INTERNAL PROMOTION AND EXTERNAL RECRUITMENT: A THEORETICAL AND EMPIRICAL ANALYSIS

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1 INTERNAL PROMOTION AND EXTERNAL RECRUITMENT: A THEORETICAL AND EMPIRICAL ANALYSIS by Jed DeVaro * Department of Management and Department of Economcs College of Busness and Economcs Calforna State Unversty, East Bay Hayward, CA E-mal: jed.devaro@csueastbay.edu and Hodaka Morta School of Economcs Australan School of Busness The Unversty of New South Wales Sydney 2052, Australa E-mal: h.morta@unsw.edu.au May 15, 2009 Abstract: A crucal personnel decson employers face s whether to fll a lmted number of manageral postons wth nternal hres or external recruts. We present a theoretcal and emprcal analyss of ths decson and how t relates to wage settng and the provson of general tranng. The theoretcal framework s a promoton tournament nvolvng M competng frms wth heterogeneous productvtes, two-level job herarches, and a fxed number of manageral postons. Employers provde general tranng to ther workers, some of whom are promoted nternally or raded by competng frms. We also consder an alternatve model based on varaton n the qualty of the worker-employer match. Both models predct the followng results: As the number of workers at the lower level of the herarchy ncreases, holdng fxed the number of managers at the top, 1) nternal promoton ncreases relatve to external recrutment, 2) employers provde more general tranng, 3) the percentage of employees n the upper tal of the wage dstrbuton decreases, 4) proftablty ncreases. We test these predctons usng data from the 2004 wave of the WERS, a natonally-representatve cross secton of Brtsh establshments. The emprcal results are supportve and contrbute to the lterature some new stylzed facts concernng how key employer decsons vary wth both the sze and shape of the organzatonal herarchy. Keywords: Internal Promoton, External Recrutment, General Tranng, Tournaments, Fxed Slots, Job Herarches * The authors acknowledge the Department of Trade and Industry, the Economc and Socal Research Councl, the Advsory, Conclaton and Arbtraton Servce and the Polcy Studes Insttute as the orgnators of the 2004 Workplace Employee Relatons Survey data, and the Data Archve at the Unversty of Essex as the dstrbutor of the data. None of these organzatons bears any responsblty for the authors analyss and nterpretatons of the data. We thank Jonathan Lm for research assstance and numerous colleagues for helpful comments, ncludng semnar partcpants at the 2009 Socety of Labor Economsts meetng, Htotsubash Unversty, USC Marshall School of Busness, UC Merced, and the 2008 conference on Tournaments, Contests, and Relatve Performance n Ralegh, NC. 1

2 1. Introducton The number of manageral postons s lmted n most organzatons, and employers fll those lmted postons wth ether nternal hres or external recruts. Ths external-versusnternal-hrng decson s mportant, because manageral capablty s a crtcal determnant of the proftablty of an organzaton. Our objectve s to explore how ths decson s related to the shape of the organzatonal herarchy, presentng a new theoretcal model that descrbes the nterconnectons among employers competton for scarce manageral talent, ther proftablty, the shape of ther organzatonal herarchy, the dstrbuton of wages wthn the organzaton, and ther ncentves to tran workers. Our model delvers testable mplcatons concernng how these concepts are related, and we test these predctons emprcally usng the Brtsh WERS, a largescale, natonally-representatve, cross secton of employers surveyed n Our results support each of the model s predctons and ntroduce a new set of emprcal results to the lterature on nternal hrng versus external recrutment. We fnd that, controllng for employer characterstcs, ncreases n establshment sze that make the job herarchy more bottom heavy are assocated wth: 1) a greater lkelhood of hrng nternally versus recrutng externally, 2) a hgher level of proft, 3) a lower fracton of workers n the upper tal of the organzaton s wage dstrbuton, and 4) a greater lkelhood of provdng tranng to workers. Our analyss contrbutes to the theoretcal and emprcal lteratures on promotons n general and nternal hrng versus external recrutment n partcular. 1 Gven that two mportant functons of promotons are creatng worker ncentves and assgnng workers to jobs, the two man buldng blocks for theoretcal analyses of promotons are tournament models and job assgnment models (Baker, Jensen, and Murphy 1988; Gbbons and Waldman 1999a). Ours s a job-assgnment model that ncorporates a central feature of tournament models, namely a herarchy wth a fxed number of manageral postons. In contrast, most job assgnment models assume flexble job slots n whch any number of workers could be promoted to CEO, gven suffcently strong job performance. The noton of fxed job slots s an mportant feature of most wthn-frm job herarches, as dscussed n DeVaro (2006), so t s worthwhle explorng the jobassgnment aspect of promotons under the realstc assumpton of fxed manageral job slots. On the other hand, the noton of an actve outsde market n whch competng frms bd for a worker s 1 A survey of the lterature on nternal promoton versus external recrutment s contaned n Waldman (2007). 2

3 servces s a plausble feature of employment relatonshps that s captured n many job assgnment models (ncludng ours) but that s absent from tradtonal tournament theory, except nsofar as a partcpaton constrant n the worker s utlty maxmzaton affects how the employer sets wages across herarchcal levels. Furthermore, an mportant dstngushng feature of our model s that, unlke most exstng models of promoton, ours explctly analyzes strategc nteractons among heterogeneous employers n ther efforts to fll ther manageral postons wth capable canddates. In our model, frms herarchcal structures are endogenously determned, where frms wth hgher returns from ther managers adopt more bottom-heavy herarchcal structures. Ths results n a set of novel testable predctons concernng nternal promoton versus external recrutment and the shape of the job herarchy. To see the model s man deas, consder a labor market consstng of M ( 2) frms, each of whch has a two-ter herarchy consstng of one manageral poston and a varable number of subordnate postons. The frms are heterogeneous n that they have dfferent returns from ther managers capabltes. Each frm decdes how many young workers to hre and makes ntal wage offers to a large number of ex ante dentcal young workers that choose between employment and self-employment. When the hred young workers become old, ther manageral capabltes (whch are transferable across any frms n the market and modeled as random draws from a known dstrbuton functon) are revealed to themselves, to ther employers, and to all other employers n the labor market. 2 We assume that employers have symmetrc nformaton about manageral capablty and that employers compete aganst each other by smultaneously makng wage offers to employ one worker n the manageral poston. Productve workers who are not hred as managers reman wth ther current employers as subordnates, whle unproductve workers ext the market to pursue some outsde opton (e.g. self employment). Our model, and an extenson that ncorporates frm-sponsored general tranng, yelds the followng set of testable predctons: As the number of subordnate workers at the lower level of the herarchy ncreases (holdng fxed the number of managers at the top): 1) nternal promoton 2 The symmetrc learnng assumpton n whch a partcular worker s ablty s revealed durng the course of hs career to all employers n the labor market at the same rate has appeared n a number of models n the job assgnment lterature (e.g. Gbbons and Waldman 1999b, 2003). An alternatve strand of the lterature focuses on asymmetrc learnng n whch a worker s current employer obtans nformaton about hs ablty at a faster rate than competng employers (e.g. Waldman 1984; Mlgrom and Oster 1987; Rcart Costa 1987; Waldman 1990; Bernhardt 1995; Zabojnk and Bernhardt 2001; Owan 2004; Golan 2005; DeVaro and Waldman 2007; DeVaro, Ghosh, and Zogh 2008). 3

4 ncreases relatve to external recrutment, 2) proftablty ncreases, 3) the percentage of employees n the upper tal of the wthn-establshment wage dstrbuton decreases, 4) employers provde more general tranng. 3 The logc behnd these predctons can be explaned as follows: As the number of productve workers n the ndustry ncreases, each employer can hre a manager wth a greater manageral capablty. Ths beneft s ncreasng n the return from manageral capablty, and hence an employer wth a hgher return from manageral capablty has a greater ncentve to ncrease the number of ts productve workers by employng more tranees and provdng them wth a hgher level of general tranng. An employer wth a larger number of productve workers, n turn, has a greater probablty of fllng ts manageral poston wth an nternal hre, wth a larger number of productve workers remanng as subordnates. Our analyss relates to the lterature on radng (e.g. Lazear, 1986; Bernhardt and Scoones, 1993; Km, 2007). Lazear (1986) explored a model consstng of two frms, wth a rad occurrng when a worker s worth more to a competng employer than to the current employer, and demonstrated that an nformatonal asymmetry between the two frms concernng the worker s productvty gves rse to a number of mplcatons on radng and offer-matchng. Buldng on Lazear s model, Km (2007) explored a model that lnks employee movement and product-market competton, demonstratng that a frm may poach ts rval s key employees n order to nduce the rval s ext. Bernhardt and Scoones (1993) examned the strategc promoton and wage decsons of employers when employees may be more valuable to competng frms. In all of these models, the fundamental drvng force for radng s the qualty of worker-employer match. In contrast, n our model the drvng force for radng s the combnaton of fxed manageral job slots and employers heterogenety n ther returns from manageral capablty, though, as n the models based on match qualty, our model also captures the dea that radng occurs when a worker s worth more to a competng employer than to hs current employer. In Secton 3, we present an alternatve model based on match qualty that yelds the same predctons as our man model, and we dscuss how both models compare. In our man model, returns from manageral capablty are assumed to be dfferent across frms. In the equlbrum, frms wth hgher returns employ more young workers, yeldng our key predcton that an employer wth a more bottom-heavy herarchcal structure s more lkely to 3 The fourth predcton offers a new explanaton for the exstence of frm-sponsored general tranng, a topc of recent nterest n the tranng lterature. Alternatve explanatons for ths practce have been offered n earler work (e.g. Acemoglu and Pschke 1998, 1999a, 1999b). 4

5 hre ts manager from ts nternal canddates. A smlar assumpton was made by Zábojník and Bernhardt (2001), whch proposed an asymmetrc learnng model n whch tournament przes are determned compettvely. That analyss ncorporated frm heterogenety by assumng a fxed number of hgh-productvty frms and free entry of low-productvty frms. As n our model, hgh-productvty frms n ther model adopt a more bottom-heavy herarchcal structure than lowproductvty frms n the equlbrum. However, the Zábojník and Bernhardt model does not yeld predctons concernng nternal promoton versus external recrutment; there s no labor turnover n the equlbrum, and all promotons are nternal n ther model. 4 Another purely theoretcal analyss that relates to ours s Demougn and Sow (1994), whch ncorporates tranng n a smlar manner to the extenson of our man model. Demougn and Sow consder an overlappng-generatons structure n whch frms are nfntely lved and each cohort of workers partcpates n the labor market for two perods. In any perod, a frm employs a sngle manager and an endogenously-determned number of unsklled workers. The frm can tran any or all of ts young workers, where a hgher level of tranng ncreases the probablty that an unsklled worker becomes sklled and therefore capable of becomng a manager. In the equlbrum, each frm promotes nternally f at least one young worker s tranng succeeds, and promotes externally otherwse. A fundamental dfference between the Demougn and Sow model and ours s that n thers the equlbrum herarchcal structure (bottomheavness) s the same across frms, whereas n ours t s dfferent. Ths s crucal, because the focus of our analyss s on dervng and emprcally testng new predctons concernng how varaton n herarchcal structures across frms affects the lkelhood of nternal promoton, proftablty, wage structure, and tranng ntensty. In contrast, the focus of ther theoretcal analyss s explanng a pre-exstng pattern of evdence concernng career moblty, up-or-out rules, nternal labor markets, the span of control, and senorty wage prema. Other theoretcal analyses of nternal hrng nclude Chan (1996) and Waldman (2003), and a recent emprcal analyss s Chan (2006). These analyses dffer from ours n ther 4 Our model also predcts that an employer wth a more bottom-heavy herarchcal structure makes more proft, has a greater fracton of workers appear n the upper tal of the frm s wage dstrbuton, and provdes more tranng. Although these addtonal predctons also arse from the Zábojník and Bernhardt analyss, our work offers a contrbuton n two ways (apart from our unque theoretcal predcton concernng nternal hrng). Frst, our model establshes the robustness of these addtonal predctons n the context of a model wth a very dfferent focus; whereas Zábojník and Bernhardt focus on the ncentve mechansms of promotons wth asymmetrc learnng, we focus on the job-assgnment mechansms of promotons wth symmetrc learnng. Second, whereas the Zábojník and Bernhardt analyss s purely theoretcal, we emprcally test all of our model s predctons. 5

6 motvatons and n that they do not focus on the mplcatons of employer heterogenety. In partcular, they am to explan why nternal canddates are frequently preferred for promoton over equally-qualfed external canddates. Chan s (1996) model conssts of two ex ante dentcal rsk-neutral frms, whle Waldman s (2003) model consders a sngle rsk-neutral frm. In contrast, our study focuses on the mplcatons of employer heterogenety n the returns from manageral capablty, and ths yelds a set of new predctons concernng how a frm s tendency to hre nternally, ts proftablty, ts wthn-frm wage dstrbuton, and ts decsons regardng tranng relate to ts chosen shape of the job herarchy. Before presentng our man model n the next secton, we note that our theory offers a potental explanaton for a well-establshed emprcal fndng that nternal hrng of CEOs s more prevalent than external recrutment n large frms (e.g. Dalton and Kesner, 1983; Lauterbach and Wesberg, 1994; Parrno, 1996; Lauterbach, Vu, and Wesberg, 1999; Agrawal, Knoeber, and Tsoulouhas, See Murphy, 1999 for a survey). Although ths nternal successon frm sze relatonshp has been documented emprcally, to our knowledge, no theoretcal models have been proposed that yeld ths predcton. Our model s frst predcton relates to ths stylzed fact, though we emphasze that our predcton pertans to changes n sze of a partcular type, namely ncreases n sze at the lower (.e. non-manageral) levels of the herarchy. Thus, ncreases n frm sze n our model also mply changes n the shape of the herarchy, n partcular a flattenng of the herarchy or an ncrease n bottom heavness. However, the emprcal regularty pertanng to frm sze n general mght well be consstent wth the predctons of our model to the extent that frm sze n general s postvely correlated wth sze n the lower levels of the herarchy, and thus our model can be nterpreted as offerng a theoretcal explanaton for the nternal successon frm sze relatonshp for CEOs. Whereas the prevous emprcal studes smply focused on frm sze wthout dstngushng how ths sze was dstrbuted across herarchcal levels, the data we use allow us to nvestgate emprcally the more refned predcton regardng sze (and shape) from our theoretcal model. We fnd clear support for ths predcton, thereby ntroducng a new stylzed fact to the lterature as well as a theoretcal ratonale for t. 2. A Theoretcal Model of Internal Promoton Versus External Recrutment In the followng subsectons we present our model, analyss, testable predctons, and an extenson to consder employer-sponsored tranng. 6

7 A. Model Consder an ndustry consstng of M ( 2) frms n a two-perod setup. Heterogeneous frms are characterzed by parameters V, where ndexes frms and V 1 > V 2 > > V M. The parameter V determnes frm s return from ts manager, as descrbed later. 5 In realty, frms n the same ndustry adopt dfferent strateges to satsfy needs of dfferent types of customers. For example, some frms produce lower qualty, standardzed products whle others produce hgherqualty products talored to specfc customer demands. For the latter type of frm, a manager's ablty to understand the changng nature of customer needs and to propose correspondng changes n the frm s busness strategy (such as product desgn, product delvery, advertsement, etc.) s more mportant than n the former type of frm. Our mode captures ths mportant dfference across frms by assumng that the returns from manageral capabltes are dfferent across frms. In the begnnng of perod 1, a large number of ex ante dentcal ndvduals exst. Every frm (= 1, 2,, M) smultaneously makes take-t-or-leave-t frst-perod wage offer w 1 > 0 to nˆ 0 ndvduals. If an ndvdual accepts frm s offer, he s employed by frm n perod 1. Let n denote the number of frm s frst-perod employees (call them young workers). If an ndvdual s not employed by a frm, he becomes self-employed. To smplfy the descrpton of the model, assume that such an ndvdual stays self-employed untl the end of perod 2, earnng w > 0 per perod. Frms and ndvduals are both rsk neutral and do not dscount the future. Every young worker s assgned to a subordnate poston. Due to lack of experence, each young worker requres supervson from the employer. Assume that each frm s young worker s output s η s(n ), where η > 0 s a gven constant and s(.) s a dfferentable functon wth s (.) > 0. That s, as the number of young workers ncreases, each young worker s output declnes because each young worker receves less supervson from the employer. 6 To smplfy the analyss, let s(z) = bz where b > 0. 7 At the end of perod 1, each young worker j exhbts manageral capablty m j, whch s randomly drawn from a unform dstrbuton between α and β, 0 α < β. To keep the analyss smple and the notaton compact, let α = 0 and β = 1. If worker j s assgned to a subordnate poston, hs second-perod output s y η, requrng no supervson from the employer. Each 5 For smplcty, we assume that every employer knows ts own V and those of the other employers n the market. Ths assumpton can be relaxed a bt, so that employers observe ther locaton n the dstrbuton wth some error, and our qualtatve predctons would reman unchanged. The assumpton that employers would have a farly accurate sense of where they fall n the dstrbuton of returns to manageral capablty seems reasonable. 6 See Zábojník and Bernhardt (2001) for a smlar specfcaton. 7 We allow the possblty that a young worker s output s negatve. Ths can be avoded by nterpretng η to be each young worker s (postve) output and s(n ) to be a per-worker supervson cost that frm must ncur n perod 1 when t employs n young workers. 7

8 worker s productvty s completely transferable across frms n the market, and the realzaton of each worker s manageral ablty s observable by all M frms. In perod 2, each frm can fll one manageral poston and an unlmted number of subordnate postons. Each frm s gross output from ts manager s gven by V (m + q), where m denotes the manageral capablty of the manager n frm, and q denotes frm 's manager's productvty f he has zero manageral capablty. Assume V M > y/q, whch mples that each frm s gross output from any worker s hgher when the worker s assgned as a manager than when he s assgned as a subordnate. Each frm s perod-2 gross output s then gven by V (m + q) + n O y, where n O denotes the number of frm s subordnates (the superscrpt O stands for old workers) n perod 2. Frm s overall proft s the gross output mnus wage blls. The tmng of the game can be summarzed as follows: Stage 1: Every frm (= 1, 2,, M) smultaneously makes take-t-or-leave-t frst-perod wage offer w 1 > 0 to nˆ 0 ndvduals. Indvduals that are not employed by a frm become selfemployed. Stage 2: Each young worker exhbts manageral capablty, m j, whch s a random draw from a unform dstrbuton between α and β. The realzaton of each worker s manageral capablty s common knowledge. Stage 3: Each frm smultaneously makes wage offers, denoted w r, to every young worker r (ncludng the workers employed at other frms). Each worker chooses the hghest wage offer, and n case of a te stays wth hs current employer. 8 Each frm then assgns one worker to ts manageral poston and all others to subordnate postons. Fnally, each frm realzes output. The job assgnment lterature makes an mportant dstncton between asymmetrc and symmetrc learnng, and nfluental models have been proposed under ether set of assumptons. Although we assume symmetrc learnng, the basc logc underlyng our results should also apply n an asymmetrc learnng model. Suppose that the current employer observes ts old workers manageral capabltes after the frst perod of employment, whereas competng employers only observe a nosy sgnal of these manageral capabltes. In that case, our results should hold n expectaton, though there would be some mstaken bds by outsde employers, resultng n some neffcent separatons and job assgnments. Another mportant ssue n the job assgnment lterature concerns the tmng of the wage offer process, n partcular whether offers are smultaneous or allow for counteroffers from the current employer. The smultaneous offer assumpton has been crtczed by Golan (2005) who showed that outcomes can be frst-best 8 The results are qualtatvely unchanged under an alternatve assumpton that each worker ncurs an nfntesmally small movng cost when changng employers. 8

9 effcent even n the presence of asymmetrc nformaton (where the outsde frms are less nformed than the current employer regardng worker productvty) when the current employer s allowed to match outsde offers wth counteroffers. In our symmetrc learnng model, t makes no dfference whether wage bds are smultaneous or f the current employer can make a counteroffer. However, t s unclear how an assumpton of asymmetrc learnng combned wth a counteroffer from the current employer mght affect the analyss, snce n that case an offer made by a current employer reveals some relevant nformaton to other potental employers. B. Equlbrum and Analyss We now derve Subgame Perfect Nash Equlbra n pure strateges. To focus our analyss and smplfy the descrpton of the results, we assume that an old worker s second-perod output, y, s suffcently hgh so that every frm employs at least one young worker n perod 1 n the equlbrum. A suffcent condton for ths s y > 2(w + b) η, whch we assume throughout our analyss. 9 Note that we focus on equlbra n whch n = nˆ holds: that s, n equlbrum, every frm employs all ndvduals to whom t made a frst-perod wage offer. Suppose that each of the M frms employs at least one young worker at stage 1. Let N ( M) denote the total number of young workers n the market and m(k N) (k = 1, 2,, N) denote the k th hghest realzaton of manageral capablty n the market, across the young workers n all M frms. It can be shown that, n the equlbrum of the subsequent Stage 3 subgame, each frm employs a worker wth m( N) as ts manager at the wage of w m (N), where M 1 m (1) m w ( N) = y + Vψ + 1 [ m( ψ N) m( ψ + 1 N)] for = 1, 2,, M 1, and wm ( N) = y. ψ = Ths result can be explaned as follows. Snce frm 1 has the hghest return from ts manager, t hres the worker wth m(1 N), the hghest realzaton of the manageral capablty, and frm 2 hres the worker wth m(2 N), and so on. We fnd that w 1 m (N) = w 2 m (N) + V 2 [m(1 N) m(2 N)] holds n the equlbrum. Note that V 2 [m(1 N) m(2 N)] captures the ncrement of frm 2 s gross proft 9 Suppose that frm employs n young workers at the frst-perod wage w. If a young worker s assgned to a subordnate poston n perod 2, hs second-perod output s y, and hence Bertrand wage competton mples that the worker s second-perod wage s y. Also, f a young worker s assgned as a manager, the worker s second perod wage s at least y. Ths mples that w 2w y, gven that any ndvdual can earn w per perod by choosng selfemployment. Hence, frm s perod-1 proft s at least n [η bn (2w y)] = n [y + η 2w bn ], whch s maxmzed when n = (y + η 2w)/2b. Then, (y + η 2w)/2b > 1 y > 2(w + b) η guarantees that every frm employs at least one young worker n any equlbrum of the game. 9

10 by hrng the worker wth manageral capablty m(1 N) nstead of the worker wth capablty m(2 N) as ts manager. The mnmum amount that frm 1 must offer above and beyond the wage w 2 m (N) to prevent frm 2 from successfully hrng the worker wth manageral capablty m(1 N) s V 2 [m(1 N) m(2 N)]. Smlarly, we fnd w m (N) = w +1 m (N) + V +1 [m( N) m(+1 N)] for all = 1, 2,, M 1. Ths provdes an explanaton for (1). Each frm s Stage-3 proft from ts manager n the subsequent equlbrum, denoted π m (N), s π m (N) = V [m( N) + q] w m (N), whch gves M 1 m (2) π ( N) = ( Vψ Vψ + 1 ) m( ψ N) + VM m( M N) + Vq y for = 1, 2,, M 1, and = ψ m π ( N) = V m( M N) + V q y. M M M Concernng other workers who are not assgned to manageral postons, Bertrand wage competton mples that each frm retans ts frst-perod workers at the wage of y, makng zero profts from them. The expected value of each frm s perod-2 proft s then E[π m (N)]. Gven the assumpton of a unform dstrbuton for manageral capablty, we fnd (3) N ( ψ 1) N ( M 1) E[ π ( N)] = ( V V ) + V + Vq y for = 1,, M 1, M 1 m ψ ψ+ 1 M ψ = N + 1 N + 1 m N ( M 1) and E[ π M( N)] = VM + VMq y. N + 1 Now suppose that there exsts an equlbrum n whch each frm offers w 1* to ndvduals and employs n * = * n ˆ young workers at Stage 1. Let N M * * n = 1 * n ˆ > 1. In the equlbrum, each young worker becomes frm s ( = 1, 2,, M) manager and earns second-perod wage w m (N * ) wth probablty 1/N *, and remans a subordnate of hs frst-perod employer earnng second-perod wage y wth probablty (N * M)/N *. Each young worker s expected secondperod wage n the equlbrum s then gven by w 2 (N * ), where (4) where w N) M 2 = 1 ( 1 ~ M = 1 V V + 1. m E[ w ( N)] N M + N N ~ V y = y +, N( N + 1) 10

11 At Stage 1, each ndvdual receves at most one frst-perod wage offer n the equlbrum, and every ndvdual who receves an offer s ndfferent between takng and not takng the offer. ~ 1* V Snce a self-employed ndvdual s lfetme wage s 2w, we have that w + y + = 2w * * N ( N + 1) holds for all = 1, 2,, M, and hence w 1* = w 1 (N * ) for all = 1, 2,, M, where ~ V (5) w 1 ( N) 2w y. N( N + 1) * * Then each frm s expected overall proft s Π ( n, N ) n the equlbrum, where m 1 (6) Π ( n, N ) E[ π ( n + N )] + n [ η bn w ( n N )] where + ~ m V = E[ π ( n + N )] + n[ y + η 2w + bn ] ( n + N )( n + N + 1) * N n j and N j * n j j. We have Vˆ 2 ~ 2 N + V [ N + N (2N + 1) n ] (7) Π ( n, N ) = + y + η 2w 2bn 2 2 for = 1, 2,, M, n N ( N + 1) where V ˆ V + V+ 1 + V VM for = 1, 2,, M 1, and Vˆ M MVM. Treatng the number of workers as a contnuous varable, (7) gves us necessary frst order condtons for the equlbrum numbers of each frm s young workers to satsfy. That s, n Π ( n *, N * ) = 0 must hold for all = 1, 2,, M. We fnd that ths condton s not only necessary but also suffcent, and the game has a unque equlbrum (see the proof of Proposton 1). Our man result s descrbed n Proposton 1, where the number of workers s treated as a contnuous varable. Proposton 1: The game has a unque equlbrum n whch each frm employs n * ndvduals n perod 1, where n * 1 > n * 2 > > n * M > 1. The logc behnd ths result can be explaned as follows. Consder frm s choce of the number of ts young workers, holdng the number of other frms young workers fxed at N - 11

12 ( M 1). The mnmum possble wage at whch frm can employ n young workers s w 1 (n + N - ) where w 1 (.) s as defned n (5), because each ndvdual s ndfferent between beng employed by frm at w 1 (n + N - ) and beng self-employed. Frm s perod-1 proft s then (8) n s n w n N n y w bn V% n N n N, 1 [ η ( ) ( + )] = [ + η 2 + / ( + )( + + 1)] and (y + η 2w)/2 > b mples that each frm employs at least one young worker gven any N -. In Perod 2, frm employs a worker wth m( N), the th hghest realzaton of manageral capablty n the market, as ts manager at the second-perod wage of w m (n + N - ). Snce m( N) s the th order statstc among N = n + N - young workers n the ndustry, frm can ncrease the expected manageral capablty of ts manager by ncreasng the number of ts young workers n, holdng N - constant. Comparng frm and frm j where < j, frm s ncremental proft from employng an addtonal young worker s greater than frm j s ncremental proft, because frm s return from manageral capablty s greater than frm j s return from t (that s, V > V j ). On the other hand, the ncremental frst-perod proft (the ncrement can be negatve) from employng an addtonal young worker s the same across all M frms. Hence, the ncremental overall expected proft from employng an addtonal young worker s also hgher for a frm wth a hgher return from manageral ablty, whle the ncremental cost of employng an addtonal young worker s the same for all M frms. Ths mples that a frm wth a hgher return from manageral ablty employs a larger number of young workers n perod 1, so n * 1 > n * 2 > > n * M > 1. C. Testable Predctons We now derve testable predctons that serve as the bass for our emprcal tests n Secton 4. In the equlbrum, each frm has n * young workers, and all of them are assgned to subordnate postons. There are N * young workers n the market, and every young worker has an equal probablty 1/N * to become frm s ( = 1, 2,, M) manager n perod 2. Hence, the expected number of frm s subordnates n Perod 2 n the equlbrum s [(N * M)/N * ]n * n O*, and n * 1 > n * 2 > > n * M mples n O* 1 > n O* 2 > > n O* M. Frms n our model adopt two-ter herarches, consstng of a manager at the hgher herarchcal level and subordnates at the lower herarchcal level. Then, n * 1 > n * 2 > > n * M and n O* 1 > n O* 2 > > n O* M mean that frm 1 adopts the most bottom-heavy herarchcal structure, frm 2 s the second most bottom-heavy, and so on. In Secton 4, we descrbe how a measure of herarchcal bottom-heavness can be constructed n our data set. 12

13 The followng three testable predctons emerge from our model. Testable predcton 1: An employer wth more bottom-heavy herarchcal structure s more lkely to hre ts manager from ts nternal canddates. Testable predcton 2: An employer wth more bottom-heavy herarchcal structure makes more proft. Testable predcton 3: An employer wth more bottom-heavy herarchcal structure has a lower percentage of ts employees located n the upper tal of the wthn-frm wage dstrbuton. Snce every young worker n the market has an equal probablty, 1/N *, of becomng frm s manager, the probablty that frm hres ts manager from ts nternal canddate s n * /N * P *, and n * 1 > n * 2 > > n * M > 1 mples P * 1 > P * 2 > > P * M, yeldng predcton 1. Regardng proftablty, gven V 1 > V 2 > > V M we fnd 1 (n * 1, N * -1 ) > 2 (n * 2, N * -2 ) > > M (n * M, N * -M ), yeldng predcton 2. Fnally, gven the natural assumpton that managers are located n the upper tal of the frms wage dstrbutons and subordnates are n the lower tal, we have predcton 3. D. An Extenson: Frm-sponsored tranng Employers often provde tranng, at ther own cost, to ther employees. In ths subsecton, we consder an extenson of the model that ncorporates frm-sponsored tranng to explore the robustness of our theoretcal predctons n the presence of tranng and to obtan an addtonal testable predcton. 10 Suppose that every frm (= 1, 2,, M) smultaneously makes take-t-or-leave-t offers (w 1, x ) to nˆ 0 ndvduals at Stage 1. After the frst-perod employment s settled, each frm provdes a level of tranng, x [0, 1], to ts young workers at a tranng cost of c(x ) per worker, where c(.) s a standard, twce-dfferentable cost functon satsfyng c(0) = 0, c (.) > 0, and c (.) > 0. To smplfy the analyss, let c(z) = az 2, where a > 0. Gven the tranng, φ(x n ) tranees become productve workers and the others become unproductve workers n perod 2, where φ(x) denotes the nteger closest to X R satsfyng φ(x) X. Thus, tranng ncreases the number of productve workers. Each frm s young worker s output s η s(n ) as n the orgnal model, 10 The full descrpton of the extenson s presented n a Supplementary Note that s avalable upon request. 13

14 where η > 0 s a gven constant and s(.) s a dfferentable functon wth s (.) > 0. Assume η < w; that s, each young worker s output s lower than hs self-employment output. 11 At the end of perod 1, each productve worker j exhbts manageral capablty m j, whch s randomly drawn from a unform dstrbuton between 0 and 1, as n the orgnal model. Each productve worker s output n a subordnate poston s y, where y > w. On the other hand, unproductve workers do not exhbt manageral capablty and ther output n a subordnate poston s η (< w) n any frms n the market, and hence unproductve workers leave the market and become self-employed n perod 2. Human captal s general and nformaton s symmetrc. That s, each worker s productvty s transferable across frms n the market, and the realzaton of each worker s manageral ablty s observable by all M frms n the market. We consder the Subgame Perfect Nash Equlbra, treatng the number of workers as a contnuous varable. Let n * and x * denote the number of frm s young workers and the level of tranng frm provdes, respectvely, n the equlbrum. If n * > 1 and 0 < x * < 1 for all = 1, 2,, M, we say that the equlbrum s an nteror equlbrum. It can be shown that n the case of M = 2, there exsts a range of parameterzatons for whch nteror equlbra exst. Detals of the analyss are avalable n the Supplementary Note. If an nteror equlbrum exsts, t can be shown that n * 1 > n * 2 > > n * M > 1 and 1 > x * 1 > x * 2 > > x * M > 0 both hold n the equlbrum. The logc behnd ths result, whch s smlar to the logc behnd Proposton 1 of the orgnal model, can be explaned as follows. Let N M xn denote the total number of productve workers n the market, and let N, P = 1 x n P j j j denote the total number of productve workers n the market that are not employed by frm. In Perod 2, frm employs a worker wth m( N P ), the th hghest realzaton of manageral capablty n the market, as ts manager. Snce m( N P ) s the th order statstc among N P = x n + N P,- productve workers n the market, frm can ncrease the expected manageral capablty of ts manager by ncreasng the number of ts productve workers, x n, holdng N P,- constant. Comparng frm and frm j, where < j, frm s ncremental proft from ncreasng the number of ts productve workers s greater than frm j s ncremental proft, because frm enjoys a hgher return from manageral capablty (.e., V > V j ). Ths mples that the ncremental frst-perod proft from ncreasng the number of productve workers s hgher for a frm wth a hgher return 11 For example, the need for learnng-by-dong may reduce young workers output below the self-employment wage. 14

15 from manageral ablty, whle ts ncremental cost s the same across M frms. Ths results n x * n * > x * j n * j for < j. That s, a frm wth a hgher return from manageral ablty has a larger number of productve workers n the equlbrum, and the convex costs for tranng and supervson of young workers result n x * > x * j and n * > n * j for all and j such that < j. In the equlbrum, each frm has x * n * productve workers, and there are three employment possbltes for each productve worker: () employment as a manager for the current employer, () employment as a manager for a competng employer, or () employment as a subordnate for the current employer. The expected number of frm s subordnates n Perod 2 n the equlbrum, denoted n O*, s then gven by (9) n N M = for = 1, 2,, M, N * O* * * x * n where N M * * * xn = 1 =. It can then be shown that x 1 * n 1 * > x 2 * n 2 * > > x M * n M * mples n 1 O* > n 2 O* > > n O* M, whch n turn mples, as n the orgnal model s equlbrum, that frm 1 adopts the most bottom-heavy herarchcal structure, frm 2 adopts the second most bottom-heavy structure, and so on. Concernng nternal promoton and external recrutment, each frm hres a worker wth the th hghest manageral capablty as ts manager. Gven that there are M = 1 x n * * productve workers n the ndustry and x * n * of them are n frm, the probablty of nternal promoton n each frm s x * n * / M = 1 x n * *, whch s strctly decreasng n. Hence Testable predctons 1-3 are robust n ths extenson of the orgnal model. In addton, the extenson yelds the followng testable predcton, snce x * 1 > x * 2 > > x * M holds n the equlbrum. Testable predcton 4: An employer wth a more bottom-heavy herarchcal structure provdes a hgher level of general tranng to ts employees. 3. An Alternatve Model: Manageral Match Qualty In our model, stochastcty n manageral capablty plays an mportant role n nducng external recrutng. In an alternatve model, the stochastc component mght nstead represent 15

16 frm-specfc manageral match qualty. To explore such an alternatve model, consder the twofrm case (M = 2). Suppose that f frm 1 employs young worker k n perod 1, worker k s match qualty wth frm 1, denoted m k1, s realzed by both frms and by the worker at the end of perod 1. However, worker k s match qualty wth frm 2, m k2, s stll unknown to both frms and to the worker. Assume that m k1 and m k2 are both randomly drawn from a unform dstrbuton between 0 and 1, where each worker s match qualty wth frm 1 s ndependent of hs match qualty wth frm 2. If frm employs worker k as ts manager, frm s gross output from that manager s V (m k + q). The other specfcatons of the model are the same as n our orgnal model. We now derve Subgame Perfect Nash Equlbra n pure strateges of ths alternatve model, assumng throughout that an old worker s second-perod output as a subordnate, y, s suffcently hgh so that each frm employs at least two young workers n perod 1 n the equlbrum. A suffcent condton for ths s y > 2(w + 2b) η, whch we assume throughout our analyss. Suppose that there exsts an equlbrum n whch each frm employs at least two young workers (that s, n 2, = 1, 2) at stage 1. Let m (1 n ) denote the hghest realzaton of match qualty among frm s n young workers. If frm employs one of frm j s (j ) young workers as ts manager, the manager s expected match qualty wth frm s 1/2. Ths mples that each frm employs the worker wth m (1 n ) as ts perod-2 manager at the wage y f m (1 n ) 1/2, and employs one of frm j s (j ) young workers as ts perod-2 manager at the wage of y f m (1 n ) < 1/2. Hence, the expected match qualty of each frm s perod-2 manager n the equlbrum s g(n ) where (10) 1/2 1 1 n 1 n 1 n + (1/2) g( n) nz dz + znz dz = 0 2 1/2 n + 1 antcpates that, f he s employed by a frm, hs second-perod wage wll be y. Hence, each frm employs n young workers at the wage of 2w y at stage 1 n the equlbrum, and each frm s expected overall proft n the equlbrum s π (n ), where 16 n+ 1, and each frm s expected proft from ts perod-2 manager n the equlbrum s (11) V( g( n ) + q) y. For workers who are not assgned to manageral postons, Bertrand wage competton mples that each frm retans ts frst-perod workers at the wage of y, makng zero profts from them. Each frm s perod-2 expected proft s then V( g( n ) + q) y. At stage 1, each ndvdual

17 (12) π ( n) V( g( n) + q) y+ n[ η (2 w y) bn]. Treatng the number of workers as a contnuous varable, we fnd that π (n) s strctly concave for all n 1, and that there exsts a unque value n * > 0 ( = 1, 2) satsfyng π (n * ) > π (n) for all n 1, n n *, where V 1 > V 2 n * 1 > n * 2. Ths mples the result analogous to Proposton 1 of our orgnal model: that s, the alternatve model has a unque equlbrum n whch each frm employs n * ndvduals n perod 1, where n * 1 > n * 2 > 2. In the equlbrum, frm employs ts perod-2 manager nternally wth probablty P *, where (13) * n * P = 1 (1/2). Snce n * 1 > n * 2 P * 1 > P * 2, the alternatve model yelds qualtatvely the same predcton as Testable predcton 1 of our orgnal model. Also, V 1 > V 2 and n * 1 > n * 2 together mply π 1 (n * 1 ) > π 2 (n * 2 ), whch yelds qualtatvely the same predcton as Testable predcton 2 of our orgnal model. Whle Testable predctons 1 and 2 of the orgnal model also hold n the alternatve model based on frm-specfc manageral match qualty, Testable predcton 3 does not hold n the alternatve model, because all managers and old workers earn the same wage, y, n equlbrum. Ths s because of our assumpton that frms make take-t-or-leave-t offers to workers. If we consder an alternatve wage-settng process n whch an employer and ts manager share the surplus assocated wth the employment, then the expected wage of managers wll be hgher than y, and ths wll n turn mply that the predcton 3 also holds. Furthermore, although we do not show t formally here, an extenson of ths alternatve model could also yeld our Testable predcton 4 concernng tranng. In summary, the four testable mplcatons arsng from our model based on employer heterogenety n the returns to manageral capablty could also arse from a model based on heterogenety n the qualty of worker-employer matches. Whle from a theoretcal standpont the predctons can be generated from ether source of heterogenety taken alone, n the real world we suspect that both sources are relevant and mportant. It s reasonable to expect that an ntegratve model that ncorporates both sources of heterogenety would also yeld the same four predctons, and such a model would lkely be more realstc than ether the model of Secton 2 that neglects heterogenety n match qualtes or the model n Secton 3 that neglects employer heterogenety n the returns to manageral capablty. Nonetheless, an mportant result of ths paper s that ether 17

18 heterogenety n match qualty (taken alone) or employer heterogenety n returns to manageral capablty (taken alone) s suffcent to generate the four testable mplcatons for whch we fnd emprcal support n the followng secton. 4. Data and Emprcal Analyss Our data source s the management questonnare from the 2004 Brtsh Workplace Employee Relatons Survey (WERS), jontly sponsored by the Department of Trade and Industry, ACAS, the Economc and Socal Research Councl, and the Polcy Studes Insttute. Dstrbuted va the UK Data Archve n November 2005, the WERS data are a natonally representatve stratfed random sample coverng Brtsh workplaces wth at least 5 to 9 employees, except for local unts n Northern Ireland and those n the followng 2003 Standard Industral Classfcaton (SIC) dvsons: agrculture, huntng, and forestry; fshng; mnng and quarryng; prvate households wth employed persons; and extra-terrtoral organzatons. The 2004 WERS was the ffth such survey, followng earler waves n 1980, 1984, 1990, and The samplng frame used for WERS 2004 s the Inter-Departmental Busness Regster (IDBR) whch s mantaned by the Offce for Natonal Statstcs (ONS). As noted by Chapln et al. (2005), The IDBR s undoubtedly the hghest qualty sample frame of organsatons and establshments n Brtan. The frame s contnuously up-dated from VAT and PAYE records and establshments that no longer exst are removed reasonably quckly. Some of the workplaces targeted were found to be out of scope, and the fnal sample sze of 2295 mples a net response rate of 64%, or 64.8% among establshments havng 10 or more workers, after excludng the out-of-scope cases (Chapln et al., 2005). Data were collected va personal ntervews of approxmately 2 hours n average duraton, between February 2004 and Aprl 2005, usng Computer Aded Personal Intervewng. The respondent n the management questonnare was usually the senor manager dealng wth personnel, staff or employment relatons at the workplace. In the vast majorty of cases ths respondent was dentfed and ntervewed at the locaton of the sampled establshment, though n some cases the ntervew occurred elsewhere n the parent organzaton (though stll focusng on the sampled establshment). Our theory requres a measure of bottom heavness of the herarchy, and the WERS contans ths nformaton n the form of numbers of workers employed n varous types of 18

19 postons n the organzaton. We defne Managers to be the number of workers at the establshment n the occupatons descrbed n the WERS as ether Managers and senor offcals or Professonals, and Subordnates to be the number of workers at the establshment n the followng (typcally) lower-level occupatons: Assocate professonal and techncal, Admnstratve and secretaral, Sklled trades, Carng, lesure, and personal servce, Sales and customer servce, Process, plant, and machne operatves and drvers, Routne unsklled. The occupatonal categores underlyng Managers and Subordnates are descrbed n detal n Appendx B along wth all of the other varables used n the analyss. Observng both Managers and Subordnates for each establshment allows us to measure the noton of bottom heavness that s relevant to our theory. In partcular, holdng constant Managers, ncreasng Subordnates amounts to an ncrease n the bottom heavness of the herarchy. We therefore nclude both varables on the rght-hand sde of all of our emprcal models, and the sgn of the coeffcent of Subordnates s of nterest from the standpont of testng the theoretcal predctons. Alternatve functonal forms would be less approprate for addressng our theory. For example, a control for frm sze cannot be ncluded n the model along wth Managers and Subordnates, due to perfect mult-collnearty snce Sze = Managers + Subordnates. Furthermore, ncludng the rato Managers/Subordnates on the rght-hand sde, ether alone or n conjuncton wth a control for sze, would also be problematc from the standpont of the theory. The coeffcent of such a rato n the presence of a control for sze would capture the effect of changes n the herarchy s shape n a way that leaves sze unchanged (.e. redstrbutng a fxed sze across the levels of the herarchy), and the coeffcent n the absence of a sze control would smply capture the effect of a change n herarchcal shape. None of these alternatves captures what our model addresses, whch s an ncrease n sze of a partcular type, namely an ncrease n sze that makes the herarchy more bottom heavy. Thus, the approprate functonal form s one n whch sze appears on the rght-hand sde dsaggregated nto ts two subcomponents (Subordnates and Managers), n whch case the coeffcent of Subordnates pertans to changes that broaden the bottom of the herarchy (and therefore ncreasng frm sze) whle holdng the top fxed. Our emprcal results are based on the full sample of establshments, though we drop the relatvely small number of observatons for whch the respondent employer reports that the establshment s largest occupatonal group s ether managers and senor offcals or 19

20 professonals, snce ths stuaton suggests a top-heavy herarchy whereas our theoretcal model s desgned to explan nternal hrng decsons, tranng decsons, and wthn-establshment wage structures for the more typcal cases nvolvng a fxed small number of managers supervsng a larger number of subordnates. Ths reduces the sample sze to To a large extent our results stll hold, though a bt less strongly, even n the absence of ths sample selecton crteron. Imposng ths selecton rule, we also conducted the analyses on the subsample of 1567 establshments n the prvate sector, producng results that are qualtatvely smlar to those we report usng the full sample and ncludng n our multvarate statstcal models a bnary control varable ndcatng prvate sector. Descrptve statstcs for all varables n the analyss are dsplayed n Table 1; we use establshment samplng weghts when computng the statstcs n ths table and n all of our subsequent analyses. Some of the varables n our multvarate statstcal models contan mssng values, and we estmate all of our models usng lst-wse deleton. 12 Our analyses nclude controls for ndustry and employer characterstcs, and we defne these n Appendx B. Testable predcton 1 we vew as the central predcton of our model. It states that organzatons that choose more bottom-heavy herarchcal structures are more lkely to promote nternally rather than recrut externally. We address ths predcton by estmatng ordered probt models that use the followng WERS measure as a dependent varable: Internal Hrng: qualtatve response to the queston Whch of these statements best descrbes your approach to fllng vacances at ths workplace? 1 = External applcants are only source, no nternal recrutment, 2 = External applcants are gven preference, other thngs beng equal, over nternal applcants, 3 = Applcatons from nternal and external applcants are treated equally, 4 = Internal applcants are gven preference, other thngs beng equal, over external applcants, 5 = Internal applcants are only source, no external recrutment As seen n Table 2, ths predcton s emprcally supported n that the coeffcent of Subordnates s postve and statstcally sgnfcant at conventonal levels. To nterpret the magntudes mpled by the reported ordered probt coeffcents, consder an ncrease of 100 n the number of Subordnates at an establshment. On average, n the most controlled specfcaton, ths change s assocated wth decreases n the probablty that Internal Hrng = 1, 2, or 3, an ncrease of In Table 1, we use all avalable observatons for each varable to compute summary statstcs. Analogous tables that compute summary statstcs based on the smaller subsamples on whch the multvarate statstcal models are estmated closely match Table 1. 20

21 percentage ponts n the probablty that Internal Hrng = 4, and an ncrease of 0.04 percentage ponts n the probablty that Internal Hrng = 5. Testable predcton 2 states that organzatons wth more bottom-heavy herarchcal structures earn hgher proft. To address ths predcton we use a qualtatve dependent varable, Fnancal Performance, ndcatng the employer s ratng of the establshment s fnancal performance relatve to that of other establshments n the same ndustry, wth 1 = a lot below average, 2 = below average, 3 = average, 4 = above average, 5 = a lot above average. We estmate ordered probt models usng Fnancal Performance as the dependent varable, Managers and Subordnates as the key ndependent varables, and a set of controls for ndustry and employer characterstcs. Testable predcton 2 mples that the estmated coeffcent of Subordnates should be postve and statstcally sgnfcant; n other words, holdng constant the number of managers at the top of the organzatonal herarchy, ncreasng the number of workers lower down n the herarchy mples hgher proft. As revealed n Table 3, n all specfcatons ths result s strongly supported emprcally. To nterpret the magntudes mpled by the reported ordered probt coeffcents, consder an ncrease of 100 n the number of Subordnates at an establshment. On average, n the most controlled specfcaton (column 3), ths change s assocated wth decreases n the probablty that Fnancal Performance = 1, 2, or 3, an ncrease of 1.6 percentage ponts n the probablty that Fnancal Performance = 4, and an ncrease of 1.1 percentage ponts n the probablty that Fnancal Performance = Testable predcton 2 pertans to proft, whereas the precedng emprcal test pertans to fnancal performance as nterpreted by the respondent employer. In some cases, the employer mght nterpret fnancal performance to mean somethng other than proft. Followng the survey queston pertanng to fnancal performance, the WERS asks the employer to state how fnancal performance s nterpreted. The dstrbuton of responses to ths clarfyng queston s dsplayed n Table 4. Snce Testable predcton 2 pertans to proft, we estmated the fnancal performance ordered probt models on the subsample for whch the employer nterpreted fnancal performance to mean proft, fndng agan that the coeffcent of Subordnates s postve and statstcally sgnfcant as our theory predcts. Results are dsplayed n Table 5. To 13 These margnal effects, and others we report throughout the analyss, were computed usng STATA s mfx command, n whch other covarates are evaluated at ther mean values. 21