IZA DP No. 3096 Interactions Between Workers and the Technology of Production: Evidence from Professional Baseball Eric D. Gould Eyal Winter DISCUSSION PAPER SERIES Forschungsinstitut zur Zukunft der Arbeit Institute for the Study of Labor October 2007 Interactions Between Workers and the Technology of Production: Evidence from Professional Baseball Eric D. Gould Hebrew University and IZA Eyal Winter Hebrew University Discussion Paper No. 3096 October 2007 IZA P.O. Box 7240 53072 Bonn Germany Phone: +49-228-3894-0 Fax: +49-228-3894-180 E-mail: iza@iza.org Any opinions expressed here are those of the author(s) and not those of the institute. Research disseminated by IZA may include views on policy, but the institute itself takes no institutional policy positions. The Institute for the Study of Labor (IZA) in Bonn is a local and virtual international research center and a place of communication between science, politics and business. IZA is an independent nonprofit company supported by Deutsche Post World Net. The center is associated with the University of Bonn and offers a stimulating research environment through its research networks, research support, and visitors and doctoral programs. IZA engages in (i) original and internationally competitive research in all fields of labor economics, (ii) development of policy concepts, and (iii) dissemination of research results and concepts to the interested public. IZA Discussion Papers often represent preliminary work and are circulated to encourage discussion. Citation of such a paper should account for its provisional character. A revised version may be available directly from the author. IZA Discussion Paper No. 3096 October 2007 ABSTRACT Interactions Between Workers and the Technology of Production: Evidence from Professional Baseball * This paper examines how the effort choices of workers within the same firm interact with each other. In contrast to the existing literature, we show that workers can affect the productivity of their co-workers based on income maximization considerations, rather than relying on behavioral considerations such as peer pressure, social norms, and shame. Theoretically, we show that a worker’s effort has a positive effect on the effort of co-workers if they are complements in production, and a negative effect if they are substitutes. The theory is tested using panel data on the performance of baseball players from 1970 to 2003. The empirical analysis shows that a player’s batting average significantly increases with the batting performance of his peers, but decreases with the quality of the team’s pitching. Furthermore, a pitcher’s performance increases with the pitching quality of his teammates, but is unaffected by the batting output of the team. These results are inconsistent with behavioral explanations which predict that shirking by any kind of worker will increase shirking by all fellow workers. The results are consistent with the idea that the effort choices of workers interact in ways that are dependent on the technology of production. These findings are robust to controlling for individual fixed-effects, and to using changes in the composition of one’s co-workers in order to produce exogenous variation in the performance of one’s peers. JEL Classification: J2 Keywords: peer effects, team production, externalities Corresponding author: Eric D. Gould Department of Economics Hebrew University of Jerusalem Mount Scopus Jerusalem 91905 Israel E-mail: mseric@mscc.huji.ac.il * For helpful comments and discussions, we thank Todd Kaplan, Daniele Paserman, Victor Lavy, Daron Acemoglu, two anonymous referees, and seminar participants at Hebrew University, the European University Institute, the Norwegian School of Economics, Tel Aviv University, and the University of Texas. 1 Introduction This paper examines how t he effort ch oices of workers within the sam e firm in teract with eac h oth er , and how this interaction depends on the techn ology of production. In contrast to the existing liter ature, w e focus on show ing h ow t he effort choice of one w orker can affect the effort choices of his co-workers based purely on income-m aximizing considera- tions, rather than relyin g on behavio ral explanations such as peer pressure, sha me, etc. In addition, w e break from the existing literature by s ho wing t hat the effortchoiceofone worker could have a po sitive or negative e ffect o n his c o-wo r ker s. For e xam p le, a mec h a- nism based on behavioral considera tions like peer pressure or shame predicts that a high level of effort by one wo rker will induce oth er workers to increase their effort level, or that alowereffort b y one wo rker cau ses other wo rkers to follow suit. We refer to both of these cases a s a “positive interaction ” in the sense th at a change in e ffort by one wo rker causes others to change their effort in the same direction. Howe ver, we show that a “ neg ative in tera ctio n” between wo rke rs is also possible, in the sense that a ch an ge in effort by one worker causes other wo rkers to c h ange their effort in the opposite direction. Therefore, this paper con trib utes to the existin g literature by sho w ing that the in- teraction of effort choices could work in both directions, ev en within the same firm at the same time. In partic ular, we sho w that a “positive in teraction” should exist bet ween comp lem entar y wor kers, while w o rkers who are substitutes may free ride off the effort of eac h other, and th us genera te a “negative int eraction” in the effort choices of co-worke rs. The theory is tested using panel data on the performance of baseball pla yers from 1970 to 2003. The game of baseball p rovides a clear case where pitchers and non-pitc hers can safely be defined as substitutes fo r eac h other in team performan ce — since p reventing runs and sco ring runs are perfect substitutes in th e team’s goal of scoring mor e runs th an the o pposing t eam . In addition, p laye rs who are not pitc h ers are o ften comp lem ents with eac h other since it u su ally takes more t han one player to get a h it in order to sco re a run for the team . The empirical analysis show s that a pla ye r’s batting averag e significant ly increases with the batting perform ance of other players on the team, but decreases with the quality of the team’s pitch ing . Furth erm ore, a p itcher’s performance increases with the 1 pitching qualit y of the o ther pitchers, but is unaffected by the batting output of the team. These results are in consistent with beh avioral explanations for how one w orke r affects the per form ance of other w orkers, since a t y pical behavioral response should c ause w o rkers to c hange their effort in the same direction regardless of the other player’s role or function. Thu s, psychologic al conside ratio ns are unlike ly to exp lain o ur findings that players respond differentially to th e actio ns of th eir co-workers according to their role a nd function on the team. Ov erall, t he results a re more consistent with an interaction of effort c ho ices within the team t hat a re based on a rational response to the tec hnology o f production. Our empirical findings are robust to controlling for individual fixed-effects, expe- rience, year effects, team, home ballpar k ch aracteristics, and managerial qualit y. The inclusion of individual fixed-effects mea ns that the results canno t be e xp lain ed by assorta- tiv e matching bet ween complementa ry o r su bstitutable p layers at the team lev el, since th e analysis is exp loitin g variation o ve r time wit hin a give n player’s pe r formanc e. In ad dition , the results a re rob ust to using a first-differences specification, as well as restricting the sample to only those workers who cha nge teams (chan ging all of their co-workers), or using a s ample of only t hose wo rkers who re main with the sam e team, manager, and h ome ball- park in consecutiv e years. Furtherm or e, in order to cont rol for unobserv ed yearly shocks which ma y a ffect the performance of the whole team, we instrum ent the yearly performance of one’s t eam mates with the lifetime performa nce of his teammates. Yearly variation in this instrument stems only from ch anges in the composition of on e’s co-wo rkers, sin ce each pla yer’s lifetim e performance is constant for ea ch ye ar. Results using this instrument are v e ry similar t o the O L S estimates. There is a grow in g literature that stresses the im portance of the environ m ent in deter- mining the outcomes of individuals. Most of this literature is concerned w ith examining ho w peers and environ m ental factors affect y outh behav ior regarding their educational ac h ievem ents, h ea lth, criminal invo lvem ent, wo rk status, and other economic va riab les. 1 This paper differs by looking at the in teraction o f adult beha v ior in the wo rkp lace. Th e 1 See Angrist and Lang (2004), Guryan (2004), Hoxby (2000), Sacerdote (2001), Zimmermann (2003), Katz, Kling and Liebman, (2001); Edin, Fredriksson and Aslund (2003); Oreopoulos (2003); Jacob (2004); Weinberg, Reagan and Yankow (2004), Gould, Lavy and Pa serman (2004a and 2004b). 2 literature on the in tera ctio n of worke rs within a firm is not extensive. Winte r (2004) demo nstrate s the ore tically the o ptim a lity o f offerin g differen tial in centive c ontra cts in or- der to elicit worker effort whic h genera tes externalities on other workers. Kandel and Lazear (1992) examine the theory of team production within the firm and focus on how teams produce social pressure to solve the free-riding problem. The most related papers to ours are by Ichino and M aggi (2000) and Mas and Moretti (2006). Ic hino and M aggi (2000) examine shirking behav ior within a large banking firm, and show that a worke r’s shirking beha vior significant ly respo nd s to the beha v ior of his co-worke rs when they move across branches within the sam e firm. Using data on workers from a large g rocery story c hain, Mas and Moretti (2006) e xam ine ho w the productivity of a worker varies according to the productivity of other w orkers on the same sh ift, and provid e additional evidence that be havior consideratio ns such as peer pressure and social norm s are significan t. Som e of our empirical specifications emplo y a similar identification stra tegy in the sense tha t we exploit differences in the composition of one’s co-workers to explain var iation in an indi- vidual’s performan ce level over time and across workp laces. However, o ur paper differs b y examining the theoretical and empirical di fferences in the natur e of the interaction across workers depending on whether they are substitutes or complements w ith eac h other. In this m anner, o ur paper contributes to the literature by pro viding a theoretical foundation and empirical evid en ce for both positiv e a nd negative interactions in the effort c h oices of workers i n a real work environment. 2 The model In this section, we show h ow the effort choices of workers within the same firm interact with each other, and ho w this interaction depends on the tec hnology of the team production function. To do t h is, we presen t a parsimonious p rincipal-a gent model where t h e o p tim al contract is derived und er two d ifferen t scenarios. I n o ne scen ario, players are co mp le- mentar y to one an other, and in th e second scenario, workers are consid ered substitutes. In order to characterize the two different types of techn olog ies, we borro w t he co ncep t o f strategic substitution and complemen tarit y (see Milgrom and Shannon (1994) a nd Topkis 3 (1998)). Our model is similar to Holmstrom (1982) and Holmstrom and Milgrom (1991) in the s ense that the outcome of effo rt i s u n certain, b ut risk aversion p lays n o role in our model. Th at is, our model is based on ly on th e issue of mor al hazard . A t eam consists of two agen ts {1,2}. Eac h agen t is respo nsible for a task. A worker’s task is successful with probab ility β if he exerts effort, but is successful with probabilit y α<βif no effort is exerted. We assum e that the cost of effort is c for both agents. 2 On eac h team, the tasks of the two worker s jointly determine the success of a project according to a techn ology p : {0, 1, 2} → [0, 1], where p(k) is the proba bility that the project succeeds giv en that exactly k agents have successfully com p leted their tasks (the assum ption of symmetry is used only for t he sake of simplicity). In order to allow wor kers to ba se th eir e ffort choices on th e performance of other workers, we a ssum e th at player 1 performs his task first, and then play er 2 ch ooses his effort after ob ser ving the o utcome of the t ask perform ed by agen t 1. We derive th e o ptim al contra cts for two teams — each team representing a d ifferent t ype of technology. The production function for team 1 is c haracterized by comple- mentar ity or superm odularit y between the agents, which is represen ted by p(2) − p(1) > p(1) − p(0). In con t rast, team 2 is char acterized by substitution bet ween workers, which is represen ted by p(2) − p(1) <p(1) − p(0). This fram ework captures the b asic intuition that, in the case where w orke rs are complements in prod uction, the success of one agen t in com pleting his t ask c ontrib utes m ore to the prospects o f the entire p roject succeed ing if the other ag ent s ucceed ed a s we ll. In contrast, in the case where workers a re sub stitutes, the marginal con tribution of a successfully completed task by one w o rker is higher when the other worker fails in his task. The principal is facing moral h azard. He cannot monitor the effort of his workers, nor is he informed about which tasks ha v e ended successfully. Instead, h e is informed only about w h ether the project as a w h ole is successful. Therefore, the principal offers contracts to a gents that are contin gent only on the wh ether the ove rall project su cceeded or no t. 2 In reality, the cost of effort would be a function of a person’s innate ability. Also, as we later discuss, the probability of the task succeeding conditional on effort would also be a function of personal characteristics. However, we maintain the assumption of a uniform cost for the sake of simplicity. 4 Specifically, t he p rinc ipal offers a contra ct to each member of the team, repr esented by a v e ctor of reward s v =(v 1 ,v 2 ) w ith agen t i receiving v i if the project succeeds a nd zero otherwise. For a mechanism v, we have an extensive f orm game G(v) between the two play ers. If the overall team project is successful, the project generates a benefit B for the principal. Given a mechanism v, let q(v) be the probab ility of success in the uniqu e 3 (subgame per fect) equilibrium of the game G(v). The principal designs the incentiv e mechanism v optima lly, s o as t o maximize his net rev enu e, represen ted as v =argmaxq(v)[B − P j v j ]. We assu m e that th e ove rall p roject is valuable en ou gh so tha t the o ptim al m ech an ism a wa rd s each player with a positive reward if the project is successful. That is, B is sufficiently high (B>B ∗ ) so that v j > 0 for both players in the optimal mech anism . N ote that th is assumption implies that player 1 exerts effort. If this were n ot the case, then v 1 > 0 cannot be optimal since the principal would be better off paying zero t o playe r 1. Depending o n the value of B as well as the values of the other parameters in the game, the optima l mec han ism must yield one of the follow in g equilibria in the co rresponding game: 1. Player 1 exerts effort and player 2 exerts effort if and on ly if the first task succeeded. 2. Player 1 exerts effort a nd play er 2 exerts effort if and on ly if the fir st task failed. 3. Player 1 e xerts e ffort and player 2 e xerts effo rt regardless of the o u tcom e of the first task. If B is sufficiently high (B>B ∗ ), then the project is so v aluable that the princi- pal will induce equilibrium 3 so that pla yer 2 always finds it worthwhile to exert effort regardless of wheth er playe r 1 succeeded an d regardless of wh ether th e tec h n ology is one of substitution or complementarit y. If, ho wev er, B is high enough to induce the prin- cipal to prov ide incen tives to exert effort but not so high that this is alw a ys the case (B ∗ <B <B ∗ ), the optimal str ategy will depend on the technology of production. The follo w in g p roposition states wh at h ap pens whenever B is sufficien tly h igh (B>B ∗ ) so that the principal provid es at least some i nc entives to exert effort. 3 We assume that indifference is resolved in favor of exerting effort. 5 Proposition 1 (1) If th e team ’s technology satisfies c omplementarity, then the optimal mecha n ism induces either equilibrium 1 or equ ilibrium 3. (2) If th e team’s tech nol ogy s at - isfies su bs titutio n , t h en the op timal mech a nis m induces either equilib rium 2 o r equ ilibr ium 3. Proposition 1 asserts that unless it is a dom in ant strategy f or agen t 2 to always exert effort (B>B ∗ ), the optim a l pattern o f behavior in equilibrium will be co nsist ent with our em pirical resu lts. If workers are com p lem entary, a fa ilure on th e part of p layer 1 will trigger player 2 to shirk. In contra st, if workers are substitutes in pr oduction, a failure on the part of player 1 w ill trigger p laye r 2 to exert e ffort. The intuition for Proposition 1 is straigh tforw ard. In general, the principal will find it co st effectiv e to pro vide incen tives for the agent to exert effort when the ma rginal return to the w orker’s effort is high. So, if w orkers are complementary to eac h other, player 2’s effort will have a b igg er impact on the o verall success of the team if pla yer 1 succeeded rather tha n failed. Therefo re, i n order for player 2 to exert effort, he will need to be com pensated fo r the lower probability of team success in the case w h ere player 1 failed versus the c ase where p layer 1 succeeded. If the project’s value is sufficien tly h igh (B>B ∗ ), the principal will find it profitable to pro vide incentives to player 2 even if pla yer 1 failed. But, if the project’s va lue is lo wer than this threshold (B ∗ <B <B ∗ ), the princip al w ill findittoocostlytoprovideincentivestoplayer2toexerteffort if pla yer 1 failed. Althou gh it might seem in tuitive that the principal would create an incen tive mechanism to counter the urge for pla y er 2 to shirk when pla y er 1 fails, the model shows that this is only the case w h en the value of the project is sufficiently h igh. In intermediate cases, it is o ptim al for the p rincipa l not to waste his money on provid ing in centive s to player 2 when the chances are low that player 2’s effort will result in the overall success of a p roject which is no t sufficien tly valuable. In con tra st, if workers are substitutes in pr oduction, playe r 2’s effort is more effective if player 1 fails in his t ask. If p layer 1 succeeds, then player 2 knows that his effort is not as crucial for the team to be successful, and therefore, player 2 wou ld need a higher pa y m ent to exert effort in the case where player 1 succeeds. If the project i s worth a lot (B>B ∗ ), 6 then the prin cipa l will find it profitable to incur this cost in order to im prove the chances of team success even w h en the success of player 1 has already rendered pla ye r 2’s effort to be less crucial. But, in the interm ed iate case (B ∗ <B <B ∗ ), the principal will find it optimaltopayenoughtoplayer2toexerteffort only when pla ye r 1 fails, s ince this is the case where playe r 2’s effort i s more critical to the success of th e team. Once again, we see that the principal will not a lways design the optima l con tract to guard against shirking in all cases — i f wo rke rs are s ub stitu tes, it is o ften th e ca se tha t it i s n ot p rofitable to g u ard against shirking by p laye r 2 if p layer 1 h as alread y d one m ost of th e wo rk th at is cr itical for team success. Proof of Propositio n 1: We start b y deriving the optimal mechan ism for a team where w o rkers are complementary with each other. Let u s examine the behavior of p layer 2, who is paid v 2 if the o ver all project is successful. Con sider playe r 2’s decision node after t ask 1 succeeded. Player 2’s expected payoff will be [βp(2) + (1 − β)p(1)]v 2 − c if he exerts effort and [αp(2) + (1 − α)p(1)]v 2 if he sh irks. T h e o ptimal rewa r d for playe r 2 should make him indifferent among these two options. Hence v 2 = c (β−α)[p(2)−p(1)] ,and pla yer 2 w ill exert effort un der this contract if pla yer 1 succeed ed in his task. Furthermore, bec au se the two worke rs are com p lem e ntar ity, player 2 will shirk if player 1 failed in his task. This follo ws from th e fact that player 2’s effort has a lower m arginal effect when play er 1 fails and from the fact that play er 2 is indifferent between sh irking a nd exerting effort wh en p layer 1 succeeded. Hence v 2 is a mecha nism which indu ces equ ilibriu m 1. Consid er now a mechanism v 0 2 under wh ich pla ye r 2 exerts effort when player 1 fails in h is task. The incentive con straint for th is mech an ism must be [βp(1) + (1 − β)p(0)]v 0 2 − c ≥ [αp(1) + (1 − α)p(0)]v 0 2 and v 0 2 ≥ c (β−α)[p(1)−p(0)] . D ue to the complementarity co nd ition [p(2) − p(1)] > [p(1) − p(0)], it follows that v 0 2 >v 2 . Hence, if the contract is v 0 2 , it is a dom inant strategy fo r player 2 to exert effort in t he comp lementarity case. Th is proves that the optimal me chanism in the ca se where worke rs are com plem ents induces either equilibriu m 1 or equilibrium 3. We now exam ine the case where workers are substitutes in production. We have seen th at a mech an ism that in duces player 2 to exert effort when player 1 fails in his task must pay v 0 2 = c (β−α)[p(1)−p(0)] . C on sider an alternativ e mec hanism which i nduces pla yer 2 to exert effort w hen player 1 succeeds. In this type o f mechan ism , 7 [...]... considerations Rather, our purpose is to demonstrate that these interactions could result from fully rational (income maximizing) considerations without relying on behavioral responses Indeed, the remainder of the paper presents evidence from professional baseball that these types of interactions between workers are significant, and appear to be based on a rational response to the technology 3 The Data and Background... pressure, guilt, and social norms These types of explanations would predict that any type of workers will work harder when his co -workers are working harder, regardless of the function of his job in relation to the function of his co -workers Therefore, the differential responses according to the role of each type of player can be viewed as evidence in favor of the idea that workers adjust their effort in... Overall, the results are consistent with the theory that players should be positively affected by the performance of their fellow workers when they are complements in production (like batters between themselves), but negatively affected by the performance of their fellow workers when they are substitutes in production (like batters and pitchers) Although the finding that a pitcher is positively affected by other... (not including the batting performance of pitchers), the ability of player i represented by µi , other observable control variables, and the unobserved random component, εit The other control variables include: the batting average in player i’s division (excluding his own team) in year t which controls for the quality of the pitching and batting in the team’s division in the same year, the team manager’s... rational way which is dependent on the technology of team production This interpretation is strengthened by the many robustness 20 checks with different samples and specifications, as well as instrumenting the performance of one’s co -workers with their lifetime performance All of the variation in this instrument comes from changes in the composition of one’s co -workers, and therefore, is unaffected by transitory... examine whether the results in Tables 2 and 3 are robust to using different measures of a player’s performance As a basis for comparison, the first column in the upper panels of Tables 4 and 5 replicate the batting regression results already seen in Tables 2 and 15 3 for the fixed-effects and first-differences specifications respectively The first column in the bottom panels of Tables 4 and 5 use the “on-base-percentage”... quantify and where the actions of one player, which do not always show up in statistics, can complement or come at the expense of the performance of his teammates In addition, baseball players are easily divided into two distinct types: pitchers and batters The function of pitchers is to prevent the other team from scoring runs, while the function of a batter is primarily to help score runs for the team... harder, regardless of whether they are complements or substitutes in team production This prediction is clearly rejected in the analysis So, the differential responses according to the role of each type of player can be viewed as evidence for the idea that the technology of production significantly influences the interaction of effort choices across workers 5 5.1 Alternative Explanations and Robustness Checks... pitchers as explanatory variables, and the results are essentially unchanged Thus, the results are robust to estimating the effect of pitchers and batters separately (columns (1) and (2)) or when they are estimated together in column (3) Therefore, the results are not a product of a high correlation between the two variables Columns (5)-(7) present the basic results for pitchers, and show that a pitcher performs... but there is no significant effect of the team’s batting performance on a pitcher’s performance — a finding which repeats itself throughout the paper Again, the effect of the player’s fellow pitchers on his own performance is robust to the inclusion or exclusion of the team’s batting performance Regarding the other control variables, they all have the expected signs and are generally significant for the . Interactions Between Workers and the Technology of Production: Evidence from Professional Baseball * This paper examines how the effort choices of workers. Arbeit Institute for the Study of Labor October 2007 Interactions Between Workers and the Technology of Production: Evidence from Professional Baseball