What does economic theory tell us about labour market tightness?

Transcription

1 What does economc theory tell us about labour market tghtness? Andrew Brgden and Jonathan Thomas Workng paper no. 85 Bank of England, Threadneedle Street, London, EC2R 8AH. The vews expressed here are those of the authors and do not necessarly reflect those of the Bank of England, or the Monetary Polcy Commttee. The authors gratefully acknowledge comments receved from Larry Ball, Ian Bond, Mke Joyce, Stephen Nckell, Chrs Pssardes, Mark Schwetzer, two anonymous referees, and semnar partcpants at the Bank of England. Copes of workng papers may be obtaned from Publcatons Group, Bank of England, Threadneedle Street, London, EC2R 8AH; telephone , fax , e-mal Workng papers are also avalable at The Bank of England's workng paper seres s externally refereed. Bank of England 2003 ISSN

2 Contents Abstract 5 Summary 7 Introducton 9 2 Labour market models 2 2. The standard compettve model Effcency wage models The model of Layard, Nckell and Jackman (99) Models of skll msmatch Models of matchng frctons Summary of model mplcatons 37 3 From labour market tghtness to nflatonary pressure 38 4 Conclusons 4 References 43 Appendx: The wage bargan 45 3

3 Abstract Labour market tghtness s a phrase often used by commentators and polcy-makers, but t s rarely defned. In ths paper, the phrase labour market tghtness s nterpreted as descrbng the balance between the demand for, and the supply of, labour. A logcal consequence of ths approach s that tghtness s not a helpful concept n those models of the labour market, such as the standard compettve and the basc matchng model, where there are nsuffcent rgdtes to create mbalances between labour demand and supply. It s proposed that changes n the labour share of ncome are a convenent yardstck for measurng changes n labour market tghtness. In response to certan knds of shock, changes n the labour share wll gve msleadng sgnals, but ths s lkely to occur less frequently than wth other oft-cted tghtness ndcators such as the unemployment rate or the employment rate. The paper concludes by consderng the lnks between labour market tghtness and nflaton. A key lesson from ths analyss s that any attempt to nfer the relatonshps between labour market tghtness, varous market ndcators of t, and nflaton, requres both a clear defnton of tghtness and depends on the specfc model of the labour market. Key words: Labour market tghtness, labour share, nflaton. JEL classfcaton: E240, E30, J230. 5

4 Summary The am of ths paper s to offer a coherent framework for examnng the underlyng drvers of labour market tghtness, and the relatonshp between labour market tghtness and nflaton. Our motvaton stems from the fact that although the phrase labour market tghtness s frequently used n the economcs lterature, t s rarely defned. Nonetheless, a varety of emprcal evdence on labour market quanttes and prces, such as unemployment and average earnngs growth, s often cted as evdence of changes n the tghtness of the labour market. Wthout a clear defnton of the phrase t s dffcult to evaluate the usefulness of any evdence offered; and a proper understandng of the relatonshp between tghtness and nflaton s also problematc. In our vew labour market tghtness can be defned n terms of ts mplcatons for the labour share of ncome. Ths follows from the noton that the labour market s tght (loose) when there s an mbalance between labour demand and labour supply, whch wll exert upward (downward) pressure on real unt labour costs, or equvalently on the labour share. Because the words tght and loose mply a degree of mbalance, we assert that the labour market can only be consdered tght or loose out of steady state. Ths has two mportant mplcatons. Frst, no shock can cause the labour market to become tght or loose unless t pushes the labour market away from ts steady state. In practce, ths s not too restrctve, snce the knds of rgdty that are present n most popular macro-models are suffcent to do ths. Second, any shock that alters the steady-state value of the labour share cannot be sad to have made the labour market permanently tghter or permanently looser. Ths s because movements n the steady-state do not nvolve any change n the balance between the demand for, and supply of, labour. We use our defnton of labour market tghtness and ts assocated propertes to examne the tghtness mplcatons of several popular labour market models. We start wth the basc compettve model, and then work through models of effcency wages, nsder power, skll msmatch and matchng frctons. A key message of ths exercse s that the mplcatons of much-cted ndcators of changes n labour market tghtness, such as unemployment, depend crtcally upon both the underlyng economc shock and any market rgdtes. For example, n the model of nsder power a postve shock to nomnal money balances leads to a tghtenng of the labour market that s accompaned by a declne n unemployment, whch subsequently rses over tme back to ts unchanged steady-state value. On the other hand, an adverse labour supply shock n the perfectly compettve or effcency-wage models leads to a tghtenng of the labour market that s accompaned by a rse n unemployment to a hgher steady-state value. 7

5 We then turn to the relatonshp between tghtness and nflaton. By our defnton, a tghtenng of the labour market wll cause the labour share of ncome to rse. Snce labour market tghtness s a real phenomenon, t wll have no mplcatons for nflaton unless the economy s subject to some form of nomnal rgdty. Examples of such rgdtes that could plausbly underpn a lnk between tghtness and nflaton nclude stcky prce expectatons, and restrctons on the frequency wth whch frms can alter prces. If such frctons are present, t s possble for out of steady-state movements n the labour share to nfluence nflaton. A key lesson from ths analyss s that any attempt to nfer the relatonshps between labour market tghtness, varous market ndcators of t, and nflaton, requres both a clear defnton of tghtness and depends on the specfc model of the labour market. 8

6 . Introducton Labour market tghtness s a phrase often used by economc commentators and polcy-makers alke, yet t s rarely defned. Nonetheless, a varety of emprcal evdence on labour market quanttes and prces, such as unemployment and average earnngs growth, are often cted as evdence on changes n the tghtness of the labour market. Wthout a clear defnton of the phrase t s dffcult to evaluate the usefulness of any evdence offered. A proper understandng of the relatonshp between tghtness and nflaton s also problematc. Wth these ssues n mnd, ths paper has two key ams. The frst s to outlne what popular labour market models have to say about the drvers of labour market tghtness as we nterpret t. To ths end, we start wth the basc market-clearng model, and then work through models of effcency wages, nsder power, skll msmatch, and matchng frctons. The second am s to nvestgate the lnkages between tghtness and nflaton. Polcy-makers and commentators tend to speak n terms that mply a lnk between a tghtenng of the labour market and nflaton. However, labour market tghtness, as we nterpret t, s fundamentally a real concept. A tghtenng of the labour market may cause frms to pay more n real terms for a gven qualty of labour, but t does not necessarly follow that there are consequences for the general prce level. Gven plausble nomnal rgdtes n the economy, t s, however, possble for movements n labour market tghtness to have nflatonary consequences. Several examples of such nomnal nerta, such as stcky prce expectatons, are dscussed. Before we go any further, t s worth settng out some mportant concepts. Frst, what does labour market tghtness mean? Ideally, one needs a workng defnton that s suffcently broad to embrace all of the models consdered. To ths end, we propose that labour market tghtness be taken to descrbe the balance between the demand for, and the supply of, labour. If the demand for labour ncreases relatve to supply, the labour market tghtens, then we can expect some upward pressure on the real prce of a gven quantty of labour. So a tghtenng of the labour market s lkely to produce an ncrease n real unt labour costs, or equvalently an ncrease n the labour share of ncome. () Ths suggests that movements n the labour share can be used to measure changes n market tghtness. However as the paper proceeds, t wll soon become apparent that, even n the smplest () The labour share s the fracton of total output that goes to workers. In our context t should be thought of as excludng the self-employed as they are gnored n the labour market models we consder. Batn, Jackson and Nckell (2000) consder a measure that () ncludes the self-employed and publc sector, () ncludes the self-employed and excludes the publc sector. Ther excluson of the publc sector can be justfed by the fact that they are prmarly nterested n modellng the prcng decsons of prvate sector frms. Both measures gve smlar results n regressons explanng the behavour of nflaton. 9

7 labour market models, focusng on the labour share can lead to stark, and arguably counter-ntutve, conclusons. To llustrate, when the producton functon s Cobb-Douglas, both product and labour markets are perfectly compettve, and frms have the rght to manage, the labour share s constant and equal to the exponent on labour n the producton functon. Ths means that shocks to labour supply, caused perhaps by a change n the replacement rato, whch ntutvely one mght assocate wth a tghtenng or loosenng of the labour market, have no effect on our proposed ndcator. The flp sde s that shocks to the exponent on labour n the producton functon, or (f we relax the assumpton of perfectly compettve product markets) shocks to the degree of product market competton, cause a permanent shft n the labour share, and therefore market tghtness. To address these ssues, we shall argue that shocks to labour supply can only affect labour market tghtness f they move the economy out of steady state n such a way as to generate mbalances between the demand for and supply of labour. Ths wll occur f there are certan rgdtes n the economy, such as sluggsh employment adjustment, or adaptve wage and prce expectatons. These sorts of rgdty are bult nto some of the labour market models we consder, but they are not present n all of them. For example, the textbook compettve and matchng models are always n equlbrum. As a result the noton of a tght or loose labour market s not a helpful concept n these cases. Moreover, we assert, for reasons that we hope wll become clear, that shocks to labour demand whch cause a permanent shft n the labour share do not ndcate a permanent shft n labour market tghtness. As Chart below shows, the UK labour share has tended to fluctuate around a well-defned mean, suggestng that permanent shocks to the UK labour share have been ether very nfrequent, offsettng, or small. Chart The labour share of ncome n the Unted Kngdom (a) (a) The numerator s compensaton of employees. The denomnator s GDP at factor cost mnus an estmate of selfemployment ncome. 0

8 Our framework mples that t s more convenent to judge whether the labour market has become tghter or looser by lookng at labour market prces. But changes n labour market tghtness often have mplcatons for labour market quanttes. Indeed, t s sometmes argued that the effects of changes n labour market tghtness wll be seen n labour market quanttes before they are seen n prces. Ths belef s mplct n the structure of the Bank of England s macroeconometrc model (Bank of England (999)), where a shock to aggregate demand frst rases hours worked. Other thngs equal, ths ncrease n hours worked rases the number of people n employment and reduces the number of people n unemployment. It s ths reducton n unemployment that fnally puts upward pressure on real unt wage costs, or equvalently the labour share of ncome, through pay growth. So n the Bank of England s macroeconometrc model a tghter labour market mples a lower unemployment rate. As we revew the dfferent theoretcal models, we shall note what each has to say about the knd of changes n labour market quanttes that one mght see when the labour market becomes tghter. In some cases we fnd that unemployment s lkely to be fallng, but n other cases t s lkely to be rsng. Thus one of the key lessons from ths paper s that focusng on quantty-based measures can sometmes gve a msleadng mpresson about the evoluton of labour market tghtness. To sum up, we defne labour market tghtness as descrbng the balance between labour demand and supply. Changes n labour market tghtness are lkely to produce changes n real unt labour costs, or equvalently, changes n the labour share of ncome. In our vew, the labour market can never be consdered permanently tghter or permanently looser: demand/supply equlbrum must eventually be re-establshed. Consequently, economc shocks can only affect labour market tghtness f, and for as long as, they move the labour market away from that steady state. A tghtenng of the labour market, n our terms, wll cause the labour share of ncome to rse. But snce we defne labour market tghtness as a real phenomenon, such movements wll have mplcatons for nflatonary pressure only f the economy s subject to some form of nomnal rgdty. Examples of such rgdtes that could plausbly underpn a lnk between tghtness and nflaton nclude stcky prce expectatons, and restrctons on the frequency wth whch frms can alter prces. Naturally, none of ths affects the concluson that the rate of nflaton s ultmately determned by the monetary stance. The layout of the paper s as follows. Secton 2 sets out a number of popular labour market models and outlnes what each model has to say about the determnants of the labour market tghtness. Whle there s some overlap n the underlyng drvers, several of the models pont to determnants that are not covered by others. In Secton 3, we outlne several mechansms by whch a tghtenng of the labour market wll lead to an ncrease n nflatonary pressure. A fnal secton concludes.

9 2. Labour market models 2. The standard compettve model Background The standard compettve model assumes that frms and workers are prce takers n the product and labour markets, and that wages and employment are set at the level where aggregate labour demand and aggregate labour supply are equalsed. Thus unemployment s voluntary and s defned as the dfference between some exogenous tme endowment and actual hours worked. We begn wth a very smple structure. On the demand sde, output s produced accordng to a Cobb-Douglas producton functon wth labour and captal and as factor nputs. Ths generates a conventonal downward slopng labour demand curve. We assume that frms are always on ther labour demand curves whch means that they set employment (frms have the rght to manage ). The labour supply curve s derved from a utlty functon defned over consumpton and lesure and s assumed to be upward slopng. Equlbrum wages and employment are affected by technologcal changes that are based towards a partcular factor nput, and by changes n the level of unemployment benefts. Technologcal changes shft the labour demand curve, whle beneft changes shft the labour supply curve. Key equatons Labour demand s derved by assumng that each dentcal frm faces a Cobb-Douglas producton functon gven by (2..). Y N K (2..) Y s output, N s employment and K s the (fxed) captal stock at frm. For smplcty, we assume that 0 <N< so that N s also the employment rate. Proft () s gven by: PY WN rk (2..2) where P s the prce level, W s the wage rate, and r the rental rate of captal. Dfferentatng (2..2) wth respect to N and usng (2..) leads to the followng labour demand equaton, W Y (2..3) P N 2

10 The supply sde of the labour market s based on an aggregate utlty functon of workers, whch s defned over a composte consumpton good, C, and lesure, -N. Utlty s descrbed by the followng CES utlty functon: ( ) / ( ) / /( ) U [ C ( )( N) ] (2..4) 0<< captures the weght whch workers place on consumpton and lesure, whle s the elastcty of labour supply. Let b < W be the real level of unemployment benefts. Then the workers budget constrant s the sum of wage and benefts weghted by the share of tme allocated to employment and unemployment respectvely. Followng Pssardes (998), ths budget constrant can be wrtten as: C NW ( N) b (2..5) Substtutng (2..5) nto (2..4), t follows that workers choose N to maxmse the followng utlty functon: U [ ( NW ( N) b) ( ) / ( )( N) ( ) / ] ( ) / (2..6) Maxmsng utlty wth respect to N leads to the followng labour supply schedule: N /( N) [( ( W b) /( )) b] / W (2..7) Dfferentatng the labour supply schedule wth respect to W shows that t s upward slopng f we assume that > - b/w. Market equlbrum s gven by the ntersecton of labour demand (2..4) and labour supply (2..7) whch can be solved for wages and employment. The exogenous varables n the model are, the exponent on labour n the producton functon, whch shfts the labour demand functon, and b, the real level of benefts, whch shfts labour supply. 3

11 Implcatons for labour market tghtness Chart 2 Compettve model wth nstantaneous employment adjustment: adverse labour supply shock W/P L S * J L S E* E L D N 0 Chart 2 plots the labour demand and labour supply curves n real wage/employment space. Suppose that unemployment benefts, b, rse. The labour supply curve shfts from L S to L S * and the equlbrum moves from E to E*. The real wage s now hgher, and employment s lower, but what of the labour share? Lookng back at equaton (2..3), we can see that all along the labour demand curve, the labour share (W.N / P.Y) s constant and equal to. And snce frms have the rght to manage, we know they are always on ther labour demand curve. As the economy moves from E to E*, the real wage ncreases but employment falls. As employment falls productvty rses. Indeed, employment falls and productvty rses just enough such that the labour share s unchanged. Does ths mean the labour share s not a good ndcator of labour market tghtness? Not necessarly. In the above example, there s no mbalance between the demand for and the supply of labour. At pont E*, and at pont E, frms are operatng on ther labour demand curve and workers are operatng on ther labour supply curve. When unemployment benefts rse, frms ratonally cut producton and hence ther need for labour declnes. In ths perfectly compettve model, the economy s always n steady state and, accordng to our defnton, the labour market can be nether tght nor loose. In practce, t seems unlkely that frms wll mmedately adjust employment followng an economc 4

12 shock, perhaps because of hrng and frng costs. (2) Consder nstead how the labour share would respond f employment were fxed n the short term. Followng the shft n the supply curve from L S to L S *, the system must jump to a pont lke J. Now there s an mbalance between the demand for and supply of labour. In order to mantan staffng levels, frms must pay a hgher real wage. But employment and productvty are unchanged. Hence the labour share rses. It s not optmal for frms to mantan such hgh levels of producton, so employment starts to fall, and we move back down L S * to the fnal equlbrum at E*. In an economy where the labour supply curve s ht by a seres of nfrequent shocks, and frms cannot adjust employment mmedately, the labour share wll vary over tme but have a constant mean. Ths seems to be a reasonable descrpton of the data n Chart. (3) In ths example, an assumpton that employment s fxed n the perod mmedately followng a shock s suffcent to push the economy out of steady state. It s ths departure from steady state that allows scope for the labour market to be ether tght or loose for short perods of tme. Chart 3 Compettve model wth sluggsh employment adjustment: postve labour demand shock W/P J E* L D * L S E L D 0 N Equaton (2..3) shows that the poston of the labour demand curve L D depends only on, the exponent on labour n the Cobb-Douglas producton functon. Chart 3 shows how the labour demand (2) Nckell (986) and Bentolla and Bertola (990) provde emprcal evdence that such costs are mportant. (3) If the producton functon s of the CES form then an adverse labour supply shock wll lead to a rse n the labour share f the elastcty of substtuton between captal and labour s less than one. The labour share wll fall f ths elastcty s greater than one. In the Cobb-Douglas case ths elastcty s equal to one. 5

13 curve mght shft followng a rse n Sluggsh employment adjustment means that wages jump up n the short run to a pont lke J. Snce J s on a hgher labour demand curve, we know that the labour share has rsen. Ths new hgher labour share s mantaned as real wages declne, employment rses and we reach a new steady state at E*. In the ntroducton we stated, wthout attemptng to justfy the statement, that we dd not beleve that a permanent shft n the labour share ndcated a permanent shft n labour market tghtness. We hope ths example goes some way towards explanng our reasonng. At pont E* there s no mbalance between the demand for, and the supply of, labour. Frms are operatng on ther labour demand curve and workers are operatng on ther labour supply curve. Workers enjoy an ncreased share of natonal output snce, followng the shock, they are producng an ncreased share of natonal output. In models that have staggered wage and prce settng and nomnal rgdtes, such as the one due to Layard, Nckell and Jackman (99) that we consder n Secton 2.3, then shocks other than to the exponent on labour n the producton functon can seemngly cause a labour demand curve that s drawn n actual real wage (W/P) employment space to move. That s because the labour demand curve s only stable when drawn n expected real wage (W e /P) employment space. Consder a postve shock to nomnal money balances that occurs after prces have been set. Demand and employment are lkely to ncrease n the short term causng an ncrease n nomnal wages that frms had not expected when they set prces. One could argue that ths amounts to a temporary upward shft n the labour demand curve L D as drawn n Chart 2. Yet we would argue ths s not really a shock to labour demand n the true sense, rather that the rgdtes n the model have forced frms to employ, temporarly, more labour than they would lke to and hence operate off ther labour demand curve. (4) Notce that L D and L D * cross as N moves towards zero. At very low rates of employment, technology shocks that are based towards labour and away from captal cause the real wage to fall. That s because such technology shocks are harmful to output when the captal stock s relatvely large and hence reduce average labour productvty. Ths stuaton s unlkely to occur n practce. 6

14 Table A: The consequences of dfferent shocks n the standard compettve model Shock Postve labour demand ( up) Adverse labour supply (b up) (nstantaneous adjustment) Adverse labour supply (b up) (sluggsh adjustment) Unemployment Real wages Labour share Table A lsts the responses of three dfferent varables (unemployment, the real wage rate, and the labour share) to shocks n the standard compettve model. The frst column outlnes the mplcatons of a labour-based technology shft (e a postve labour demand shock). Unemployment falls, real wages rse and the labour share rses. Yet we do not beleve ths sgnals a tghter labour market as there s no resultng mbalance between the demand for and supply of labour. An ncrease n unemployment benefts (adverse labour supply shock) has no mplcaton for the labour share and therefore market tghtness, unless suffcent rgdtes exst to shft the economy out of steady state. One such rgdty s a restrcton that output cannot change n the mmedate perod. Ths would cause real wages to overshoot, and the labour share to jump up. In the long run, unemployment would rse, real wages would fall back slghtly and the labour share would return to ts (unchanged) steady-state value. 7

15 2.2 Effcency wage models Background The key assumpton here s that worker productvty s ncreasng n the wage pad by the frm. Ths may reflect the dea that more productve workers set hgher reservaton wages, so that hgher pay attracts better job applcants and rases workforce qualty. Alternatvely, a hgher wage may dscourage worker shrkng because t rases the cost of beng unemployed. Ths lnk between worker productvty and pay provdes a ratonale for the exstence of nvoluntary unemployment because frms have an ncentve to pay wages above the level that clears the market. We consder the shrkng varant of effcency wages developed by Shapro and Stgltz (984). In ths case, frms cannot perfectly observe worker behavour. So to dscourage shrkng they attempt to pay a wage premum whch exceeds any premum pad by ther compettors. Such behavour by all frms pushes average wages above the compettve equlbrum whch generates nvoluntary unemployment. Ths unemployment acts to further reduce shrkng because t rases the cost of job loss f the worker s dscovered shrkng and fred. Compared to the compettve model, the effcency wage model delvers a rcher set of demand and supply-sde varables that can nfluence the labour market equlbrum and thus the labour share. For example, monopoly power n the goods market can feed through to labour demand because the margnal product of labour s equal to the product of the mark-up and the real wage. On the supply sde, changes n the ablty of frms to montor workers or the rate of labour turnover can also affect market tghtness. We employ a standard prce-settng and wage-settng framework n real wage / employment space (Layard et al (99), Blanchard (997)). Specfcally, dentcal mperfectly compettve frms produce a sngle good under a Cobb-Douglas producton technology, and set employment to maxmse profts. Ths leads to a downward slopng prce-settng curve. Once agan t s assumed that employment adjustment s sluggsh. The wage-settng schedule, whch Shapro and Stgltz (984) call the no-shrkng condton s upward slopng, reflectng the dea that hgher real wages are necessary to nduce postve effort as the economy tends towards full employment. Key equatons Each frm faces a Cobb-Douglas producton functon gven by (2.2.) and a constant-elastcty of substtuton demand functon gven by (2.2.2). 8

16 9 K N Y (2.2.) d Y P P Y (2.2.2) Y s the output of frm, N s the number of people employed n frm, K s the (fxed) captal stock at frm, P s the prce charged by frm, P s an aggregate prce ndex, s the elastcty of demand, and Y d s an aggregate demand ndex. Proft ( ) s gven by: rk WN Y P (2.2.3) where W s the wage rate (common to all frms) and r the rental rate of captal. Usng (2.2.) to substtute for N then (2.2.2) to substtute for Y and rearrangng we obtan: d d rk K Y P P W Y P P (2.2.4) Dfferentatng wth respect to frm s prce, settng ths dfferental to zero, and usng the assumpton that all frms are dentcal, P = P gves: where d K Y W P (2.2.5) Usng ths n the demand functon (2.2.2), we can see that actual output for all frms (Y ) s equal to the demand ndex, Y d. Makng ths substtuton back nto (2.2.5), and usng the producton functon to remove K, we obtan: ) / ( N Y W P (2.2.6) (2.2.6) says that product prces are equal to a constant mark-up over margnal cost (where margnal cost s the wage rate tmes the nverse of the margnal product of labour, W/(Y/N). The mark-up s

17 / = /( -). Snce we are conductng our analyss n real wage / employment space t s useful to rearrange the prce-settng curve accordngly. Thus: (5) W P Y (2.2.7) N The man nnovaton n the shrkng model concerns the determnants of the supply sde of the labour market whch s gven by the no-shrkng condton. The argument s neatly summarsed by Pssardes (998). Consder a statonary envronment where dentcal rsk neutral workers can be employed or unemployed. Let the expected returns n each state be E and U respectvely. Workers have a utlty functon U (w, e)=w - e, where w s the real wage and e s the level of effort devoted to the job. The effort level s 0 f the worker shrks or e > 0 f he or she does not. All shrkers face the probablty, q of beng caught and dsmssed nto unemployment. Utlty s zero f the worker s unemployed. Further suppose that there s an exogenous rate of job separatons, s, and that workers dscount the future at rate r. Let the expected returns of a non-shrker and shrker be ns E and s E respectvely. For a non-shrker, these returns are the dscounted value of utlty, w - e, less the dscounted expected utlty loss from ns exogenously losng the current job and movng nto unemployment se U. Thus, re ns ns w e s( E U ) (2.2.8) In the case of a shrker the utlty of the job s w but the probablty of enterng unemployment s s + q. Thus we can wrte, re s s w ( s q)( E U ) (2.2.9) Frms offer a wage that makes the ndvdual ndfferent between shrkng and non-shrkng. Thus n equlbrum E ns E s E. From (2.2.8) and (2.2.9) t follows that E = U + e/q. Substtutng ths (5) Notce that ths rearrangement makes the prce-settng schedule look lke a standard labour demand schedule. But the two are fundamentally dfferent. The labour demand relaton s derved under the dea that frms take wages and prces as gven because they operate n compettve labour markets. However, the prce-settng curve allows frms to set prces. Therefore the level of competton n the goods market wll affect the prce-settng curve but not the labour demand curve. Smlarly the standard labour supply curve gves the wage at whch a gven number of workers are wllng to work, whle the wage-settng curve s the outcome of worker-frm barganng or the unlateral decsons of frms. Therefore factors such as the decentralsaton of pay barganng wll affect the wage-settng curve but not the labour supply curve. 20

18 nto (2.2.8), solvng for w and mposng symmetry so that w = w allows us to derve the aggregate real wage n terms of U. Therefore, w ru ( r s q)( e / q) (2.2.0) The return from unemployment can be defned as the dscounted value of unemployment benefts, b, plus the probablty of movng from unemployment to employment (sn/u) multpled by the dscounted expected gan from ths transton. (6) Thus, ru b ( sn / u)( E U ) (2.2.) Substtutng (2.2.) nto (2.2.0) and usng the fact that E U = e/q leads to the followng wage-settng curve whch s ncreasng and convex n the employment rate, N: (7) w b ( r s q)( e / q) N /( N)( se / q) (2.2.2) Implcatons for labour market tghtness The equlbrum s gven by the ntersecton of equatons (2.2.7) and (2.2.2). As n the compettve model technologcal shfts towards labour cause a permanent rse n the labour share. A rse n product market competton has a smlar mpact because the resultng rse n output demand feeds through to the demand for labour. However, n both cases labour market tghtness s unchanged. Thus the outcome follows Chart 3 n Secton 2. where the labour market jumps to pont J n the short run and the labour share rses. In the long run the labour market moves to pont E* where the new hgher labour share s mantaned. On the supply sde, recall that the compettve model ndcated that only movements n b affect the labour share. The shrkng model delvers a rcher set of tghtness factors. Specfcally, changes n the probablty of job separaton, s, and the probablty of beng caught shrkng, q, are also mportant. For example, suppose that s rses. Ths ncreases the ncentve to shrk because the worker faces a hgher chance of enterng unemployment. Thus the wage-settng curve or no-shrkng condton shfts to the left. Lke a rse n b, the sluggsh adjustment of employment means that market tghtness wll temporarly rse. In ths case the outcome follows Chart 2 n Secton 2., where the labour market moves to J n the short run, and the labour share rses. In the long run the labour market moves to E* as the labour share declnes to ts orgnal value. In contrast, an ncrease n q lowers the expected returns to shrkng so that the (6) The probablty of movng from unemployment to employment s sn/u because the hrng rate equals the separaton rate (sn) n statonary equlbrum and all hrngs are from the unemployed (U). (7) Shapro and Stgltz (984) call ths the no-shrkng condton as t shows the wage that frms must pay to nduce workers to supply a non-zero level of effort, condtonal upon the employment rate. 2

19 wage-settng curve shfts to the rght. Consequently, labour market tghtness declnes n the short run before returnng to ts long-run value. Table B: The consequences of dfferent shocks n the effcency wage model Shock Postve labour demand ( up) Adverse labour supply (b up, s up, q down) (nstantaneous adjustment) Adverse labour supply (b up, s up, q down) (sluggsh adjustment) Unemployment Wages Labour share Table B lsts the responses of three dfferent varables (unemployment, the real wage rate, and the labour share) to shocks n the effcency wage model. Whle the effcency wage framework allows a wder varety of shocks than the standard compettve model, the underlyng message remans the same. Postve labour demand shocks cause a permanent reducton n unemployment, a permanent ncrease n the real wage and a permanent ncrease n the labour share. There are no mplcatons for labour market tghtness. An adverse labour supply shock wll cause a temporary tghtenng of the labour market (accompaned by a rsng unemployment and hgher real wages), but only f output cannot adjust mmedately. 2.3 The model of Layard, Nckell and Jackman (99) Background In chapter of ther book, Layard, Nckell and Jackman (99) sketch out a small-scale macro-model based on a labour market charactersed by nsder power. Ther model dffers from those we have consdered so far n two mportant respects. Frst, the authors mpose a nomnal rgdty, n the form of stcky prce expectatons, whch acts as an alternatve to the stcky employment assumpton that we have mposed thus far. Second, they nclude money n ther model. Ths allows us to trace out the effects of shocks that orgnate outsde the labour market, and whch move nether the labour supply nor the labour demand curve, yet affect market tghtness. It also allows us to consder the lnkages between labour market tghtness and nflaton. 22

20 Models of nsder power are charactersed by the noton that frms rank exstng staff (the nsders) above unemployed workers (the outsders). Ths rankng gves the nsders a source of monopoly power when settng the wage, and provdes mcro-foundatons for a wage-settng curve that s upward slopng n real wage / employment rate space. Unemployment perssts n these models because, at low rates of unemployment, the competng clams of frms and workers over what s produced are ncompatble. As the economy nears full employment, nsders know that, should they leave the frm, they can fnd another job very quckly. In order for them to stay wth the frm they must therefore be offered a hgh real wage (hgh w-p). At the same tme, as the economy nears full employment, labour productvty falls. By mplcaton, the margnal cost of producton rses whch leads frms to push for a hgher mark-up of product prces over the wage rate (hgh p-w and hence low w-p). The functonng of the labour market n many large scale macroeconomc models of the UK economy, such as those employed by HM Treasury, NIESR, and the Bank of England, s essentally the same as that envsaged by Layard, Nckell and Jackman (99) model. Key equatons Perod by perod, the sequence of events s as follows:. There are many mperfectly compettve frms ndexed by. Each frm sets a prce p for ts product, maxmsng expected profts condtonal on the expected level of demand and expected money wages. 2. A demand shock s realsed. From here on the model s determnstc, and the followng three events can be regarded as occurrng smultaneously: d 3. Each frm supples whatever s demanded ( y ) after the demand shock at the prce (p ) whch they set at the begnnng of the perod. Ths assumpton s crucal because t means that frms can be operatng neffcently, and produce more than they would choose to f prces could be mmedately adjusted. It prevents frms from cuttng output mmedately followng an adverse labour supply shock, and hence plays a smlar role to the arbtrary restrcton on employment adjustment that we made n earler sectons. 4. Captal s fxed. A Cobb-Douglas producton functon s suffcent to determne unquely the 23

21 amount of labour (n ) that each frm needs to hre n order to produce d y. 5. The wage rate s determned as the outcome of a Nash barganng process between frms and trade unons. It can be shown that the labour demand and labour supply curves take the followng general form. (8) e e p w 0 u (2.3.) e w p u (2.3.2) 0 (2.3.) s the labour demand curve (or prce-settng rule). It s based on the dea that prces (p) are set as mark-up over the expected margnal cost. (9) (2.3.2) s the labour supply curve (or wage-settng rule). The Nash barganng process produces an expected real wage that vares nversely wth the unemployment rate. As unemployment falls, nsders know that, should they be lad off, they could quckly fnd work elsewhere. Ths rases the value of ther fall-back pont. The four parameters 0,, 0 and should not be regarded as deep structural parameters. Rather they are functons of other parameters, such as the level of unemployment benefts, the degree of product market competton, and a measure of trade unon power all of whch may change over tme (see appendx). The aggregate demand sde of the model s represented by a reduced-form equaton lnkng the unemployment rate to real money balances (m p): u m p (2.3.3) In steady state, all expectatons are fulflled. Usng p = p e, w = w e and u = u e n equatons (2.3.) and (2.3.2) we obtan the followng expresson for the unemployment rate n steady state (u*): * 0 0 u (2.3.4) (8) The labour demand curve or prce-settng rule s a transformaton of the standard labour demand curve derved n Secton 2.2. Mcro-foundatons for the wage-settng rule are set out n the appendx. (9) In general terms, the expected margnal cost s equal to the product of the expected wage and the nverse of the expected margnal product of labour. Under a Cobb-Douglas producton functon, the expected margnal product of labour s ncreasng n the expected unemployment rate (u e ), whch means ts nverse s decreasng. 24

22 To examne behavour out of steady state, we need to specfy some process for w e, p e and u e. Layard, Nckell and Jackman (99) assume that () errors n the forecast for w e and p e are the same and () expectatons for nflaton and the unemployment rate are formed adaptvely. Usng w-w e = p-p e, p e = p - and u = u e n (2.3.) and (2.3.2) we obtan: where p 2 u u * p (2.3.5) Equaton (2.3.5) says that, whenever u les below u*, nflaton wll be rsng and whenever u les above u*, nflaton wll be fallng. Inflaton can only be stable when u equals u*, hence u* s referred to as the non-acceleratng nflaton rate of unemployment (or NAIRU). Usng the model outlned above, we can analyse the consequences of many dfferent knds of shock (recall that 0,, 0 and are all functons of other parameters). For our purposes, the shocks can be splt nto two camps: shocks to aggregate demand (whch move u), and shocks ether to labour demand or to labour supply (whch move u*). Startng from a poston of long-run equlbrum (where u = u*), let us consder frst what happens followng a shock to aggregate demand. Ths takes the form of an unantcpated ncrease n nomnal money balances. Prces are fxed n the mmedate perod, so from (2.3.3) unemployment must jump down below u*. From (2.3.5) ths wll be assocated wth a subsequent ncrease n nflaton. What actually happens s as follows: to cope wth the ncrease n demand, frms need to employ more labour than they had expected when product prces were set. Ths leads to a reducton n the cost to an nsder of beng fred (snce mmedate re-employment s more lkely), and hence to an ncrease n the wage rate determned by the Nash bargan. Temporarly, nsders enjoy a hgher real wage. But frms have been caught out on two fronts: not only have nomnal wages gone up aganst a fxed product prce, but ncreased employment means that, under Cobb-Douglas producton, labour productvty has fallen. Consequently, frms amng for a constant mark-up over margnal cost wll rase ther prces, and by more than the prevous ncrease n nomnal wages. Ths s the begnnng of the classc wage-prce spral. Perod by perod, wages ncrease more rapdly than frms had been expectng, and product prces ncrease more rapdly than workers had been expectng. Ths wll take place untl prce rses have eroded the ntal shock to nomnal money balances and the level of demand mpled by (2.3.3) s agan consstent wth employment at u*. Shocks to labour demand or labour supply cause a jump n u* rather than a jump n u. Agan, startng from a poston of equlbrum, consder the case where unemployment benefts rse. Now at any gven unemployment rate, nsders are less concerned by the prospect of becomng unemployed. That means the real wage rate determned by the Nash bargan s hgher at any gven unemployment 25

23 rate. From the labour demand curve, we know that f real wages are to be hgher, productvty must rse, hence employment must fall and unemployment must rse. As n the case of demand shocks, the assumpton of adaptve expectatons means the economy does not jump mmedately to the new equlbrum. Followng the ncrease n benefts, workers push for a hgher money wage. Frms rase ther prce n response, real money balances fall and through (2.3.3) unemployment begns to rse. Implcatons for labour market tghtness In the Layard, Nckell and Jackman (99) model, u-u* provdes a convenent quanttes-based measure of labour market tghtness. Chart 4 LNJ (99) model: postve nomnal demand shock W / P L S* L S^ E L D^ L D* O N* N^ N But t turns out that there s no smple mappng between u-u* and the labour share. We use Chart 4 whch plots labour demand (or prce-settng), and labour supply (or wage-settng) curves n actual employment / actual real wage space, to llustrate ths pont. In steady state, when wage and prce expectatons are fulflled, the economy wll be at pont E, at the ntersecton of L D * and L S *. Now consder what happens followng an unantcpated ncrease n nomnal money balances. Prces are fxed n the mmedate perod, so more goods wll be demanded than frms had ntended to supply. That means N must rse above N* to a pont lke N^. In order to attract extra staff, frms end up payng a hgher real wage than they had antcpated. When drawn n actual employment / actual real wage space, the effectve labour demand curve jumps to L D^. Real wages are hgher, and productvty s lower, so the labour share has rsen. Next perod, the frm wll rase ts prce to offset not only the rse n money wages, but also the declne n productvty. Frms are back on ther 26

24 long-run labour demand curve, L D *. Now t s the nsders who are fooled. When drawn n actual employment / real wage space, the effectve labour supply curve jumps to L S^ and the labour share s back at ts steady-state value. Ths process contnues untl prce rses have fully eroded the real effects of the ncrease n nomnal money balances. The labour share flps from beng above ts steady-state value, to beng at ts steady-state value, as the economy flps from beng off the labour demand curve and on the labour supply curve, to beng on the labour demand curve and off the labour supply curve. The model of Layard, Nckell and Jackman s of nterest n part because t allows for varatons n the labour share under Cobb-Douglas technology, but also because t suggests a lnk between tghtness and nflaton (see (2.3.5)). But recall that (2.3.5) s only vald under adaptve expectatons. When a shock to nomnal money balances pushes u below u*, workers bd up money wages on a vew of product prces that turns out to be wrong. Then frms rase product prces on a vew of money wages that turns out to be wrong. As ths wage-prce spral escalates, both partes are fooled perod by perod. Both partes fal to perceve that the shock was a nomnal one and can have only nomnal consequences n the long run. If nstead expectatons were formed ratonally, the ncrease n m would stll cause a jump down n u below u* (because prces are fxed n the mmedate perod). But p would then rse by the same amount as the rse n m, real balances and hence demand would be unchanged and u would return to u*. In ths example, tghtness s only nstantaneous and s assocated wth jumps n the prce level, rather than sustaned ncreases n the rate of nflaton. The assumpton of adaptve expectatons s one knd of nomnal rgdty that s suffcent to provde a lnk between real developments n the labour market and nflaton. For those who are uncomfortable wth adaptve expectatons, then other forms of nomnal rgdty (such as overlappng contracts) could be used n conjuncton wth ratonal expectatons to derve smlar results. Table C lsts the responses of unemployment, the real wage rate and the labour share to a postve nomnal demand shock n the LNJ (99) model. Ths s one case where a reducton n unemployment s a relable ndcator of a tghter labour market. A postve nomnal demand shock causes unemployment to jump down and then drft back up to ts startng value. Under a strct nterpretaton of the LNJ (99) model, both the real wage rate and the labour share would oscllate. Ths oscllaton would go away f we assumed that dfferent frms adjusted ther wages and prces at dfferent tmes. For example, one group of frms mght set ther prces n perods and 3 and ther wages n perods 2 and 4 whle a second group mght set ther prces n perods 2 and 4 and ther wages n perods and 3. 27

25 Table C: The consequences of a demand shock n the LNJ (99) model Shock Postve nomnal demand shock (m up) Unemployment Wages Labour share 2.4 Models of skll msmatch Background The models consdered so far have all focused on aggregate shfts n labour demand or supply. In contrast, models of skll msmatch emphasse changes n the composton of aggregate demand and supply. In partcular, these models focus explctly on the consequences of a change n balance between the demand and supply of sklled labour. The standard msmatch model s based upon a labour market that s comprsed of sklled and unsklled employees. A shft n labour demand towards sklled workers whch s not met by a commensurate rse n supply, wll tend to rase ther wages and reduce ther unemployment rate, whle lowerng the wages and rasng the unemployment rate of the unsklled. Gven a wage-settng functon for each skll group that s decreasng and convex n unemployment, ths wll lead to a rse n aggregate unemployment. The magntude of ths extra unemployment depends on the flexblty of real wages, whle ts persstence wll depend on the speed of adjustment of the relatve supply of sklled workers. (0) Our analyss s based on Manacorda and Petrongolo (999) who develop an ndex of skll msmatch whch captures the changes n the balance between the demand and supply of labour nputs dfferentated by skll. The basc dea s that a net shft n demand for sklled workers wll ncrease (0) The msmatch dea also extends to shfts n the composton of demand across specfc regons, ndustres, or occupatons (Llen (982), Blanchard and Katz (997)). 28

26 ther share of the aggregate wage bll followng upward pressure on sklled employment and wages. On the other hand, a net shft n the supply of sklled workers ncreases ther share of the labour force. The ndex compares these relatve demand and supply changes. Key equatons The model has two central elements. The frst s a producton functon wth heterogeneous labour nput whch s used to derve the msmatch ndex. The second element s a wage-settng functon for each labour group whch s convex n ther group-specfc unemployment rates. These wage functons are used to show how a rse n msmatch affects aggregate unemployment. To fx deas, suppose that the aggregate producton functon has three nputs: captal (K) sklled labour (N s ) and unsklled labour (N u ) where captal s fxed. The producton functon takes the Cobb-Douglas form: Y k s u AK (2.4.) N s N u s, u and k are the relatve demand ndcators for each nput where s + u + k =. Followng Nckell and Bell (995), we defne a relatve demand shft towards sklled labour as d s = -d u >0. A captures general technologcal progress. If W s and W u are the real wage rates of each skll group, then proft maxmsaton mples: s u Ws N W N u s u (2.4.2) Let L s and L u be the labour force of each skll group. Thus E = N /L s the group employment rate. Dvdng both sdes by L s /L u gves: s u L L s u Ws ( N s W ( N u u / L / L s u ) ) (2.4.3) Now let l =L /L be the labour force share of group, where L s the total labour force. Takng logarthms of both sdes and totally dfferentatng throughout leads to: s ls Ws E (2.4.4) s d ln d ln d ln d ln u lu Wu Eu The left-hand sde of (2.4.4) can be nterpreted as the dfference n the growth rates of the demand and supply of sklled labour relatve to ts unsklled counterpart. Ths makes t a natural ndex of 29

27 movements n skll msmatch, whch we denote by dlnsm. A change n the relatve demand for sklled labour s captured by dln( s / u ), whch s the growth of the rato of sklled and unsklled wage bll shares. l s /l u s the rato of the sklled and unsklled labour force shares. So dln(l s /l u ) traces movements n the relatve supply of sklled labour relatve to unsklled labour. The rght-hand sde of (2.4.4) expresses the ndex n terms of relatve wages (W s /W u ) and employment rates (E s /E u ). An ncrease n market mbalances translates nto ether a rse n the relatve wages of sklled workers, a rse n ther relatve employment rates (whch s nterpreted as a rse n the unsklled unemployment rate relatve to the sklled unemployment rate), or a combnaton of both. () The model s completed by assumng that the wage functon for skll group, s of the form: ln(w )=z - ln(u ). (2) Thus wages are a decreasng convex functon of unemployment. Ths convexty means that wages are more responsve to changes n unemployment when unemployment s low than when t s hgh. Wth these wage functons t can be shown that an ncrease n msmatch leads to a fall n the sklled unemployment rate, and a rse n the unsklled unemployment rate. The convexty of the wage-settng functons mean that the aggregate unemployment rate ncreases when the sklled have hgher employment and/or wage rates. In practce, the sklled have hgher rates of both employment and wages. Smlarly, sklled wages rse, unsklled wages fall, and the aggregate wage rate rses. A skll-based demand shock has no permanent effect on the labour share, s l. = s + u. Ths s because d s = -d u. Chart 5 shows the results of such a shock. The demand curve for sklled labour, L Ds shfts rghtwards to L Ds. Ths s offset by a leftward shft n the demand curve for unsklled labour from L Du to L Du so that total labour demand s unchanged. Wth no restrcton on employment adjustment, the equlbrum n the sklled market moves from E s to E s, whle the unsklled market moves from E u to E u. Sklled wages and employment rse, whle unsklled wages and employment declne. The convex wage settng schedule (WS), means that aggregate wages and unemployment rse but market tghtness s unchanged. Ths neutral effect of skll-based shocks wll also occur f employment adjustment s sluggsh and the real wage s fully flexble. In ths case, sklled wages () Equaton (2.4.4) assumes that the relatve demand and relatve supply of workforce sklls are ndependent. Ths helps to smplfy the analyss, but s unlkely to hold n practce. Consder a shft n demand towards sklled workers. Any resultng ncrease n the returns to sklls should serve to ncrease the share of workers who wll nvest n acqurng the relevant attrbutes. Ths wll eventually boost the relatve supply of sklls. Skll demand may also respond to an ncrease n supply. For example, a jump n the relatve supply of sklled workers may nduce frms to create sklled jobs. (2) z ncludes the standard factors whch move the wage-settng curve, ncludng the level of benefts, worker barganng power, and the long-term/short-term composton of the unemployed pool. The mcrofoundatons of ths double-logarthmc wage-settng functon nclude the models of effcency wages and nsder power dscussed n Sectons 2.2 and 2.3 respectvely. It can also be shown that the double-logarthmc specfcaton s a log-lnear approxmaton to the frst-order condtons for wages n the wage barganng model developed by Mannng (993). 30