Connective Capital: Building Problem-Solving Networks Within Firms. Casey Ichniowski Columbia University and NBER

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1 Very prelmnary. Please do not quote. Comments welcome. Connectve Captal: Buldng Problem-Solvng Networks Wthn Frms Casey Ichnowsk Columba Unversty and NBER Kathryn Shaw Stanford Unversty and NBER October 11, 2005 We thank the Natonal Scence Foundaton and the Alfred P. Sloan Foundaton for ther generous support, and the many partcpants at semnars at Cornell Unversty, Harvard Unversty, London School of Economcs, MIT, Northwestern Unversty, Stanford Unversty, Unversty of Chcago, Unversty of Illnos, UCLA, the Socety of Labor Economcs, the Amercan Economc Assocaton meetngs, and Jon Gant, and dscussant Edward Lazear for hs detaled suggestons.

2 Captal conssts n a great part of knowledge and organzaton. -- Alfred Marshall, Prncples of Economcs Socal captal s ncreasngly dscussed as an mportant fabrc of communtes and of frms. Very loosely, socal captal s the set of network relatonshps among people that they tap nto to solve problems. For example, n a communty, turnng to frms, n the press, we hear a great deal about the mportance of networkng and of workers and frms relyng on networkng to ncrease problem-solvng performance. However, economsts have tended to ntroduce network relatonshps ndrectly nto our models of the frm, through models of nformaton flows wthn the frm or models of herarches. Busness researchers have modeled socal networks for many years, and have a very deep lterature, but ths lterature has tended to focus more on the value of the socal network to ndvduals rather than the frm, and wth most emprcal evdence on the value of networks to ndvduals. Our goal s to emphasze the captal component of socal captal, by ntroducng socal captal drectly nto the frm s producton functon as a non-lnear form of human captal. We defne connectve captal as the employees human captal obtaned from the knowledge base of co-workers that he taps nto when faced wth a problem to solve. 1 Just as economsts have modeled the nvestment n human captal by ndvduals and by frms, we ntroduce connectve captal nto the frm s producton functon, and model what nduces ndvduals to nvest n connectve captal, and what nduces frms to nvest n t. And, ust as there are many forms of human captal (such as frm specfc sklls or occupatonal sklls), we treat connectve captal as a specal form of human captal and we dentfy the propertes of connectve captal that produce dfferental nvestments n t across ndvduals and frms. Due to the network externaltes and group-based rewards of connectve captal, workers wll under nvest n t. Therefore, frms that value problem solvng wll nvest n organzatonal practces to ncrease ndvduals nvestments n human captal. Gven some predctons from the model concernng the worker s and frm s decsons to nvest n connectve captal, we analyze a unque data set that measures the presence and absence of connectons among co-workers n a sample of 642 steelworkers. These data are used to 1 We develop the label connectve captal rather usng the term socal captal because some elements of socal captal le outsde the boundares of what s emphaszed n our model. 2

3 measure the amounts of connectve captal for each ndvdual n these organzatons, and test several predctons of the model. Frst, we show that workers wth lower apparent costs of communcatons are formng more connectve captal. Second, consstent wth our hypotheses, we show that frms wth human resource management practces that support connectve captal development are those wth more workers nvestng n connectve captal. In keepng wth the quote by Marshall above, our overarchng goal s emphasze, as many organzatonal or personnel economsts have done, that the returns to human captal, or to the frm s knowledge base, depend on how the frm s organzed. Our model s an extenson of the lterature on teams, n that we emphasze the value to frms of employees workng together n a complementary fashon to solve problems. In many frms today, sklls are so deep, or expertse s so mportant, that ndvduals must specalze and the frm s success depends upon the collectve nteracton of these experts on ther connectve captal. In secton I, we develop the model, and n secton II, we provde emprcal evdence on the determnants of the nvestment n connectve captal. I. A Model of Investments n Connectve Captal Ths secton develops a model of connectve captal nsde organzatons. After defnng connectve captal, we ncorporate t as an nput n the frm s producton functon. Snce ndvduals or frms do not smply maxmze nvestments n productve captal nputs, the model of ths secton also consders the optmal nvestment n connectve captal for ndvduals and frms. Defnng Connectve Captal and the Producton Functon The dea that workers human captal rases productvty s a bedrock prncple of economcs. The dea of connectve captal elaborates on ths dea by argung that spllovers of knowledge among co-workers serve as a way to multply the expertse of sklled workers. A knowledgeable or experenced worker may ndeed perform work tasks well, but he can also mprove the performance of others f that expertse s shared. We capture ths mechansm for 3

4 ncreasng productvty wth the basc dea that connectve captal s shared human captal, and defne connectve captal for worker, CC,, as: 2 N (1) CC = Σcc HC where cc = 1 f worker communcates wth worker = 0 f worker does not communcate wth worker and HC s dfference between the human captal of person and, or HC HC -HC. Thus, to calculate worker s connectve captal over a gven tme perod, one frst measures whether or not he communcates wth each of hs coworkers, =1,..,N ( ), and weghts each exstng communcaton connecton by the human captal he gans (or HC -HC ) through those communcatons. The defnton of an ndvdual s connectve captal therefore has two man components worker s cc vector measures the worker s communcaton network, whle the HC -HC s reflect gans n human captal that are transmtted over those network channels that do exst. Next, denote the general producton functon for frm output (Q) as: (2) Q = f(hc, CC; K) where HC and CC are the vectors of tradtonal human captal and connectve captal, respectvely. Accordng to (2), ncreases n connectve captal rase output as long as f CC >0, condtonal on physcal captal, K. 3 An example helps llustrate how knowledge transfer among workers mproves productvty beyond the drect effects that knowledge and sklls have on an employee s own ndvdual performance. The example we develop below focuses on the problem-solvng actvtes of producton workers n a sample of steel fnshng lnes. Employees routnely encounter problems n the steelmakng producton process, such as deteroratng steel surface qualty durng a producton run. But to dentfy the actual reason for ths problem from among many possble sources and then solve the problem, an employee can draw upon hs own tranng and experence, but can also tap nto expertse and experence of others. Co-workers can have dfferent human captal that s relevant for ths problem for many 2 Because we wll be focusng on dfferences n productvty n technologcally comparable producton processes, we assume that number of labor hours s comparable across observatons and therefore s not ncluded n the L functon. 3 The equatons (1)-(2) model s analogous to models of the productvty effects of spllovers of R&D knowledge across frms n an ndustry. See for example Grlches (1979). 4

5 reasons. Co-workers may have superor techncal knowledge of chemcal coatngs or they may smply be workng n dfferent areas where steel nputs had prevously been treated. Worker may not be able to solve the surface qualty problem on hs own and worker may not even be aware of the problem f t shows up elsewhere n the plant. Communcaton (cc s) and dfferences n knowledge (HC -HC s) are both mportant for problem solvng and together these factors determne a worker s connectve captal. The central pont here s that access to others knowledge and sklls can promote problem solvng and therefore elevate overall levels of productvty n many organzatons, ust as t does n the llustraton from steel mlls. Snce connectve captal s a functon of human captal, output s a non-lnear functon when we rewrte (2) as (2 ' ) Q = f (g(hc);k) where g(hc) = g(hc,cc) snce CC s a nonlnear functon of HC. Gven ths producton functon arsng from the defnton of connectve captal, below we develop the model of connectve captal to show not only that f ' (HC)>0, but that the effect of human captal on output s lkely to accelerate n some range of HC before turnng down, or that g '' (HC)>0 and g ''' (HC)<0. An ndvdual who s very good at problem-solvng wll be asked to solve numerous problems and hs human captal wll multply throughout the organzaton. Thus, as human captal s ncreased, the productvty of human captal accelerates before deceleratng n the producton functon. That s, the creatve problem-solvers are extremely valuable to frms that value problem solvng. Summary of the Model To gude the reader through the detals of the model that follows, we summarze the results as follows. A prmary feature of connectve captal s recprocty a valuable knowledge lnk occurs only when two people share nformaton, thus when one person asks for help the sharer must respond wth help. Ths requred recprocty produces a network externalty n the model. An ncrease n one person s propensty to share wll ncrease all propenstes to ask (because there s more askng f the probablty of a sharng response s greater). And greater askng produces more sharng, because no sharng occurs wthout askng frst. Thus, we have the network externalty that sharng s contagous ncreased sharng by one, ncreases sharng by all, and therefore ncreases connectve captal for all. Indvduals have an ncentve to ask and 5

6 share because they are rewarded through group-based ncentve pay. Frms have an ncentve to nvest n connectve captal f they have hgh returns to problem solvng (as wll frms wth more human captal and lower dscount rates). When the value of connectve captal s hgh, frms wll nvest n norms of hgh sharng to nduce greater ndvdual nvestment n connectve captal to reduce the free-rder problem of connectve captal. The recprocty n socal networks s not the standard contractual recprocty between two people. Standard contractual recprocty would dctate that f I share today wth you, you wll recprocate by sharng wth me tomorrow t s a blateral contract wth long term enforcement. However, the pont of recprocty n socal networks s that n large socal networks, you may be asked to share wth someone whom you wll never see agan sharng must occur wthout blateral contracts. We model how the frm s norm-settng nvestments drve such sharng. The Worker s Investment n Connectve Captal If connectve captal does ncrease productvty, what determnes the decsons of two workers to connect and what determnes the overall extent of connectons and knowledge sharng wthn the frm? Let workers and be two employees faced wth a problem the former s the asker and the latter s the potental sharer. A = 1 f worker decdes to ask for nformaton from worker and s zero otherwse, and S = 1 f worker decdes n turn to share wth the asker and s zero otherwse. Rewrte the communcaton lnk between and as: (3) cc = A S The connectve captal for worker (cc ) s the amount of new human captal shared by worker when a communcaton lnk s establshed between the two workers (cc = 1). The frm s qualty output, Q, s a functon of tradtonal human captal and connectve captal of all employees, so rewrte (2) assumng lnearty n human captal and connectve captal (4) Q t = α'hc t + δ'cc t-1 Perod t qualty output, 4 Q t, s a functon of both the vector of human captal of the N-person workforce, HC t, 5 and of the pror problem-solvng actvty δ'cc t-1. The vector CC t-1 s also an 4 Q t should be consdered as qualty-adusted output because problem-solvng actvtes n many producton settngs are assocated wth seekng methods to mprove product qualty. 6

7 N-element vector. These elements equal zero for workers who have not receved any human captal from co-workers and are postve for any worker who has developed connectve captal n perod t-1. Connectve captal, CC t-1, s weghted by the vector of coeffcents δ n the producton functon, and these coeffcents have an mportant nterpretaton. We assume that δ s an ndex of the value of problem-solvng actvty: δ s hgher when the frms profts rse because the market values the qualty of the output (so low-qualty products have low δ). Thus, we assume that all frms face contnuous shocks to producton problems arse constantly. Frms wth hgh δ are those frms that have a hgh return to solvng the problem that has surfaced. We also make some assumptons about the nature of the problems that arse and the dstrbuton of human captal n solvng these problems. We assume that problems of dfferent types arrve randomly for person and then that person seeks the person who s the expert n solvng that problem, or seeks the person for whom (HC -HC ) s greatest for the relevant problem that can solve. Clearly, f there were only one type of problem, then there would be only one person whom every person n the frm would call. Furthermore, we assume that dfferent people are experts on dfferent problems, so that once agan, multple people are called. Clearly, t s mportant to vew human captal as havng many dfferent types, and we do so shortly n a subsecton below, but for smplcty, we avod the messy ntroducton of vectors of human captal types at ths pont. There are two types of costs assocated wth the nvestment n connectve captal. The frst s drect opportunty cost of tme the tme spent solvng a problem that could have been spent drectly producng output nstead: t(α HC - α HC ), where t s the percent of tme spent on ont problem solvng actvtes by and. The second cost s the person-specfc personal dsutlty of communcatng (or the utlty for those who enoy t). These costs are thngs lke the followng. Askers face costs assocated wth dentfyng co-workers, wth contactng people, pullng co-workers together, and other search costs. Sharers also face the logstcal costs of respondng to the request for assstance, such as attendng a meetng, or puttng other work asde. These workers may also experence dsutlty later on f sharers receve less credt or 5 For smplcty, we assume that human captal HC s separable from connectve captal CC, though multplcatve nteractons between all these forms of human captal would complcate the analyss but not change the essental ponts. Note also that past stock of connectve captal should lower the costs of nvestng n current connectve captal, because workers buld knowledge about who to contact to solve problems. Such a state dependence effect past CC bulds current CC s assumed here to occur wthn the frst perod. Addng a state dependence effect would sgnfcantly complcate the model, but would mply that there are adustment costs that further lmt frms ablty to ump between dfferent states of CC. 7

8 compensaton than askers for solvng problems. Askers and sharers therefore ncur personal costs C A and C S of communcatng. Workers maxmze the net benefts of connectve captal nvestments. Output s reduced durng the perod when the communcatons occur, ndvduals bear the personal costs of communcatng, and then there s a payoff n ncreased problem-solvng productvty n subsequent perods. We llustrate the worker s cost-beneft calculaton n a two perod model n whch workers can decde to ask and share durng the frst perod. To capture the dea that problem solvng s a team-based actvty that affects the output of groups of workers, let worker compensaton be determned by a group-based ncentve pay so that all workers dvde net revenue among themselves each worker gets Q/N. 6 Askng and sharng would then take place for representatve workers and accordng to: A (5) A = 1 f PR[ d( δhc) t( α HC + α HC )]/ N > C s (6) S = 1 f R [ dδ HC t( α HC + α HC )]/ N > C gven A = 1 where (5) s the expected gan to worker from askng, P s the probablty that worker wll share (or Pr(S =1)), R s the percent of net revenue allocated to workers as compensaton, 7 d s the dscount factor (1/(1+r)), and t s the percent of tme (or percent of base perod human captal) that s spent communcatng rather than producng. The probablty of sharng s P = B o f ( ϕ ) dϕ. Workers are rsk neutral, so workers ask when the expected monetary gans s s 6 In problem-solvng contexts, group-based pay s commonplace (Cte??) perhaps because of lmts on observablty of sharng or on abltes to measure the contrbutons from dfferent deas. Undoubtedly, alternatve compensaton schemes could be developed that focus on elctng optmal levels of connectve captal. For example, f sharng s observed, then 360% peer evaluatons could be used to reward sharng. Subectve evaluatons have also been suggestve as a possble way to reward hard-to-measure nputs lke teamwork (Baker, Gbbons, and Murphy, 200x). Here, we assume that, on average, t would be too costly to develop reward schemes due to lmts on observablty or measurement, and assume the Q/N compensaton levels to emphasze the problem-solvng s a team process that affects a group s output. Moreover, we assume that groups of askers and sharers are large enough that each (,) par does not form a long term relatonal contract such as, f you help me today, I ll help you tomorrow. The pont of connectve captal s that people from many parts of the organzaton share even when they wll not be drectly rewarded n the next round by ther asker. 7 Thus, we assume that the frm allocates a percent (R) of net revenue to workers and retans a percent for shareholders, as s typcal for proft-sharng plans or worker-owned frms. We wll assume R s fxed (obvously related to workers alternatve wages, etc.) and not address ts value heren. 8

9 exceed the monetary and personal costs. Thus, Rdδ HC N s the ncome gan n perod 2 and / Rt( α HC + α HC ) N s the opportunty cost of communcatng tme n perod 1. / Assume that the person-specfc costs of askng and sharng are dstrbuted randomly across the populaton, so that A C = ϕ and A s C A s = ϕ, wth densty functons f ( ϕ ) and f ( ϕ ), s and for the moment assume become: A s ϕ and ϕ are be ndependently dstrbuted. Then (5) and (6) (7) (8) A S B s s f ( ϕ dϕ > ο = 1 f B ) B > s ϕ = 1 f ϕ gven A = 1 A whch states that worker wll ask when the benefts, B ( R[ dδ HC t( α HC + α HC )]/ N ), A tmes the probablty that worker wll share, P, exceed the costs of askng, ϕ. Person shares when asked f the benefts exceed the costs n (8).When we turn to the frm s decson to nvest n connectve captal below, we wll emphasze how the frm wll tend to choose human resource practces to shft the dstrbuton of costs relatve to benefts and thus to nduce employees to choose hgher levels of connectve captal. Thus, the model mples that connectve captal s hgher when the expected costs of both askng and sharng are less than the mnmum beneft threshold of B. Or, problem-solvng occurs when cc =1, whch by combnng (7) and (8) wth equaton (3) above can now be expressed as: (9) cc = 1 f B A > ϕ / P and B > ϕ s Thus, connectve captal ncreases when ndvduals have dfferent sklls, or when HC HC s large (all else constant, such as the opportunty cost of tme, whch rses wth HC ), and when sharng costs are low, when the dscount rate d s low, and when the ncome returns to problem solvng as a functon of S, R, and N are hgh. In ths model, there are two reasons for the underprovson of connectve captal. Frst, there s the free-rder effect, or the underprovson of effort n any workplace that s governed by group-based ncentve schemes. The level of sharng mpled by (8) wll be suboptmal from the 9

10 group s (and frm s) perspectve because the worker s only takng nto account hs share of benefts, and ths underprovson ncreases wth the number of workers, N (Kandel-Lazear (1992), other references ). That s, when worker decdes whether to ask worker for assstance, worker asks only f the margnal cost of ths effort equals 1/N of the expected margnal benefts to the frm. Second, the most mportant underprovson outcome n our model of connectve captal comes from the network externalty n the model. The network effect s as follows: an ncrease n sharng, S, by one person wll ncrease the askng and sharng of all other workers. One can see these network effects by consderng the effect of an exogenous drop n the sharng costs of person so he shares more. The ncrease n hs sharng ncreases the overall probablty of sharng, P, whch ncreases the probablty of askng for all employees. These network effects reflect the standard externalty of networks: sharng s contagous. An ncrease n the communcatons of one person wll ncrease the connectve captal of all others. For these two reasons, there s underprovson of connectve captal, whch the frm can address by ntroducng polces that ncrease the personal rewards to connectve captal. When the personal rewards to connectve captal are ncreased, nvestment rses. We turn to that topc n the next subsecton after we determne extensons of the model. s ϕ Extensons of ths Basc Model A few addtons to the model are useful n addng further mplcatons. Expand the cost functons: (10) C A A = a Ζ + ϕ A (11) C S S = a Ζ + ϕ S where for some people, there s a utlty or dsutlty assocated wth who they are callng for example, women may be more comfortable callng women, so that costs are a functon of vector Z characterstcs that are specfc to the (,) par of communcators. Some characterstcs of the partner, such as demographc smlarty or physcal proxmty, mply lower costs to person. The mplcatons of ths extenson are clear. When people are close, or have low costs arsng from the Z effect, connectve captal wll rse. Moreover, f we drop the assumpton that 10

11 A assume ϕ and ϕ are be ndependently dstrbuted, permttng the ont dstrbuton f( ϕ, S A S ϕ ) then communcatons wll rse when costs are postvely correlated. That s, connectve captal wll rse ether when frms par (,) workers who have smlar costs of communcatng, or t wll rse when low-cost workers select frms n whch exstng employees have low costs of communcatng. In other words, frms wll have an ncentve to match workers based on communcatons costs and workers wll tend to self select nto frms based on low personal communcatons costs. A second extenson s to recognze that workers have dfferent types of expertse n solvng problems. That s, some workers may have an expertse at solvng operatng problems, whereas others mght be experts at solvng desgn problems. Then the output from person now looks lke: J ο ο o o d d d d (12) Q = αhc + δ p cc ( HC HC ) + δ p cc ( HC HC ) = Where ndvdual faces a probablty of operatng problems arsng, equal to ρ, and chooses to communcate wth workers from a set of workers, J, who are the operatng experts; or when workers faces a desgn problem wth probablty ρ d and chooses to communcate from a set K of workers who are the desgn experts. The basc model s unchanged, expect that now we recognze that connectve captal s valuable when there are dfferent types of human captal formng the human captal gap, HC HC, and therefore when person has the sklls that are relevant to solvng the operatng problem, or that come from set J for operatng problems or K for desgn problems (Lazear, 1999). Gven multple types of problems and sklls assocated wth solvng these problems, the value of CC to the frm or ndvdual depends on the levels of δ k, p k, and HC k - HC k, for k=o and D: hgher levels of all of these varables produce more value to CC all else constant. However, t s the dstrbuton of these varables that s partcularly mportant n assessng the value to the frm of connectve captal. Skll dstrbutons are shown n Fgures 1 and 2. In Fgure 1, there are four types of ndvduals, where ndvduals have two sklls each (HC O, HC D ). In Fgure 1, Person 4 has more of both sklls, Person 1 less of both sklls, Person 3 s a relatve expert at desgn, and Person 2 s a relatve expert at operatng. Assume Person 1 randomly receves a problem that requres both an operatng and desgn soluton then he wll always call Person 4 because Person 4 s better at solvng both desgn and operatng problems. K k k 11

12 In other words, f sklls are postvely correlated (note n Fgure 4, the regresson lne through ndvdual skll sets would be upward slopng to reflect ths correlaton), that mples that there are some people who are experts at everythng, and everyone calls the expert. For example, everyone would call the engneer or plant manager f he s good at solvng all problems he s person 4 n Fgure 3. Therefore, when Person 1 receves a problem that s desgn and operatng, he wll make only one call to 4, or he wll have only one cc 14 =1 lnk to the expert and no other lnks (cc 12 =0, cc 13 =0). That s a herarchcal frm. On the other hand, n Fgure 4 there s no Person 4 no expert at everythng. In ths case, when faced wth an operatng and desgn problem, Person 1 wll call both Persons 2 and 3 CC wll have two lnks (cc 12 =1, cc 13 =1). As you can see n Fgure 2, sklls are negatvely dstrbuted across ndvduals. So the pont s, f sklls are negatvely dstrbuted, then there are no experts at everythng, and the total value of CC s hgher. Ths s a flat frm wth fewer layers and more connectve captal. Note fnally that the value of CC depends on the dstrbuton of problems to solve. If a frm faces only desgn problems, then Person 1 wll always call only Person 3, and wll never communcate wth Person 2 (gven skll dstrbuton of Fgure 2). Therefore, connectve captal s hgher when the problems to be solved requre multple sklls. In summary, connectve captal wll be hgher when 1) Sklls are negatvely dstrbuted there are no experts at everythng, each employee has a dfferent expertse that s valued as dfferent problems arse. In the world of manufacturng, ths means that operators know more about some problems than do engneers. In the world of hgh tech, t means that there are some experts at network technologes and some experts at wreless technologes and the frm needs both sklls, but no one person has them. 2) Problems arse that constantly requre a combnaton of sklls to be solved, not ust one skll. Then the person recevng the problem wll call several ndvduals to solve the problem (assumng pont 1, that there are no experts on everythng). 3) Tme costs of communcatng are not prohbtvely hgh. For example, f the operatng expert s tme costs are too hgh, then Person 1 wll solve the problem alone. 12

13 Ths detaled example does not change any of the conclusons of our basc model, but smply clarfes the structure of the problem. In the basc model, we are assumng that problems arse randomly and contnuously, that they requre multple sklls, and that sklls are not postvely correlated across the workers. Thus, when worker receves a problem, he wll know to call worker for that partcular problem, and then worker k for a dfferent problem. We assume that all workers have the same rates of problem arrval and that they know whom to call. Of course, a very mportant part of networkng s knowng who to call. We assume here that knowng who to call s a functon of tenure (or frm-specfc human captal) and do not emphasze t here, but clearly callng dfferent people whle searchng for the rght person wll ncrease CC. Fnally, our basc model then uses δ as the ndex for the frm of the value of problem solvng, and thus s a functon of product qualty and the lkelhood that qualty problems arse. 13

14 Desgn D D HC 3 4 D HC 2 3 D HC Operatng O 0 HC 1 0 HC 2 0 HC 3 Fgure 1 Desgn D D HC 2 3 D HC Operatng O 0 HC 1 0 HC 2 Fgure 2 14

15 The Frm s Decson to Invest n Connectve Captal The frm s ultmately makng the decsons that determne ndvduals nvestments n connectve captal, and thus the frm s decdng how much to nvest n connectve captal. The returns to connectve captal depend on the frm s technology, δ, that values problem solvng, and the human captal of ts workforce, HC, that rases the value of connectve captal. Thus, n the long run, the frm should take connectve captal nto consderaton when makng physcal and human captal nvestment decsons, and gven the technology and HC, employees wll optmally nvest n connectve captal. Technology ntensve companes (wth hgh δ), wll have more connectve captal. But we focus here on the short run. In the short run, how can frms that have the greatest returns to problem solvng (due to hgh technology or human captal), further elevate the frm s returns to captal by ncreasng ts workers desre to nvest n connectve captal? Frms that value connectve captal the hghest (due to ther technology) can ncrease connectve captal by convncng workers that sharng knowledge s a requred standard operatng procedure for employees, and that all wll beneft from sharng. Thus, we develop a model here n whch frms decde how much to ndoctrnate workers wth a sharng norm, gven that such ndoctrnaton s costly. In ths secton, we show that the optmal outcome for frms s that they wll ether nvest heavly n developng the sharng norm, or not at all. That s, frms wll tend to ether have a culture of sharng that bulds connectve captal, or they wll have a culture of ndvdual effort and low levels of connectve captal. The Frm s Influence on Workers Costs of Sharng Assume that frms that value connectve captal hghly can ndoctrnate workers wth a workplace norm that conveys to workers that the frm values hgh levels of sharng of knowledge, and the frm often renforces that norm through peer pressure to share. The peer pressure model of Kandel and Lazear (1992) emphaszes the value of norms and ndoctrnaton under condtons when ndvduals wth group-based ncentve pay have the ncentve to free-rde or underperform, as s the case here wth connectve captal. Frms can reduce free-rder problems by nsttutng standards or norms of workplace behavor where the norm s the expectaton that all workers wll to contrbute effort towards achevng the group reward (and 15

16 thus all wll gan from the hgher effort levels). 8 Akerlof and Kranton (2003) elaborate on the use of norms by hypotheszng that a worker s personal utlty s hgher when hs self mage, or dentty, matches the frm s deal behavor for ts employees. Very smply, defne ndoctrnaton of a sharng norm as: when the worker s actons fal to lve up to the frm s deal sharng behavor, the worker s utlty falls because hs self mage fals to lve up to hs own deal. s Ths norm therefore enters the worker s perceved cost of sharng, or ϕ. Assume a standard of a hgh value of the SharngIdeal causes the worker to feel less dsutlty (or less cost) of sharng: ( ) s s (13) ϕ = γ ( SharngIdeal) Effort s As a result, the frm can shft the cost of sharng dstrbuton for workers the dstrbuton of costs of sharng condtonal on standards of a sharng culture become: (14) f( ϕ SharngIdeal) = f( ϕ S S I=ndoctrnaton of sharng norm) so that workers n frms wth a norm of sharng wll have lower sharng costs, because they gan utlty from sharng when sharng s part of the ther dentty or when peer pressure rewards sharng. The development of a sharng norm s not free to the frm, so the frm bears two costs n perod 1 the costs of nvestng n the sharng norm, and the opportunty cost of the employees communcatons tme when sharng occurs. In perod 2, the frm earns the returns to these nvestments as returns to problem solvng. The frm s expected proft functon n the two-perod model s (π (αhc-w) + pr( cc = 1)[ dδhc t( α HC + α HC )] ηi ] (15) E ) = (1 R)[ ( 1+ d ) N N where (1-R) s the percent of the frms net revenues reserved for shareholders, W s wage and materal costs, ηi s the cost of nvestng n ndoctrnaton a sharng norm, and d s the dscount rate for the perod 2 profts. Recall from the ndvdual s perspectve, the probablty that cc s equal to one s 8 See MacLeod (1988, 1987) for an alternatve approach to solvng the free-rder problem n teams. Note that Kandel and Lazear (1992) emphasze that frms do two thngs to enforce ths norm. Frst, they convnce employees to use peer pressure to montor behavor: workers who free-rde are shamed by ther peers nto performng. Second, frms use heavy up-front ndoctrnaton to make workers feel gulty when they underperform, so no drect montorng s needed because workers self-montor. 16

17 (16) pr(cc )=1 s B BP f ( ϕ, ϕ I) ϕ ϕ 0 0 A so substtutng (16) nto (17) produces (17) E ( π ) = (1 R)[(1 + d) (αhc-w) N N + B 0 0 BP A S f ( ϕ, ϕ S A A S I) ϕ ϕ [ dδ HC S t( α HC + α HC )] ηi ] where the frm chooses the optmal level of ndoctrnaton to maxmze profts, or E( π ) (Total Expected Gans) = η I I where the total expected gans defned n (17) are (18) (1 R)( A S f ( ϕ, ϕ A S I) ϕ ϕ [ dδ HC t( α HC and for smplcty wage and materal costs are assumed to be fxed. + α HC )] To see the frm s optmal nvestment n ndoctrnaton, Fgure 3 dsplays a total expected gan functon (18) wth potental alternatve cost functons, the horzontal axs s the quantty of ndoctrnaton, I ndex: Total Indoctrnaton Cost Total Gan I I * I Index 17

18 Fgure 3: The Total Gans to Investng n Connectve Captal Relatve to the HR Costs where the costs of the sharng norm, ηi, are lnear n cost functons Cost 1 through Cost 3, but could be nonlnear as shown n cost functon Cost 4. Gven ths structure of the costs and benefts of connectve captal to the frm, the overall concluson s that frms wll tend to poston themselves n extreme postons frms wll have ether farly hgh levels of connectve captal or no connectve captal as a functon of ther ndoctrnaton costs. Because the beneft functon accelerates and then plateaus n Fgure 3, the frm wth Cost 2 wll nvest n I*, or wll nvest n a hgh level of the sharng norm that wll produce a hgh level of connectve captal. Dfferent frms have dfferent costs of sharng norms. Frm 1 wth Cost 1 wll never nvest n sharng or connectve captal because the costs are always too hgh. However, for all other frms cost functons shown n Fgure 3, the nonlnear expected gans functon mples that the optmal nvestment n the sharng ndex wll the hgh level of I*, so frms wll tend to have ether hgh connectve captal or low connectve captal. 9 The expected gans functon s nonlnear for two reasons. Frst, the ndvdual s decson to share hs knowledge s dscrete, so sharng occurs for each person when the benefts of sharng exceed sharng costs, or S =1 when B >φ,. However, each frm has a dstrbuton of sharng costs across people Fgure 4 dsplays dfferent possble dstrbutons of costs relatve to the benefts of connectve captal. In Fgure 4a, the benefts B are low, so gven a dstrbuton of costs of sharng, f(), the number of people who share s the small number n the shaded regon. In Fgure 4d, the benefts are hgh relatve to costs, and a large percent of people are n the shaded regon of sharers. But these fgures can be used to show that, gven a fxed beneft level for the frm, f the frm ntroduces a sharng norm that shfts the dstrbuton of costs to the left, connectve captal wll rse non-lnearly: sharng wll rse a lot from Fgure 4a to 4b, as large numbers of people see ther sharng costs fall, but then from Fgures 4b to 4d there s lttle addtonal ncrease n sharng from further decreases n costs (because most people are already sharng, and sharng s dscrete once person shares wth person, t s not further ncreased). Therefore, the bggest gans to ndoctrnaton for a frm come when lttle sharng s takng place 9 Ths result focuses on dfferences n the cost functon across frms, but of course dfferences n technology δ or human captal wll shft the beneft functon across frms, and thus shft the nvestment n connectve captal. However, the key pont of Fgure 3 s that the beneft functon s nonlnear (across dfferent amounts of technology), and that causes the hgh or low levels of connectve captal across frms. 18

19 at pont 4a; f the frm s already at the poston of Fgure 4d. (Ths pont s explaned further more n the next subsecton.) 19

20 4a 4b 4c 4d Fgure 4: Shftng the Cost Dstrbuton Left Through the Benefts Lne Second, the nonlnearty n the gans to connectve captal n Fgure 3 arse from the network effects of sharng. If the sharng norm lowers the costs of sharng for a few workers, that rases the probablty of sharng for all, so that the probablty of askng rses for all 20

21 employees, whch wll n turn ncrease the probablty of sharng, and so on. As a result of the network effect descrbed above for worker nvestment n CC, the pr(cc )=1 rses slowly then accelerates: pr(cc )=1 s B BP A S A f ( ϕ, ϕ I) ϕ ϕ 0 0 S and thus the total gans to nvestng n a sharng norm are small at low values of ndoctrnatng I, but accelerates as ncreases n HR nduce network effects to accelerate. Mechansms for Inducng Sharng by Workers Thus, there are two mportant conclusons. Frst, that frms wll tend to ether have a culture of sharng or a culture of ndvdual effort. Second, when a frm wants to transton to a sharng culture, early nvestments n ndoctrnaton I wll have lttle effect on sharng, but as ndoctrnaton ncreases t wll suddenly have a bg mpact on sharng. To emphasze ths latter pont, let us recall that f the frm decdes to ndoctrnate to rase the SharngIdeal, ndoctrnaton s wll only have an effect f the worker s close to the margn n sharng, or f costs ϕ, are close to B for worker. Thus, small nvestments n ndoctrnaton or peer pressure wll have no effect on connectve captal f these nvestments are not suffcent to nduce sharng. In Fgure 4a, very few workers are close to the margn, and there s not much ncrease n sharng when costs are lowered wth HR from that pont. But movng from poston 4a to 4c nduces a bg ump n sharng as many workers costs fall below the fxed beneft B. So the effect s nonlnear, or at low levels of peer pressure there s no effect of HR on connectve captal, but as peer pressure rses and to nduce more workers to share, HR begns to have an effect. Because ndoctrnaton must reach a crtcal level before t nduces connectve captal from sharng, frms may fnd t optmal to ntroduce multple HR practces smultaneously to ncrease the lkelhood of reachng that crtcal level. 10 Frst, a more homogeneous workforce wll ncrease the probablty that frms wll move from the low-sharng to the hgh-sharng 10 The nonlnearty of the effects of ndoctrnaton on connectve captal can also be produced by models of the complementarty of human resource practces. In the dscusson above, we emphaszed that multple HR practces are valuable n ncreasng the lkelhood of recprocty. For example, frms need to establsh a norm of recprocty, encourage peer pressure when that norm s gnored by an employee, tran the employees for problem solvng actvtes, organze them n teams to undertake actvtes and montorng, and lastly to select workers who have low cast so of communcatng. As emphaszed by Mlgrom and Roberts (19xx), these ndvdual HR practces are complements: ncreasng the value of any one practce wll ncrease the value of the others. Thus, as n Fgure 1, the nonlnear nature of returns to human resource practces mples that frms wll ether have low levels of these practces, or hgh levels of these practces. 21

22 workplace by shftng the gans functon left n Fgure 3. If the dstrbuton of personal sharng costs n Fgure 4 are more homogeneous, so the dstrbuton has a lower varance and hgher peak, then ncreasng I wll created an accelerated ncrease n sharng (as the frm moves from poston 4a to 4d more rapdly). Thus, f frms select more homogenous workers, they wll select more nnovatve ndoctrnaton of sharng norms (or none at all), because n ths case, small ncreases n I wll have a bg effect on connectve captal. Second, f frms match a subset of workers from type who have low costs of askng wth a subset of workers from type who has low costs of sharng, then for each value of I, the gans to I are greater, or the total gans functon shfts leftward. In effect, ths matchng ntroduces a postve correlaton between the costs A S A S dstrbutons of askers and sharers, so that cov( ϕ, ϕ ) > 0 and thus F( ϕ, ϕ ) > F( ϕ ) F( ϕ ) for ndependent dstrbutons of formng F( ϕ ) and F( ϕ ). Thrd, frms can also shft the gans A dstrbuton leftward by hrng workers selectvely by hrng those wth low costs of sharng. Fourth, gven the complementarty of sklls descrbed n secton xx, by hrng a more dversely sklled workforce, connectve captal wll ncrease (or large HC -HC ). Frms wth hgh returns to problem solvng, δ, but low costs of selectng workers, wll gan more from ths selecton process. Fnally, frms can lower the personal costs of sharng by placng people n teams where sharng s drect, or by organzng nformaton sharng sessons durng certan perods. Recall also that our model assumes group-based ncentve pay. Personal returns to connectve captal can be ncreased by alterng the forms of ncentve pay, but we take the group-based ncentve pay n the model as gven. 11 S A S II. Emprcal Evdence on Connectve Captal Usng Data from Steel Mlls The model of the frm s and worker s decson to nvest n connectve captal produced a seres of mplcatons above, and a number of these mplcatons can be examned usng data that we have gathered from steel mlls. We focus frst on the lnk between organzatonal practces and connectve captal, then on the worker s nvestment n connectve captal, and fnally on the lnk between connectve captal and productvty. Frst we descrbe the data. The Producton Process 11 For example, one form of ncentve pay s that frms that sharng n value problem solvng can promote workers n part on subectve evaluatons of ther collegalty. 22

23 Our goal s to confne our analyss to technologcally comparable producton lnes, so that we can examne the extent of connectve captal and the effects of organzatonal practces on CC wth no varaton n technology. Of course, the dsadvantage s that we cannot test the degree to whch technology, or dfferences n the value of problem-solvng, δ, cause dfferences n connectve captal. The sample for ths study comes from fnshng lnes n the ntegrated steel ndustry. In ths producton process, very thn sheets of steel are treated n some manner, such as coatng or softenng or stretchng the steel. The sheets of steel are typcally four feet wde, about 1/16 nch thck or less, and about a mle long, so the steel s stored n cols weghng about 12 tons each. To process t, the col s loaded on to the entry end of the lne and the end of the new col s welded to the steel that s currently runnng n the lne. The new col unrolls as the strp s processed contnuously through the lne. Machnery on the lne cleans, heats, stretches, or coats the steel, and fnally the steel s recoled and cut at the end of the lne. It s a contnuous process that s very captal ntensve. If connectve captal s to have any value on these lnes, t s mportant that workers efforts at problem solvng can potentally rase productvty. The productvty of these fnshng lnes can vary n a number of ways. Often the lne shuts down due to a "delay," where a delay s an unscheduled lne stoppage when some problem s found on the lne. For example, delays occur f the steel has a surface qualty problem requrng correcton, or a trackng problem causng the steel edges to crumple. Cols that break n the lne or mechancal falures n the rollng process also cause lne delays. Productvty s also lower f the lne s up and runnng but producng poor qualty steel that cannot be sold to ts ntended customer whch s a loss n lne "yeld." Thus, worker actvtes to solve problems n delays or surface qualty wll ncrease the productvty of the lne. Ste Selecton and Survey To obtan nformaton on workers communcatons regardng problem-solvng ssues, we survey all the employees n seven of the types of ntegrated steel lnes descrbed above. These seven lnes were selected so that three of the lnes have HR practces supportng problem solvng we refer to these lnes as nvolvement-orented (IO) lnes. The organzatonal practces these lnes have are: strong group-based ncentve pay for qualty output, formal processes for nformatve sharng, formal problem-solvng teams, hgh levels of tranng, and careful selecton of new employees who have the sklls and postve atttude towards problem solvng. The other 23

24 four steel lnes have none of these HR practces we refer to these lnes as control-orented (CO) lnes because they are run wth more manageral control and less emphass on employee nvolvement. These lnes were chosen from the set of 36 steel lnes that we vsted and used n our prevous study of the productvty effects of HR practces (Ichnowsk, Shaw, and Prennush, 1997). In that study, we dentfed four types of HR systems, from tradtonal havng no nnovatve HR practces, or hgh-performance havng all the nnovatve HR practces. From ths set of 36 mlls we randomly selected the seven to represent the hgh and low end or the HR spectrum. 12 The survey of workers communcaton patterns has three man features (see Appendx A for a sample of the survey). Frst, t asks the employee put a check mark next to the name of each person wth whom he typcally communcates, where the names of all people wth responsbltes for runnng or managng the lne wth whom the respondent works are lsted. Second, as the respondent checks off these names, the survey asks employees to dentfy the topc area of the communcatons wth other employees: operaton-related ssues, customerrelated ssues, and work routnes. Thrd, respondents dentfy the frequency of ther nteracton wth other workers for the varous communcaton topcs. The three categores are daly, weekly, or monthly. There are typcally about 90 workers per lne, rangng from 87 to 118 workers. The number of blue-collar workers operators and mantenance workers ranges from 47 to 51 workers across most lnes. Samples n regresson analyses below nclude responses for up to 642 employees across the seven lnes. The Frm s Investment n HR Practces and Connectve Captal Our model of the frm s nvestment n nnovatve HR practces and thus n connectve captal, mples that: Hypothess H1: Frms wth hgher levels of nvolvement-orented practces wll have greater amounts of connectve captal frms wll use ndoctrnaton, norms, peer pressure, tranng, 12 We conducted new vsts to these steel fnshng lnes between May 1996 and May Intally, we spent about three weeks n one IO mll and three weeks n one CO mll observng the day-to-day actvtes and talkng wth producton workers, supervsory staff, and managers about ther obs. Durng ths perod, we conducted plot tests of data collecton survey nstruments. After these ntal vsts to two of the stes, we vsted each mll ste between June 1996 and October 1997 for about one week each. Durng these vsts, we made more drect observatons of the workers, conducted further ntervews, and collected certan survey data. A fnal set of vsts to each ste was conducted between March 1998 and May 1998, wth each vst lastng about three days. 24

25 careful selecton of employees, nformaton sharng, and ncentve pay to nduce greater nvestment n connectve captal by workers. 13 Hypothess H2: Connectve captal s not equvalent to Human Captal they may or may not be correlated. Recall that our measure of connectve captal, from equaton (1), s N Connectve Captal CC Σcc HC for person, where cc = 1 f worker communcates wth worker = 0 f worker does not communcate wth worker and HC =HC -HC. Because t wll be hard to measure human captal, we also consder an alternatve proxy for connectve captal, that we call connectve captal tes %: N Connectve Captal Te% (CC Te%) Σ cc /N where n equaton one we set HC =1, so that we assume that the gans of worker talkng to are the same across all workers (and thus normalze the value to 1). Because fnshng lnes can be of slghtly dfferent sze, we dvde the number of tes by the sze of the mll, N, to create a varable that s comparable across mlls Connectve Captal Te% s smply the percent of all people n the mll whom worker talks to wthn a specfed perod about specfc problems. The basc means n our data seem to support Hypothess H1: nvolvement-orented lnes have much more connectve captal. Usng tradtonal measures of human captal, of ether educaton or tenure as proxes for HC and HC, we fnd that the IO lnes have approxmately twce as much connectve captal as the CO lnes (Table 1, columns 1 and 2). However, these proxes for human captal are lkely to be very nadequate measures of ndvdual-specfc problem-solvng sklls n steel mlls. Therefore, we assume no dfferences across ndvduals n human captal, and look only at the CCTe%. Once agan, IO mlls have much greater amounts 13 There s one set of mplcatons of the model that cannot be tested usng the steelmll data. We cannot test whether mlls are selectng workers or tranng workers to encourage connectve captal development (for example, selectng workers wth more homogenous costs of sharng). In other words, we cannot test whether there are specfc HR practces that are used to enhance the development of connectve captal. 25

26 of connectve captal as measured only by ther volume of communcatons (column 3, Table 1): the CCTe% s more than three tmes as great on IO lnes as on CO lnes across all ndvduals. In Hypothess H2 we ask whether human captal and connectve captal are correlated n our data there s very lttle correlaton between human captal and connectve captal across these lnes. Though these IO and CO lnes have very dfferent apparent amounts of connectve captal, they are essentally dentcal n terms of ther mean values of measured human captal. The mean values of educaton (and ther dstrbuton) are vrtually dentcal for the IO and CO lnes: the mean educaton levels are and 13.22, respectvely (columns 4 and 5 of Table 1). Tenure levels are a lttle bt dfferent CO lnes are older and thus have a subset of workers who have consderably hgher tenure. The concluson s clear: IO lnes and CO lnes have bascally equvalent amounts of human captal, when human captal s measured by tradtonal measures of educaton and tenure. Moreover, because IO lnes have the same measured human captal as CO lnes, the second concluson s clear: the IO lnes have nearly twce as much connectve captal than do CO lnes because workers on IO lnes communcate more wth fellow workers. Renforcng these conclusons, when we add controls for dfferences n ob actvty (operators vs. managers) and other factors, our regresson results show that hgh-hr IO lnes contnue to have much greater amounts of CC Tes than do CO lnes. In Table 2, we regress of CCTe% as a functon of HR envronment (IO vs. CO) and ntroduce controls for dfferences n the types of communcatons (operatng vs. customer vs. work routnes), the strength of the tes (daly vs. weekly vs. monthly), and the ob-class of the worker. Across all obs, IO lnes communcate 18 percentage ponts more (column 1). The greatest gans are for producton workers and team leaders on IO lnes (column 2). In fact, f we focus only on Strong Tes (daly communcatons), managers have no dfference n communcatons across the IO vs. CO lnes. 14 Fnally, n Table 3 we add controls for the workers human captal, and show that the concluson that hgh-hr IO lnes have much hgher levels of connectve captal remans true. Thus overall, our communcatons data suggests that n nvolvement-orented plants, both workers and frms are nvestng n greater amounts of connectve captal. Our data also shows 14 We also estmate regressons n whch we omt observatons n IO lnes wth very large numbers of tes to test whether the postve IO effect s drven by the hgher communcatons for a subset of the workforce. Even elmnatng these outlers n IO lnes, we fnd that the IO effect s very postve for all groups of workers. 26