Job Matching and TheTheory OfTurnover

Job Matching and the Theory of Turnover

Boyan Jovanovic

The Journal of Political Economy Vol 87 No 5 Part 1 (Oct 1979) pp 972-990

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Boyan Jovanovic Hul( Lnhorctlorzr~I n r nnd Collrrnh~c~b u i z ~ ~ ~ i t )

A long-run equilibriurri theory of turnover is presertted and is shoivrr t o esplaiu thc irnporta~lt regular-ities t1itr have l~erll oktser-ved by empirical investigators r or-hers procluctivit) in I pilticulnr jot) is 11ot kriotri ex ante anti Itec-ornes kllo~vn niitre prccisrly its the worker-sjob tenut-e irlcl-east9 lul-noer is genel-ated I)) the esis- tence oi I noildegerierate distr-ib~ttion of tlic wor-hers produc-tii~it~ across different jobs The noxit1ege1leracy is caused by the ass~rrrred a]-iitiori in the cluality of the svor-ker-e~nplover- tliatch

he objective of this paper is to construct and to interpret a model of pcrn-~anentjob separations A permanent job separation involves a change of employers for the worker 71-e~~~porary separatiolis (con- sisting rnairlly of temporary layoffs) have been the sul-ject of recent theoretical work by Baily (1974) Azariadis (1975) and Feldstein (1976) anti are not corlsidered here

Recent evidence or] labor turnover falls into two categories the cross-sectional industry studies (Stoikov and Rarnon 1968 Kur-ton and Parker 1969 Pencavel 1970 Parsons 1972 Telser 1972) and the more recent studies using longitudinal data on individuals (Rartel 1975 Rartel and Borjas 1976 Ereernan 1976 Jovanovic and Mincer 1078) T h e strongest and most consistent finding of all these studies is a negative relationship between quits and layoffs on the one hand and job tenure on the other This finding is equally strong for quits as it is for layoffs Jovanovic and Mincer (1978) find that roughly one-

This is a shortened versiorr of n ~ y Ph1) thesis I jvo~ild like t o thank R E 1-ucas for suggesting this problem ro me ancl foi- his co~~stariteiicorir-igerncr~r and advice thl-oughout the prepararior~ of this work 1 would also like to thank Gary Beckel- arid Lcster Ielser for their help at various stages of the pr-eparaticin o f thc thesis [[rifrrrini lt$Polrlrcai Econoni 19iY v o l 87 no 5 pr I ]

1979 by Thr Univeisr~yof Chrrago 0022-SROXi9R751-0004$015l

JOB MATCHING A N D TURNOVER 973 half of this negative relationship is explainecl by the negative struc- tural dependence of the separation probability on job ter1ure T h e rest of the observed clependence is only apparent anct is caused b y the fact that within any nonhomogeneous gr-oup a negative col~relation between job tenure anti the separation probability will exist simply because those people with a lower propensity to change jobs will tend to have longer job tenure and vice versa Other observed 1e1ationships are as fbllows women young nrorkers productioii workers those with less schooling and those in the private sector tend t o turn over more as do those workers not cover-eci by a pension plan atit1 those ~ v h ocvork in industries with loxver conce~itratiori ratios ox- with snlaller average firm size None of these relationships is nearly as strong as that bct~veen job te~iur-e and sep~t-ation pl-obabilities

Existing ~nodels of iurnovel- (that is the pel-manent separations component of turnover) all involve irnperkct information Net in- fhrnration arrives either about ones current match o r about a possitde alternative match that leads to a job change In fact a natural distinc- tion among the rnodels call he made along these lines In one citcgory are models in which turnovet- occurs as a result of tlie arrival of infor-mation about tlie current job match and the present moctel ftlls into this category as do the ~nodels of Viscusi (1976) Milde (I$) and Jo l~nson (1978) These are niodels i t1 which I job is an experi-ence good in the tcl-minology of Nelson (1970) that is the only viy to determine the quality of a par~icular rnatcll is to fi)rni the match and experience it I11 the second category are pure search-gooct tnocfels of job change (Kuratani 1973 1ucas and PI-escott 1974 Rur-dett 1977 Jovano1-ic 19780 Mortensen 1978 lilde 1978) In those motlelc jobs are pure sear-ch goods and matches dissolve because of the an-ivnl of new information about an alternative plospective match Hil-shleifer (1973) introduces the inol-e appropriate designa- tion inspection goods Iti~b~c-tionis evlluition that car1 take place prior to purctiase r~purirncuonly after purchase

In this paper ajob match is treated ts a pure experience goort T h e paper makes two separate contributions First i t is the only explicitly ec1uilib1-iun~ treatment of tur-nover in its category An ecjuilibriu~n wage contract is provect to exist itrid a particular wage cotitrict is demonstrated to be an equilibriunl one This particular wage co11- tract has he propert) that at each nioment i t1 time tlie ro~ker- is paitf his ~narginal ~ I O ~ L I C ~conditional upon all the tailalle inf0rnlation at that time

Second the c11tracterization of the inodels implications I-egarding

1 bec~nirawcre of the ark o f thew three author aftcl- tllc present vc~tkas la rgc l~li~lishctl

974 JOURNAL OF POLITICAL ECONOMY

the tenure-turnover relationship arlcl the tenure-wage relationship is more esplicit than that of earlier models and the predictions are largely consistent I$-it11 the evidence T h e rnodel predicts that worker-s

- rernain on jobs in whicl-1 their productivity is reve~led to be relatively high and that the select themselves out of jobs in ivhich their productivity is I-evealecl to be low Since wages always eclual expected mai-ginal prodi~cts for all vorker-s the nod el generates (011 average) Mage gl-owth as tenure increases Since job tenure and lahor market expel-iet~ce are corr-elateel across workers this also implies wage g r o ~ ~ t hover the life cycle T h e model also pi-edicts that each corkers separation probability is I of his job tenure clec~-easing f i~~ lc t i on Ioosely speaking this is 1)ecausc a mismatch betiveen a torker and his employer is likely to he detected early on rattler than late T h e learriirlg mechariisrn is such that longel- job tellure has a negative s tructu~al effect on tile vorkers sepaiation probability After cor- recting till- the regression hias that arises becruse of the spurious correlation between job tenure and the separation probability in a hetcrogcneous group of workers Jovanovic a n d llincer (1978) find tliat this structui-al tiepe1ldence is very strong

Befor-e (leveloping the model we summarize the major assumptions of the jot)-matching approach t o turnover Ei1s~ i t is assumetl that for each worker a nondegerier-ate distribution of productivities exists across different jobs T h e same is true Lhr thc employer-~vorkers d i f k r in their productivities in a given task that the ernployel- needs to have performed T h e problenl is one of optirnallp assigning ~vorkers to jobs

T h e second assumption is that employers ctn contract vith workers on an iildiviclual basis T h e employel- is then able to revirti a ivorker with vho~n he matches well by paying the corker relatively more 111dividtttI contracting creates a structure of re~vai-ds thit PI-ovictes p rope~ signals fbr the attainment of optimal rnitches In extreme exa~riple of individual coritr~cting is a piece-rate ivage scale A less extreme and a widely prevalent esanlple is i s)stenl of pr-ornotion o r dela)-eci pay increases based on the quality of the woi-kers perfi)l-- Itlance on the jol ovel- a past period of time of sorrle given length These are examples vtlere workers pay is c o r ~ t i n g e ~ ~ t on their- per- forni~nce

Ihe third major assumption of the job-matching approach is that imperfect information exists o n both sides of the rnarket about the exact location ~f ones optirnal iissignn~erlt Follo~vi~rg an initial as- sig~~rrient inforrn~ition lteco~nes availalle and I-eassignnient be- r m v comes optirnal in certain cases T h e job-matching model ger-rerates turnover as the phenomenou of optiinal reassigrt~nent cztused 11)- the accumulation of ttette~ iiiforn~ation with the passage of time

JOB MATCHING A N D TUKNOVER 975 The Model

Assume that firms production functions exhibit constarit returns to scale and that labor is the only factor of prod~~ctiori Cnder conipeti- tive conditiorls the size of firm is tllen intieterminate Each workers output is assumecl to be obsered instantaneously by the worker and by the ernployet- so that infbrmational asymmetries do not arise Let S ( t ) be the contribution by a worker to the total output of the firni over- a period of length t and let

X ( t = pt + m ( t ) (for each t gt 0) ( 1 ) where p and cr a le constants and a gt 0 and where z(t) is a standal-d normal rtriable with meall 7ero and variance t (a stanclartl Wiener process with indepentient iricrernerits so that cov lz(t) z(t)] = nrin [t If])Then X(t) is nor-n~ally distrib~ttecl with mean yt arid ~ i t h variance CT )~ Assun~e that (T is the same lor each firm-worker rnatch while in general p cliffel-s across matches T h e interpretation of p is not one of I-1-ker- ability but a nieasure of the cjuality of the match When the ~rratclr is forrned p is unknown As the nratch continues further intormation (in the f i~rn i ofoutput as given by eq [ I ] ) is generated A gootl match is one possessing a large p Let p he nornlally distributed XI-ctss matches with niean m ant1 with variance J and assurne that job dianging involves drawing a new value of p from this dis- tl-ihution and the successive drawings are independent he latter assu~nption guarantees that the workers prior history is of no rele-vance i r i assessing his p on a newly formed match T h e only way to learn about p is to observe the worker on thejolgt for a period of time Ihis inclependeuce assunlption also means that the i~iforrnatiorlal capital thus generated is con~pletely nratch specific and is analogous to the conrept of firm-specific human capital

For a worker with job tenure t and cumulative output X(t) = x the above assumptions irnply that the available information on p on his current job can be characterized by a posterior distribution that is norriial (see Chel-noff 1968 p 266) with

posterior mean -E(p) = (wzs- + xa-)(s- + t a -~~) - (2)

posterior v~riarice = S i t ) = (-I + tcr-)-

llie pair- [X(t) t ] is thu-efi~re a sufficient statistic for the information co~ttainect in the entire posterior distribution (Ihis property is essen-tially due to the independent increments property of the Wiener

10 elaborate Clhcn tlealing wit11 rarrtion~ variables the corlcept of inforrrration spccificit) is associatet with the conccpt o f i~ltlependcnce while perfect informational generalits is associatecl wit11 perfect correlation

976 JOURNAL 01 POLITICAL ECONOhlY

process) Furthermore IlY(ttt (p) is 110r1na11y distributed with mean m irid variance - S ( t ) ((her-noff 1968)

Firms are assumed to be risk neutral and to nlaxirnize the rnatlie- matical expectation of revenues discounted by the rate of interest r The) cornpete tbr workers by offering wage contracts In a long-~-un equilibrium the payments practices of each firm ~ ~ ~ o u l d be well under- stood and would not need to be explicitly written An implicit contract equilibrium is studied here T h e present model al~stracts entir-el) from the cctnsideration of shocks stemming from the product market A11 firms face the same product price uorrnalized at unity so that a mairitaineti h-pothesis of the model is that demand conctitiorls are stationary Assume that the firms wage policy can be characterized by a wage function ul[X(t) t ] -Phis is the wage paid to the I-orker with tenure t if his cumulative output contrihution is ecjual to X(t) I f the firm tvishes to fire a certain worker rather than doing so directly the firm is assumed to lo~ver his wage by an arnount sufficient to itrctuce him tct quit 411 the job separations are therefore at the rvor-kers initiatke but since sorne of the separations are disguised layoffs their empir-ical counterpart is really total separations (quits p l~ is layoffs)

Yorkers are assumed to live for-ever ancl this assumption justifies the exrlusio~i of age as an explicit argument from the wage function As long as he remains with the firm the ~vorker receives payment according to tlie wage functiorl w ( ) He has the option of quitting at any time Let Q be the present value of quitting a job and then pursuing the best a1ternatixe T h e infinite horimn constant discourit rate and the independence ofthe successive drawings o f p imply that Q is a constant 1et a(Q[ic])be the present value to the worker of ohtainilig a job with a finn which offers ) IS its age contrict and when the value of quitting is Q Then ifc represents tIre direct ancl the foregone earnings costs of job changing

T h e constant c is assunled to be parametrically given for each vorker although i t may vary icross workers Let T he the quitting tirne and let H(xt I [w]Q) = prob ( X [ t ]s x and 7 gt f given [a]and Q) and F(t [ u ~ ] (2) = prob (7 G t given [as]and Q) I hen F is the probability that the 15orker quits befigtre tenure t while N is the probability that he does not quit before tenure I and that by that time his cu~nulative output

klorc gcrierall) otie coulil rsstlrnc thaf orlers lifetinres arc csponc~nti+ll tlistrib- utrrl implvitry the tt)srtice of aging+)nc trultl not r~litkerl diffcr~tltpledic-tion ihouc the Irt~gth of tlw trtniining litc of a or-ket- tvho has iIrc~dv liveti d lor~giirr~cth~n for a worke r who tias onI liztl t shor-I tirne

4 1 he c-oristarlc- o f Q over t i t~lr tnrr~-rs that (lie war-ker never returns to a jot) from ~vhich he once separarect 111 other- vo~tls if i t esistetl the optiori of I-cc~llW O L I I ~ rrever be exrrcisrd b ttle wet-kcr

JOB MATCHING A N D TURNOVER 977

doe4 not exceecl x Ihen define the appropnate ctens~ties h (r t 1 [u l ] Q) and f ( t 1 [zo] Q) b) h = dNIdv a n d j = dFldt Both f and h are chosen b~ the ~voi kei In respon5e to a wage function X I ( ) and I p~esentvalue of quitting Q -1 hen

Equition (4) holds at the optimall chosen f~inctions h and f Since f integrates to a number not exceeding unity aaaQ = Spirfi1t lt 1 Then it is easi1)- seen that for given functions h f and zu equations (3) and (4) possess exactly one solution for the pair of scalars (a(2)

All new workers look alike to the firm and each ~vorker is offered the same wage cor~tract ~ In differential form equation (1) reads d X i t ) = pdt + cdz(t) Letting E be the mathematical expectation operation conditional on X(t) = x at t the disco~~nteci revenue from the output of a single worker is ~ f p - d ~ ( t ) = =Ef Te-vflv fd~(t) EfreF E(p)dl + E f Tu - ~E~ di(t)lhe stochastic integrals are It6 integrals (see fiushner [1971] for their definition) anct the last integral is therefore zero b y the indepenclent increments property of the Wiener process so that Efe-$ix(t) = ~ f ~ ~ - ~ ~ ~ ~ ( ~ ~ ~ ( ~ ) d tfcrt= f z_E(p)hixt [XI]Q)dxrlt = P(Y [il~]) Firnis are aware of the workers optiinal quitting response to the wage contract zu) and this is re- flected in the above equation Now let n(Q fur)) be the discounted expected net revenue from the employment of a given worker who is offerect the contract ui) and who has a present value of quitting equal to Q Then

where y = ~ f T a - ~ y1 [ul]Q)d t ( t In maximizing n(Q [ X I ] ) over functions [ w ] the film treats Q as

gihen since Q is determined by the wage policies of other firms

Let 13 be the set of competitive equilibrium wage contracts and for an 7 ~ ( )let Q([ro]) denote the unique solution for Q from equation (3) hen if us()E B (E 1) each worker fcgtlloclr his optimal quitting

Sirnilarl) all f i r - l r i look alike to the worket- ex ante Straightfortvarii estensions of the nod el t o the case where there art observable differences in characteristics anlong workers are outlined at the enti of the paper Salop (1973) takes up the search problem when the fcorher is able to distil~guish among firnrs ex ante arld has partial inful-niatioti riot only about the wage offerrd by the firm hut also about the likelihootl that he will receive an emplovmeiit offrl- Yrotn the firrn in the event that he saniples it 1x1 Salops analssis the most attractive opportunities are saniplect first arid the job seehet- lowers Iris acceptance wage with his iiuration of unernplo~rnent as his ~retnair~ing opportunities ~OrSCrl

Ya JOURNAL OF POLITICAL ECONOMY

poll~v in lesponw to zu() anti to Q([w]) (E2) TQ([zL~I)[zL])3

n-Q([IP])[GI) for all in() 1 711 ( ) so that ZLI( ) maximizes expected profits (E3) n-Q([w])[ul])= 0 (zero expected profit ~ortstraint) Let

1 ) = t o r 1 ( t ) contlact stntes tl-lit the ~ o r k e l I hi +ige 111 be paid hls eupecter-i (1n11 glrlnl) p~octrlc t it each rnomerlt 111 ttrne 1x1Qv =Q([itx4])

h r o ~ ~ nI -70X E R Ploof -ES I tiearl sat15fled bgt 711 1o plole E1 anti E2 ilppoe

t x ( o n t r a d ~ t t l o ~ ~that F2 1s ttot ltlshed b wv 40 thit t h e ~ c eilst sorne 711 E H such that a d e ~ l a n tf t r m offers ~t

while the ilo~ kel must be tfolng at least a tvcll 1s uncle1 711

(The value ofquittirlg the deviant firm is unchanged at Q) From (5)

hen equations (6) illri (7) imply that the left-hand side of (8) is strictly positive But the right-hand side of (8)is equal to JTe rlJw (xt)h(~tI [itl]Q) - h ( ~ tI [w] Q))d~dt + QJp-~f(t [ i ~ ] Q) -

(t 11711]p ) gt c l t and this expression cannot be positive since the quitting policb implied by h ( ~ t [ a i ] (I) j ( t Q)) is optimal fhr [ z r l ]

the workers when facet1 with t ) anti the the wage contract ~L(Y present value of quitting Q QED

Since workers and firrrls are risk neutral ul(x f ) is rlot a unique equilibrium contract any random variable [ possessing the property I([) = u(xt) would also qualify A pure piece-rate wage involving a payment ofX(i + At) -X(t) over the interval ( t t + At) theretbl-c also qualifies as eqttilihriurri since EldX(t) = ) d t + crEclz(t) ilr(x~L(Y = t ) t i t Ally such contract leads to idetitical turnover behavior as under ZL~(Xt ) Ever1 within the class o f functiorls o f s and t alone u(x t) may not be unique he following theorern guarantees however that tul-nover behaviol- is unique

~ ~ P O T P W ~2-If 71 E H the11hx t 1 [n] Q([il])) = h ~ t 1 [ill] Q([uI]) and j t Q ( [ ~ L ] ) ) = 1 [711] Q([af])) [~LI] Jf

Proof-See Jovanovic 19780 The proof is lengthy and rlot par- ticularl) instructive Theoren 2 states that the separation policy of the worker is unique even though the wage contract leading to it is not This turnover behavior is identical with that which results in a situa-tion i r l which each firm offers a wage corttract zom(x t ) = E(p)

Purcto optirnnlity rft~irriozlrr-Sinte all the agents are risk tleutl-al the

979 JOB MAICHING A N D TURNOVER

correct optirnality cr-iter-ion is the maximization of the discounted expectation of aggregate output Theorem 2 inlplies that whatever the prevailing equilibrium wage contract the worker behaves so as to maximize his own expected discounted output He collects all of the rent associateti with the match arld the decision about -tlether or- not to terminate the match rests with hirn (although the tirni is equally involveti in the sepal-ation decision since i t lowers the workers wage to the point where it knows the worker will quit) Therefore a separation occur-s if and only if the rent associated with the match falls to rero A central planner could improve on this situation onlv if he krielv zcjhich workers and it~hirhfirms would make good matches

Assume that the worker is faced with the wage contract zir(x t ) = E(p) and a present value of quitting Q The sufficient statistics (state variables) areX(t) and t I t is more convenient to use instead w ( t )and t as the two state variables where ul(t) = EX(p)Since ~ ( t )is normally tlistributed with mean 7n i-tnd variance r - S ( t ) for all t it satisfies the stochastic differential equation

so that the workers wage folIows a driftless random process with ever-decreasing incremental variance that tends to zero as tenure tends to infinity Let V ( w t) be the (current) value of the game to the worker rvho has tenure t and wage ~ ~ ( t j= w Then letting Ert denote the nlathernatical expectation operator conditioned upon zc and t 6

~ ( Z U t ) = i ~ lA t+ P - ~ E ~ Y + At] t ) + o(At)(~~t[t (10)

Subtracting (XI t ) from both sides dividing through by At taking the limit as At tends to 7er0 and applying ItOs Lemma (5ee Kushner 197i ) j ieIdc

As with most optimal stopping problems involving Mai-kov processes the space of points ( w t )can be divided into a continuation region and a stopping region (see Shiryaev 1973) The continuation regiori con- sists of those wage-tenure cornbinations at which it is optimal for the worker to remain with tllc firm Equatioris (10) and (1 1) hold for all

( ) ( S t )represertts ttarlns rentling to zero faster than At does Note that the optiort of stopping or1 ( t t + At) (in wtlich casc a rcwartl Q is rollectecl) is exercised wirh a probibilitr that hehaves esser~tiall as does

I (At ) 1 1 - lt- I 1 - q v 5 z CXP 1- (At) 2 1 = ( ) ( A t )(At) -

(see Feller I)6t5 p 171 xvhrr-e thc inec1ualitv follows by a ~vell-knowt~ on theresult hlills I-atio atitl whel-r s is eclnal to 11 - ( I )


wage-tenure combinations that belong to the continuation region Let [O(t) t] be the boundary of the continuation region so that along the boundary V[O(t) t] = Q and O(t) may be thought of as the reservation wage at which the worker quits the firm Evaluating equation (1 1 ) at = O(t) O ( t ) = rQ - [s(1)~2~r~] l [e(t) - V[e(t) I] A welI-knoilmt ] smooth-fit condition of optimal stopping (see Shiryaev 1973) states that along the boundary V[O(t) t ] = aQat = 0 implying that

$ ( t ) = rQ - -V0) [ $ i t ) t ] 2aZ In the interior of the continuation region V(u8 t ) gt Q Since at the reservation wage V[O(t) t] = Q and since V[O(t) t] = 0 this implies that V[O(t) t] 3 0 Note that S ( t ) declines monotonically to zero which suggests that H(t) should be rnonotonically increasing up to rQ It is possible to prove [see the Appendix) that H ( t ) lt rQ for all t that (IOldt 3 0 and that im O(t) = rQ so that the reservation wage increases up to its limit froni below T h e reason fhr the increase in the reservation wage is the decrease of the incremental variance of the wage process as tenure increases A large incremental variance implies a large dispersion in possible future wages If wages turn out to be very high the worker does not quit If they become very low the worker partially avoids this adverse outcorne by quitting attd collecting Q In the absence of the opportunity to quit the risk-neutral torkers welfare would be unaffected by changes in the incremental variance T h e limit of the reservation wage is rQ This is because the wage tends to a constant as t tends to infinity There is nothing further- to be learned and at the point of indifference between staying and quitting the capitalized value of this constant trage must be equal to the present value of quitting Q

T o obtain an approximation to the probability of job separation by tenure set H(t) = rQ for all t Then for this approxinlation to the reservation wage

A n infbrnral proclf is as fbllo~vsV ( W 1 ) = Q + jiVfv )rlv is rnaxinrircd with respect to () (the reservatiotl wage at t ) Therefore dtfferentiating both sicies with I-espect to ()setting the result equal to zero anti taking thc limit as uptends to (0one obtains that V[(t) t ] = 0 which in turn implies V[(t ) = 0 since V [ ( t ) = (2 = I t i constant

In the Appendix it is shown that B ( t ) lt rQ for all t implying that V gt 0 along the boundar-y where it is also true that E = 0 So if it was true that the continuation region was boundeci from above this would imply that V lt Q for some point in the interior of the continuation region sufficiently close to the boundary which cannot be true Therefore H(t) is single valued and it bounds the continuation region from below so that the optimal policy does hale the reservation wage property This is not surprising since it is known (Rothchild 1974 p 709) that optimal search rules from normal distributions with unknown mearls and known variance have the reservation price property when the prior distribution is also normal

T h e wage is a standard Wiener process in the s - S ( t ) scale (see the discussion

JOB MATCHING AND TURNOVER

where iY(s) = (~T)-Samp~dz iwhere p(t) = s - S ( t ) is the precision lhe unique mode of this distribution is (171 - 70) After the mode the prohalility of turnovei- ciecliries rapidly to zero Sonle ivorkers never change jobs since lim F(t ) lt 1

r+= 10detel-mine thi- p eciicted behavior of the separation probability

by tenure consider the hazard rate 4(t)-f(l - F)Then + ( t ) is the density of separation conditional upon an attained level of tenure t The rnodel predicts I nonrnonotollic relationship first [4(t)] gt 0 and then 4(t) lt 0 as t gets relatively large That $ ( t ) must eventually decline figtllows since limf(t) = 0 while 1 - F(t) is bounded away from

I--zero The precise inarheliiatical expression hl-the tenure level t X at which 4(t) changes sign and finally becomes negative cannot be obtained in closed form but sincef gt 0 implies + gt 0 clearly t 2 m - rQ = the model off If the mode off is close to zero 4( t )is likely to become riegative early on as appears to he the case empirically (see Jovanovic and Mincer 1978)

The tenure-wage profile (defined as the conditional expectation of the wage given that the worker has attained tenure t ) may also he calculatedland is equal to 6 ( t )= (n + (nr - ~ - Q ) ~ ( - N [ s- S(t)]-11 - 212-n[s - S ( t ) ] ) ) Note that GI([) increases nionotonically from ~ I I

when tenure is zero up to [m + ( m - rQ)LS(-crs-I )l - 2Y(-(rCs2)] when tenure tends to i~lfiriity Therefore as low-wage workers quit arid high-wage workers stay the model iniplies that the average wage of a coho^-t of workers increases with tenure eventually at a decreas-ing rate In the limit as tenure becomes indefinitely large the average wage of those members of the cohort who have not quit approaches a constant as the wage of each worker becomes constant and equal to his true productivity Ihis then is an alternatike explanation for -ivage gr t~othon the joi

preceriirig eq 191) Therefore the fhrmula represents the first passage probability for a Wiener p t - t~es r through a linear Iottndar) (Cox and Miller- 1965 p 221)

lhe prolmhility that a Wiener process will rlot c-ross a linear hotindary by a partic-uiar time and that it will etrd up at a particular value at ttiitt time is also aiailable in closeti form (see Cox and Lfiller 1965 p 221 eq 71) 4fter appt-opriate adjustment the conditional density of M-ages ( b y tertur-e leel) is obtained atid ri(l) is the rr~athemarical expectation of this distt-ibution

982 JOLTRNAL OF POLITICAI ECONOMY

A mismatch leads to a lobver rage and an early separation 7hus holding constant market experience average past earnings are likely to be lo~ver tor a worker ivho has experienced many job separations This prediction appeii1-s to be consistent ~vi th evidencc from the National longitudinal Stud) (NI-S) mature mens sarnple (see Bal-tel arid Borjas 1976)

Job durations over the life cycle itre identically and independerltly distributed ~andoni vitriahles The turnover generated 1)) the model therefore fi)~-ms a pure renebval process (see Feller- 1966 chap 11) Let y denote the ivorkers labor market experience and 11(3) + o ( A J ) denote the pl-oljability that the worker experiences a job separation on the market experience interval ( y u + A y ) -1hen R ( J )is the renewal (lensit whictt satisfies the equation

Jovanovic and Sfincer (1978) prove that a monotorrically declining $ ( t ) irnplies a rrlonotonicall) cleclining K (J) I n other isorcis a mono-tonically declining separatior~ pr-obattility hy tenure isI)j itvclfsufficicnt to cause turnover t o tieclinc monotonic~lly ove1 the life cycleI2

Last the model ge~ier~lizes stl-aightfol-avaiicilyt o incorportte pel- miinent cliffel-ences in rvor-kcrs cfiiiractel~istics such as lewl of school- itlg ability race sex ant1 so on l h e pal-alnetel-s of the rnotiel (S 771

a J ) can then be 1egal-der1 as fi~nctions of these ~ariahles with each distinct group of vat-kers treated as though they belonged to a distinct lnarkct of vorke~-sof that type T h e entire tiialysis I-emains valiti co long as infi)rmational synirnetr- let~veen wolkers and ernploers is rnaintainetl so that issues of sigr~aling artrl self-selection are side- stepped 1-he riatul-e of the assurrietl functional deperitlencc bet~vecn w t - r n and $ on the one hanti anti the votkers persorltl character-istics o r 1 thc other will drterminc the preclicted relationships hetvcer~ turnover and these personal charactel-istics This is not pursuer1 here hut is a11 ir~teresiing probleln fi)r future research

Holding evcr)thing else constlrtt This statentrtlt shoulti ilot Ie inter-pretcti is sring t1ilt vithir~I group olobsc~itioniIl) t-quitletit prople t l ~ o e that have changed jot~s often in tlic pit hate had lvcr artage past r ir t~ing thin those rhai hit not changed jobs often In other wortis the rnotiel does [tot inrpl rllat tnovers st~ould do $or-se than ttrrs c3veit though ernpit-ic11ly thi ippett-s t o be trut

A sirnilrt- rrlaiionship holtfc fhr wage 1ttI() he thr rrtarhcr~t~tical crpec-tation of the wagc II a giben level of lahoi- niir-krt expcrirtice J Ihert I() sitifies the equition L(Y)= i gt ( j ) i l - I ( Y ) ~+ [ ~ ( O L ( ~- tjdt Ici (13) amp kr~ortt is the retiewil ecluation which fbr- all giveti continuocis tlcr~sit I ( ) possessea a utticlue solurion K ( J ) (Feller 1966) sucft that K ( 0 ) = f (0) ailti lim Ii() =[I(0dir1

0- i

JOB hlATCHING A N D TLTRNOVEK gH3 Appendix L V t x now pro-lt the assertiol~s niadr in the text following equation ( 1 2 )ahout ( I ) the bourlci~~-) of the optinlal contirtuatiori region We pr-ove that H ( t ) lt1-Q tbl all I that ( I ) is r~ontlecre~sirig and that i t approaches t-Q as t tends to irifinity Sorric transfolrrlitior~s of the original problcrri ere rlccessary before these ~sscrtions co~tl(l Ilc proved anti since tllese trinsforrnaticrls move orle att frorn rhct ecor~omics of the protlerri it seenied preferal)le to incliitle these proofs ill t hc pper~diu

Suppose hat a probahilit space (0F P) is giverr with w heirig the elenier~taryeverits (wE0t)For any real-valued F-n~eisurable function f ( w ) the rrittherrlatical expcctitiori operator E is tlefir~eti as E V ( w ) ]= J j ( w ) d P Let S ( t ) E K 1be a hIarkov process cletincd on the above space A particular sample path of the process is written as [ X ( t o ) ] T f Let E he the expectation opertrcx cortdrt~onrl upon Y ( 1 ) =

( on5ltler the follot~ rng pr ohlenr of optir~illl stopplng t ( t ) Lcr 1 utrlrt fi~rlctror~ Igte g i ~ c r ~ to the t i ( ) the11 u ( ) deliotes the Irrrnntltlneous pioft 1111cr at trnw 1 ~f the p~irrrc~ 1s st111 111 progless ~ 1 tt a~rctr f ( 1 ) = 1Let Cr (1) be the rc1 rr1111rl p ~off furrct~oli cler~oting the utrllt to the plarer if the g~lrne13

stopped clctl at I rritl S ( I )= I he players otqectle 1s to rnnlrrirle h ~ s epecttcl tlrscourrtcd i ~ t ~ l r t frorir pla ~ n q ) 11it t l ~ sco~ l~ r trlre garrre ( ~ t ~ t h = late)

over- F-rrleasural~lr stopping tirrle functions 7(w) X flirther restl-icrior~ or1 T ( w ) is that i t must not anticipate the future A rigorous discussion of this ~cquir-enrent ippears in S1tirviev (1973) For rnost stoppirrg problems itrtd certlinl fill the problems discussed hclov this reqitireirlent niearis that thc solutiorl to the optinral stoppiirg problerrl car1 bc charac terizeci by a co~itiiiui-tiori regiorl for thc pr-ocrgts X(1) so thit the first exit tinre fronr the I-egioli is the oy)tiriril stoppirig tirnc for X(r ) Let C(n I ) he the value of t h ~ gaiitt to the pIacr lt I corrtlitio~ril uporr X ( t ) = s therr

where (a) is the optinial stopping policy and C ( x 1 ) is the current value furlction Lct

1xt q( t ) = ((L) - L7( t ) for 111 ( 1 ) ancl let ( ) = ~ ~ ~ ~ - r r 7 ( ~ ) - t l w ~ T ( ~ ) ) g i ~ i ~ ( w ) (14)

~rtd co~~sitler- the problem of irtaxirnizing

F 6 g ( Y [ I ( w ) 01 7 ( w ) = I g X [ T (a)w ] 7 ( w ) ) iA5) over s~oppirig-tirrle turictions 7(w) Ier f ( w ) be the optirnal policv for rhis pr~ohlerr~llierr the follo~virig tt~eorern t~olds

7h~orrm3-If E J I - ~ ]ulY(t w ) I ~ I Ilt r then f ( w ) = 7(w) a t d

g84 JOURNAL OF POLITICAL ECONOMY

Proof-Shiryaev 1973 p 101 Theorern 3 asserts that stopping problenis such as ( A l )which itivo1ve a n instantaneous utility obtainable ~ r h i l e the gitrnc is plavetl cart be transfotmed into problenis such as (A5) ~hich involve ol-rl a trrrninal paoff function g(x ) Note that C(r t ) is the current value of the policy never stop the garne no mattel- wh~t hippe~-rs to X(t)

Let X ( t ) satisfv the stochastic Ith equation

(A 7 )

(or (1X(t)= ( t [ X ( i ) t ld t + b[X( t ) t ] d v ( t ) in differential form) Here r(t)is the stai~tlard Vierter procrss a r ~ d X ( ) is I llatkov pl-occss jith instantaneous nrean n ( ) and instantaneor~s variarice [ b ( ) I 2

-1 he following theoretn cotrtains the basic resulls associrted it11 thc proh- Icni of optirnall stopping Y(i) when X ( ) is tiefined hv ecjuatiorl ( A 7 )

7Jzcotcnr -Let X ( t ) he itefi~ietl b ecjuation ( A i ) a n d let the stopping 1-oblem be given 1)y ei1uatio1-r(A5)Let 7lt -c be given a t ~ t l in atf(litior-1 to the other requirements on T ( w ) let T ( w j E 10 TI] for i l l wEIZ 1etJ = ( t x ) tE[O 7 l sER1)arid let V(x t )= supEampX[T(w)wj - (w)) where the s u p is taleri over the atlrnissahle filnctio~is T ( 0 ) Assume that the firtictiorts c r ( ) h ( ) anti (() a r e dl t~vice contitluouslv differentialgtle in x ant1 once it1 I tnti t1itt for all

1 -( x t ) ~ J itl+ itrl+ ~t~is k t l + 1 ~ ) ~ ~ l+ 111r 1 + I ( ( + ~ I I ~ amp ( I + 1 Y ) and that a 1 + h k where ancl k a re positive (onstants

1etD = [(t x)Vgt 51 and A + (z()tx() gt 0) = ( t x ) t t ( ) + (112)[8()j2[() T h e n the follorvirtg pi-opositions holtl ( 1 ) V 3 (o n J (2) I f V is differetltiahle then Z7() + n( )C ( ) + ( 1 2 ) [ b ( ~ ) ~ V ( )= 0 for ( t s ) E ] ( 3 ) T h e first exit time of the process L t X ( t ) ]from D is a n optimal stopping time Therefin-e L) is the region of the continueti observations and along its bourirlary I = 5(4) 4 C D (5) If 4 is connected so is I)

Procf-Miroshriichenko 1975 p 387 Consider riow the workers problem Let i i~[X(i)t]= Ex(p)= IV(t) be the basic l larkov process defined on (a F P ) The worker rllaxirnizes discou~itect expected earriings His instal-i- tatleous utility is I t ( ) while the tcrrninal p a ~ o f f ftinctiorl is a colrstint (2 Iheref(re the counterpart o f ccluatiori 011) is

7 heprocess IV()has ~ e r o drift I heretorc the courlterpart of I ( x t ) is E JP-s-w(s w)dc = r-lLlr 7herefitre g(x t ) = Q - r-lV Since E J ~ P - I IV(t w ) 1 tit lt x t heo~ern3 ma) he applieti to the pro1lenr to cortclutle tltat the solution t o the worler ~ prohlenr o f r r~ax in~i~ i r rgthe espr-cs- sion in ( A 8 ) is itientic~l ~ r i t h the solution to the problern of rnasirrri7ing

If T(w) is the op t i~na l solution then equation (A6) ielcls

whtrc ((I t ) is the worhcrs currellt value function N o w let Cl(r) he the stant1ircl Viener- process with Il(O) = 1 1 1 12t) is I stantiirtl icner ptoctlss in t h e - S ( t )scale (Chernoff 1968 p 22ti) L c r t i n g ~- a - S()+ I = rr21(-V ) -~ ~ ~ - 1 art0 k(w) -- - S[ (w)]


~vhere 7(w)E[Om) -+ Y(w)E[O r) he prohlern has therefore been trans- fortned illto orie of stopping a stal~tlard tierler process M(J) on the illterval LO s) kith only a terminal payoff function

1 heoren] 4 miI no be appllecl to tht problem ~ r t h ( I ( ) = 0 b ( ) = 1 Lct V(iZ J ) bc the ptesent ~ l ~ i e funttton for thts prohlenl ticfinetl b~

11o~x)~tt10t14of the theorern nssel ts that I C I ) hrre I1 15 the contitluatlon regtot] for the proces L1Z (I) 1J Ict [$(I) I ] he [he t)ouritlai of the corrttnu- tlon rcglori I hen [B() 3) Ff A +

0 ) I for teurolO 0 (I15)

-1 he 8 ( gt )i i ~ t r eresctitiotl lge I the (It ) piltc Let 6it) be the ~cse r ~a t io t~ age in the (bt t ) spice 1 hen B(t) = 01 - ([)I

r h r o ~ p m5 4 0 ) lt rQ f o ~)euroLO 5 )

Proof -Along the boundar)

l lO1 I = ) I I (I I ti) In view of (415) it is sufficietlt to prove that B(J) rQ fitr ariyjE[O s) By

contradictiol~suppose that fitr rotnejOeuroLOs) f)(jO)rQ Equation (A16) then= implies chat V[f)(y0) y o i = [()(iso) = 0 Consitier ria thc value of the follo~-ingpolic) it ( ~ ( 1 yo) For some 8 such that y o + 6 lt continue thc game ~tr i~i ly o + 8 hen if 71(yo + 8) lt 4 2 stop the galilc at y o + 6 anit collect 5[z1(11

+ amp) yo + 61 gt 0 If7(j+ 8) gt rQ cot~till~ie = 5 ancl collect a the ganir urttilr pi~koff ccliial to zero But putb Iv(y0+ 6) lt JQgiver] that 71(y0) = rQ] = 112 allti so there is a positive cxpectcti pavoftund(r this policv Since this policy is feasible C[0(j0) yo] rllust also be positive This colnpletes the proof of the theorern

Let F(y) be the probability that the vorkrr-s optinlal policv will lead hirn tit quit beforej 17henF (yo)= prob inf [Ctr(j) - 0 ( ~ ) ] 0) Ietf(y) he the density Then O = s y

(A 17)

Let cu ancl R be two partmerers Assun~e rllat the evolution of X(t) is not affected t q (1 anti Let u(v t a ) be the instantar~eous utility firnctiori in present valrrc terms and let G (x I p) be the tel-rninal payoff function also in present value terms Let I f ) ( a p)I ] be the optimally cletermitled bourtciary of the contintration region for tile process IX(t) 11 T h e function O( t a P ) is assumed to he sir~gle valuect Let h(s 1 a p) be the probability (density) that the game will not have been stopped befi~re t and that X(t) = r and letf( a

986 JOURNAL OF PO1ITICAL ECONOhiY

p) 1)rthe piobrb~lrt~ (clenit) th~t the ganie it111 be stopped elic t l nt t It rs t leal th~tH( nit11 olle ) ht ) and f ( ) lie In one-to-orlc co r~e$po~l t l e~ l t e ~r lo the~inti ilroultl be thought of d5 decrsrori $$I ~~tbicsLet I be the hort~oi 0 lt I -r I ct I (a p) be the ltiluc of the g~trr~t ~ t tlllte relo I her1

1l i r o t ~ n ~ 1 l ~ ( o r ~ t n ) a lnd 3 do riot i f f t ~t the e~olutron ot Y (1)6 ( l 117(~0po -11 ind r f I ( ( ) (j ) h ( ) f (I aild V() ~ I C ~ t l rrespcct to a and 8cl~fft~ierlt~able tiler clVria = iJVi)a = f 1-1u ( 1 cr)h ( 1 (I P)dcil lnd ((1 rip = OVia8 = f(~e(c( 2 p) t PI((CY p)dt

Proof-Cnless s t ~ t t ~ l ) (() A t ) f ( ) ~nci0( ) allother~trcz c ( eaiult~tedit ( 1 a p) Ful the rilo~e sllrce the proof f o ~ a I 111trost ~den t~ca l lth the proof f o ~p oul thc lltter is p e n

the theole111 will have Iteen pioveti Since tht worket-s policy i t r rcsporlse to a a r ~ d 3 is optiliial

fol a1101p 0 Subtldc tlng (a 3) from borh s~cics of ( A y l ) tlilil~rlg thlough In (la auri taLlrig the llrnlt JS d p - 0 the ierult i

A change i r ~ 3 i lr~plie~ a charrge in the optirrial stopping polic in genei~l But the polic which lvas optinral prior t o the shift i l l 8 iernains a feasible polic lhcreforc

Kcluations (-123)tntl ( A I Y ) ~rnply that

and (121)and (Al t f ) 1111pl that (A20) holds -+ tlVcl = i3Vla ilrd the theor em rs p i o ~ e d

I he results of I heoiern f i ale nou used to obtiin ciualrratie 11rfo1 nritloii about the t l e~~~ i t lve ( ( k t lnceof the uorkers cuixcnt a l~ ie f u l ~ t l o r ~ 1 ) IV(0) = rn

JOB MATCHING A N D TURNOVER

BL the envelopr theorem slntr- [[Ots) 1 = 0

Since ( v ) is a (iensit i t is rionnegitivc vhilr theor-em 5 implies that ampH(Y) J gt O foryElOs) Therefore (acas)(ni0) gt 0 But the state ( m 0 ) isarbitrarj-If the state is ( I t - r ) wher-eY = - S()the ar~aloguc of the right-hand side of ec~u~t ion replac cd b S ( 0 I he onlp $a in which the (42i) nou1t-i holtl rith rrolLers clfu-e is affecteci b the nler-e passage o t time is thl-ough the drcr-case in S ( t ) Since a( ( iV4 I)iaS(i) gt 0

I he envelope tlieor-em cannot be clirectly applied it1 ( X 2 5 ) to calculate il(li3rti btgtciuseni is the s t a r t i ~ ~ g point of the stanctarci tiietler process f l r ( y ) and if i t is changed it changes the probabilities of reaching a given bourltlar-v H ( v ) However ( so )is the derivative of F ( y 0 )which i r ~turn is tlehried h

-1his means that if lo() f ( I ) ] was a feasible policl pair- prior to the ch+rigth in )a then the new feasible policy pair is [ H ( T ) + dtnf ( ~ ) ] In other words after the change in m the boundary [ ( j )+ rlm] induces the same first-pilssag-e (tensity ( Y ) as did the bi)unda~-y ()prior to the change in r n and this holds for all boul~dal-ies N v ) I herefore the c h a n ~ e ft-on] rn to rtl + ilrri car1 be

1 7

considereti as having n o effect on the feasibilit) o f reaching a boundar) but sir~lplas changing the form of the pa)offfunction frorn 5(11 Y ) to [(It + iim y ) Application of ~heot-cnl (5 then viclcls

and sit~cef(v) is I density a(latri gt 0 iIain the rate (171o) is arbitrar-y ancl a siniilar ICSLIII tloltis f i ~ r (irCiilll)(lt gt) 1ettirig f ( 1 ) - ( r ) ( d ~ M t )he the first- passage probabilitv in the oliginaI rirne scale

7 h ~ o t - ~ t n is norlctecreasing in t7-$(t) Prorj-By contraciiction suppose that at t H(t) is decreasing Then

there exists ari E gt 0 sufficier~tly small such that the points [H(l)t + T] for T E [ O euro1 all lie in the continuation region Therefore since C gt Q in the continuation region

~ [ $ ( t ) 1 + euro1 gt c [ ( l ) I = Q (A31)


But

In vie of (A27) S~nce (A32) is a contradiction to (A31) the theorem ici proved

7 I ~ ~ o 7 ~ m 6( t ) = r (28 -11m 1-z

Proof--Since 6 ( t ) = B[s - S(t)] = (y) it is sufficierlt to prove tllal

lim O(y) = rQ (A33)V -s

Bp contradiction suppose that lim (y) = q and that q lt rQ Now choose6 gt 0 u-L

such that q + 8 lt rQ By theorem 7 H(y) is nondecreasing iny Tllerefore the point (q + 6 s - E ) 111ust lie in the continuation region for all)- E gt 0 In terms of the present value function V(trJ ) and the present value of the payoff function lt(WJ ) this 111eans that

where ffq + 8 ( - ~ y )is the probability (density) that the game will end aty E [r - E J ) given that Mfs - E ) = r) + 6 Since is decreasing in Mr and decreasing in jarid since H(y) is nondecreasing 4[8 (s - E ) s - euro1 gt lt[H(J)y] for y E (r - E 5 ) Iherefi~re

V(q + 8 s - t) lt lt[H(s - euro1 s - euro1S f + 6 s - E J (A351S-f

Furthermore f ( q + 6 s - t y) is the first-passage density of the standard Wiener process (originating at q + 6 at s - t ) through the boundary (y) on the interval [A - t s) Then the integral on the right-hand side of (A35) is smaller than the probattilit)- that the same standard Wiener process will cross the threshold sup B(y) = 7) From Feller (1966 p 171) this latter probability is

C=--e

equal to 2[1 - T(t- 8)] whereV(u) = Im(2rr)-2exp[- 112u 2 ] ~ l z c z Therefore

Equat~ons (236) (A34) and (A12) then imply that

[Q - r - H ( c - ~)]2[1- A(E I )] gt [Q - r (q + 6)] gt 0 (A37) But since 6 0 ) 1s nondecreasing and since by assumption linl O(y) = q lt rQ

u-8

(Q - rq)2[1 - A(t-L6)] gt [Q - r-I(q + 6)] f438) The right-hand side of (A38) is positive and does not depend on E Therefore t may be chosen sufficiently snlall such that the inequality in (A38) does not hold he theorem is proved

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JOB 3fATCHING AND TURNOVER g89

Baily Martin N 14ages and Employriierlt untier Uncertain Dctnind Rrcb Ecorr Stzcdirc 4 1 no 1 (Januar) 1974) 37-50

Aartel A P lsquoJob Lfobility ant1 Earnings (t-o~th orking Papel Nat Bur Econ Res 1975

Barrel A P and Boriis G I Zliddie-Age Job Xiobilit orking Paper Sa t Bur Econ Res 1976

Bnrdett Kerlncth Thcorgt of Ernploee Search Quit Katcs zlbIi 68 (blar-ch 1978) 2 12-20

Rurtori J o h n F and ParLer- soh11 E Inter-i~rdustr Iariations in oluntary Lahor IIot)ility Ir~dus clnd 1rrhot R r l lt ~ t i o ~ l (j~rluir 1960) Nril 22 rio I 199-2 16

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(ox David K and hfiller- H I) 7 ~7t~orof Stocitcrstic Irocrcr~s Sew York iiley 1965

Feldstein hiartin S Ienlporargt laofZs in the Theory of I~rlcriiploymelit JPE 84 no 5 (October 1976) 937-55

Feller Williarn 4tr I~rtrodzrctio7~to Probcrhilitj Throry iitrcl Its A~~gtlzc(ttiort 1012 2d ed New York Itiiey 1966

Freeman K B Exit Voice Tradeoffin the Iahol- Il~rket Inionisln Quits anti J o b T e n ~ ~ r e Unpnhlished paper- Harvard Univ 19715

Hirslrleifer Jack iCller-e Are Ve in the Theory of Info~-~ii ~t iol i 4Eli 87 (XIay 1973) 31-39

Johrison W A LIheorgt of J o b Shopping Ql1E 92 (bra 1978) 26 1-77 Joanovic Bo)ari Joh Xfatching and the Thcor of Turnover PhD dis-

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1abor Iurnovet Whel-r J o t ~ s Are Pure S e ~ ~ r c h (oods Inp~tblisheci paper Colurribia Liniv Fet~ruary 1978 ( h )

Jovanovic Ro)an and Minter Jlcoh 1tl)or Mobility and 17~ges Inpub- listied paper ltolumbia Utliv Julie 1978

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Kushner Harold introductinn to S t o ~ h ( t ~ t ~ ~ Co~ltr-01KC York 1folt Kinctit~t 8r Viriston 1971

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Shiryaev AIBert N Stcrtiticnl S ~ q ~ ~ r ~ l t i n I Opt in1~~1 Provi-d 4 ~ ~ ( ~ l j ~ i ( S~o~~p i r rg~Kz i l r ~ dence K I Anlerican Ilathern~tical Society 1973

9g0 JOURNAL OF PO1ITICAL ECONOMY

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Job Matching and the Theory of TurnoverBoyan JovanovicThe Journal of Political Economy Vol 87 No 5 Part 1 (Oct 1979) pp 972-990Stable URLhttplinksjstororgsicisici=0022-38082819791029873A53C9723AJMATTO3E20CO3B2-Q

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5 Systematic Job Search and UnemploymentS C SalopThe Review of Economic Studies Vol 40 No 2 (Apr 1973) pp 191-201Stable URLhttplinksjstororgsicisici=0034-65272819730429403A23C1913ASJSAU3E20CO3B2-N

References

Wages and Employment under Uncertain DemandMartin Neil BailyThe Review of Economic Studies Vol 41 No 1 (Jan 1974) pp 37-50Stable URLhttplinksjstororgsicisici=0034-65272819740129413A13C373AWAEUUD3E20CO3B2-4

Systematic Job Search and UnemploymentS C SalopThe Review of Economic Studies Vol 40 No 2 (Apr 1973) pp 191-201Stable URLhttplinksjstororgsicisici=0034-65272819730429403A23C1913ASJSAU3E20CO3B2-N

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Boyan Jovanovic Hul( Lnhorctlorzr~I n r nnd Collrrnh~c~b u i z ~ ~ ~ i t )

A long-run equilibriurri theory of turnover is presertted and is shoivrr t o esplaiu thc irnporta~lt regular-ities t1itr have l~erll oktser-ved by empirical investigators r or-hers procluctivit) in I pilticulnr jot) is 11ot kriotri ex ante anti Itec-ornes kllo~vn niitre prccisrly its the worker-sjob tenut-e irlcl-east9 lul-noer is genel-ated I)) the esis- tence oi I noildegerierate distr-ib~ttion of tlic wor-hers produc-tii~it~ across different jobs The noxit1ege1leracy is caused by the ass~rrrred a]-iitiori in the cluality of the svor-ker-e~nplover- tliatch

he objective of this paper is to construct and to interpret a model of pcrn-~anentjob separations A permanent job separation involves a change of employers for the worker 71-e~~~porary separatiolis (con- sisting rnairlly of temporary layoffs) have been the sul-ject of recent theoretical work by Baily (1974) Azariadis (1975) and Feldstein (1976) anti are not corlsidered here

Recent evidence or] labor turnover falls into two categories the cross-sectional industry studies (Stoikov and Rarnon 1968 Kur-ton and Parker 1969 Pencavel 1970 Parsons 1972 Telser 1972) and the more recent studies using longitudinal data on individuals (Rartel 1975 Rartel and Borjas 1976 Ereernan 1976 Jovanovic and Mincer 1078) T h e strongest and most consistent finding of all these studies is a negative relationship between quits and layoffs on the one hand and job tenure on the other This finding is equally strong for quits as it is for layoffs Jovanovic and Mincer (1978) find that roughly one-

This is a shortened versiorr of n ~ y Ph1) thesis I jvo~ild like t o thank R E 1-ucas for suggesting this problem ro me ancl foi- his co~~stariteiicorir-igerncr~r and advice thl-oughout the prepararior~ of this work 1 would also like to thank Gary Beckel- arid Lcster Ielser for their help at various stages of the pr-eparaticin o f thc thesis [[rifrrrini lt$Polrlrcai Econoni 19iY v o l 87 no 5 pr I ]

1979 by Thr Univeisr~yof Chrrago 0022-SROXi9R751-0004$015l




















































































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Job Matching and TheTheory OfTurnover