n equaton (25) s that neutral techncal change s not neutral. The reason for ths s that t affects dfferently the effort ncentves of the two types of workers and hence elcts dfferent wage responses on the part of frms. The mpact of techncal change on the relatve wage s n prncple ambguous. The cause of ths ambguty s twofold. Frst, as we saw n secton 4, slower technologcal progress may ncrease or decrease productvty-adjusted wages dependng on whether the captalzaton or the job creaton-destructon effect domnates. Second, knowng the sgn of the change n ω L and ω H s not suffcent, as both can move n the same drecton mplyng that we also need to know ther magntude. Two parameters dffer across the two labour markets and hence allow us to pnpont some of the crcumstances under whch neutral techncal change wll unambguously ncrease or decrease the skll premum. Suppose frst that s L =. Substtutng for t n equaton (25) we have (ω H /ω L ) g = 1 ω L s Hε H E H 1 α E H be H +(1 η H) g. (26) HE H ω H H E H Slower neutral techncal change decreases the relatve wage for E H > be H, and ncreases t otherwse. The ntuton for ths result s straghtforward. Because shrkng s mmedately detected, there s no need to use a hgh wage as a dscplnary mechansm. Frms wll smply compensate workers for the cost of effort, and pay them ω L = z + ε. The unsklled wage s consequently ndependent of the rate of techncal change. A fall n g then ncreases the relatve wage f and only f t ncreases the sklled productvty-adjusted wage. A second parameter of nterest s the extent of job-to-job reallocaton. Job-to-job reallocaton s mportant because t determnes the strength of the job creaton-destructon effect of techncal change and hence whether t ncreases or decreases wages. Consder the extreme case n whch η L = α and η H =1; that s sklled workers who are fred mmedately fnd a new job, whle unsklled workers always enter the unemployment pool. Then we have that be L =0and be H = H, and equaton (25) mples 24

26 (ω H /ω L ) = 1 α g ω L H E H s H (H E H ) ε α g ω H HE H H E H + ω H ω L s L(L EL ) ε E L + g LE L ω L L E L < 0. (27) A hgh value of η H mples that the job creaton-destructon effect dsappears n the sklled labour market. Slower techncal change has only a captalzaton effect, whch ncreases the equlbrum sklled wage. In the unsklled labour market, low reallocaton makes the job creaton-destructon effect domnate, resultng n a lower unsklled wage. That s, ω H ncreases and ω L falls, leadng to a hgher skll premum. 4.3 Calbraton In order to look at possble patterns of wage nequalty followng a reducton n the rate of neutral techncal change, we calbrate the model and obtan numercal examples. Recall that the equlbrum of the model s gven by the ntersecton of the followng curves: ω = αap, E 1 α ω = z + ε + ε s ρ + ε s 1 η 1 E (1 α) g, where A s a scale parameter n the producton functon ntroduced n order to get reasonable values for wages and employment, and the sklled and unsklled labour forces have been normalsed to 1. We choose the followng parameter values: Preferences: ρ =0.04, ε =1 Labour market: L =1, H =1, z =0 Technology: α =0.6,A=4.1 s H =0.02,s L =0.2 Prces: P H =1,P L =0.66 η H =0.99, η L =

27 The values of ρ and α are standard, correspondng to a rate of tme preference of 4% and an the elastcty of labour of 60%. The cost of effort and the scale parameter A have been arbtrarly chosen. The prce of the skll-produced good s used as a numerare, and t s assumed to be 50% hgher than that of the unsklled good n world markets. There are no unemployment benefts. The probablty of a shrker beng caught s assumed to be 10 tmes as large for unsklled than for sklled workers, reflectng the dea that montorng those performng menal tasks s much easer. The choce of job-to-job reallocaton parameters s not obvous, as the evdence s sparse. Evdence on transfers followng job destructon suggests that n Germany 32% of all separatons result n re-employment wthn one week, and n Canada 53% of workers where n a new job wthn 3 weeks. 12 Because we are usng annual values n the calbratons, the correspondng rates of job-to-job reallocaton should be much hgher. We can obtan an ndrect estmate from the evdence presented by Davs and Haltwanger (1992). They fnd that, n the US, total worker reallocaton n a year -.e. the proporton of workers that change employers or transt from employment to joblessness durng a year- was 36.8% over the perod the We can then use the unemployment rates to proxy whch proporton of those separated from an employer have another job wthn a year. Durng ths perod the unemployment rates for hgh-educaton and low-educaton workers were 2% and 7.8%, respectvely. 13 The flow nto unemployment of type workers can be expressed as f =0.368 E (1 η ), (28) assumng the same reallocaton rate for sklled and unsklled workers. If the flow were equal to the stock,.e. all those unemployed would fnd a job wthn the year, the mpled job-to-job reallocaton rates would be and 0.77 for sklled and unsklled workers, respectvely. Of 12 See OECD (1996). 13 See Nckell and Bell (1996). These are unemployment rates for the perod

28 course, not all workers do fnd a job wthn a year, mplyng that these fgures provde only a lower bound. Supposng that only 10% of those unemployed fnd a job wthn the perod, the correspondng rates would be η H = and η L = We can vew these numbers as lower and upper bounds for our proxy. In our benchmark calbraton we use the values η H =0.99 and η L =0.75, representng the greatest dfference between the two categores of workers mpled by these estmatons. We wll then perform comparatve statcs on them. The above parameters are used to obtan values for the benchmark economy, depcted n the frst three columns of table 3. We consder the effect of a reducton n the rate of productvty growth from 5% to 1% on the benchmark economy. We can see that a reducton n g, ncreases ω H and reduces ω L. The productvty slowdown thus results n an ncrease n the skll premum accompaned by a reducton n the real unsklled wage. These results depend strongly on the degree of job-to-job reallocaton for the sklled. Table 3 shows that as η H changes we obtan anumberofdfferent patterns. 14 Forhghvaluesofη H,e.g. η H =0.99 and η H =0.95, the reducton n the rate of techncal change ncreases the skll premum. For η H =0.8, both the sklled and the unsklled wage fall wth g. In ths partcular case, the two wages change proportonally and the skll premum s unaffected by the productvty slowdown. For an even lower rate of job-to-job reallocaton, η H =0.75, the sklled wage falls by more, leadng to a reducton n the skll premum. In other words, a reducton n the rate of neutral technologcal change may ncrease, decrease, or keep constant the skll premum dependng on the rate of job-to-job reallocaton for sklled workers. Tables 3, 4, 5 around here 14 Note that the unsklled wage s only reported once, as t does not depend on η H. 27