Hiring as Investment Behavior

Transcription

1 Review of Economic Dynamics 3, Ž doi: redy , available online a hp: on Hiring as Invesmen Behavior Eran Yashiv 1 The Eian Berglas School of Economics, Tel Ai Uniersiy, Israel yashiv@pos.au.ac.il Received December 18, 1998 This paper explores he deerminans of hiring a he macroeconomic level. I reas he hiring decision as an invesmen decision, similar o he one aken for physical capial or for financial asses. A is core is a presen value relaion which defines he worker s asse value for he firm and deermines opimal hiring. The paper validaes his relaion using volailiy ess and infers he unobserved asse values by esimaing i. Hiring and asse values are found o be weakly correlaed wih he business cycle and much more volaile. The paper also demonsraes he links beween models employed and issues examined in finance and he labor marke Academic Press Key Words: aggregae hiring, presen value relaion, business cycles, unemploymen, srucural esimaion, asse pricing, hiring subsidies. 1. ITRODUCTIO While gross invesmen in capial has been he subjec of exensive sudy in macroeconomics, he parallel concep for laborhe gross flow of hiringhas received much less aenion. This is so because he underlying assumpion in many macroeconomic models is ha he labor marke is fricionless; hence, employmen adjusmens, including hiring, are cosless and insananeous. However, heoreical worksuch as he search and maching models of Diamond Ž 1982., Morensen Ž 1982., and Pissarides Ž has emphasized he role of fricions in his marke, modeling 1 I have benefied from useful suggesions made by an anonymous referee and he co-edior Dale Morensen. I am graeful o Bernard Dumas, Zvi Ecksein, Bruno Solnik, and seminar paricipans a Tel Aviv Universiy, he Recanai Business School ŽFinance in Tel Aviv Workshop., HEC School of Managemen, and he Hebrew Universiy for commens on previous versions of he paper. I am graeful o Michael Ornsein and Rafal Wojakowski for excellen research assisance and o he HEC Foundaion for financial suppor. Any errors are my own $35.00 Copyrigh 2000 by Academic Press All righs of reproducion in any form reserved. 486

2 HIRIG AS IVESTMET BEHAVIOR 487 hiring as a ime-consuming, cosly aciviy. Empirical work on labor marke flowssuch as ha of Blanchard and Diamond Ž 1990., Burda and Wyplosz Ž 1994., and Merz Ž has demonsraed ha gross hiring is a volaile and sizable flow which is imporan for he undersanding of he workings of he labor marke. In his paper, we underake an empirical exploraion of hiring in he presence of fricions. We rea he hiring decision as an invesmen decision, similar o he one aken for physical capial or for financial asses. When he firm decides o hire a worker, i is as if i buys an asse: i pays screening and raining coss in he expecaion of receiving a sream of reurns in he form of fuure profis. These profis consis of he worker s produciviy less he wage paid. These dividends are discouned by a discoun facor ha akes ino accoun boh he probabiliy of worker separaion from he job and ineres rae. The opimal rae of hiring is derived from he presen value relaion linking marginal hiring coss wih expeced discouned marginal profis. We sudy his relaion in an aggregae, macroeconomic conex. We es is validiy, quanify he asse value of workers, and explore is sochasic properies. The resuls enable us o explore he behavior of hiring over he business cycle and o analyze is sensiiviy o various deerminans. The main difficuly in sudying hiring empirically from his perspecive is ha, unlike invesmen models which use firms marke value Žby compuing average q, for example., or asse pricing models which use sock prices, here is no explici marke price for he asse value of workers. Thus, we have o infer his value from he FOC for opimal hiring. We do so using wo inference procedures and obain wo independen ses of esimaes of asse values. Afer comparing hem, we focus on a specificaion ha holds rue for boh. The daa used are Israeli labor marke daa, which are paricularly useful in he presen conex as hey provide a highly reliable gross hiring flow series covering a large segmen of he marke raher han a series derived from a sample. We find ha he daa corroborae specific formulaions of he presen value relaion, yielding reasonable asse values equivalen o approximaely wo monhs of worker pay. The flucuaions in asse values are shown o sem mosly from flucuaions in expeced, fuure marginal profi raes, as well as in bank credi raes. The laer resul highlighs he role of financial variables in generaing labor marke flucuaions. We also find ha hiring and asse values are weakly correlaed wih radiional measures of he cycle and exhibi much higher volailiy. Wihin a cerain range, he dynamic demand curve for labor is quie fla. The paper makes several conribuions: i validaes he presen value model of opimal hiring, demonsraes alernaive ways o infer worker asse values, and offers quaniaive esimaes of hese in a macroeconomic

3 488 ERA YASHIV conex. The paper hen delineaes he implicaions for he sudy of aggregae flucuaions. Finally, i demonsraes he links beween models employed and issues examined in finance and he labor marke. This demonsraion has several aspecs: i is shown how economeric mehodologies used in finance may be applied o explore issues in he labor marke, how ineres raes on bank credi play a very imporan role in driving flucuaions in hiring, and how he sudy of he asse value of workers can conribue o he lieraure on financial asse pricing. One can look a he resuls of his paper as a firs sep oward he consrucion of a more comprehensive producion-based asse pricing model. For example, he resul obainedha he asse value of workers is weakly relaed o conemporaneous measures of he business cycle, while i is srongly relaed o expeced presen value of fuure profismay have imporan implicaions for characerizing he cyclical behavior of sock prices. The paper proceeds as follows: Secion 2 presens he model of firms behavior, deriving he FOC which defines opimal hiring. Secion 3 presens he daa. Three secions hen deal wih he esimaion of he unobserved asse values: Secion 4 does so using srucural esimaion employing he GMM mehodology, Secion 5 approximaes he presen value relaion and infers asses values from i, and Secion 6 selecs paricular specificaions from hese alernaive esimaes, sudies heir magniudes and sochasic properies, and examines he sources of heir flucuaions using a variance decomposiion analysis. Two secions hen look a he implicaions of hese resuls: Secion 7 sudies he behavior of hiring and asse values over he business cycle, while Secion 8 examines he sensiiviy of hiring o is driving facors using he non-sochasic seady sae. Secion 9 concludes. 2. THE MODEL The following is a parial equilibrium model of opimal hiring of labor by a represenaive firm. I is closely relaed o he lieraure on dynamic labor demandsee Sargen Ž and Hamermesh Ž1993, Chaps. 6 and 7.. We regard he firm s hiring decision essenially as a problem of invesmen under uncerainy. Conrary o he implicaions of he neoclassical model, workers are no coslessly fired a he end of every period and coslessly hired a he beginning of each period. Raher, employmen evolves in a way similar o he evoluion of he capial sock. In he same way as capial is accumulaed hrough gross invesmen, workers are accumulaed hrough gross hiring; as capial depreciaes, workers separae from jobs. The model hus emphasizes he fricions in he labor

4 HIRIG AS IVESTMET BEHAVIOR 489 marke. I is precisely hese fricions, which generae he forward-looking aspec of firms behavior, ha are a he hear of he analysis. The objecive funcion of he firm is o maximize he sum of expeced discouned profis where is decision variable is gross hiring Ž H.. The firm s problem may be examined wih he ools of sochasic dynamic programming in he same way as hey have been used for capial invesmen problems, 2 so he model is he analogue of Tobin s q model of invesmen in physical capial. The iming is as follows: he firm makes is hiring decisions in period using he informaion se. The hired workers ener producion in he following period Ž 1.. Separaion of workers from jobs occurs a rae s. The sochasic dynamic programming problem is formulaed as subjec o 1 max E Ý Ł j 4 Ž 1 r. H j0 i0 i1 Ž. Ž. F, A W H, B, Ž 1. j j j j j j 1 Ž 1 s. H, Ž 2. where E denoes expecaions formed in period based on he informa- ion se, F is he producion funcion wih employmen Ž. and oher facors of producion Ž conained in he vecor A. as is argumens, and real wage paymens are denoed by W. We represen by he coss of hiring which are of wo ypes: Ž. i he cos of adverising, screening, and selecing new workers and Ž ii. he cos of raining. This funcion has as is argumens he number of hires Ž H. and possibly oher variables Ždenoed by he vecor B; one such variable could be he employmen sock. and we explore i in deail in he empirical work below. The firm uses he relevan ineres rae r o discoun fuure sreams. The FOC Ž he so-called sochasic Euler equaion. is 1 F1 1 1 E W1 Ž 1 s 1.. Ž 3. H 1 r H The inuiion here is ha he marginal cos of hiring Ž he LHS. equals expeced discouned marginal profis Ž he RHS.. The laer consiss of wo erms: he expeced marginal profi a period 1, which is made up of he marginal produc and he reducion in hiring coss due o he addi- 2 Ž. See, for example, Sargen 1986, Chap. 14.

5 490 ERA YASHIV ional hire less he wage paid and he expeced savings of hiring coss if he worker does no separae in he following period. Hence flucuaions in hiring reflec flucuaions in marginal profiabiliy, he separaion rae, and he ineres rae. Ieraing forward he expression on he RHS of Ž. 3 and imposing he relevan ransversaliy condiion, we obain j Ž i1. E Ý ½Ł 5 j1 i1 Ž i1. 1 s 1 H 1 r 1 s ž / j j Fj j Wj. Ž 4. The expression in he square brackes on he RHS is he presen value of fuure marginal profis. While his formulaion of he firm s problem could fi in a number of macroeconomic models, i is paricularly relevan o he search and maching approach o labor markes see Diamond Ž 1982., Morensen Ž 1982., and Pissarides Ž In ha conex, he model presened here formalizes cosly search by firms, whereby he firm decides on he number of vacancies Ž V. o open and akes he probabiliy of filling a vacancy Ž Q. as given so H QV. These models posi ha wages are deermined hrough bargaining beween firms and workers over he surplus creaed afer a mach is formed. The wage soluion, using generalized ash bargaining, is hus given by Ž. J F Ž 1. J J U, Ž 5. where J F is he firm s ne value of he mach, J J U is he worker s ne Ž U value of he mach J being he gross value and J being he value of unemploymen., and is he worker s share of he mach surplus. Following Eq. Ž. 3 a mach ha is formed and is o begin producion a ime is worh o he firm F Ž 1 s1. F F J W E J 1. Ž 6. 1 r For he unemployed worker he presen value of unemploymen consiss of he sum of Ž. i he value of unemploymen benefis as well as any non-pecuniary value, such as ha derived from leisure aciviies, a ime, o be denoed b, and Ž ii. he expeced fuure value which akes ino accoun he probabiliy of maching ino employmen he nex period,

6 HIRIG AS IVESTMET BEHAVIOR 491 P H U, and he coninuaion value of employmen J : U U J b E P1 J1 Ž 1 P1. J 1. Ž 7. 1 r Similarly he presen value of employmen consiss of he sum of Ž. i he wage a ime and Ž ii. he expeced fuure value which akes ino accoun he probabiliy of separaing from employmen ino unemploymen in he nex period, s 1, and he coninuaion value of unemploymen J U : 1 U J W E Ž 1 s1. J1 s1 J 1. Ž 8. 1 r The ne value of he mach for he worker is hus Ž 1 s1 P1. U U J J W b E Ž J1 J 1.. Ž 9. 1 r Ž. Ž. Ž. Insering 6 and 9 ino 5 yields F Ž 1 s. W E J 1 r 1 F 1 Ž 1 s1 P1. U Ž 1. W b E Ž J1 J 1.. Ž r Ž. Solving for he wage, using he fac ha 5 holds rue also a ime 1 gives ž / F J F W EP 1 Ž 1. b. Ž r In he empirical work he wage equaion Ž 11. will be joinly esimaed wih he Euler equaion Ž. 3. In he following, i is worhwhile o noe wo addiional feaures of his seup: Ž. i The model describes invesmen in workers by firms wihin an aggregae, homogeneous seup and worker separaion, hough sochasic, is exogenous. I should be emphasized ha his framework is applied o he aggregae labor marke, where he employmen sock keeps growing over ime. Evidenly, such irreversible invesmen in workers fis a marke

7 492 ERA YASHIV wih high firing coss or insiuional consrains on firing beer han i does a more flexible marke. The quesion of his model being a useful approximaion of aggregae behavior in he real world is, herefore, an empirical one, and he resuls below seem o sugges a posiive answer. Moreover, informal evidence relaing o his daa se suggess ha here was very lile firing aking place in he sample period. oe, oo, ha in he empirical work below s, he exogenous rae of worker separaion, is aken a is acual value raher han being se o be some fixed parameer and ha is sochasic properies Ž see Appendix A. seem o furher jusify his way of modeling. Ž ii. The FOC in is wo forms ŽEqs. Ž 3. and Ž 4.. is analogous o he asse pricing equaion used in he financial lieraure, j D1 P1 ž / Ýž Ł i/ 1 r i1 j j1 P E E D, Ž 12. where P is he sock price, r is he discoun rae, and D are dividends. In he curren conex P represens marginal hiring coss Ž. H and hence he asse value of he worker, is he appropriae discoun facor Žincluding s and r., and D is marginal profis. 3. THE DATA We use Israeli labor marke daa aken from he Employmen Service Ž ES. affiliaed wih he Minisry of Labor. This daa se has several useful qualiies, due o he insiuional srucure ha generaed i. This srucure may be briefly described as follows: he ES is he main insiuional inermediary in he marke. From 1959 unil March 1991 privae inermediaries were illegal, and he ES handled all job openings ha did no require a universiy degree. The hiring of workers for hese jobs was required by law o pass hrough he ES, making he daa coverage quie comprehensive. The hiring series we use is he number of vacancies filled by he ES each monh. The reliabiliy of he series is reinforced by he availabiliy of a similar series for workers referred o he vacan jobs. In comparison, daa aken from populaion or labor force surveys usually suffer from a number of problems, such as misclassificaion of employmen saus generaing spurious gross flows, missing observaions ha are correlaed wih labor marke saus, and oher measuremen errors see Abowd and Zellner Ž We use 180 monhly observaions in he years We do no use pre-1975 daa, as vacancy definiions were changed; we do no use

8 HIRIG AS IVESTMET BEHAVIOR 493 pos-1989 daa for wo reasons: as of March 1991 vacancy posing was no longer mandaory, and he ES vacancy measure became jus a parial indicaor of he relevan worker flows, and in 1990 here were disrupions in daa collecion. The sample monhly average rae of hiring is 1.8% Žou of employmen.. This figure is comparable o hose repored for oher economies: 1.7% in he U.S. for he unemploymen o employmen flow Ž Blanchard and Diamond, 1990., beween 1.5% and 1.9% in France Ž Burda and Wyplosz, 1994., and 2.1% in Danish manufacuring ŽAlbaek and Sorensen, Table III Ž in Secion 6. below repors several descripive saisics for his hiring rae series, in he conex of a discussion of he sochasic properies of he asse value of workers. We use sandard macroeconomic daa on producion, employmen, wages, unemploymen benefis, and ineres raes from he Cenral Bureau of Saisics, he aional Insurance Agency, and he Bank of Israel. To be consisen wih he model, we resric aenion o he business secor. Full definiions and a lis of sources for all he daa series are given in Appendix A. 4. IFERECE OF ASSET VALUES USIG EULER EQUATIO ESTIMATIO In his secion, we infer workers asse values hrough srucural esimaion of he Euler equaion. We briefly discuss he economeric mehodology, specificaion issues, and he ess used, including volailiy ess of he ype employed in he asse pricing lieraure Ž We hen repor and discuss he resuls Ž Mehodology Ž. 3 We use Hansen s 1982 GMM mehodology o esimae he firms Euler equaion ŽEq. Ž 3. above., which deermines he evoluion of hires. Following esimaion, we examine he resuls in erms of wo ess prevalen in he asse pricing lieraure: he so-called volailiy ess and an orhogonaliy es. The former uses he inequaliy varžežx y.. varž x. and posis ha asse prices should vary less han he ex-pos presen value of dividends hey forecas. Here hey perain o he asse value of he marginal worker and ex-pos presen value of marginal profis from he worker. The orhogonaliy es is a es of Euler equaion s overidenifying resricions see he discussion in Cochrane Ž This es is based on he noion ha reurns are unforecasablei.e., hey are orhogonal o 3 We use he HansenHeaonOgaki GMM Package in Gauss version 3.01.

9 494 ERA YASHIV any variable in he informaion se. These orhogonaliy condiions are esed using Hansen s Ž J-saisic es. In order o ake he model o he daa, several specificaion issues mus be addressed. These relae o he use of discoun raes, funcional forms, he variables o be used in he hiring cos funcion, he iming of hiring coss relaive o producion, saionariy of he variables, and he insrumen se: Ž. i For discouning, we explore several alernaive specificaions: one is he ex-pos, real rae of ineres charged on bank credi. This was he major form of firm financing and he mos reliable marke ineres rae series in he sample period. Anoher is he rae of growh of non-durable consumpion. 4 As a hird alernaive we use a consan rae of r 0.4% in monhly erms, which ranslaes ino a 5% annual rae of ineres, which we deem a plausible value. Ž ii. The funcional form of he producion funcion Ž F. is o be specified. We ake a radiional roue and specify a CobbDouglas funcion; his enables us o use he average produc, which is proporional o he marginal produc, in esimaion: F F. Ž 13. Ž iii. The variables o be included in he hiring cos funcion Ž. have o be considered. Basically we focus here on gross hiring coss as disinc from ne coss Hamermesh Ž 1993, Chap. 6. elaboraes on his poin. By gross coss we refer o boh he coss of screening Žinerviewing, esing, ec.. and he coss of raining. In order o ake ino accoun he size of he firm in erms of employmen and oupu, we model hese coss as a funcion of hiring raes ou of employmen and as proporional o oupu, H i.e., Ž. F, where is some increasing funcion. This implies ha coss are inernal o he producion process. Observed oupu is herefore ne of hiring coss and should be modeled accordingly, i.e., F F. Ž iv. The funcional form of hiring coss Ž he shape of. is anoher key issue. We ry wo power funcions Žhe quadraic and a general, unconsrained power which could also be linear. and polynomials of 4 In a general equilibrium seing, such as RBC models, he rae of ineres in equilibrium is defined as g lnžuž C. už C. 1, where is a subjecive discoun facor of he represenaive consumer and už C. is hisher marginal uiliy from consumpion a period. r If his funcion is a CRRA funcion wih parameer, hen g ln lnž C C. 1. Thus g r is a linear funcion of he growh rae of consumpion. In esimaion we use r g lnž C C. Ž i.e., 1. 1 and discuss he consequences of using oher values for or.

10 HIRIG AS IVESTMET BEHAVIOR 495 degree 2, 3, or 4 as he alernaive funcional forms: 2 H 1 F 2 ž / 2 1 H ž / 2 d i H Ý i ž / F Ž 14. i1 i F d 2,3,4. Ž. v As o he iming of hiring coss, we ry wo formulaions: in one, coss occur in he monh before producion akes place; in he oher, we caer for he possibiliy ha he hiring process is compleed wihin he monh and so hiring coss are incurred in he monh of producion. Ž vi. As some of he variables are non-saionary, we run he equaion divided hroughou by he average produc a period 1. Thus all variables included in he equaions are saionary. Ž vii. For he insrumen se, we ried differen lag srucures of he variables Ž he hiring rae and profiabiliy. and esed he equaions for robusness wih respec o changes in his se. In order o see if his equaion can be linked o a maching model, where he wage ha appears in he Euler equaion is deermined by he ash bargaining soluion, we also run he GMM procedure on he Euler equaion Ž. 3 joinly wih he wage equaion Ž 11.. To do so we posulae ha oal income during unemploymen, b, is given by b z, Ž 15 F F. where z are unemploymen benefis on which here are daa Žsee Appendix A.; any non-pecuniary value, such as ha derived from leisure aciviies, is capured by he consan Ž a parameer. plus an i.i.d process ; and he variables are expressed in erms relaive o average oupu. Insering his specificaion ino Ž 11. yields 0 W H z EP Ž 1., Ž 16 F F 1 F F. 0

11 496 ERA YASHIV where we have used he CobbDouglas specificaion for he producion funcion Žsee Eq. Ž 13.., divided he equaion hroughou by F o Ž. F induce saionariy and used Eq. 3 o replace he erm J11 r by Ž H. Ž F.. The error in his equaion is given by Ž Resuls We sar wih esimaion of Eq. Ž I urns ou ha a general power funcion using bank credi rae discouning performs he bes. In columns 17 of Table I we repor he key resuls for his specificaion under alernaive insrumen ses. We repor oher esimaes and robusness ess in Tables BI and BII of Appendix B. The able repors he esimaed parameers he parameers of he hiring cos funcion Ž. and, he coefficien of labor in he producion funcion, he es saisics of he overidenifying resricionsorhogonaliy ess Ž he J saisic., and he variance of each side of he equaion o es for he variance bound condiion. The resuls validae he presen value relaion and poin o a highly convex power funcion. The power Ž. 2 esimaes vary in he range , mosly around 4.7. This degree of convexiy Ž. 2 reflecs he elasiciy of hiring wih respec o he expeced presen value, implying a relaively fla dynamic labor demand curve. The poin esimaes and he sandard errors of he scale parameer, 1, exhibi much greaer variaion, ranging from 296,348 o and 5,209,596. The evidence presened below sheds furher ligh on his issue. Across all specificaions, he producion funcion parameer Ž. is precisely esimaed a a value of around This value is consisen wih he resuls of oher sudies, which have direcly esimaed he CobbDouglas producion funcion. Column 8 of Table I presens esimaes of he equaion joinly wih esimaes of he wage equaion ŽEq. Ž This is a more resriced form of esimaing he parameers 1, 2, and because while boh equaions use acual wage daa, Eq. Ž. 3 does no resric W in any way bu Eq. Ž 16. does. In specifying he ash soluion i adds wo more parameers o be esimaed:, he worker share in he wage bargain, and he unemploymen income parameer. The resuls indicae ha he esimaes of columns 17 are robus. Furher experimenaion wih he insrumen se and wih he sample periodrepored in Table BIII of Appendix Bshows ha varies again around 4.7, and ha he esimaes of vary in he 2 1 range of 67,000 o 711,000, a somewha narrower and lower range han 5 oe ha he srucural esimaion mehodology employed is consisen wih he wage Ž W. being an endogenous variable, even if an explici formulaion of he deerminans of wages is no esimaed. We reurn o his issue below, when we discuss he join esimaion of he Euler equaion and he wage equaion.

12 HIRIG AS IVESTMET BEHAVIOR 497 TABLE I The Euler Equaion Ž. Ž. Ž. Ž. Ž. Ž. Ž. Ž , , , , ,567 5,209, , ,517 Ž 127,876. Ž 221,459. Ž 181,279. Ž 159,326. Ž 213,963. Ž 13,705,868. Ž 145,901. Ž 501, Ž Ž Ž Ž Ž Ž Ž Ž Ž Ž Ž Ž Ž Ž Ž Ž Ž Ž J-Saisic p-value VAR LHS VAR RHS oes: H F Ž. 1 In column 1 he insrumen se conains a consan and four lags of and W. In column 2 he iming of hiring coss and producion is se o occur wihin he same monh. In columns Ž.Ž. 3 5 he lags used are 2, 3, and 5 respecively. F H In column Ž. 6 is dropped and in column Ž. W 7 is dropped from he insrumen se. In column Ž. 8 he equaion is esimaed joinly wih he wage equaion and he insrumen H F z se includes a consan and four lags of, W, and F. Ž. 2 Sandard errors are in parenheses. Ž. 3 VAR LHS is he variance of asse values Žwhich appear on he LHS of he Euler equaion.. VAR RHS is he variance of he ex-pos presen value of marginal profis Žwhich appear on he RHS of he equaion.. ha repored above. The esimae of he worker share Ž., which is 0.17 in column 8, varies across insrumen ses in he range of 0.2 o 0.4. This seems reasonable for wo reasons: he share of unemployed workers in maching is around 0.2 o 0.3 according o he resuls of srucural esimaion of he Israeli maching funcion repored in Yashiv Ž 1999a.; for he U.S. Morensen Ž presens empirical consideraions ha place i a IFERECE OF ASSET VALUES USIG THE PRESET VALUE RELATIO In his secion, we approximae he presen value relaion driving hiring Ž. Ž. see Eq. 4 above using a mehodology proposed by Cochrane 1992 for

13 498 ERA YASHIV sock pricedividend raios. This approximaion separaes ou he differen deerminans of asse valuesfuure produciviy growh, marginal profi raes, separaion raes, and discoun raes. We use i for several purposes: Ž. i While he Euler equaion esimaes repored in he previous secion were based on a mehodology which uses informaion from pairs of consecuive periods along he firms opimal pah, he approximaion mehodology akes many more periods ino accoun. I hus offers he opporuniy o infer he hiring cos funcion parameers, and hence asse values, independenly of he GMM resuls, using a differen mehodology and wih differen informaion. Ž ii. I faciliaes he decision as o which of he GMM specificaions discussed above should be preferred. Ž iii. I permis us o do a variance decomposiion analysis o deermine he relaive role played by he differen deerminans of asse values. We begin by discussing he approximaion mehodology Ž 5.1., leaving he full derivaion o Appendix C. We hen repor he esimaes of he funcion parameers inferred from he approximaion Ž An Approximae Presen Value Relaion The approximaion elaboraed in Appendix C is based on he exac presen value relaionship Ž. 4 divided hroughou by average oupu: 0 Fj j Wj j H Ž 1 s. 1 j i1 j E F Ý ½Ł 5 1 r F j1 i1 Ž i1. 1 s. Ž 17. The LHS expresses he asse value in erms of average oupu. For noaional simpliciy i shall be denoed P. The RHS expresses he expecaions of fuure marginal profishe dividends from he job worker machdiscouned by boh he separaion rae and he real rae of ineres. The idea is o separae ou hese differen elemens. The approximaed relaionship, derived in Appendix C, implies he expressions for he uncondiional mean and he uncondiional variance of asse values, j EŽ P. EŽ MP. covž w, w 2 Ý j Ž. j j Ý j j j1 Ž. cov MP, w Ž 18.

14 HIRIG AS IVESTMET BEHAVIOR 499 Ž. EŽ MP. j f j s Ý Ž j. Ý j j1 j1 E MP var P cov P, n cov P, g 1 1 Ž. Ž. Ž. j r j Ž j. j E MP Ý cov P, g Ý covž P, MP. 1 j1 j1 Ž 19. where 1 W F F ž / ž / MP, 1 s Ž. n f ln 1 g f g s lnž 1 S. 1 1 r g ln Ž 1 r1. F f g F1 1 w Ž n f g s g r. and e EŽw.. The uncondiional mean ŽEq. Ž 18.. is he sum of wo erms: he firs, EMP Ž. 1, represens asse values in a cerainy world, wih all variables evaluaed a heir mean. This is he average, discouned marginal profi. The second consiss of wo elemens: one is a weighed sum of co-variances of dividend growh raes, separaion raes, and real ineres raes. The oher elemen is a weighed sum of co-variances of marginal profi raes and he differen raes conained in w. The greaer he co-variance of dividend growh or of he marginal profi rae wih separaion raes or ineres raes, he lower he mean asse value. The variance of asse values ŽEq. Ž 19.. and consequenly he variance of hiringis decomposed ino four erms. These are weighed infinie sums of he co-variance of asse values Ž P. wih he fuure produciviy growh rae Žn f., wih Ž he negaive of. he fuure separaion rae Žg s., wih Ž he negaive of. he fuure real ineres rae Žg r. and wih he

15 500 ERA YASHIV fuure raes of marginal profis Ž MP.. I is imporan o noe he paricular feaures of his decomposiion: as he co-variance erms may be negaive and as he four erms are no orhogonal, each erm as a fracion of varž P. may be above 100% or below 0. oe, oo, ha high asse values Žand hiring raes. may be associaed wih low fuure produciviy growh raes or wih high fuure separaion raes if hey are also associaed wih much lower fuure ineres raes or wih much higher marginal profi raes Esimaion of Asse Values We now use Eqs. Ž 18. and Ž 19. o infer asse values. To do so, we need o posulae he funcional form of hiring coss. We use a general power funcion, so marginal coss are given by Ž H. Ž F. Ž H We hen compue, for alernaive values of he power 2, he value ha would saisfy Eq. Ž and, separaely, he value ha would saisfy Ž 19.. For he mean and variance expressions ha appear in hese equaions we use he sample momens. The values for he power Ž. ha we consider are 2 Ž he quadraic funcion. 2, 3, 4, 5, and 4.7, he laer being he resul of he GMM esimaion in he previous secion. These compuaions involve wo furher assumpions: firs, we use 0.68 o calculae marginal profi raes, as his value was fairly robus in he Euler equaion resuls and corresponds o sandard producion funcion esimaes. Second, we need o runcae he infinie sums in he wo equaions a some finie period J. We did so afer esing values of J from 1 o 100 monhs and ook J 75, afer which he expressions did no change much. We examined he robusness of he compuaion o modificaions in J. Table II repors he resuls, including he inferred 1 values and asse values ŽP Ž H hey imply. One se of resuls perains o he values saisfying Ž 18. and he oher se o hose saisfying Ž 19.. We look for values of 1, for a given 2, ha saisfy boh equaions. We differeniae beween he various discoun rae models. The key resul is ha only in he bank credi discouning case and only for he case 2 4 do here exis esimaes of 1 ha saisfy boh equaions. In all oher cases eiher he 1 esimaes are very differen across he wo equaions, or one of he equaions is no saisfied by any posiive value of 1. 6 These resuls narrow down he range of specificaions o a highly convex funcion using he bank credi ineres rae. 6 Using oher consumpion-based raes wihin a CRRA framework does no change his conclusion.

16 HIRIG AS IVESTMET BEHAVIOR THE SOURCES OF FLUCTUATIOS AD STOCHASTIC PROPERTIES OF HIRIG AD ASSET VALUES The aim of his secion is wofold: o deermine which specificaions ou of all he differen resuls repored in he preceding wo secions should be preferred and o sudy heir sochasic properies. As asse values are TABLE II Inferred Asse Values Using he Approximaed Presen Value Relaionship a. Bank Credi Raes Discouning variance mean Specificaion 1 P 1 P , , ,300, ,150, ,600, ,300, b. Consumpion-Based Discouning variance mean Specificaion 1 P 1 P , ,230, ,670, c. Consan Discouning variance mean Specificaion 1 P 1 P , ,265, ,750, oes: H Ž. Ž The firs column specifies he 2 used in compuing he asse value, P 1 Ž. 2 The second column repors he value of 1 ha saisfies he variance decomposiion. Ž. 3 The hird column repors he sample average value of P implied by his specificaion. Ž. 4 The fourh column repors he value of 1 ha saisfies he uncondiional mean equaion. Ž. 5 The fifh column repors he sample average value of P implied by his specificaion. Ž. 6 The sign indicaes ha no posiive saisfies he equaion. 1

17 502 ERA YASHIV unobservable, here is no obvious way in which he various esimaes may be evaluaed. However, reviewing he evidence presened in Tables I and II, here is one specificaion ha sands ou as saisfying all he crieriahe power funcion, using bank credi raes for discouning. This specificaion passes he orhogonaliy and variance bounds ess of he Euler equaion and saisfies boh he mean and variance equaions of he approximaed presen value equaion. Moreover, in he former case i proved o be robus o he modificaions repored in Appendix B. As o he values of is parameers, he esimaes of he degree of convexiy Ž. 2 are similar across inference mehodologieshey are 4.7 in he GMM case and 4 in he approximaion case, wih 4.7 being accepable, oo. In fac, a major difference is found only in he scale Ž. 1 esimaes. The GMM esimaes vary across specificaions. In all cases hey are lower han hose repored for he approximaion in Table II using he same power Ž In wha follows, we herefore narrow down he se of specificaions and aemp o evaluae hree alernaive parameer ses: Ž. i 2 4.7, 1 450,000 reflecing he GMM esimaes; Ž ii. 2 4, 1 200,000, which is he preferred esimae using he approximaion as repored in Table II; Ž iii , 1 3,150,000, which represens a combinaion of he wo mehodologies; he preferred specificaion of he power Ž. 2 from he GMM esimaes Ž Table I. and he 1 value ha saisfies he mean equaion of he approximaion Ž Table II.. Table III repors he properies of hese hree specificaions. Panel Ž. a looks a hiring raes and a marginal and oal hiring coss. I presens heir sample momensmean and sandard deviaionin monhly erms. Panel Ž b. compues he goodness of fi of hese specificaions. This is done by plugging he alernaive parameer ses ino he Euler equaion Ž. 3 and H solving for he hiring rae Ž.. The soluion is obained by solving he equaion period by period, using he acual values of he exogenous variables and of lagged hiring. We hen repor he correlaions Ž. beween he solved, fied hiring series and he acual one. Panel Ž. c repors he auocorrelaion of he differen series. Panel Ž d. presens a variance decomposiion analysis of asse values using Eq. Ž The wo specificaions based on he approximaion specificaions Ž ii. and Ž iii. in Table II give similar magniudes for hiring coss: marginal cossi.e., he coss of he marginal hireare, on average, 140% of monhly oupu or a lile over wo monhs of wages. Toal coss are abou 0.7% of oupu. The specificaion based on he GMM esimaes se Ž. i above gives far lower values, a consequence of he lower scale esimae discussed above. 7 We do no repor he variance decomposiion for he GMM esimaes se Ž i. above as i does no saisfy Eq. Ž 19..

18 HIRIG AS IVESTMET BEHAVIOR 503 How plausible are hese esimaes? Based on casual observaion and inuiion one should expec he value of screening and raining coss o be equivalen o a few weeks or monhs of pay. The exising micro-based empirical evidence is scarce and repors diverse esimaes, bu generally confirms his inuiion. Surveys of micro sudies in ickell Ž1986, pp. TABLE III The Sochasic Properies of Hiring and Asse Values a. Momens H Hiring raes mean sd. 1.84% 0.36% Marginal coss H F specificaion average oupu erms wage erms w H H mean sd. mean sd ,000; % 13% ,000; % 82% ,150,000; % 104% Toal coss relaive o oupu F specificaion mean sd ,000; % 0.07% 1 200,000; % 0.56% 1 3,150,000; % 0.58% b. Goodness of Fi ž / specificaion 21 H H 1ž / H ,000; ,000; ž / 3,150,000;

19 504 ERA YASHIV TABLE IIIConinued c. Auocorrelaions H ž / H H 1ž / 1 2 H specificaion ,000; ,000; ž / 3,150,000; d. Variance Decomposiion ž / ž / 21 H H f s r specificaion P, n P, g P, g P, MP 200,000; ,150,000; oes: Ž. 1 In panel Ž. a, he mean and sandard deviaion refer o he monhly sample values. H Ž. 2 In panel Ž. b we solve he Euler equaion for Ž. 1 using he acual value of all he oher variables and repor he correlaion wih he acual series. Ž. 3 In panel Ž. c, i is he ih auocorrelaion. Ž. 4 In panel Ž. d, columns 3, 4, 5, and 6 repor he fracion of var Ž P. explained by he differen P, x, each of which sands for J EŽ MP. j Ý cov P, xj 1 j1 var P Ž. where x n f, g s, g r, MP, and J 75. Ž and Hamermesh Ž 1993, p indicae ha coss are in he order of one o hree weeks of pay for low-skilled workers and in he order of a few monhs of pay for medium- and high-skilled workers. From he findings of a recen deailed sudy by Abowd and Kramarz Ž 1997., one can derive a lower bound on hiring coss in French esablishmen level daa. This urns ou o be, on average, 60% of monhly wages, inclusive of axes,

20 HIRIG AS IVESTMET BEHAVIOR 505 wih he acual level poenially much higher. Thus boh inuiion and micro sudies are in he range of he saisics of Table III. The goodness of fi measures suppor all specificaions, bu in paricular parameer ses Ž ii. and Ž iii., where he correlaion values are quie high Ž The able shows ha here is lile difference in he sochasic properies of asse values wheher we use a convexiy parameer 2 equal o 4 or o 4.7, provided ha he scale parameer Ž. 1 is adjused accordingly. The differences across inference mehodologies perain o his scale and hey are no surprising. The wo mehodologies relae o wo differen dimensions of he daa: he Euler equaion is based on he sochasic behavior of reurns, i.e., changes in asse values Ž P and P. 1. The approximaion mehodology bases inference on a presen alue specificaion. Thus he Euler equaion is more sensiive o high frequency aspecs of he daa. The more persisen are marginal profis, he higher will asse values be. Therefore, he mehodology ha picks up more high frequency movemens relaes o less persisen daa and infers lower asse values. Asse values inheri he auocorrelaion srucure of hiring raes and, herefore, on his dimension here is hardly any difference beween he differen parameer ses. The ineresing finding is ha hiring and asse values are only moderaely persisen: he auocorrelaion is 0.6 a he firs lag, weakens afer one year, and diminishes considerably afer hree years. Panel Ž d. sheds ligh on a key issuehe sources of flucuaions in hiring. The variance decomposiion analysis of asse values shows ha flucuaions in fuure marginal profi raes and in ineres raes play an imporan role. The relaive conribuion of he marginal profi rae is around 60%, while ineres rae flucuaions conribue abou 40%. The laer finding highlighs he role of financial variables in generaing labor marke flucuaions. The variance of fuure produciviy growh raes and separaion raes conribues relaively lile. Moreover, he resuls imply ha higher asse values oday are associaed wih lower fuure produciviy growh raes or higher raes of worker separaion. As noed above, his is consisen wih much lower fuure ineres raes andor much higher profi raes. In he nex wo secions we use parameer ses Ž ii. and Ž iii. o explore some of heir broader implicaions. 7. THE BEHAVIOR OF HIRIG AD ASSET VALUES OVER THE BUSIESS CYCLE The preceding resuls allow for an examinaion of he cyclical behavior of labor marke variables in he presence of fricions. This secion describes he business cycle properies of hiring and asse values. We follow

21 506 ERA YASHIV he approach aken in he business cycle lieraure and sudy he co-movemen and relaive volailiy of he relevan variables. oe ha he sandard analysis of flucuaions assumes a fricionless marke wih no adjusmen cossi.e., cosless and insananeous hiring and firing. One idea, which has been proposed in he conex of labor markes wih hiring coss, is ha if he firm opimizes ineremporally, hen recessions represen imes of low opporuniy cos. Thus one should expec o see more re-srucuring of he workforce, including hiring, in hose imes. In such a case hiring would be couner-cyclical. The curren model encompasses his ype of argumen. Looking a Eq. Ž. 3, we see ha if F is relaively low, hen, oher hings equal, curren hiring raes H should be relaively high. However, as i has been sressed, hiring is a forwardlooking decision based on a presen value expression. One should herefore examine wha happens o he differen componens of he asse value of workers a hose imes when F is relaively low. Table IV presens he dynamic cross correlaions and relaive sandard deviaions of hiring and asse values wih radiional measures of cyclical aciviy and wih he variables ha acually appear in he presen value 8 relaion. The former are he sock of employmen Ž. and real GDP Ž F.; F we add labor produciviy Ž. in order o be consisen wih he model s F Ž. W formulaion. The laer se of variables includes profiabiliy, bank credi raes Ž r., he separaion rae Ž s., and he rae of produciviy growh Ž g f.. We employ wo alernaive derending mehods: exponenial derending, which is relevan in he case of a deerminisic rend, and he HodrickPresco Ž HP. filer, which is relevan in he case of a sochasic rend. These are repored in wo panels. All variables used perain o he business secor and are a he quarerly frequency. Before discussing hiring and asse values, noe ha, in he Israeli economy, he correlaion beween employmen and oupu is low: 0.32 Ž conemporaneously. in he HP case. This is idenical o he value Backus e al. Ž repored for Europe and much lower han he U.S. value of 0.88 see Backus e al. Ž 1995, Table Employmen is less volaile han oupu; in his case, he Israeli value for he relaive sandard deviaion of 0.67 is closer o he U.S. figure of 0.61 raher han he European figure of Three broad conclusions emerge from Table IV. Firs, he correlaion of hiring wih employmen is weak Žin he exponenially derended case even weakly negaive. and wih oupu i is moderae. Second, hiring raes and asse values are much more volaile han he cyclical measures. Third, he co-movemen wih he variables included in he presen value relaion is 8 Dynamic cross correlaions are he same for hiring raes and for asse values, so only he former are repored.

22 HIRIG AS IVESTMET BEHAVIOR 507 Ž. no sronger a mos 0.3 and ofen swiches signs across lags and leads. A closer look a he resuls reveals some differences beween he derending mehodologies, bu hese do no change he picure in any essenial way. The underlying resul, hen, is ha hiring and asse values are no srongly relaed o radiional measures of he cycle or o he variables included in he presen value relaion. How can his be reconciled wih he previous resuls, especially hose of Table III? There are several, relaed answers o TABLE IV Business Cycle Properies I Exponenially Derended Variables a. Dynamic Cross-Correlaions Ž F, H, ž / H ž / H F ž / H F ž W / H ž / H ž / H f ž /, F , , , r , s , g b. Relaive Sandard Deviaions.. 1 Relaive o employmen 2 Relaive o oupu H sd sd sd P1 sd sd P2 sd sd 1.8 sd F 1.1 H 5.3 sd sd F 1.6 sd P1 6.6 sd F 4.8 sd P2 sd F 5.9

23 508 ERA YASHIV TABLE IV Coninued II HP-filered Daa a. Dynamic Cross-Correlaions Ž F, H, ž / H ž / H F ž / H F ž W / H ž / H ž / H f ž /, F , , , r , s , g b. Relaive Sandard Deviaions.. 1 Relaive o employmen 2 Relaive o oupu H sd sd sd P1 sd sd P2 sd sd 4.1 sd F 0.67 H 12.4 sd sd F 2.2 sd P sd F 6.7 sd P2 sd F 8.3 oes: Ž. 1 All variables are in naural logs. H Ž. 2 is he rae of hiring. P is he asse value as defined in Table 3: Ž H P1 uses 1 200,000; 2 4. P2 uses 1 3,150,000; is business secor employee poss. F is real GDP of he business secor. For full definiions see Appendix A. Ž. 3 For each pair of variables he longes sample H period is used. For and F his is 68:196:4. For and P i is 75:189:4. H Ž. 4 For he cross-correlaions, and he Pshave he same cross-correlaion so only he former is repored.

24 HIRIG AS IVESTMET BEHAVIOR 509 his quesion. One is ha he radiional measures of he cycle do no appear in he presen value relaionship. Anoher is ha he variables ha do appear are no represened in Table IV by heir presen alue expression, bu raher by heir conemporaneous, lagged, or lead value; compare, for example, he saisic Ž P, r. in Table IV o he expression J j Ý covž P, r. j1 j ha appears in Table III. Finally, he presen value relaion is highly non-linear, so correlaion coefficiens are no very adequae. We use hem here in order o be consisen wih he mehodology adoped in he business cycle lieraure. The posiive lesson o be drawn from hese findings is he need o examine hiring in erms of he relevan presen alue variables. The resuls do no suppor opporuniy cos argumens like he one cied above for a similar reason: while hiring raes should move counercyclically according o hese argumens, we find a posiive correlaion beween hiring and produciviy. When curren produciviy changes, componens of he asse value are changing oo, and in ways which offse he prediced negaive relaionship. 8. THE SESITIVITY OF HIRIG How does hiring respond o changes in asse values, and how are hese affeced by heir various deerminans? While his quesion may be answered in several ways, one naural case o consider is he non-sochasic seady sae. Looking a he seady sae, he focus of his secion is fundamenally differen from he cyclical issues ha were jus explored. 9 Through examinaion of he seady sae, we are able o explore he sensiiviy of hiring o is deerminans and o poin o some policy implicaions. The seady sae is given by / ž / 1ž / r s 1 g g H W H ž F 1 H 2. Ž 20. Ž. f 1 g f f All variables are a heir seady sae value. I is imporan o recognize he dynamic, flow aspec of he hiring decision. When he asse value of workers rises, no only does he number of hires go up, bu also he rae of 9 Examinaion of his quesion in a cyclical, sochasic conex would require lenghy analysis beyond he scope of his paper for such analysis using U.S. daa and a search and maching model see Yashiv Ž 1999b..

25 510 ERA YASHIV FIG. 1. Profiabiliy. hiring increases. The firs quesion of ineres for quaniaive exploraion H W is: wha is he relaionship of o each of is driving facors, i.e., F, r, s, and g f, or in oher words, wha is he slope of he dynamic, flow demand curve? Figures 14 use Eq. Ž 20. o simulae he changes in he rae of hiring as a funcion of hese variables, using he case of 1 200,000 and 2 4. In each panel he origin is he sample average of he FIG. 2. Ineres rae.

26 HIRIG AS IVESTMET BEHAVIOR 511 FIG. 3. Separaion rae. exogenous variable under sudy, and he hiring rae is he soluion of Eq. Ž 20., wih all oher exogenous variables valued a heir sample averages. The figures illusrae he elasiciy of he rae of hiring wih respec o he various deerminans of asse values. While he response of hiring o changes in he profi rae is almos linear in he relevan range, he FIG. 4. Produciviy growh.

27 512 ERA YASHIV response o he ineres rae, separaion rae, and produciviy growh rae is non-linear and asymmeric. The higher hiring raes are, he more sensiive hey become o changes in hese raes. In he erminology of labor demand curves, a hese values he demand curve is relaively fla Ž swiching he variables on he axes.; i.e., here is a relaively big response of labor demand o relaively small changes in he relevan deermining facor. 10 However, for lower values of he hiring rae he curve is seeper. Thus if hiring raes are relaively high, small increases in ineres raes can reduce hem considerably. If hiring raes are low, big reducions in ineres raes are required o bolser hem. This analysis may be applied o quesions of policy. Two widely discussed policy insrumens are subsidies or axes on hiring coss and wages. Hiring subsidies have ofen been suggesed or applied in dealing wih European unemploymen in recen years. Taxes on hiring may come in direc as well as indirec form, such as various regulaions or bureaucraic procedures. The effecs of hese insrumens may be analyzed by muliplying 1 by Ž h. Ž w. Ž. h w 1 and W by 1 in Eq. 20, where, are he hiring and wage subsidy raes, respecively. Figures 5 and 6 show he effecs of hese subsidies Ž or axes. on he rae of hiring. Some numerical compuaions are repored in Table V. Figure 5 shows ha a subsidy for hiring Ž h. displays increasing reurns in erms of he hiring rae. The higher he hiring rae, he higher 10 oe ha unlike demand curves in he neo-classical model his is a case of flow demand Ž raher han sock demand. and ha i is cas in erms of raes, no workers or hours. FIG. 5. Hiring subsidyax.

28 HIRIG AS IVESTMET BEHAVIOR 513 FIG. 6. Wage subsidyax. he impac of a marginal increase in he subsidy. Table V quanifies his asymmery in he response of he hiring rae: a 42.5% ax reduces he hiring rae from he benchmark of Figs. 14 Ž he origin. by 0.25 percenage poins, while a 22% subsidy raises he rae of hiring by he same amoun. Figure 6 shows ha a subsidy for wages Ž w. displays he same W linear behavior as he rae of profi Ž. which i affecs. F TABLE V Subsidies and Tax Effecs H h ž / 1.3% 42.5% 0.4% 1.55% % 21.9% 0.4% oes: Ž. 1 Hiring rae of 1.55% a monh is he benchmark value of Figs. 14. Ž. 2 0 is a subsidy; 0 is a ax. w

29 514 ERA YASHIV 9. COCLUSIOS The paper has sudied he deerminans and sochasic behavior of he gross flow of hiring. The empirical work examined alernaive specificaions primarily wih respec o he funcional form of hiring coss and discoun rae models. Using wo alernaive mehodssrucural esimaion and approximaioni inferred he unobservable asse values of workers, quanifying hem a reasonable magniudes. The resuls were subjeced o a variey of ess frequenly used in he financial asse pricing lieraureorhogonaliy ess, variance bounds, and mean-variance resricions. These corroboraed some of he specificaions, validaing he presen value relaionship driving hiring. I was shown ha he volailiy in asse values sems mosly from flucuaions in expeced marginal profis and in bank credi ineres raes. These flucuaions were found o be only weakly correlaed wih cyclical flucuaions in GDP and in employmen. Hiring displays high sensiiviy o is driving facors and moves asymmerically in response o changes in he componens of he discoun facor. More work is needed o fully undersand he asse pricing and business cycle implicaions of hese resuls. In he asse pricing conex, he noion of asse value of workers could be embedded in a full-fledged producionbased asse pricing model encompassing boh labor and capial. Then he consequences for asse prices could be elaboraed. In he business cycle conex, he resuls pose a challenge o exising models: wih fricions, firms behavior is shaped by ineremporal relaionships of he ype analyzed here. This calls for analysis in erms of he relaionship beween he relevan presen value variables and he cyclical measures. Such analysis would include examinaion of he shocks driving asse values and he propagaion mechanisms generaed by he coss involved in hiring. APPEDIX A: DATASOURCES AD DEFIITIOS The daa se includes 180 monhly observaions in he years In wha follows we use he following abbreviaions for he agencies ha are he sources of he daa: ES Ž Employmen Service., CBS ŽCenral Bureau of Saisics., BOI Ž Bank of Israel., and IA Žaional Insurance Agency.. ES daa are aken from is monhly and quarerly saisical publicaions. All oher daa appear in he monhly bullein of he CBS. 1. Hires Ž H.. Source: ES. umber of vacancies filled by he ES each monh. 2. Separaion rae Ž s.. Source: compued on he basis of IA and CBS series. Lacking a direc measure of he ime-varying separaion rae