Endogenous Pricing and Multitasking: A Sales Agents Contract

Transcription

1 Endogenous Pricing and Multitasking: A Sales Agents Contract Maria D. Palacios March 2017 Abstract I construct and use a new database to analyze the implications of a change in the contract of sales employees on their behavior. An important feature of the firm in question is that sales workers set prices (p) and are payed a share of sales or revenues (p q). Before the change, sales agents receive a fixed share of the sales they make. With the new contract, the share of revenues payed to workers increases as the price-cost margin ((p c)/p) of the product sold increases. Particularly, I analyze two interesting features that the contract change gives rise to: an increase in average price and a shift in workers effort toward activities that are more compensated and away from the less compensated ones (i.e., toward products with a demand that allows higher price-cost margins). First, I find that weekly average price and profits increase 9% after the announcement of the new contract, while there is no effect on quantity sold. Second, in line with theoretical predictions from the simple model developed, I provide evidence that workers reallocate effort toward the sales of high-margin goods and away from low-margin ones even if financial incentives increase for all products sold. I am grateful to Kevin Lang, Jordi Jaumandreu, Andrew Newman, Claudia Olivetti and Marc Rysman for helpful discussions and to participants in the Boston University micro dissertation workshop for their comments and suggestions. Boston University. doloresp@bu.edu.

2 I Introduction Both theoretical and empirical research indicate that in general stronger financial incentives bring about higher effort from workers. But what happens in a context where sales employees have two tools to influence demand, in a context where they decide how much effort to exert and are in charge of setting prices? What is the optimal effort and price when workers are rewarded based on sales revenues? How do employees adjust their behavior if we change the compensation structure by increasing financial incentives as the price price-cost margin 1 ( p c ) of a sale increases? Finally, in a multi-product firm would there be a differential p effect between goods that have distinct demands and therefore different optimal price-cost margins? A new administrative dataset collected from a Mexican firm specialized in selling electrical products that changed the contract of its sales employees allows me to delve into these questions. The firm studied changed sales workers compensation scheme from a linear wage contract to a piecewise linear one. Prior to the change workers received a fixed commission 2 on the revenue of each sale. With the new incentives scheme commissions can take four different values and increase as the price-cost margin of the sale increases. For most transactions the new contract implies that workers receive a higher commission than before, so in general financial incentives are stronger. I abstract from the optimal contract choice problem and focus on the workers response to the change in incentives. An important feature of the firm in question is that sales workers set the price of each sale (as long as it is larger or equal to the cost of the product sold). To guide the analysis of the effect of the contract change, first I develop a simple theoretical model in which I assume that workers influence demand by choosing an unobserved effort level and the price for each sale. By solving the workers maximization problem it becomes clear that price is an increasing function of effort. The new contract brings about an increase in the optimal effort level and therefore in the price chosen by sales employees. The theoretical framework allows me to also draw conclusions on profits and quantities. This study contributes to the development of the organizational industrial organization (OIO) literature as described by Legros and Newman (2014) by exploring the relationship between organizational design (a change in workers wage contract) and traditional industrial organization (IO) variables: price, profits and quantity. With the firm selling multiple products we can also investigate how stronger financial incentives affect the allocation of effort between tasks. Understanding how incentive contracts 1 The price-cost margin is the price minus the cost over the price, p c p. This ratio is also known as the Lerner Index. In the remainder of the paper I refer to this index as the price-cost margin or margin which is the term employed by the firm. 2 I refer to commission as the percentage of revenue that the employee receives as part of her wage. 1

3 affect agents effort allocation in different dimensions is an important step in the study of contract design when there are multiple tasks involved. The theory on this matter is well established. In the model by Holmstrom and Milgrom (1991), the principal is concerned not just with the overall level of effort but also with how the agent allocates effort across the various tasks. When the components of tasks are substitutes the principal needs to take into account how offering stronger incentives on one task will affect the agent s effort allocation on other tasks. Stronger financial incentives could, for instance, result in a reallocation of activities toward those that are more compensated and away from the less compensated ones (Prendergast, 1999). Yet, empirical work is far behind multitasking theory and not all studies have found support for the theoretical predictions. I also contribute to this literature by providing empirical evidence that stronger financial incentives do not imply higher effort for all tasks in a multitasking context. More specifically, I show that sales employees decrease effort on the sales of certain types of products even when on average financial incentives increase for all goods sold. The theoretical predictions when the payment scheme changes on price and profits are different depending on the assumptions about the interaction of efforts allocated to each task. On the one hand, if efforts are independently costly, the new contract increases workers effort and both price and profits for every product increase. Alternatively, if efforts are substitutes for workers, with the new incentives scheme employees reallocate effort between tasks decreasing price and profits of products that usually have low-margins and increasing price and profits of products that usually have high-margins. A complex feature of the context studied for the multitasking analysis is that price, and therefore price-cost margin, is endogenous. But, an attractive feature is that performance on different tasks (sales of different products) is measurable. The empirical analysis is based on data from all twelve stores of the Mexican company. The effects, that are estimated by examining the behavior of 75 workers over 103 weeks are in line with the theoretical framework s predictions. First, the switch to the piecewise pay has a positive and significant effect on average price and profits per worker. Second, I find evidence on effort reallocation from low-margin products to high-margin ones. Due to the new payment scheme the price of high-margin products increases more than 20% while the price of low-margin goods decreases about 10%. The effects on profits are also consistent with the model. For high-margin products, profits increase around 14%, while for low-margin goods profits decrease about 14%. The remainder of the paper is organized as follows. After a brief literature review, Section II describes the institutional context of the firm and discusses in more detail the change in the wage contract. Section III proposes a theoretical framework and establishes testable predictions of the contract change for the non-multitasking and multitasking cases. Section IV presents the data and descriptive evidence on the effect of the new scheme on average 2

4 price and profits. Section V formalizes the analysis and uses worker level data to estimate the effect of the new policy on workers performance. Section VI, presents some robustness checks. Finally, section VI concludes. I.A Literature Review There are two literatures that I briefly discuss: (1) on the effect of incentives on workers behavior and (2) on the relationship between organizational design and traditional IO variables such as price and quantity. On the one hand, there is a large literature that studies the effect of incentives on employees behavior. For a more complete review on hiring and incentives see Oyer and Schaefer (2011) or Lazear and Oyer (2013). Several empirical studies in personnel economics examine the effect of a particular choice of payment scheme on output or productivity and conclude that financial incentives modify workers behavior. For example, Lazear (2000) analyzes the effect of the introduction of a piece rate contract on both effort and worker selection. He reports that piece rate system increases productivity by about 44%. This gain comes from two sources: an increase in individual level-productivity as a result of the stronger incentives and self-selection of more productive workers into the firm s workforce. Following the seminal work by Lazear (2000) there are other empirical papers that use firm level data to analyze the effect of compensation contracts. Shearer (2004) shows that piece rates affect the productivity of tree planters in British Columbia. He finds that workers paid through a piece rate are approximately 20% more productive than those paid by the hour. Bandiera et al. (2009) also present evidence that incentives change employees behavior. They study a change in managerial incentives in an English fruitpicking operation. When managers are paid using fixed wages, they tend to favor workers with whom they are socially connected. However, when managers get paid on a bonus based on the overall output, managers change their behavior and begin favoring the most able workers. This increases both the mean and dispersion of worker productivity. These are only some examples of studies that show that financial incentives do change behavior in organizations and that indicate that stronger financial incentives induce employees to improve measured performance. Nonetheless there is also a large literature on unintended consequences of financial incentives. For instance, Oyer (1998) show that since firms often base their incentives on a fiscal year, salespeople and executive workers have incentives to manipulate prices, influencing the timing of customers purchases, and vary effort over their firm s fiscal year. For example, a salesperson who is under pressure to meet a quota near the end of the year may offer a customer a bigger price discount if the client orders immediately. He shows that, indeed firms tend to sell more (and at lower margins) near the end of fiscal years than they do in the middle of the year. 3

5 Larkin (2014), investigates pricing distortions that arise from the use of non-linear incentive schemes. He uses data from a large software company and finds that salespeople adjust the timing of deal closure to take advantage of the firm s accelerating commission scheme. Specifically, salespeople significantly cut prices in the quarter where they have a financial incentive to close a deal. He estimates that such behavior costs the firm between 6 and 8% of potential revenue. A particularly complex context in which financial incentives can bring about undesirable consequences is when the agent performs different tasks. The multitasking problem is well described by Holmstrom and Milgrom (1991) and Baker (1992). Paarsch and Shearer (2000) suggest that, for a British Columbia tree-planting firm, the change from fixed wages to piece rates caused a 22.6% increase in productivity but that workers also respond to incentives by reducing quality. Feng Lu (2012) shows that after the introduction of a mandatory quality disclosure policy in the nursing home industry, the Nursing Home Quality Initiative (NHQI), scores of quality measures improve for the publicly reported dimensions but deteriorate for the unreported ones. Finally, Hong et al. (2013) test the theory of multitasking using a field experiment in Chinese factories. They find that as a result of a piece rate bonus scheme, workers trade off quantity at the expense of quality. However, in the experiments described by Shearer (2004) and Bandiera et al. (2005) the authors find no evidence that agents disregard activities that are not rewarded. Although, Shearer (2004) is not aiming at directly testing multitasking, his study suggests that there is no difference in quality under two compensation systems: fixed wages and a piece rate contract. Bandiera et al. (2005) compare productivity under a piece rate and under a relative incentives scheme (where individual effort imposes a negative externality on others) in a fruit farm. They also find that the higher productivity of the piece rate scheme does not come at the expense of the quality of fruit picked. My paper contributes to the literature by providing empirical evidence in line with multitasking theory: in the firm studied stronger financial incentives bring about a reallocation of effort between tasks. 3 Interestingly, rewards increase for all tasks but there is still a decline in the effort allocated to one of the tasks. On the other hand, the literature on organizational industrial organization (OIO) as described by Legros and Newman (2014) is at an earlier stage (see their paper for a more comprehensive review). The authors argue that a complete theory of the relationship between organizational design and traditional IO variables such as price, quantity, or welfare has yet to be developed. One of the main matters reviewed in their paper is the effect of market competition for incentive provision and strategic decisions. The competitive context of the industry is key for understanding the organizational decisions of a particular firm such as financial incentives and delegation. Fershtman and Judd (1987) is one of the first papers 3 Even if I do not describe any of the consequences observed as undesirable. 4

6 to consider incentives schemes in an oligopoly context. Owners delegate strategic decisions to managers who, in turn, receive as compensation a convex combination of profit and sales. The Cournot-quantity game described rationalizes the decision of owners to deviate from a profit sharing incentives scheme. In other papers (such as Wickelgren (2005) and Alonso et al. (2008)), the authors suggest that it might be desirable to allow managers to choose prices either because it gives them better incentives to exert unobservable effort that increases profits when there is intra-firm competition or because demand conditions are privately observed by local managers. In addition to setting prices agents might be able to undertake non-price actions that influence demand. As described by Wickelgren (2005) and Sæthre (2016), in several markets sellers impact consumer choice through channels other than price, such as quality, marketing or other unobservable measures that require effort. Sæthre (2016) argues that when these unobservable actions are correlated with profit margins, estimating demand using standard methods (i.e.: instrumenting for price using cost) yields biased estimates; and he proposes a model to infer non-price actions of the firms. Although not developed by the author, the idea that unobservable effort influences demand can also have important considerations for organizational design. I also contribute to the OIO literature by providing an empirical analysis of a firm that switches from rewarding workers based on revenues to rewarding them based both on sales and profit. Moreover, the firm in question delegates pricing decisions to sales workers. Similarly to Wickelgren (2005) and Sæthre (2016), I consider a model that allows for unobservable actions or effort that influence demand. Still, even if we share this conceptual feature, my paper focuses on understanding the behavioral change of workers after their contract is modified and not on intra-firm competition or demand estimation. With the theoretical framework developed and the data collected from the natural experiment used, I analyze how the change in workers incentives affected the firm s price, profits and quantity, linking organizational design to traditional IO variables. II II.A Context and the Incentives Change Context The firm studied is a branch of an international company specialized in distribution of electrical products and related services. The period that is analyzed in this study is During these two years the firm was divided into twelve storehouses across the Latin 4 I exclude the first week of 2008 because it is incomplete. 5

7 American country in which it operated, had around 250 workers and sold almost 18,000 different products. Since then the company has been rapidly growing in terms of sales and number of employees and is currently one of the most important electrical distributors in the country. At the end of June 2008, the wage contract for sales personnel was modified. The goal of this paper is to understand the effect that this change in workers financial incentives had on their behavior. The company s sales workforce consists of two main types of workers: sales agents and counter employees. Sales agents have a portfolio of clients allocated to them whom they visit constantly. Counter employees, in contrast, work in a store and are in charge of selling products to any incoming client. Every storehouse has a sales manager to which all workers report. I study the performance of sales agents and exclude counter employees from the analysis because they have a very different incentive scheme and cannot influence price. An important characteristic of this firm is that sales agents can modify the price at which they sell each product, as long as the price is greater or equal than the cost of the product. 5 Thus, agents can affect the profit made in each transaction. From now on I refer to sales agents indistinctly as employees or workers. II.B The Contract Change As in many companies, under the original incentives scheme sales workers received as payment a fixed salary and a commission on the revenues they made from sales. In order to induce higher effort, employees base wage was low compared to the income they received from commissions, and still is after the change. Before mid-2008, sales commissions were a fixed percentage of the client s payment. 6 In 2008 this scheme changed. Now, the commission percentage varies among transactions 7 and increases as the price-cost margin ((p c)/p) of the transaction increases. This policy was implemented in order to encourage sales employees to protect profits. At the same time, a minimum quota requirement was introduced establishing that workers need to satisfy a monthly quota in order to be in good standing (i.e. every month workers need to sell at least x dollars). Failure to meet the quota in several successive months may result in termination of employment. However, although the concept of the quota was introduced in 2008 it was not enforced until the end of Promotions for sales workers are very 5 In some very particular cases sales can be arranged below cost (if it is part of a bargaining strategy with a client, for instance), but approval from upper-level management is needed. 6 Sales workers get paid as long as the customers they sell the products to pay the firm what they owe; no payment by the client means no commission for sales employees. 7 One transaction is composed of a sale of one product at one price to a given client, i.e.: the sale of five light-bulbs for $1 per light-bulb to client A is one transaction. 6

8 rare. Thus, the main tool for aligning sales personnel incentives in this company is the commissions scheme. The monthly wage w(p, q), as before, has a fixed component s and a variable one j b j(p j q j ) where b is the commission specified by the firm, p is price, q is quantity and j denotes each transaction. Such that: J w(p, q) = s + b j (p j q j ) With the introduction of the new contract, the sales workers wage went from having a fixed commission for all transactions to a piecewise linear one. Thus, with the old contract: j=1 b j = b, j With the new contract, the commission for each transaction depends on the price-cost margin of that transaction: b j = b A b B b C b D if p j c j p j < x if x < p j c j p j x + k 1 if x + k 1 < p j c j p j x + k 2 if x + k 2 < p j c j p j where b A < b B < b < b C < b D. With the new payment structure: a higher price-cost margin translates into a higher commission. Also, if the price-cost margin of the transaction is above x + k 1, compared to the previous scheme, workers receive a higher commission. On the other hand, if the price-cost margin of the transaction is below x + k 1 with the new contract workers get paid a lower commission than before. It is important to mention that workers do not negotiate the provision of goods to the firm so cannot directly affect costs. This implies that they can only modify margins by changing the price. III Theoretical Framework The basis of the theoretical framework developed in this section is the classical moral hazard model, where there is an agent (the sales worker) who takes action or chooses an effort level to generate output and a principal (the firm) who owns the output. The principal specifies a contract to share the output with the agent by paying a wage that depends on output 7

9 (Gibbons, 2005). The main difference with the basic principal-agent model is that I allow the agent to decide not only effort but also price of each sale. More precisely, the timing of events is the following: 1. The principal and the agent sign a compensation contract w(p, q) that depends on the revenue and price-cost margin of each sale that the agent does. 2. The agent chooses actions or effort levels a = (a 1, a 2,..., a J ) for each transaction, but the principal cannot observe these choices. At the same time, the agent chooses prices p = (p 1, p 2,..., p J ). 3. The effort and price, given the demand functions q(a, p), determine the quantity sold q = (q 1, q 2,..., q J ), revenue and profits. 4. The agent receives compensation specified by the contract. In addition, I assume that quantity for transaction j is a function of effort and price for that transaction only. Also, that quantity is increasing in effort, decreasing in price and that the cross partial derivative of quantity with respect to effort and price is positive: q j a j > 0, q j p j < 0, 2 q j a j p j > 0. The agent is risk neutral with utility U = w(p, q(a, p)) γ(a), where w(p, q(p, a)) is the wage received by workers and γ(a) is the convex cost of effort (i.e.: γ j (a) > 0, γ jj (a) > 0). Finally, for simplicity, in order to get testable predictions of what the contract change causes, I transform the discrete linear and piecewise linear schedules into a continuous one: Setting b j (p j ) = b w(p, q) = s + J b j (p j ) (p j q j ) j=1 j replicates the old contract. As for the new contract, the piecewise scheme implies the commission is increasing in price-cost margin. Since workers cannot affect cost, 8 the commission received for the sale of each good can be thought as an increasing function of price. Thus, setting db j /dp j > 0 approximates the new contract. 8 In very extreme cases sales agents could affect cost. For instance, if they sell an unusual large amount of a good then managers could potentially buy that good at a better price from producers. 8

10 With the old contract, sales employees care only about maximizing revenues while with the new contract a higher price also means they receive a higher share of revenues. I illustrate the differences in the share of revenues received by workers as the price-cost margin increases between old, new and continuous contracts in figure 1. Figure 1 Share of Revenue Received by the Worker depending on the Price-Cost Margin The agent s maximization problem is the following: max {a,p} J s + b j (p j ) [p j q j (a j, p j )] γ(a 1,..., a J ) j=1 Workers maximize utility by choosing effort (a) and price (p) for every transaction j. I start by setting up the case with no multitasking problem in order to contrast it later with the case that results in substitution of effort between tasks. Thus, in a first instance I assume that there is no relation between goods in the cost of effort function (i.e., γ jm (a) = 0). With γ jm (a) = 0 price and effort for all goods change in the same direction. So, for the following propositions and proofs I drop the j subscripts and use a, p, q and c as scalars. Proposition 1.1: If b(p o ) b, where p o is the equilibrium price with the old compensation scheme, 9 with the new contract both price and effort increase. 9 This condition means that using the prices chosen by workers with the old contract to calculate the commission with the new incentive scheme b(.), they would receive at least the same percentage b of sales as before. 9

11 Proof: First order conditions with respect to p and a, respectively, are b(q + p q p ) + db dp pq = 0 bp q a γ a = 0 Fully differentiating [ u pp db p q + bq dp a a + bp 2 q a p db p q + b q + bp ] [ ] [ ] 2 q ( ) dp a a a p dp pq db = d da 0 dp u aa where u pp and u aa are the second order conditions and the 2x2 matrix is the Hessian, so u pp < 0, u aa < 0 and det(hessian) > 0. The assumption that 2 q/ a p > 0 is sufficient for the remaining term of the Hessian to be positive. Then, applying Cramer s rule, dp > 0 and da > 0. Proposition 1.2: If dp > 0 and da > 0, then profits increase while the overall effect on quantity is ambiguous. Proof: Profits Π = (p c) q(a, p) dπ = dp q + [ q q da + dp](p c) a p using the first order condition on price when db/dp = 0, we can rewrite the effect on profits as dπ = dp Since dp > 0 and da > 0, dπ > 0. ( q ) c + da (p c) q p a Quantity q(a, p) dq = dp q p + da q a The first term of the change in quantity is negative (the price effect ) and the second term is positive (the effort effect ). So the overall effect of the new contract on quantity is ambiguous. In summary, with the introduction of the new contract workers increase price and effort. Therefore profits increase while the overall effect on quantity is ambiguous as higher prices 10

12 reduce quantity and higher effort increases it. The intuition for this result is strong. If workers do not raise price, with the new contract they do just as well as previously but now they can do even better by raising price which increases the marginal commission and therefore the optimal effort level. The old payment scheme only required workers to maximize revenues, while the new contract aligns better workers incentives with profit maximization. III.A Multitasking Case Now, I consider the case when efforts for selling different products are substitutes in the sales agent s cost function. For simplicity, I assume that there are two products {L, H}, one that usually has low-margins and another that is usually sold at higher margins before the new contract is implemented. To provide actions a L and a H the agent faces an effort cost of γ(a L, a H ), where: γ(a L, a H ) is strictly convex and continuously differentiable and 2 γ(a L,a H ) a L a H γ LH is strictly positive. The second condition implies that increasing effort in one product increases the marginal cost of effort in the other. Therefore, increasing effort in one product leads to some negative externality on the other product. A strong assumption that I impose is that demand functions for all goods are independent. Repeating the same analysis as before we get theoretical predictions of the effect of the change in the incentive scheme on prices and efforts for both products. Proposition 2.1: If the increase in price ( sensitivity ) ( of the commission for good H is db greater than the change for good L (i.e., d H db dp H > d L dp L )) and γ LH is sufficiently large, then price and effort increase for product H and decrease for good L. Proof: Using the first order conditions with respect to p L, a L, p H and a H and fully differentiating u pl p L u pl a L 0 0 dp L p L q L d u pl a L u al a L 0 γ LH da L 0 0 u ph p H u ph a H dp H = 0 p H q H d 0 γ LH u ph a H u ah a H da H 0 ( db L dp L ) ( db H dp H ) where u pj p j and u aj a j are the second order conditions, u pj a j are the cross partial derivatives of utility for j = {L, H} and the 4x4 matrix is the Hessian. Thus, u pj p j < 0, u aj a j < 0, 11

13 ( db u pj a j > 0 for j = {L, H} and det(hessian) > 0. Start by setting d L p L ) = 0. Then, using Cramer s rule and the first order conditions one can show that dp H > 0, da H > 0, dp( L < ) 0 and da L < 0. By continuity, with a γ LH sufficiently large this is the case even when db d L p L > 0. Proposition 2.2: If dp H > 0, da H > 0, dp L < 0 and da L < 0, then profits increase for H goods and decrease for L goods while the overall effect on quantity is ambiguous. Proof: For H products the proof is the same as in the non-multitasking case depicted above. For L goods it is quite similar. Profits of L product Π L = (p L c L ) q L (a L, p L ) Using the first order condition on price we can rewirte the effect on profits as dπ L = dp L Since dp L < 0 and da L < 0, dπ L < 0. ( q ) L c L + da L (p L c L ) q L p a L Quantity of L product q L (a L, p L ) dq L = dp L q L p L + da L q L a L The price effect is positive (since price decreases quantity increases) while the effort effect is negative. So the overall effect of the new contract on quantity of good L is ambiguous. Workers trade off effort on one task (or product) at the expense of another task as a result of the new bonus scheme. Moreover, this theoretical framework yields testable predictions: price and profits decrease for low-margin goods while they increase for high-margin goods. IV IV.A Data and Descriptive Evidence The Data I exploit the firm s commissions and sales records, which contain detailed information on every transaction since The data compiled include a product ID number, 10 the revenue 10 The product ID number is constant through time but unfortunately I cannot observe what the product sold is. 12

14 made on the sale or transaction, the price-cost margin, price and quantity of each transaction, employee who closed the deal, commission earned, customer, invoice number, invoice date and payment date. Information on about 20% of all transactions is incomplete: on the sales records quantity sold, product price and cost are missing. To address this and use as many observations as possible for the statistical analysis, I calculate weekly average cost for every product (and monthly average cost for goods that were not sold every week). Then, I impute cost using the averages per product for the transactions with incomplete information. With the imputed cost, revenue and price-cost margins, I back out price and quantity. Finally, I drop observations that have prices above $25,000 that represent sales of special products. The dataset contains almost 1.4 million transactions and different variables that allow me to analyze in detail the effect of the contract change. The new scheme was announced at the end of June 2008 in three out of twelve stores that the company had at that time. I refer to these stores as the main offices stores, since the central offices are located in two out of these three storehouses. In the other nine stores the new policy was announced and explained to the sales workforce by the end of September of the same year. This offers the possibility of a difference-in-differences analysis, between the main offices stores and the other stores employees, of two experiments: the announcement of the new contract in the first group of 29 workers and then on the second group of 46 workers. The difference-in-differences specification is critical for identification, for instance, it allows me to control for the decrease in sales and profits induced by the financial crisis. One potential concern is that the human resources team was not able to implement the new incentives scheme as planned. In spite of the announcement in which it was specified that starting the following month the wage contract for all workers of the relevant storehouses would change, the new contract was gradually introduced and it was not until December 2008 that all workers were shifted to the new incentives scheme (see figure 2). However, employees were not aware that the introduction of the new payment scheme would be gradual. Therefore, one would expect to see a change in their behavior in the weeks following the announcement. 13

15 Table 1: Descriptive Statistics per Transaction Mean Std. Dev. Min Max Revenue ($) (1,609.63) , Profit ($) (375.43) , Unit price ($) (192.22) , Quantity 85 (555) 1 123,300 Price-cost margin (%) (12.60) Transactions per week 13,407 (2,272) 7,122 20,012 Notes: All the variables that contain monetary values are in dollars of January Number of observations: 1,380,871. Figure 2 Timing of the Introduction of the New Incentives Scheme IV.B Descriptive Evidence I observe 75 workers and almost 18,000 different products during the period studied. On average sales employees closed 13,407 deals every week making a profit per transaction of 40.5 dollars. Some other general descriptive statistics per transaction are depicted in table 1. With the new contract, transactions with a price-cost margin below x + k 1 receive a lower commission than before. However, as can be seen in both figures 3 and 4 most sales register a margin above this threshold. Two interesting features are worth pointing out in these figures. First, looking at figure 3 we see that there is not a first-order stochastic dominance of the old cumulative distribution function over the new one. Actually, the share of transactions 14

16 with lower price-cost margins is higher after the new contract is announced. Yet, there also seems to be a higher proportion of transactions with very high price-cost margins after the contract announcement. Moreover, there does not seem to be any bunching (see figure 4) after the x and x + k 1 cutoffs imposed by the new incentives scheme. However, for the last cutoff of x + k 2 I test and reject the null hypothesis of continuity of the density using the McCrary test. Figure 3 Cumulative Distribution Functions Before and After the Contract Announcement Figure 4 Transactions by Price-Cost Margin After the Announcement of the New Contract 15

17 The three variables that I consider to measure workers performance and analyze the effect of the new contract are profits, average price and quantity. Profits is what ultimately matters for the policy evaluation and what the firm was seeking to increase when it decided to introduce the new incentives scheme. Figures 5 and 6 provide graphic evidence on workers performance in 2008 and The first figure of the two shows profit per week in the main offices and in the other stores averaged over the workers of each group. The second one shows average weekly item price per worker. The two vertical lines correspond to announcement dates in the main offices stores at the end of June 2008 (solid line) and in the other stores at the end of September 2008 (dashed line). The horizontal lines are the means for both groups in each of the relevant periods: (1) when both groups know nothing, (2) when only the main offices employees know about the new contract and finally, (3) when both groups of workers know about the new scheme. By observing these figures we can see that right after the announcement of the new incentives scheme in the main offices stores, both the mean of the average profit per worker and the mean of the average price per worker increase in the main offices. In turn, as would be expected, the mean of the profit per worker in the other stores remains fairly similar after June 2008 while average price slightly decreases. As can be seen in both figures at the end of 2008 and beginning of 2009 both the mean of the average profit per worker and the mean of the average price in the main offices stores decreases (probably due to the financial crisis). However, thanks to the new incentives brought by the announcement of the new contract in the other stores workers manage to maintain similar levels of profits and prices as before. Figure 5 Average Weekly Profits per Worker in Main Offices and Other Stores 16

18 Figure 6 Average Weekly Item Price per Worker in Main Offices and Other Stores V Effects on Workers Performance The old contract was based on revenues subject to a price floor (p c), while the new contract also includes profits as a variable that determines workers payment. In response to this change we expect workers to modify their behavior. In the following subsections, I analyze the effect that the announcement of the new incentive scheme has on workers sales performance. First, I look at workers weekly measures (average price, profits and quantity sold). Then, to start disentangling the different mechanisms behind these weekly aggregate effects I analyze worker-product weekly measures and estimate the effect of the new contract on prices, profits and quantities within products. I consider and test the hypothesis that workers reallocate effort among products and focus more on goods that give them a higher reward given the new payment scheme (i.e. high price-cost margin products). V.A Evidence on Effort Increase When considering that γ jm = 0, the predictions from theory are that average effort and price increase with the new contract which means that profits increase, while the effect on quantity is ambiguous. To investigate the effect of the new incentive scheme on overall average price, profits and quantity sold I start by aggregating transactions at the worker-week level. I add revenue, profits and quantity from all transactions that worker i registered every week to calculate weekly revenue, profits and quantity sold, respectively. Then, I divide weekly revenue by quantity to calculate average weekly price. The panel data specification that I 17

19 Table 2: Effect of the New Incentives Scheme on Weekly Measures Dependent variable log(price) log(profits) log(quantity) (1) (2) (3) (4) (5) (6) New contract announcement dummy 0.093* 0.089* (0.051) (0.048) (0.082) (0.064) (0.092) (0.073) Main offcies stores dummy *** 0.554*** (0.024) (0.039) (0.043) Age (0.007) (0.011) (0.012) Age (0.000) (0.000) (0.000) Male *** *** (0.029) (0.047) (0.052) Tenure *** 0.105*** 0.125*** (0.003) (0.005) (0.005) Individual fixed effects No Yes No Yes No Yes R-squared Notes: *** denotes significance at 1 percent, ** at 5 percent and * at 10 percent. Standard errors are clustered at the employee level (i.e., there are 75 clusters). Estimates are calculated using data for years 2008 and Number of observations: 7,120. estimate using these aggregated data is: y it = τd it + λ t + γ i + x it β + u it (1) where y it is the log of average price, the log of profits or the log of quantity of all products sold by employee i on week t, D it is a dummy equal to one after the announcement of the new contract was made in the store where worker i belongs to, and zero otherwise. The λ t are a full set of week time effects, the γ i are individual fixed effects which capture permanent differences in the ability across sales personnel. The x it are individual specific covariates: age and age squared. Finally, the u it are identically distributed error terms with mean zero. The parameters of interest are the coefficients on the new contract announcement dummy, τ. These capture in reduced form the effect of the change in the incentives scheme on the three outcome variables. Table 2 reports the estimates with and without workers fixed effects. Column (1) shows that after the announcement of the new contract there is a statistically significant increase in average weekly price. This result, as shown in column (2), is robust to introducing employee fixed effects that account for differences in individual ability. With the new payment scheme, average weekly price increases 9.29%. From columns (3) and (4) we can see that the effect on weekly profits per worker is also positive but not statistically significant. 18

20 Considering the result when including individual fixed effects, the point estimate for profits suggest they increase 8.82% with the announcement of the new payment scheme. Finally, the last two columns depict the statistically insignificant coefficient of the new contract announcement dummy for quantity sold as dependent variable. There are different approaches that workers could take that would give rise to an increase in both average weekly price and profits without any effect on quantity. One possibility is for them to increase effort on the sales of all goods. Relating to the theoretical framework this would imply that the cross partial derivative of the cost of effort between products is equal to zero (i.e.: γ LH = 0). Higher effort in all products would in turn yield higher prices and profits in all products, while the effect on quantity would be ambiguous. Another possibility that I explore in the next section is that workers change effort differentially among products. Particularly, I consider and test the theoretical case when efforts for selling different products are substitutes in the sales agent s cost function (i.e., γ LH > 0). V.B Evidence on Effort Reallocation If increasing effort in one product increases the marginal cost of effort in the other (i.e., γ LH > 0) then a higher reward for high-margin products incites the worker to substitute effort away from low-margin products. The theoretical framework described in section III.A predicts that this substitution of effort brings about an increase in price and profits for high-margin products and a decrease in price and profits (or quantity sold) for low-margin products. To test if this is the case I divide products in four groups according to their average price-cost margins using quartiles, and compare the effect of the new contract on each group. A concern is that price, and therefore price-cost margin, is an endogenous variable. Ideally, we would use only the pre-change observations to calculate the average price-cost margin per product and categorize goods into quartiles according to these pre-change averages. By doing this we would be considering the equilibrium price (and margin) for each good with the old contract, that could be expressed using the model s primitives. There are two main problems with this approach. First, only 46% of products are observed before and after the new contract is announced. Moreover, for some of these goods I only observe a small number of transactions in the pre-change period, and their pre and post-change average margins computed are very different (most likely due to the few observations used in the pre-period to calculate average margins and not to a strategic response to the contract by workers). So the category to which these products belong to (and the ranking of all goods) changes depending on what observations we consider to calculate the average margins. Still, in the robustness checks section I include the results when considering only the 19

21 pre-change observations to rank products. 11 My preferred specification is to consider all observations available to calculate average price-cost margins and rank products using these averages. I am particularly interested in comparing the effect of the contract on products below the first quartile (the most low-margin products) with goods above the third quartile (the most high-margin products). The regression estimated is: y jit = 4 µ τ (ɛ τ D it ) + λ t + γ i + θ j + x it β + u jit (2) τ=1 where y jit is one of the three outcome variables previously analyzed: the log of average price, the log of profits or the log of quantity for product j sold by employee i in week t. As before, D it is a dummy equal to one after the announcement of the incentive change was made in the store where worker i belongs to, and zero otherwise. The λ t are a full set of week time effects, the γ i are individual fixed effects, the θ j are product fixed effects and the x it are individual specific covariates. The new set of variables, ɛ 1, ɛ 2, ɛ 3 and ɛ 4 are equal to one if product j is below the first quartile, between the first and second quartiles, between the second and third quartile or above the third quartile, respectively, of the distribution of products according to their average price-cost margin. Using these new variables as shown in equation (3) allows me to analyze the differential effect of the new policy on goods that are on average sold with high and low price-cost margins by comparing the estimates on coefficients µ τ. The results of regression (3) are shown in tables 3, 4 and 5. We can see from the first and third lines of these tables the new contract does not have an homogeneous effect on the high (Q4) and low-margin products (Q1). In line with the theoretical predictions, table 3 shows that after the announcement of the new payment scheme the average price of high-margin products increased more than 20% when considering within worker changes (column (2)). In columns (3) and (4) I include product fixed effects, the within product increase in price of high-margin goods (12%) is lower than the within worker increase. This suggests that workers are both raising prices of high-margin goods and also promoting the goods that can be sold at a higher price. In contrast, for low-margin products as predicted by the theoretical framework, the new contact causes a decrease in average prices of between 7 and 10%. The effects on profits, reported in table 4, are also consistent with the model. For highmargin products (Q4), profits increase around 14%, while for low-margin goods (Q1), profits decrease about 14%. These numbers are not statistically different when we include workers and product fixed effects. Finally, the estimates of the effects on quantity for high-margin products are negative and go from -13% when considering the within worker changes (column 11 The estimated coefficients of the new contract effect on prices are similar but I lose significance when estimating the effect on profits. 20

22 Table 3: Effect of the New Incentives on Average Price by Type of Product Dependent variable: log(price) (1) (2) (3) (4) New contract Q *** 0.198*** 0.116*** 0.115*** (0.035) (0.035) (0.009) (0.009) New contract Q ** 0.068** 0.024*** 0.024*** (0.033) (0.033) (0.006) (0.006) New contract Q (0.034) (0.034) (0.006) (0.006) New contract Q ** ** *** *** (0.037) (0.038) (0.007) (0.007) Q *** *** (0.057) (0.055) Q *** *** (0.046) (0.045) Q *** *** (0.046) (0.044) Main offices stores dummy (0.053) (0.005) age (0.013) (0.001) age (0.000) (0.000) male ** (0.049) (0.005) tenure (0.006) (0.001) Individual fixed effects No Yes No Yes Product fixed effects No No Yes Yes R-squared Notes: *** denotes significance at 1 percent, ** at 5 percent and * at 10 percent. Standard errors are clustered at the employee level (i.e., there are 75 clusters). Estimates are calculated using data for years 2008 and Number of observations: 946,

23 Table 4: Effect of the New Incentives on Profits by Type of Product Dependent variable: log(profits) (1) (2) (3) (4) New contract Q ** 0.127** 0.170*** 0.154*** (0.055) (0.049) (0.048) (0.044) New contract Q (0.047) (0.042) (0.042) (0.038) New contract Q * (0.048) (0.040) (0.043) (0.039) New contract Q ** *** *** *** (0.053) (0.047) (0.043) (0.038) Q *** *** (0.035) (0.033) Q *** *** (0.031) (0.030) Q *** *** (0.026) (0.022) Main offices stores dummy 0.291** 0.257*** (0.122) (0.076) age (0.027) (0.023) age (0.000) (0.000) male ** (0.082) (0.077) tenure (0.015) (0.010) Individual fixed effects No Yes No Yes Product fixed effects No No Yes Yes R-squared Notes: *** denotes significance at 1 percent, ** at 5 percent and * at 10 percent. Standard errors are clustered at the employee level (i.e., there are 75 clusters). Estimates are calculated using data for years 2008 and Number of observations: 946,

24 (2)) to less than -4% for the within products changes (columns (3) and (4)). The quantity of low-margin goods only has a negative and statistically significant effect (-4%) when we include both employee and product fixed effects (column (4)). It is worth pointing out that in the specification used in column 4 quantity sold of low-margin goods decreases even if average price also decreases. The fact that quantity sold of low-margin goods does not change or even decreases (according to the specification estimated) goes in line with the model s intuition that workers can affect quantity by changing effort level. Still, is there anything more precise we can say about effort? The main complication when addressing empirically the question of how effort changed is that we do not observe effort. However, if quantity depends on effort and price: q = q(a, p), the change in quantity sold as described in the theoretical framework section comes from an effort effect and a price effect : dq = da q + dp q }{{ a} p }{{} effort effect price effect From workers first-order condition when the old contract is in place we know that: q b p 0 = q = b b 1 p = 0 This implies that we can calculate the price effect (dp q ) and back-out the effort effect p (da q ). I do this for both the low (Q1) and high-margin (Q4) product groups, using the a point estimates previously presented and the average weekly-worker quantities and prices before the new contract was announced. Given that: dq = da q q + dp a p q q = q a + p a p Therefore, by correcting for price sensitivities and the change in prices I calculate the effect on quantities due only to shifts in effort. The results are shown in table 6. Recall that q/ a > 0; thus, it is clear that for high-margin products effort increases while for low-margin goods effort decreases. 23

25 Table 5: Effect of the New Incentives on Quantity by Type of Product Dependent variable: log(quantity) (1) (2) (3) (4) New contract Q ** *** (0.050) (0.044) (0.042) (0.039) New contract Q (0.048) (0.042) (0.039) (0.036) New contract Q (0.050) (0.042) (0.042) (0.039) New contract Q (0.057) (0.047) (0.039) (0.035) Q *** ** (0.065) (0.061) Q *** *** (0.057) (0.054) Q *** *** (0.058) (0.054) Main offices stores dummy 0.321*** 0.277*** (0.119) (0.087) age (0.029) (0.024) age * (0.000) (0.000) male (0.094) (0.076) tenure (0.016) (0.011) Individual fixed effects No Yes No Yes Product fixed effects No No Yes Yes R-squared Notes: *** denotes significance at 1 percent, ** at 5 percent and * at 10 percent. Standard errors are clustered at the employee level (i.e.: there are 75 clusters). Estimates are calculated using data for years 2008 and Number of observations: 946,

26 Table 6: Effort Effect of the New Incentives by Type of Product q p q/ p a q/ a (1) (2) (3) (4) High-margin products Low-margin products VI Robustness Checks In the following subsections I present three robustness checks regarding effort reallocation. The first one addresses the concern that financial incentives might have decreased for some transactions. Unlike with the continuous approximation of the contract, with the piecewise linear and discrete contract that the firm implemented, sales with very low price-cost margins receive a lower commission than before. So effort for transactions with low margins could decrease even if there is no effort substitution. I show that even when considering products for which all sales receive a higher commission than before there is evidence on effort substitution. The second robustness check is designed to test whether the differential effect of the new contract between high and low-margin products can be solely explained by workers bundling the two types of products together and using discounts on low-margin goods to increase the price on high-margin ones. Finally, in the third robustness check I consider only the pre-change observations to rank products, that is I consider the equilibrium margin for each good with the old contract to define high and low-margin goods. VI.A Differences between Discrete and Continuous Contracts One potential concern stems from an important difference between the continuous contract used to draw theoretical predictions and the discrete wage contract implemented. When using the continuous wage schedule, there is no way for effort of any given product to decrease if there is not a negative externality from the increase in effort of another product (i.e., if γ LH = 0 instead of γ LH > 0). In practice, however, one could argue that for transactions with very low price-cost margins (specifically transactions with price-cost margins below x + k 1 that receive a lower commission than before) effort decreases because incentives decrease even if there is no effort substitution. Due to the definition of low and high-margin products used it is not surprising that there are more transactions of low-margin goods that occur below the x + k 1 cutoff Still, the share of transactions with a price-cost margin below x + k 1 is less than 20% for any of the two groups of products. 25

27 Figure 6 Transactions Densities by Type of Product To address this concern and provide another piece of evidence on effort reallocation I compare the effect of the new contract on products that only have transactions registered with price-cost margins on segment 3 of the piece-wise linear contract (i.e., p c between p x + k 1 and x + k 2 ) and products that only have transactions with price-cost margins on segment 4 (i.e., above x + k 2 ). With the new contract, both groups of products receive a higher commission on every single transaction, but the group of goods of the fourth segment have a higher price-cost margin and receive a stronger commission increase than those of the third segment. The panel data specification used is: y jit = 2 µ τ (ξ τ D it ) + λ t + γ i + θ j + x it β + u jit (3) τ=1 where the variable ξ 1 is equal to one if product j was only sold with a price-cost margin between x + k 1 and x + k 2 and zero otherwise, and the variable ξ 2 is equal to one if good j was only sold with a margin above x + k 2 and zero otherwise. The coefficients of interest are µ 1 and µ 2. There are 3,597 products on the segment 4 group and only 16 on the segment 3 group. The interval (x+k 1, x+k 2 ) is rather small so it is not surprising that there are few products with price-cost margins of all sales only in this interval. When we control for product fixed effects the estimates µ 1 and µ 2 are statistically different from each other and have the expected signs. For products with higher margins and reward (segment 4) prices increase while for the segment 3 group prices decrease with the announcement of the new contract. However, estimates of the effect on profits and quantities are not statistically different. 26