February 9, Tat Y. Chan is Associate Professor of Marketing, Jia Li is a doctoral student in Marketing, and Lamar Pierce is

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1 Compensation and Peer Effects in Competing Sales Teams Tat Y. Chan, Jia Li, and Lamar Pierce 1 Olin Business School Washington University in St. Louis Campus Box 1133, One Brookings Drive Saint Louis, MO February 9, 2009 Abstract. The personnel economics literature has established that co-located workers significantly impact one another s productivity. Recent work empirically demonstrates peer effects in single-firm work settings under one compensation structure, but these studies leave important questions unanswered. First, the direction and magnitude of peer effects may depend on incentives from the firm s compensation system. Second, peer effects may extend beyond firm boundaries to inter-firm competition, with individual productivity also influenced by peers outside the firm. Third, under these pressures workers may employ various strategies at their discretion to compete with co-located peers. We address these questions using a three-year dataset of Chinese cosmetic sales transactions, examining how compensation and firm boundaries influence worker productivity spillovers and competition strategies. We use a nested non-linear least squares algorithm to simultaneously estimate permanent worker productivity and the same-day peer effect on concurrently-scheduled salespeople s revenue, unit sales, discounting, and customer and product mix. We demonstrate three important new sets of findings. First, we find that under the individual-based compensation system the direction and magnitude of peer effects significantly differ from those under the team-based compensation system. Second, we find that peer effects exist across firm boundaries, with high-ability peers at competing counters hurting productivity more heavily for workers at individual compensation counters. Third, we find that workers at individual compensation counters respond to high-ability peers within and across counters by discounting prices and focusing on high-valued customers and products. This paper provides a unique contribution to the personnel economics and marketing literature by being the first to simultaneously estimate peer productivity spillovers both within and across firms under multiple compensation systems. It also first identifies peer effects under discretionary pricing, and provides important implications for managerial decisions on staffing, compensation, location, and pricing discretion. Finally, the paper implements improved methodology that generates more efficient estimators than those in previous productivity spillover studies. 1 Tat Y. Chan is Associate Professor of Marketing, Jia Li is a doctoral student in Marketing, and Lamar Pierce is Assistant Professor of Strategy, all at Olin Business School, Washington University in St. Louis. Authors can be reached at chan@wustl.edu, jli26@wustl.edu, or pierce@wustl.edu. 1

2 1. Introduction Co-located workers can significantly impact one another s productivity. These productivity spillovers may be positive, as coordination improves each worker s production through knowledge transfer (Marshall 1890; Lucas 1988) and complementarities in skills and abilities (Gant, Ichniowski, and Shaw 2002; 2003; Hamilton, Nickerson, and Owan 2003). Alternatively, workers may negatively impact their peers, either through the reduced effort of free-riding (Holmstrom 1979) or by imposing production externalities on their coworkers (Holmstrom 1982). Co-located workers have even more significant impact on their peers when they directly compete with one another under the high-powered incentives of pay-forperformance or tournament-based compensation. Workers may use social pressure or norms to reduce negative peer effects (Kandel and Lazear 1992; Mas and Moretti 2009), but these are unlikely to countervail the high-powered incentives of competition. The many ways in which workers can affect peer productivity provide a simple yet powerful implication whom you work with matters. While recent work has empirically demonstrated peer effects in work settings (Falk and Ichino 2006; Bandiera, Barankay, and Rasule 2007; Mas and Moretti 2009), it has done so exclusively within firms or groups and under singular compensation structure. While this research shows that the quality of peers influences worker behavior, these findings leave several important questions unanswered. First, the direction and magnitude of peer effects may be critically linked to the compensation system used by the firm and the incentives it provides to workers. Second, the importance of peer effects may extend beyond the boundaries of the firm to competition with other organizations. Where workers from different firms are co-located, individual productivity may be influenced not only by workers from within the firm, but also by 2

3 peers from the outside. Finally, under these peer pressures workers may actively employ various strategies at their discretion to compete with other co-located workers. In this paper we examine an empirical setting where peer effects extend across the boundaries of the firms with different compensation systems cosmetic sales in a Chinese department store. In this setting, which is similar to sales environments in many industries, multiple manufacturers employ salespeople to work at co-located counters on the retail floor. These brand-based counters compete for customers inside the department store, with some employing team-based compensation (TC) and others individual commissions (IC). Therefore, while some salespeople work as a team to compete against outside peers from other counters, others must also compete with the inside peers at their own counter. In this sales setting, each peer, whether within or outside the firm boundary, has a potential impact on a given agent s productivity. Salespeople use inherent skill, effort, and discretionary pricing to compete with competitors inside and outside the firm. We use a detailed three-year dataset of individual sales transactions to identify how compensation structure and firm boundaries influence productivity spillovers across workers. These data identify individual salesperson, prices, products, and time for each transaction of this period, allowing us to observe real-time productivity and pricing strategies for 61 workers in 11 brand-based counters. This level of detail allows us to build a simultaneous equation system to study in each period how any worker s temporal productivity is influenced by the set of peers within and outside counters working at that time. Our model allows these peer effects to depend on the compensation systems adopted by own counter and competing counters. We use a nested non-linear least squares algorithm to simultaneously estimate permanent worker productivity and the same-day peer effect on concurrently-scheduled salespeople s revenue, unit sales, 3

4 discounting, and customer and product mix. This method allows us to study the complicated within-counter and cross-counter peer effects that depend on the compensation systems of both the focal worker and her peers, and generate estimators that are more efficient than the two-step estimators adopted in previous studies. While our results confirm previous studies showing productivity spillovers to co-workers, we demonstrate three important new sets of findings. First, we find that the direction and magnitude of peer effects depend on compensation system. We find strong evidence that IC counters produce negative peer effects among employees, as salespeople compete against one another for customers. In contrast, we identify positive though small peer effects within TC counters, suggesting high-productivity peers may improve worker productivity through coordination. Second, we find that peer effects exist across firm boundaries in sales competition. High-ability peers at competing counters hurt worker productivity, as those peers outcompete for customers and sales. We also find this effect to greatly depend on compensation system. Highability workers at IC counters have much less effect on outside peers, since they focus much of their effort on inside peers. In contrast, high-ability workers at TC counters have dramatic effects on their outside peers, as they can exert the entirety of their effort toward cross-counter competition. Third, we demonstrate that workers adjust their selling strategies in response to high-ability peers. They respond by lowering prices in response to high-ability competing peers within individual-compensation counters and high-ability peers at competing counters. Workers also respond to high-ability peers by focusing on high-value customers who may be loyal to them and therefore difficult for peers to steal. Our results suggest that peer effects are important both within and across firm boundaries, and that their magnitude and direction is dependent on the compensation system of 4

5 both the focal firm and its competitors. While individual compensation may motivate workers, it also transfers much of their competitive effort to within the firm. This may reduce the firm s ability to effectively compete with rivals, and when combined with discretionary pricing, lead to lower profit margins as well. While we cannot show that one compensation system dominates another, our results suggest that TC improves a firm s responsiveness to high productivity workers at competing firms. The coordination benefits of team-based compensation appear to reduce the impact of star salespeople in competing brands. This paper provides a unique contribution to the personnel economics literature. It is the first to simultaneously estimate peer productivity spillovers both within and across firms, and does so under multiple compensation systems. It is also the first to study peer effects under discretionary pricing, contributing to the literature on the employee gaming of compensation systems (Baker 1992; Courty and Marschke 2004). Our results have important implications for managers of sales groups as well as those providing the marketplaces in which they compete. This study shows that the optimal staffing of workers may critically depend on the compensation system and the staffing choices of competing firms. Worker diversity of skills may indeed improve team productivity (Leonard and Levine 2006; Mas and Moretti 2009), but only under team-based or low-powered incentives. Under individual incentives, low-productivity workers may be unable to compete with peers, and may instead engage in strategic gaming detrimental to the firm. Under these high-powered incentives, pricing discretion may produce within-firm price wars that ultimately low profit margins. 2. Theoretical Background Sources of Productivity Spillovers 5

6 A worker may influence the productivity of her peers in a number of ways. First, she may transfer knowledge or ability to the peer. This knowledge transfer may be voluntary, where the worker actively teaches or helps the peer, or involuntary, where the peer learns from observing the coworker. Empirical work by Berg et al. (1996) supports this claim, finding teams in garment facilities commonly enjoy informal training among peers. This knowledge-transfer process implies that high-ability workers will have positive productivity spillovers onto peers, while low-ability workers will provide few spillover benefits. Several theoretical models of team-based pay suggest productivity spillovers may also occur from coordination and specialization in teamwork (Milgrom and Roberts, 1990; Kandel and Lazear, 1992). Boning, Ichniowski, and Shaw (2001) and Gant, Ichniowski, and Shaw (2002, 2003) show team production in the steel industry produces some type of coordination benefits, particularly in more complicated production processes. Hamilton, Nickerson, and Owan (2003) also show apparent gains from the coordination of teamwork, and further demonstrate that skill diversity increases these gains. Assuming that high individual productivity is associated with better coordination, high-ability workers should provide greater coordination spillovers to their peers. Productivity spillovers may also result through negative externalities from free-riding. Workers in team production may choose to reduce effort when that effort is not directly observable, and this shirking can spill over to the productivity of peers. Since workers will tend to have different intrinsic costs and benefits from effort, some will on average shirk more than others. Any worker scheduled with a low-effort peer will suffer higher externalities and carry more of the workload. Workers will therefore tend to be more productive when working with high-effort peers than with low-effort peers. 6

7 Scholars have argued that social forces, such as peer pressure or shame, might mitigate the tendency of team members to free-ride. Kandel and Lazear (1992), for example, show that peer pressure can reduce free-riding in partnerships. They argue that shame and harassment can result from deviations from social norms, and these peer pressures can limit anti-social behavior. Ichino and Maggi (2000) empirically show that social norms can also determine levels of misconduct and absenteeism by examining Italian banks, while Pierce and Snyder (2008) show the same effect for leniency in vehicle emissions testing. Recent empirical work has also demonstrated that social pressure can produce peer effects in productivity, with highlyproductive workers motivating their less productive peers to work harder. Experimental work by Falk and Ichino (2006) showed that while these peer effects worked both ways, the resulting increased productivity of the worst workers more than made up for the decrease in the best workers productivity. Mas and Moretti (2009) found a similar result in a retail setting, where supermarket checkers exerted more effort when observed by high-productivity peers. They argue that these workers suffer disutility from formal or informal sanctions and shame, and respond with increased effort to counter this social pressure. While several studies have demonstrated the existence of peer effects and the mechanisms behind them, they have done so under a single compensation system. Furthermore, these studies have identified peer effects within single firms without accounting for cross-firm competition. In Mas and Moretti (2009), for example, workers are paid an hourly wage for a relatively simple task that has no interaction with other firms. While these settings, and the peer effects embedded in them, are common and important, they do not address two additional factors that may determine productivity spillovers: compensation system and inter-firm competition. 7

8 Compensation Systems and Peer Effects There is considerable evidence in the personnel economics literature that compensation systems have dramatic effects on worker behavior. Because firms often cannot directly observe worker effort, workers choose to shirk rather than exert costly effort. When firms provide guaranteed compensation such as hourly wages, they risk workers engaging in moral hazard that reduces their costs from effort without hurting their financial gains. Firms can engage in costly monitoring of employee effort, but the marginal productivity gains from reducing moral hazard may not compensate for the marginal cost of this oversight. If effort is not directly observable, firms can make compensation completely contingent on some measure of employee output. A piece-rate system, where workers are paid for the work they accomplish, can make monitoring unnecessary. Empirical work has demonstrated that pay for performance increases productivity. Lazear (2000) showed that the replacement of hourly wages with output-based incentives for automobile windshield installation mechanics increased productivity by 35%, while wages rose only 12%. Similar results have been shown in tree planting (Paarsch and Shearer, 1996), retail sales (Banker et al, 1996), agricultural output (Groves et al, 1994), and many other industries. While performance-based compensation may provide strong incentives for effort, it can produce several other problems. With contingent compensation, employees who work hard may get unlucky and face decreased pay from exogenous economic or financial shocks. Similarly, employees who shirk may get lucky and face a positive random shock. Therefore, the risk that observable output is hurt by exogenous factors rests squarely on the shoulders of the employee. Similarly, this shock may be firm-specific, where poor products or marketing may hurt individual employee or team sales. Furthermore, employees under high-powered incentives may 8

9 attempt to game the compensation system, particularly when commissions are non-linear. Oyer (1998) first demonstrated that non-linear incentives appear to affect sales flow and margins, and that this relationship holds across many industries. Larkin (2007) similarly shows that a kinked commission curve for enterprise software salespeople leads them to game the timing and pricing of sales, costing the company 6-8% of revenue. If firms wish to implement a high-powered incentive system to reduce shirking, they can do so at two levels: the individual worker and the team. In individual-based compensation, every worker is responsible for her own productivity, and is compensated on that output. While this may considerably reduce the incentive to free-ride, it makes the employee vulnerable to productivity spillovers from other workers. It also provides strong incentives for employees to compete with one another, which may be beneficial or detrimental to firm profitability. Individual workers may focus on stealing business or work from one another rather than from competing firms. Firms may implement an alternative compensation system, team-based commissions, in order to reduce these problems. If individual production is not easily divisible, and instead enjoys benefits from cooperation and coordination, rewarding individual effort may be difficult. Firms cannot directly observe effort or productivity at the individual level, and therefore may be unable to provide high-powered individual-based commissions. Under teambased compensation systems, teammates have strong incentives to improve not only their own productivity but also the productivity of their peers. This compensation system encourages workers to internalize their production externalities. Firms must still worry about individual workers free-riding on their team members, but the ability of these teammates to locally observe effort and enforce compliance through social pressure may be possible. 9

10 Individual and team-based compensation systems therefore have different implications for productivity spillovers. In an individual-based system, high-ability workers will have no incentive to help other workers or to produce positive production externalities. Furthermore, under conditions of scarce resources or customers, individually-compensated workers may compete with one another to secure higher compensation, and due to their high ability, will likely succeed. While some learning or motivational effects may still occur, productivity spillovers are likely to be small or even negative. In a team-based system, high-ability workers have strong incentives to help other workers through teaching, coordination, and motivation. Furthermore, they have no incentive to compete with other workers, since the total of all team members productivity becomes the relevant metric for compensation. Compensation system may also have a considerable effect on spillovers across firm boundaries, as it will determine the amount of effort that workers will devote to competition with outside competitors. In individual-based systems, workers must allocate effort to compete with peers both inside and outside the firm. This within-firm competition limits the effort that can be focused on cross-firm competition. Consequently, high-ability workers in individual-based firms are likely to have less impact on their outside peers than would high-ability workers at teambased firms, who are free to devote all their effort on external competition. Similarly, workers in individual-based firms are more vulnerable to high-ability peers in competing firms than those in team-based systems, since they can devote less effort to this competition. 3. Cosmetic Sales in a Chinese Department Store We study peer effects in the context of team cosmetic sales in a department store in a large metropolitan area in Eastern China. This department store is one of the largest in China in 10

11 both sales and profit, and sells a wide range of products including apparel, jewelry, watches, home furnishings, appliances, electronics, toys, and food. One of its largest categories is cosmetics, the fifth largest consumer market in China with annual sales of $85 billion in The department store has 15 major brands in the cosmetics department, with each occupying a counter in the same floor area. These brands hire their own workers to promote and sell their products, while paying the department store a share of their revenues. The cosmetics floor effectively becomes an open market, with multiple firms competing for customers in a shared space. The department store manages the arrangement of the counters as well as the staffing of the manufacturers employees. We observe each individual cosmetic sale for 11 of the 15 counters over the period. The floor plan and location of these counters is presented in Figure 1. Figure 1: Cosmetics Floor Layout in a Chinese Department Store 2 Data from the Victorian Government Business Office. 11

12 Sixty-one female salespeople, hired by the individual brands, work in one of three overlapping shifts during the seven days per week the department store is open. First shift is from 9am to 3pm, second shift is 12pm to 6pm, and third shift is 3pm to 9pm. While workers work an average of six hours per day, they often exceed this amount on peak weekends and holidays. Since shifts are overlapping, workers need not work the same shift in a given day to share the counter. Salespeople typically rotate shifts that are assigned by the department store manager. For example, if a salesperson works the first shift on Monday, she will typically work second or third shift on Tuesday. This scheduling process, while not completely random, ensures that each salesperson will rotate workdays and times, and thereby share their shifts with a variety of their peers. In interviews with the department store manager, we observed no strategic scheduling of workers with either certain peers or during specific shifts or days of the week. One of the interesting aspects of this store is that the individual brands use two different compensation systems: team-based commissions (TC) and individual-based commissions (IC). The four brands using TC pay each worker monthly based on a tiered percentage of the monthly sales. As sales increase, the percentage commission grows. If team pay were calculated daily, then workers might decide how much to free-ride each day based on the expected productivity of their concurrently-scheduled workers. But since pay is calculated monthly and worker staffing over the month is equally distributed, each worker s compensation is based approximately equally on each peer working that month. This means that on any day, the decision to free-ride on coworkers should remain independent of concurrently scheduled peers. In essence, the common problem of free-riding in team-based compensation is independent of scheduling, and therefore unrelated with temporal peer effects. But in TC counters, whom you work with may 12

13 still be important for your own productivity. Coordination, specialization, and learning may make skilled coworkers a boon for your own individual sales. The other seven brands that we observe use individual-based commissions. 3 In these counters, workers are compensated based on an increasing tiered percentage of personal sales. Highly productive workers earn higher incomes than do low productivity workers. IC counters do not suffer from problems of free-riding, but may suffer instead from two afflictions. First, coworkers are incentivized to directly compete with one another for customers, despite representing the same brand. They may therefore focus on stealing business from one another rather than from competing brands. Second, workers have little incentive to coordinate with peers, or to work to reduce negative production externalities within the counter. Thus, while IC reduces free-riding, it creates within-counter competition potentially detrimental to the firm. In IC counters, whom you work with also matters, because they represent your competition and the source of production externalities. The nature of sales competition, whether within or across counters, is further nuanced by another interesting feature of the department store. Individual sales people in all counters have discretion to discount products from their retail prices. On average, discounting averages about 2.5% of the daily sales revenues across all counters, but this percentage is highly heterogeneous for each counter. This pricing policy is used for several reasons. First, haggling over prices is a culturally standard practice in China important in traditional market settings. Second, discretionary discounting allows skilled salespeople to use local knowledge to price discriminate and build long-term relationships with customers. It also allows them to better respond to the actions of coworkers and temporal adjustments in the market. While discretionary discounting may serve several valuable purposes, it also produces potentially problematic incentives in IC 3 The four counters for which do not have sales data also use individual-based compensation. 13

14 counters. Under individual-based compensation, workers compete against coworkers, and may do so by discounting prices. Workers within IC counters may therefore end up in an internecine price war that approximates undifferentiated Bertrand competition. This contrasts with TC counters, where workers can price based on cross-counter competition. While price competition may still occur across counters, this will be less severe due to the differentiated nature of brandbased cosmetics. Given this discretionary pricing, workers can use two important levers to increase their sales. First, they can increase their effort, which will lead to increased sales. Second, they can discount prices, which also will increase sales. In an IC counter, workers must allocate a limited amount of effort between competing with peers within their own brand and those at competing counters. In contrast, TC workers can focus all of their effort toward competing with peers at other counters. Similarly, IC workers must compete on prices both with peers at other counters and peers selling their own brand. TC workers will price only in competition with other brands. Given the differentiated nature of branded cosmetics, price competition across counters will likely be less severe than within counters. Salespeople can also alter their behavior in several other ways to account for the changing quality of peers. First, they can alter which types of products they focus on. If a highability peer is likely to focus on high-value products because of their superior revenue potential, the worker may choose to differentiate by focusing on selling lower-value products. Similarly, workers may focus on high-value repeat customers, since these customers may have some loyalty specifically to that salesperson. 14

15 Cosmetic Sales Data When an individual salesperson sells products to a customer, the cashier records the identity of that salesperson. The product types, quantities, prices, and the discount given in that sale, as well as time of transaction are also recorded in the sales database. This careful sales tracking provides the store with detailed information about every cosmetic sale in each of its brands, and also details the sales productivity of each worker in a given shift. That sales productivity will depend on a number of time-varying factors, such as the time of day, day of the week, time of the year, weather, and other exogenous factors. Sales productivity will also depend on worker specific factors. Salesperson skill or ability will influence average productivity levels, while time-specific factors such as mental and physical health, effort, and customer type may also affect specific workers. Since salespeople on average work in teams, the skills and effort of coworkers will also alter a worker s sales productivity. As explained above, this peer effect will likely depend on the compensation system of the counter. Furthermore, since workers compete with peers at other counters, productivity will also likely depend on the skills and effort of those outside peers. Details of the department store s cosmetic sales are presented in Table 1 and Table 2. Of the 11 counters in our data, four use team-based commissions and 7 use individual-based commissions. There is considerable heterogeneity in counter size. The largest brand has ten salespeople, while the smallest has three. Annual sales revenue ranges from $43,763 (US) to $631,073, with product prices from $0.11 to $ Team-based counters generally have larger total sales but lower average prices. Salespeople work alone roughly 30% percent of the time. For the smaller counters we occasionally observe all workers staffed simultaneously. This is likely due to workers staffing 15

16 multiple shifts on high volume days. We observe sales for 791 days between November 1, 2004 and December 31, During this period, no counters change compensation system, and there is 18% turnover among the workers. We cannot directly observe worker scheduling, but instead identify it by observing sales times. Although 52% of all hours involve no sales, shifts are constant and hence we assume that if we observe worker sales during a given shift, then that worker was also present during the hours without sales. Since brands did not change compensation system during our sample period, we are unable to observe any treatment effect from compensation. Consequently, we cannot analyze whether or not a brand s choice of compensation system is indeed optimal for them. Instead, we focus on how a salesperson s productivity is affected by those peers who work concurrently, conditional on compensation system. Similarly, we are unable to observe the selection of workers into employment with any given brand. It is doubtful that this selection is entirely random, with certain workers attracted to specific brands and vice versa. We must instead focus on how worker productivity is influenced by concurrently working peers, conditional on the pool of peers hired in the store. Commission Contract Table 1: Descriptive Statistics of Cosmetic Counters Annual Sales Revenue (US$) Product Price (US$) Average Transaction Size (Units) Average Price Discount Min Max Mean Brand 1 IC 631, % Brand 2 TC 626, % Brand 3 TC 553, % Brand 4 TC 229, % Brand 5 TC 108, % Brand 6 IC 142, % Brand 7 IC 285, % Brand 8 IC 43, % Brand 9 IC 195, % Brand 10 IC 133, % Brand 11 IC 128, % Total 3,078, % 16

17 Table 2: Team Size # of Team Size Salesperson Min Max Mean Brand Brand Brand Brand Brand Brand Brand Brand Brand Brand Brand Modeling Peer Effects Within and Across Counters The goal of our empirical analysis is to identify how the ability of concurrently working salespeople at the same and competing counters influences the temporal productivity of the worker. Similar to Mas and Moretti (2009), we define ability in terms of permanent productivity, or the average productivity of a given worker across time while controlling for time- and firm-specific factors. Our model differs from prior models of peer effects in three ways. First, we identify how the peer s ability relative to the focal worker influences their temporal productivity. In other words, our approach assumes that a high-ability worker influences a peer only if that peer is not of equally high ability. We believe that looking at relative, instead of absolute, productivity from peers is more reasonable especially when considering competition across counters. Suppose the peer worker has average productivity. Her impact on a highly productive worker is the same as on a non-productive worker if we only look at absolute productivity; however, our relative model allows that impact to be different on the 17

18 two co-workers. 4 Second, given our interest in the role of compensation systems on the peer effects, we estimate two separate within-counter peer effects for IC and TC counters. Lastly, our model also considers four additional across-counter effects from competing IC counters on IC counters, competing TC counters on IC counters, competing IC counters on TC counters, and finally competing TC counters on TC counters. 4.1 Econometric Specification As we have discussed, salespeople in our data work in overlapping shifts, such that a worker could work with different co-workers during different hours of her day. Taking this coworker variation into account, we begin by specifying how a salesperson s productivity is affected by her co-workers at the hour level. We assume that in any given hour, an individual s productivity is a function of the average productivity of all coworkers within and across counters relative to her. For a salesperson j working for brand i, her hourly productivity in hour h of a day, y, is specified as: y =y + γ 1 i IC +γ 1 i TC y y N 1 ; + γ 1 i IC +γ 1 i TC N y y + γ 1 i IC +γ 1 i TC N y y +Z β+ε 1 In the specification, y is measured by salesperson s dollar sales in each hour. This is consistent with the fact that in our empirical setting, a salesperson is compensated based on either her revenue sales (in IC counters) or the total revenue sales of her team (in TC counters). 5 4 We also estimate a model using absolute productivity of peers within and across counters and find that results are qualitatively very similar. 5 Alternatively we may use unit sales or number of customers served as measurement for productivity ; however, given that price of cosmetic products and total value of transaction across customers have large variations such 18

19 The worker s fixed effect y is a parameter to be estimated. It captures the worker s ability or skill-based permanent productivity, which in our setting can be interpreted as her time-invariant hourly dollar sales. The variables 1 i IC and 1 i TC are indicators that brand i is an IC counter or a TC counter, and N, N, and N denote the total number of workers working in i s own counter, in competing IC counters, and in competing TC counters at hour h, respectively. A counter is defined as competing if it is adjacent to the counter of worker j in any direction. For example, counter 1 in Figure 1 would have three competing counters: 2, 3, and 8. Thus, ; represents the average of the relative permanent productivities of all other active salespeople at worker j s counter in hour h, the average relative permanent productivity of all active peers of IC-based competing counters, and the average relative permanent productivity of all peers working for TC-based competing counters, in hour h. Z h is a vector of control variables that may affect sales. Finally, ε is an error term. Equation (1) describes productivity determinants in an environment where peer effects may operate both within and across counters and may also be linked to the compensation system used by each counter. These potential peer effects are captured by the γ parameters. Parameters γ 1 and γ 2 represent the within-counter peer effects for IC and TC counters, respectively. γ 3 and γ 4 measure the peer effects from workers at IC-based competing counters on salespeople at IC and TC counters, respectively. γ 5 and γ 6 measure the peer effects from peers who work at TC-based competing counters on salespeople at IC and TC counters, respectively. measurements may be very misleading. For example, a high-productivity worker may focus on serving high-value customers or selling high-priced products. Using such measurements may erroneously identify her as having lowproductivity. 19

20 Figure 2 provides a visual representation of the peer effects for four counters taken from Figure 1. These are competing counters as they are adjacent to each other. We represent the peer effects on two focal workers, worker A from counter 2 and worker B from counter 8, from both within and across counters. Blue represents TC counters, while red represent IC counters. Arrows from each worker to the focal workers represent the peer effects based on the permanent productivity of the eight workers. For worker A at TC counter, her peer effects are measured by γ 2 from a within-counter co-worker, γ 4 from the average relative productivity of four other coworkers from competing IC counters, and γ 6 from the average relative productivity of two other coworkers from competing TC counters. Similarly the peer effects on worker B at IC counter are measured by γ 1, γ 3, and γ 5. Figure 2: Within and Across-Counter Peer Effects 20

21 Specifying how a salesperson s productivity is affected by her co-workers at the hour level serves as the building block of our model. We then aggregate the data to the daily level used for model estimation. This is because in a market environment like our setting, selling cosmetics product usually takes effort and time (we learned from an interview with the manager that to serve a single customer can take more than an hour in the store). As a result, hourly sales may not capture contemporary peer effects. A model using daily sales to capture peer effects in the same day will provide a better measurement. Assume that on day t, salesperson j works for T hours. We sum up T equations as in (1) that becomes the following: y = T y + γ 1 i IC +γ 1 i TC y y N 1 ; + γ 1 i IC +γ 1 i TC N y y + γ 1 i IC +γ 1 i TC N y y + Z β +e 2 Where e = ε. is a vector of control variables that may affect sales, including year (Year 2 and Year 3), month (February December), and day of week (Monday through Saturday) indicators. With simple algebraic manipulation equation (2) can be re-written as: 21

22 y =[T γ 1 i IC +γ 1 i TC 1 N 1 ; γ 1 i IC +γ 1 i TC 1 N γ 1 i IC +γ 1 i TC 1 N ]y + γ 1 i IC +γ 1 i TC 1 y N 1 ; + γ 1 i IC +γ 1 i TC 1 N y + γ 1 i IC +γ 1 i TC 1 N y + Z β +e 3 where denotes the set of counter i s IC-based competing counters, and the set of i s TCbased competing counters, respectively. The notation h Tlt Tjt in (3) denotes the hour in which worker j and her coworker l working in the same hour on day t. Note that, conditional on parameters γ s, equation (3) is linear in the fixed effects y 's of all workers in the store. This is the model we estimate. 4.2 Model Estimation Equation (3) is a non-linear model since the salespersons fixed effects y 's are multiplied by the peer effects γ s. A straightforward approach would be to estimate all the parameters together using a numerical search method; however, this method is computationally 22

23 burdensome due to the number of parameters (61 worker fixed effects, γ s and β s) that must be estimated. Even if this were computationally feasible, the existence of local minima in the search process could still produce spurious results. An alternative estimation strategy is to separately estimate worker fixed effects y 's and other parameters (γ s and β s) in two stages. This is the methodology adopted by some previous productivity spillover studies (Pierce and Snyder 2008; Mas and Moretti 2009). This approach first estimates all the fixed effects accounting for potential peer effects that are a linear function of the indicators of all possible pairs of coworkers; in the second stage the estimated fixed effects are plugged into a counterpart of equation (3) in our model to estimate other parameters. While it may reduce the computational burden, applying this method in our context raises an efficiency issue. The data requirement is very high to estimate the fixed effects in the first stage. The method estimates each worker s fixed effect by including the pairing with all other coworkers using a non-parametric approach, which requires large number of observations for each possible pairing of workers both within and across counters. Many coworker pairs occur only a few times in our data; that may lead to large standard errors for our fixed effects estimates if we directly apply this method. In this paper we propose a nested optimization procedure to simultaneously estimate all parameters in equation (3) that is easy to implement and generates more efficient estimators than the two-stage estimation approach. The idea comes from the observation that, conditional on γ s, equation (3) is linear in y 's. Specifically, let Γ=(γ 1,,γ 6 ), and let 23

24 x Γ =[T γ 1 i IC +γ 1 i TC γ 1 i IC +γ 1 i TC ], ; x Γ = γ 1 i IC +γ 1 i TC, x Γ = γ 1 i IC +γ 1 i TC γ 1 i IC +γ 1 i TC, and x Γ = γ 1 i IC +γ 1 i TC, equation (3) can be re-written as y =x Γ y + x Γ y + x Γ y + x Γ y + Z β+e 4 ; We therefore start our estimation by choosing some initial values for γ s and estimate y 's. As such, the model can be estimated with standard linear methods to find the optimal y 's. Standard numerical minimization routines then can be used to search for the optimal γ s. In our implementation, we use OLS to estimate y 's conditional on γ s, and the Nelder-Mead (1965) simplex method to search for the optimal γ s that minimize the sum of squared errors as the criterion function value. Convergence is very fast using such routines given that the dimension of γ s is only six in our model. Finally we compute robust standard errors for our estimated parameters accounting for the existence of heteroscedasticity in error terms e ijt. 4.3 Identification Although our setting involves counters with different compensation systems, none of them change pay policies during the period of our data. Unlike Lazear (2000) and Hamilton, Nickerson and Owan (2003), we are therefore unable to identify how a change in compensation 24

25 system can alter worker behavior. In contrast, our setting is able to identify how changes in the mix of co-scheduled workers can impact individual and team productivity across multiple compensation systems in the presence of firm competition. Since workers at each counter are constantly changing with each shift, the combination of workers at any given time varies. Sometimes we will observe high-ability workers with other high-ability workers, and sometimes they will be with low-ability peers. This identification strategy relies on the assumption that workers are distributed approximately randomly with their peers, that is, that high-ability workers are not more commonly scheduled with low-ability peers than high-ability peers, and vice versa. While interviews with management suggest that worker assignment is independent of ability, we verify this by looking at the frequency of any two workers being concurrently scheduled. Table 3 presents the results of a brand-based chi-squared test of the null hypothesis that all worker pairings are equally frequent. Because salesperson turnover exists in our data, we separately identify coworker pairings for each brand every month. We count the number of observations for every possible pairing of salespeople (i.e., the number of times each pair of worker working together), and compare with the expected number of parings under the null hypothesis of random shift assignments. We are unable to reject this null hypothesis at the 10% level for any brand, supporting our assertion that workers are not systematically scheduled based on ability. 25

26 Table 3: Selection Tests of Worker Assignment Pearson's Chi- Square Test Statistic The 10% Critical Value of the Corresponding df Degrees of Brand Freedom (df) Brand No Brand No Brand No Brand No Brand No Brand No Brand No Brand No Brand No Brand No Brand No H 0 Rejected? One might still be concerned about that the team formation is different during different time of a day. For example, more productive workers may be systematically scheduled to work together at times of the day when demand spikes upwards. We follow the method in Mas and Moretti (2009) to examine the relationship between the number of personnel on duty and the average ability of workers. A positive relationship between the net change in personnel and the change in average permanent productivity of workers may suggest that higher ability workers will add to the shift when demand is rising. We compare this relationship across consecutive 1- hour periods for each counter, and find small change in the average permanent productivity when the number of workers increases or decreases by one. A t-test reveals that we cannot reject the null hypothesis that there is no change in average productivity at.05 significance level. 4.4 Estimation Results Table 4 reports the estimated peer effects, showing considerable productivity spillovers both within and across counters. Furthermore, these results identify key differences between IC 26

27 and TC counters. Within IC counters, peer effects ( ) are negative, indicating that a worker s productivity drops by 29% of the increased quality her coworkers. This suggests that a better coworker at IC counter has the incentive to compete with and steal sales from peers at her own counter. In contrast, peer effects (γ 2 ) within TC are positive, suggesting that better workers may improve their peers sales. While this result is consistent with specialization or coordination mechanisms, it is small in magnitude and only marginally significant. We can only safely conclude that high-ability workers in TC counters do not hurt the productivity of their peers. Table 4: Peer Effect Estimates Within and Across Counters IC Within-Counter Peer Effect (γ 1 ) TC Within-Count Peer Effect (γ 2 ) IC Peer Effect on IC (γ 3 ) IC Peer Effect on TC (γ 4 ) TC Peer Effect on IC (γ 5 ) TC Peer Effect on TC (γ 6 ) -.286*** *** -.060* -.515*** -.217*** (-0.026) (-0.034) (-0.022) (-0.023) (-0.046) (-0.034) Robust standard errors are reported in parentheses. Peer effects also exist across counters. Estimates of γ 3 to γ 6 are all significantly negative, showing that the quality of peers at competing counters reduces sales revenue, a result consistent with models of competition. But the magnitude of these competition peer effects is highly dependent on the compensation system of both the focal and peer worker. The sales of IC workers are consistently hurt more by high-ability peers at competing counters than are their TC counterparts. While high-productivity IC workers reduce sales of outside IC peers (γ 3 ) by 20% of their increased productivity, they have little effect (6%) on their TC (γ 4 ) peers. Similarly, while the spillover effect of TC workers on IC peers (γ 5 ) is about -52%, this peer effect is considerably smaller for outside TC peers (γ 6 ) at -22%. Further, TC workers have more influence on their outside peers than do IC workers (the magnitude of γ 5 is larger than γ 3 and 27

28 γ 6 larger than γ 4 ). The sum of these results suggests that TC counters are much better at competing with high-ability peers at other counters than are IC counters. This is consistent with the explanation that workers at IC counters focus much of their effort on within-brand competition, leaving little effort for cross-brand competition. TC workers, having no incentive to compete within the brand, can focus more effort on competing with other counters. Figure 3 shows the distribution of estimated worker fixed effects, and Table 5 presents summary statistics of the average fixed effects for each brand, and compares the average fixed effects under the two compensation systems. There is considerable variation in permanent worker productivity, and although the variation is much greater in some brands than others, this does not appear to be correlated with compensation system. It is important to note that we cannot directly observe one of the key costs of TC: free-riding. The reported fixed effects are a mix of workers own productivity, brand fixed effects and the overall effect on workers incentive of investing sales effort from individual- and team-based compensations. We cannot separately identify these three factors since brands do not change compensation system during our sample period. We must therefore be careful not to interpret our findings above as suggesting that TC counters are more productive than IC counters. 28

29 Figure 3: Distribution of Workers Permanent Productivities Kernel Density Estimate Density Productivity kernel = epanechnikov, bandwidth = Table 5: Worker Permanent Productivity by Brand Salesperson Permanent Productivity Mean S.D. Min Max Brand Brand Brand Brand Brand Brand Brand Brand Brand Brand Brand IC Counters TC Counters Overall