Abstract This article shows how input heterogeneity triggers productivity spillovers at the workplace. In an egg production plant in rural Peru, workers produce output combining effort with inputs of heterogeneous quality. Exploiting variation in the productivity of inputs assigned to workers, we find evidence of a negative causal effect of an increase in coworkers’ daily output on own output and its quality. We show theoretically and suggest empirically that the effect captures free riding among workers, which originates from the way the management informs its dismissal decisions. Our study and results show that input heterogeneity and information on input quality contribute to determine the shape of incentives and have implications for human resource management, production management, and the interaction between the two. Counterfactual analyses show that processing information on inputs or changing their allocation among workers can generate significant productivity gains. 1. Introduction The productivity of workers is affected by coworkers’ productivity. A number of studies analysing a highly diverse set of occupations provide evidence of these productivity spillovers. Herbst and Mas (2015) show how productivity spillovers are typically positive and their size comparable across laboratory experiments and field studies. There are several possible sources of productivity spillovers at the workplace. First, these may be built into the production technology. If coworkers are complements or substitutes in the workplace production function, the effort of one worker affects the marginal product of effort for another worker. Sport teams are a clear example of this kind (Gould and Winter, 2009; Arcidiacono et al., 2017). Second, workers may learn from each other, and therefore become more productive when working along highly productive peers (Jackson and Bruegmann, 2009; Nix, 2015; Menzel, 2016). Third, behavioural considerations may play a role, as workers may find effort less costly to exert at the margin if coworkers’ effort increases (Kandel and Lazear, 1992; Falk and Ichino, 2006). Fourth, the pay scheme, dismissal policy, or human resource management in general can generate externalities among workers. For example, relative performance or team-based evaluation make the effort choices of coworkers interdependent even in the absence of other sources of externalities (Bandiera et al., 2005; Mas and Moretti, 2009). All existing studies explore these issues in settings where output is a (noisy) function of worker’s effort only. However, in many workplaces, workers produce output by combining effort with inputs of heterogeneous quality. In Bangladeshi garment factories, for instance, the quality of textiles affects productivity as measured by the number of items processed per unit of time. The speed at which warehouse workers fill trucks is affected by the shape and weight of the parcels they handle. The amount of time it takes for a judge to close a case depends on his own effort as well as on both observable and unobservable characteristics or complexity of the case itself (Coviello et al., 2014). This article investigates whether input heterogeneity triggers productivity spillovers at the workplace. The characteristics of inputs individually assigned to workers directly affect their productivity. The amount of information on input quality and the extent to which it is shared by the worker and the management contribute to determine the shape of incentives. When incentives generate externalities among workers, heterogeneous inputs can trigger productivity spillovers. Is there any evidence of productivity spillovers of this origin? Does input allocation matter for aggregate productivity at the workplace? Measuring productivity spillovers from heterogeneous inputs is challenging for three main reasons. First, firms often do not maintain records on the productivity of individual workers. Second, even when such data exist, input quality is usually not recorded or hard to measure. Finally, to credibly identify productivity spillovers from heterogeneous inputs, these inputs and their quality need to be as good as randomly assigned to workers. We overcome these issues altogether by studying the case of a leading egg producing company in Peru. The technological and informational features of the environment at its plant are particularly suitable for our analysis. Workers operate in production units located next to the each other and grouped in several sheds. Each worker is assigned a given batch of laying hens as input in the production process. Hens’ characteristics and worker’s effort jointly determine individual productivity as measured by the daily number of collected eggs. In particular, variation in the age of hens assigned to the worker induces variation in productivity. Using daily personnel data, we exploit quasi-random variation in the age of hens assigned to coworkers to identify the causal effect of an increase in coworkers’ productivity on the productivity of a given worker. We find evidence of negative productivity spillovers. Conditional on own input quality, workers’ productivity is systematically lower when the productivity of neighbouring coworkers is exogenously raised by the assignment of higher quality inputs. A positive shift in average coworkers’ input quality inducing a one standard deviation increase in their daily output causes a given worker’s output to drop by almost a third of a standard deviation. We also find output quality to decrease significantly, with the effect in standard deviation units being similar in magnitude to the effect on quantity. We attribute these effects to a change in the level of effort exerted by the worker, which varies systematically with coworkers’ productivity. We argue that the specific source of externalities in this setting lies in human resource management practices, and the worker evaluation and dismissal policy implemented by the firm. Our conceptual framework builds upon the one in Mas and Moretti (2009), that we extend to accommodate input heterogeneity. Output is a function of effort and input quality. The latter is observable to the worker, but not to the management, which cannot disentangle the separate contribution of effort and input to output. To solve the moral hazard problem, the management combines the available information on the productivity of all workers to guess their type and make dismissal decisions accordingly. Average productivity positively affects worker evaluation. An increase in the productivity of coworkers increases a given worker’s probability of keeping the job. As a result, workers free ride on each other: when coworkers’ productivity increases, individual marginal returns from effort decrease for a given worker. His optimal effort supply falls accordingly. We use workforce turnover information in the data to investigate how employment termination probabilities correlate with individual and average productivity, and provide suggestive evidence of the mechanism identified by theory. In the second part of the article, we study whether and how the provision of social and monetary incentives can mitigate free riding and offset negative spillovers at the workplace. On the one hand, monetary incentives provide extra marginal benefits from effort, leveraged by the probability of keeping the job. On the other hand, working along friends induces peer pressure that diminishes the marginal cost of effort (Kandel and Lazear, 1992; Falk and Ichino, 2006; Mas and Moretti, 2009). Both mechanisms reduce the size of negative externalities generated by the termination policy. We test these hypotheses by exploiting the specific features of the pay regime, and elicited information on the friendship network among workers. Workers receive extra pay for every egg box they produce above a given threshold. Exposure to piece rate incentives therefore varies with input quality and the age of assigned hens. We find no effect of coworkers’ productivity when hens are highly productive and workers are more likely to hit the piece rate threshold. We also find no significant spillover effects when the worker identifies any of his neighbouring coworkers as friends. Both findings are consistent with the theory. The second result also rules out the possibility that the estimated average negative effect of coworkers’ productivity on own productivity captures the implementation of cooperative strategies among coworkers, which would be even more sustainable among friends. To the best of our knowledge, this represents the first attempt to study the implications of input heterogeneity at the workplace. We show how the presence of heterogeneous inputs and information on such heterogeneity matter for several different aspects of both human resource and production management, ranging from incentive design and worker dismissal to input assignment and replacement schedule. To shed light on the individual role of these practices, we perform a structural estimation exercise grounded in our conceptual framework. We estimate the unobserved exogenous parameters of the model, and conduct counterfactual policy analyses. We first quantify the productivity gains of processing all information on input quality, thus providing the management with a precise signal of worker’s effort. In this environment, termination probabilities are a function of individual outcomes only, and no externalities arise. We show that, holding fixed the allocation of inputs, processing information on their quality can generate significant productivity gains. Second, we quantify the extent to which input allocation affects productivity. Holding everything else constant, we simulate alternative input assignment schedules and find that daily productivity could increase by up to 20%. We discuss the limitations of our analysis, and explain what informational or technological constraints may prevent the firm from implementing these alternative policies. Our findings contribute to the literature on human resource management practices and the externalities they generate among coworkers. Bandiera et al. (2005) explore the role played by social ties in the internalization of negative externalities under relative performance evaluation, and their impact on productivity under individual performance pay (Bandiera et al., 2010). Bandiera et al. (2007, 2008, 2009) provide evidence of the impact of managerial incentives on productivity, and their consequences for lower-tier workers who are socially connected to managers. Bandiera et al. (2013) study instead the effectiveness of team-based incentives and their relationship with social connections. Mas and Moretti (2009) study peer effects among cashiers in a large U.S. supermarket chain. They show how social pressure from observing high-ability peers is strong enough to more than offset the incentives to free ride generated by the dismissal policy. Using daily personnel data from a flower processing plant in Kenya, Hjort (2014) shows that the ethnic composition of working teams affects productivity at the workplace, with the negative effect of ethnic diversity being larger when political conflict between ethnic blocs intensifies. He also shows how this effect is mitigated by the introduction of team-based pay. Our results generalize to those settings that share the same technological and informational assumptions of our conceptual framework. By technological assumptions we refer to the shape of the production function and its inputs, and the presence of heterogeneity in input quality. By informational assumptions we refer to the information available to the management and its inability to perfectly disentangle the separate contributions of effort and input to output. More broadly, our findings generalize to those settings where human resource management practices generate spillovers among coworkers, and the latter handle inputs of heterogeneous quality. In particular, the firm under investigation employs a relatively more labour intensive technology compared to firms in the same sector, but operating in developed countries. Our study is thus relevant in the microfoundation of productivity-enhancing management practices in developing countries (Bloom and Van Reenen, 2007, 2010; Bloom et al., 2010, 2013). In this respect, this article is close to Hjort (2014) in that it highlights the efficiency cost of input misallocation among workers, and explores how properly designed incentives may partially eliminate these costs. In the context of an Indian garment factory, Adhvaryu et al. (2016) show how the management can reduce the extent of negative productivity shocks by reallocating workers to tasks. 2. Conceptual Framework This section illustrates how input heterogeneity contributes to shape human resource management practices and triggers productivity spillovers among workers. $\(N\)$ workers independently produce output $\(y_i>0\)$ combining effort $\(e_i\ge0\)$ with a given input of quality $\(s_i>0\)$, with $\(i\in \{1,2,.,N\}\)$. Inputs of higher quality raise the marginal product of effort. Output at a moment in time is given by \begin{equation} y_i=s_ie_i. \end{equation} (1) Effort cost is positive and convex, with $\(C(e_i)=e^2_i/2\theta_i\)$ and $\(\theta_i>0\)$. The marginal cost of effort is decreasing in $\(\theta_i\)$, which defines worker’s type. $\(\theta_i\)$ is heterogeneous across workers, independently drawn from the same distribution. Input quality $\(s_i\)$ is identically and independently distributed across workers, and independent of $\(\theta_i\)$.1 Each worker knows his type, perfectly observes input quality and exerts effort. The management observes output, but cannot observe and thus disentangle the separate contributions of effort and input to output. The asymmetry of information between the worker and the management generates moral hazard.2 To solve the moral hazard problem, the management uses the information on output to guess worker’s type and attach to each worker a given probability $\(Q_i\)$ of keeping the job. While on the job, the worker earns a fixed salary $\(\omega\)$ from which he derives utility $\(U(\omega)\)$. In case the employment relationship terminates, the worker does not earn any salary and derives zero utility. The threat of dismissal works as an incentive device.3 Let $\(\tilde{s}_i=\ln\,s_i\)$, $\(\tilde{y}_i=\ln\,y_i\)$, and $\(\tilde{\theta}_i=\ln \theta_i\)$. We assume that $\(\mathbb{E}(\tilde{s}_{i})=0\)$, $\(Var(\tilde{s}_{i})\)$ and $\(Var(\tilde{\theta}_{i})\)$ are known to the management, but $\(\mathbb{E}(\tilde{\theta}_{i})\)$ is not. This means that the management knows only specific features of the input quality and worker’s type distributions. It has perfect information on the mean and variance of the (log of) input quality distribution, and the variance of (log of) worker’s type. But, it lacks information on where the transformed type distribution is centered. In this environment, the management estimates the log of worker’s type using a linear projection of the form \begin{equation}\label{eqexp} {P}(\tilde{\theta}_i| \tilde{y}_i,\bar{\tilde{y}})=b_0+b_1\tilde{y}_i+b_2\bar{\tilde{y}}, \end{equation} (2) where $\(\bar{\tilde{y}}\)$ is the average of $\(\tilde{y}_i\)$ among all workers. Let the retention probability $\(Q_i\)$ be an increasing and concave function of $\({P}(\tilde{\theta}_i| \tilde{y}_i,\bar{\tilde{y}})\)$, i.e. \begin{equation} Q_i=f\left(b_0+b_1\tilde{y}_i+b_2\bar{\tilde{y}}\right) \end{equation} (3) with $\(f'(\cdot)>0\)$ and $\(f''(\cdot)<0\)$. It can be shown that if $\(f''(0)/f'(0)>-1\)$ then $\(b_1,b_2>0\)$. Under this condition, output is a positive signal of worker’s type. Unobserved heterogeneity in input quality makes these signals individually imprecise. Their average provides the management with valuable information on the mean of the type distribution. To guess worker’s type, the management uses own and average output, attaching to the latter a positive weight that increases with the extent of input heterogeneity. In Supplementary Appendix A.2, we illustrate the signal extraction problem of the management, derive the equilibrium values of $\(b_0,b_1,b_2\)$, and find the sufficient condition for $\(b_1,b_2>0\)$.4 From equation (3) it follows that $\(Q_i\)$ is increasing in both own output $\(y_i\)$ and any of coworkers’ output $\(y_{-i}\)$. Moreover, the concavity of the $\(f(\cdot)\)$ function implies that the cross derivative is negative: marginal returns from own output in terms of increased retention probability decrease with coworker’s output. It is therefore possible to express $\(Q_i\)$ as a function of own and any given coworker’s output $\(q(y_i,y_{-i})\)$, with $\(q_{1}(\cdot)>0\)$ and continuously differentiable, $\(q_{11}(\cdot)<0\)$, and $\(q_{12}(\cdot)<0\)$.5 Each worker chooses the effort level $\(e_i\ge0\)$ which maximizes his expected utility \begin{equation} \underset{e_i}{\max} \ U(\omega) \ q(y_i,y_{-i})-\frac{e^2_i}{2\theta_i}. \end{equation} (4) Taking the corresponding first order condition we get \begin{equation} U(\omega) \ q_{1}(y_i, y_{-i}) \ s_i\theta_i=e_i. \end{equation} (5) We can apply the implicit function theorem to derive how the worker’s optimal effort level changes with coworkers’ output. We get \begin{equation}\label{eqift} \frac{\partial{e^*_i}}{\partial{y_{-i}}}=\frac{U(\omega) \ q_{12}(y_i,y_{-i}) \ s_i\theta_i}{1-U(\omega) \ q_{11}(y_i,y_{-i}) \ s^2_i\theta_i}<0. \end{equation} (6) Notice that the denominator is always positive, and the sign of the above derivative is uniquely determined by the sign of $\(q_{12}(\cdot)\)$. As coworker’s output increases, the worker’s optimal effort level decreases. Workers free ride on each other. This is because marginal returns from own output in terms of increased probability of keeping the job decrease with coworkers’ output, as captured by the sign of $\(q_{12}(\cdot)\)$. Workers best-respond to each other in equilibrium.6 Consider now the case in which input quality is partially observed by the management. Let $\(s_i=a_i\varepsilon_i\)$, with $\(a_i>0\)$ being observable to both the worker and the management, and $\(\varepsilon_i>0\)$ observable to the worker only. Output at a moment in time is given by \begin{equation} y_i=a_i\varepsilon_ie_i. \end{equation} (7) The management uses the available information on input quality to mitigate the asymmetry of information and derive a more precise signal of worker’s type as given by \begin{equation} z_i=\frac{y_i}{a_i}=\varepsilon_ie_i. \end{equation} (8) Let $\(\tilde{\varepsilon}_i=\ln \varepsilon_i\)$ and $\(\tilde{z}_i=\ln z_i\)$. Let also $\(\mathbb{E}(\tilde{\varepsilon}_{i})=0\)$ and $\(Var(\tilde{\varepsilon}_{i})\)$ be known to the management, which computes \begin{equation} {P}(\tilde{\theta}_i| \tilde{z}_i,\bar{\tilde{z}} )=b_0+b_1\tilde{z}_i+b_2\bar{\tilde{z}}, \end{equation} (9) where $\(\bar{\tilde{z}}\)$ is the average of $\(\tilde{z}_i\)$ among workers. If the retention probability for a given worker is an increasing and concave function of $\({P}(\tilde{\theta}_i| \tilde{z}_i,\bar{\tilde{z}})\)$, the same conditions specified above imply that $\(b_1,b_2>0\)$. Even after netting out the observable component of input quality, the residual unobserved heterogeneity $\(\varepsilon_i\)$ does not allow the management to perfectly disentangle the separate contributions of effort and input to output. The management still relies on the average of all signals to derive an estimate of the mean of the worker’s type distribution. The retention probability increases with both the individual signal $\({z}_i\)$ and any of coworkers’ signal $\({z}_{-i}\)$. Furthermore, marginal returns from own signal in terms of increased retention probability decrease with coworkers’ signal, generating free riding and negative productivity spillovers. Monetary and social incentives: We now illustrate how incentives other than the threat of dismissal can shape externalities in this environment. We model social incentives as peer pressure. In its original formulation by Kandel and Lazear (1992), this mechanism operates through the effort cost function: coworkers’ effort diminishes the marginal cost of effort for the worker.7 In the environment described here, output is a function of both worker’s effort and input quality. We thus model peer pressure as operating through a decrease in the cost of effort that follows an increase in coworker’s output $\(y_{-i}\)$. The worker’s problem becomes choosing effort level $\(e_i\ge0\)$ that maximizes his expected utility \begin{equation} \underset{e_i}{\max} \ U(\omega) \ q(y_i,y_{-i})-\frac{e_i}{2\theta_i}\left(e_i-\lambda \ y_{-i}\right), \end{equation} (10) where $\(\lambda>0\)$ is a generic parameter capturing the intensity of peer pressure mechanisms. It can be shown that, while the firm’s implemented termination policy still generates teamwork-type externalities, peer pressure pushes them in the opposite direction, possibly changing the sign of productivity spillovers.8 The basic framework can also accommodate for the presence of monetary incentives. We let the wage carry a piece rate component related to daily output, meaning $\(\omega=F+\kappa y_i\)$ with $\(\kappa>0\)$.9 The worker chooses the level of effort $\(e_i\ge0\)$ that maximizes his expected utility \begin{equation} \underset{e_i}{\max} \ U(F+\kappa y_i)q(y_i,y_{-i})-\frac{e^2_i}{2\theta_i}. \end{equation} (11) Piece rate incentives provide extra motivation for effort. Notice also that monetary incentives are leveraged by the probability $\(q(\cdot)\)$ of keeping the job. The sign of productivity spillovers is no longer uniquely determined by the sign of the cross derivative $\(q_{12}(\cdot)\)$, and own optimal effort may still increase with coworkers’ productivity. This is because coworkers’ productivity increases the probability of keeping the job. Even if marginal returns in terms of retention probability are lower, this leverages the power of incentives, as these are earned only if the job is kept. The latter effect may dominate the former, generating positive productivity spillovers. This basic framework does not incorporate other possible sources of spillovers, such as social learning, monitoring on behalf of supervisors, discouragement from highly productive peers, or the possibility that workers engage in cooperative strategies. These may potentially be incorporated in the model without changing its basic intuition on the role of the termination policy. We will discuss these other sources of spillovers and the empirical salience of alternative explanations to our findings in Section 6. 3. The Setting We take the theory to the data using records from an egg production plant in rural Peru. The establishment belongs to a poultry firm having egg production as its core business. In the plant under investigation, production takes place in several sectors, one of them being shown in Figure A.1 of Supplementary Appendix A.1. Each sector comprises several sheds. Each shed hosts one to four production units. As an example, Figure A.2 of Supplementary Appendix A.1 shows a shed that hosts four production units. Each production unit is defined by one worker and a given batch of laying hens assigned to him. Hens within a given batch have homogeneous characteristics. In particular, they are all of the same age. This is because the bird batch is treated as a single input. The entire batch is bought from an independent bird supplier company. After birth, hens are raised in a dedicated sector. The batch is then moved to production when hens are around 20 weeks old, and discarded altogether at age 80 to 90 weeks. While in production, the batch is always located in the same production unit and assigned to the same worker. Worker’s main tasks are: (1) to collect and store the eggs, (2) to feed the hens, and (3) to maintain and clean the facilities.10 Output is collected eggs. These are classified into good, dirty, broken, and porous, so that measures of output quality can be derived accordingly. The batch of laying hens as a whole is the main production input. High quality hens increase the marginal product of effort for the worker. Two specific dimensions of worker’s effort directly map from its conceptualization in the previous section. The first one relates to the logistics of egg collection. The worker walks within the production unit along cages and fills a basket of a given size with the newly laid eggs. Once the basket is full, the worker walks to the small warehouse in front of the production unit, visible in Figure A.2. There he empties the basket, then goes back to the production unit and repeats. The number of times and speed at which the worker goes back and forth from the production unit to the warehouse determines how many eggs will be counted at the end of the day. Their quality is affected as well, as eggs may break if the worker overloads the basket or is not careful in emptying it. Importantly, effort in this task is complementary to input quality as the more hens are productive the higher is the scope for going back and forth from the production unit to the storage and repeat this operation multiple times. The second relevant dimension of effort is feeding. According to the veterinary at the firm, the extent to which the same amount of food is evenly distributed across hens matters greatly for productivity, and differentially so when hens are more productive.11 Production units are independent from each other and no technological complementarities nor substitutabilities arise among them. Each worker independently produces eggs as output combining effort and the hens assigned to him as input. Egg storage and manipulation is also independent across production units, as each one of them is endowed with an independent warehouse for egg and food storage. Nonetheless, workers in neighbouring production units can interact and observe each other. The productivity of working peers can be easily monitored as they take boxes of collected eggs to the warehouse. On the contrary, workers located in different sheds can hardly interact or see each other. Workers in the firm are paid a fixed wage every two weeks. A bonus is also awarded when their productivity on a randomly chosen day within the same two weeks exceeds a given threshold. In that case the worker is paid an additional piece rate for each egg box exceeding the threshold. For simplicity, the first part of the analysis abstracts from the piece rate component of pay. Section 7 explores in detail the consequences of incentive pay and peer pressure on productivity and externalities among workers. 4. Data and Descriptives We use daily production data from one sector of the plant from 11 March to 17 December of 2012. This information is collected by the veterinary unit at the firm with the purpose of monitoring hens’ health. The unit of observation is one production unit as observed on each day during the sampling period. We observe a total number of 99 production units, grouped into 41 different sheds. The majority of sheds (21) is composed of 2 production units. A total of 97 workers are at work in the sector for at least one day, and we can identify 186 different hen batches in production throughout the period. Table 1 shows the summary statistics for all the variables we use in the empirical analysis. Our final sample comprises 21,213 observations, one per production unit and day.12 For each observation, we can identify the worker that operates the unit and the hen batch assigned to him, with information on the number of living hens and their age in weeks. Hens’ age varies between 19 and 86 weeks, with the average batch counting around 10,000 hens. There is substantial heterogeneity in the number of living hens per production unit on a given day, ranging from a minimum of 44 to a maximum of over 17,000. There are two reasons for this. First, hen batches are heterogeneous to begin with and already on the day they are moved to production. Second, within a given batch, hens die as time goes by at an average daily rate of 0.1%. Importantly, dead hens are never replaced by new hens: only the entire hen batch is replaced as a whole when (remaining) hens are discarded. This also explains why, at each point in time, all hens within a given batch have the same age. Table 1 Summary statistics Variable Obs. Mean St. Dev. Min Max Hens’ age (weeks) 21,213 45.327 17.016 19 86 No. of hens 21,213 9,947.792 3,869.995 44 17,559 Daily eggs per hen, $\(y_i\)$ 21,213 0.785 0.2 0 1 Good/total 21,044 0.857 0.093 0 1 Broken/total 21,044 0.024 0.037 0 0.357 Dirty/total 21,044 0.059 0.048 0 1 Porous/total 21,044 0.052 0.058 0 1 Deaths/No. of hens 19,623 0.001 0.017 0 0.782 Food (50 kg sacks) 21,213 22.351 8.936 0 40 Food per chicken (g) 21,213 112.029 50.154 0 5,947.137 Neighbouring coworkers 21,213 1.223 0.435 1 3 Daily eggs per hen 21,213 0.784 0.197 0 0.999 Coworkers’ average, $\(\bar{y}_{-i}\)$ Hens’ age 21,213 45.248 16.604 19 86 Coworkers’ average (weeks) Dummies $$\quad$$ Working Along Friend 16,595 0.246 0.431 0 1 $$\quad$$ Experience Above Median 16,595 0.515 0.5 0 1 Variable Obs. Mean St. Dev. Min Max Hens’ age (weeks) 21,213 45.327 17.016 19 86 No. of hens 21,213 9,947.792 3,869.995 44 17,559 Daily eggs per hen, $\(y_i\)$ 21,213 0.785 0.2 0 1 Good/total 21,044 0.857 0.093 0 1 Broken/total 21,044 0.024 0.037 0 0.357 Dirty/total 21,044 0.059 0.048 0 1 Porous/total 21,044 0.052 0.058 0 1 Deaths/No. of hens 19,623 0.001 0.017 0 0.782 Food (50 kg sacks) 21,213 22.351 8.936 0 40 Food per chicken (g) 21,213 112.029 50.154 0 5,947.137 Neighbouring coworkers 21,213 1.223 0.435 1 3 Daily eggs per hen 21,213 0.784 0.197 0 0.999 Coworkers’ average, $\(\bar{y}_{-i}\)$ Hens’ age 21,213 45.248 16.604 19 86 Coworkers’ average (weeks) Dummies $$\quad$$ Working Along Friend 16,595 0.246 0.431 0 1 $$\quad$$ Experience Above Median 16,595 0.515 0.5 0 1 Notes: The table reports the summary statistics for all the variables used throughout the empirical analysis. The unit of observation is the production unit in the sector under investigation in each day from March 11 to December 17 of 2012. Sheds hosting only one production units are excluded from the sample. Table 1 Summary statistics Variable Obs. Mean St. Dev. Min Max Hens’ age (weeks) 21,213 45.327 17.016 19 86 No. of hens 21,213 9,947.792 3,869.995 44 17,559 Daily eggs per hen, $\(y_i\)$ 21,213 0.785 0.2 0 1 Good/total 21,044 0.857 0.093 0 1 Broken/total 21,044 0.024 0.037 0 0.357 Dirty/total 21,044 0.059 0.048 0 1 Porous/total 21,044 0.052 0.058 0 1 Deaths/No. of hens 19,623 0.001 0.017 0 0.782 Food (50 kg sacks) 21,213 22.351 8.936 0 40 Food per chicken (g) 21,213 112.029 50.154 0 5,947.137 Neighbouring coworkers 21,213 1.223 0.435 1 3 Daily eggs per hen 21,213 0.784 0.197 0 0.999 Coworkers’ average, $\(\bar{y}_{-i}\)$ Hens’ age 21,213 45.248 16.604 19 86 Coworkers’ average (weeks) Dummies $$\quad$$ Working Along Friend 16,595 0.246 0.431 0 1 $$\quad$$ Experience Above Median 16,595 0.515 0.5 0 1 Variable Obs. Mean St. Dev. Min Max Hens’ age (weeks) 21,213 45.327 17.016 19 86 No. of hens 21,213 9,947.792 3,869.995 44 17,559 Daily eggs per hen, $\(y_i\)$ 21,213 0.785 0.2 0 1 Good/total 21,044 0.857 0.093 0 1 Broken/total 21,044 0.024 0.037 0 0.357 Dirty/total 21,044 0.059 0.048 0 1 Porous/total 21,044 0.052 0.058 0 1 Deaths/No. of hens 19,623 0.001 0.017 0 0.782 Food (50 kg sacks) 21,213 22.351 8.936 0 40 Food per chicken (g) 21,213 112.029 50.154 0 5,947.137 Neighbouring coworkers 21,213 1.223 0.435 1 3 Daily eggs per hen 21,213 0.784 0.197 0 0.999 Coworkers’ average, $\(\bar{y}_{-i}\)$ Hens’ age 21,213 45.248 16.604 19 86 Coworkers’ average (weeks) Dummies $$\quad$$ Working Along Friend 16,595 0.246 0.431 0 1 $$\quad$$ Experience Above Median 16,595 0.515 0.5 0 1 Notes: The table reports the summary statistics for all the variables used throughout the empirical analysis. The unit of observation is the production unit in the sector under investigation in each day from March 11 to December 17 of 2012. Sheds hosting only one production units are excluded from the sample. The data provide information on the total number of eggs collected in each production unit on each day. We divide this number by the number of hens to compute the average number of eggs per hen collected by the worker. This is our chosen productivity measure. It factors out differences across workers in input quantity, and focuses on heterogeneity in input quality. In other words, it allows to focus on differences across batches along dimensions other than their numerosity, since the latter would be a trivial source of variation for total output.13 We thus label the worker as more productive if he collects a higher number of eggs while operating the same number of hens. This is not conceptually different from what we would say of a firm that is capable of achieving higher output levels while using the same inputs. Perhaps more importantly, this measure is the one that the firm considers relevant. When specifically asked how they would evaluate workers’ productivity, the management says that they would look at the total number of collected eggs and divide it by the number of assigned hens. Table 1 shows that the average productivity in the sample is equal to 0.785 with a standard deviation of 0.2. The data also provide information on the number of good, dirty, broken, and porous eggs, that we use to derive output quality measures. On average, 86% of eggs produced by a production unit in a day are labelled as good, and are thus ready to go through packaging. In total, 6% of eggs on average are classified as dirty. Workers can turn a dirty egg into a good egg by cleaning it. Finally, we have information on the daily amount of food handled and distributed among the hens by the worker as measured by the number of 50 kg sacks of food employed. Workers distribute an average daily amount of 112 g of food per hen.14 We personally collected information on the spatial arrangement of production units within the sector, and their grouping into sheds. For each production unit, we can thus compute the average daily output of coworkers in neighbouring production units in the same shed, and the average age of their assigned hens. In March 2013, we also administered to all workers an original survey to elicit demographic and personal information about them and their social relationships. Specifically, we asked the workers to list those coworkers whom they identify as friends, with whom they would discuss personal issues, or go to lunch with. We say that worker $\(i\)$ recognizes worker $\(j\)$ as a friend if the latter appears in any of worker $\(i\)$’s above lists. In all, 63 of the interviewed workers were already employed in the period for which production data are available, so that this information can be merged accordingly for almost 80% of the sample. 5. Empirical Analysis of Productivity Spillovers 5.1. Preliminary evidence and identification strategy The batch of hens is the production input in this context. The worker is assigned the same batch of equally aged hens from the moment they are moved to production until they are discarded. Hens’ productivity varies with age, and changes the marginal product of effort.15Figure 1 plots daily productivity against hens’ age in weeks. For all given week of age, each bin in the scatterplot shows productivity values as averaged across all observations belonging to production units hosting hens of that given age. The Figure also shows the smoothed average of productivity and a one standard deviation interval around it. Productivity is typically low when hens are young and recently moved to production, but starts to increase thereafter. It reaches its peak when hens are around 40 weeks old. From that age onwards, productivity starts to decrease first slowly and then more rapidly once hens are over 70 weeks old. Hens’ age induces meaningful variation in productivity. This is especially the case through the beginning and the end of the hens’ life cycle, meaning from week 16 to week 32 and from week 75 to 86.16 Figure 1 View largeDownload slide Hens’ age and productivity. Notes: The average daily number of eggs per hen collected by the worker is plotted against the age of hens in weeks. Recall that hens in a given batch are all of the same age. The graph shows the smoothed average together with a one standard deviation interval around it. Epanechnikov kernel function is used for smoothing. Furthermore, for all given week of age, each bin in the scatterplot shows the average daily number of eggs per hen as averaged across all observations belonging to production units hosting hens of that given age. Productivity is typically low when hens are young, it reaches a peak when hens are around 40 weeks old, and then decreases thereafter until hens are old enough and the batch is discarded. Figure 1 View largeDownload slide Hens’ age and productivity. Notes: The average daily number of eggs per hen collected by the worker is plotted against the age of hens in weeks. Recall that hens in a given batch are all of the same age. The graph shows the smoothed average together with a one standard deviation interval around it. Epanechnikov kernel function is used for smoothing. Furthermore, for all given week of age, each bin in the scatterplot shows the average daily number of eggs per hen as averaged across all observations belonging to production units hosting hens of that given age. Productivity is typically low when hens are young, it reaches a peak when hens are around 40 weeks old, and then decreases thereafter until hens are old enough and the batch is discarded. The first goal of the empirical analysis is to identify productivity spillovers. Our conceptual framework shows how the individual effort choice changes with coworkers’ productivity. Workers in neighbouring production units can observe each other, while this is hardly the case for workers located farther away. We therefore hypothesize that workers’ productivity changes with the one of coworkers in neighbouring production units, as they use information on the latter to estimate the overall average productivity.17 To identify productivity spillovers, we estimate the parameters of the following regression specification \begin{equation} y_{igt}= \varphi + \gamma \ \bar{y}_{-igt} + \alpha \ age_{igt} + \beta \ age^2_{igt} + \sum^{t-1}_{s=t-3}\lambda_{s} \ {\it{food}}_{igs} + \varepsilon_{igt}, \end{equation} (12) where $\(y_{igt}\)$ is the daily number of eggs per hen collected by worker $\(i\)$ in shed $\(g\)$ on day $\(t\)$. $\(\bar{y}_{-igt}\)$ captures the corresponding average value for coworkers in neighbouring production units on the same day. Based on Figure 1, we include as regressors the age of hens assigned to the worker, $\(age_{igt}\)$, and its square.18 We also include three lags of total amount of food distributed $\({\it{food}}_{igs}\)$ as controls. This is because we want to investigate the relationship between the variables of interest at time $\(t\)$ and conditional on one relevant and observable dimension of effort exerted by the worker on previous days. Finally, $\(\varepsilon_{igt}\)$ captures idiosyncratic residual determinants of worker’s productivity. By conditioning on both own hens’ age and food distributed on previous days, we aim to identify the relationship between coworkers’ productivity and individual unobserved effort as captured by $\(\gamma\)$. OLS estimates of $\(\gamma\)$ are likely to be biased. First, the above equation defines productivity simultaneously for all workers, leading to the so-called reflection problem first identified by Manski (1993).19 Second, sorting into sheds of hens or workers with the same unobserved characteristics, or idiosyncratic shed-level shocks may push the productivity of neighbouring workers in the same direction, generating a spurious correlation between their outcomes (Manski, 1993; Blume et al., 2011). Nonetheless, hens’ age represents a powerful source of variation. Changes in the age of hens assigned to workers induce exogenous variation in their productivity that we can exploit for identification. Still, to identify a causal effect, the age of coworkers’ hens needs to be orthogonal to other determinants of own productivity, and have no effect on own outcomes other than through changes in coworkers’ productivity. Coworkers’ and own hens’ age in weeks are both a function of time. Even conditional on the full set of day fixed effects, residuals of hens’ age are still positively correlated among neighbouring coworkers, with the estimated correlation coefficient being equal to 0.89. This is because, for logistical reasons, the management allocates batches to production units in a way to replace those in the same shed approximately at the same time.20 However, the exact day in which batch replacement occurs is not the same, so that there is residual variation to exploit. The correlation between coworkers’ and own hens’ age falls to zero when computed conditional on the full set of shed-week fixed effects. The p-value from the test of the null hypothesis of zero correlation between the two variables is equal to 0.45. This means that daily deviations in the age of hens in each production unit from the corresponding shed-week and day averages are orthogonal to each other.21$$^{,}$$22 Evidence does not allow to reject the hypothesis that, conditioning on the full set of day $\(\delta_{t}\)$ and shed-week fixed effects $\(\psi_{gw}\)$, the age of hens assigned to coworkers is orthogonal to own hens’ age. Proposition 2 of Manski (1993) demonstrates how, in the absence of contextual and correlated effects, linear independence between own and peers’ characteristics is a sufficient condition to identify composite endogenous peer effects parameters. It follows that if the age of coworkers’ hens has no direct effect of own productivity, and the full set of day and shed-week fixed effects absorb all the variation in unobservables due to sorting and idiosyncratic shed-level shocks, the age of coworkers’ hens can be used as a source of exogenous variation to identify the causal effect of an increase in coworkers’ productivity on own productivity.23 5.2. Baseline results Table 2 presents the first set of results. In the first column, we regress the daily average number of eggs per hen collected by the worker over the age of hens in weeks and its square. We also include the full set of day fixed effects. This specification yields a quadratic fit of the dependent variable as a function of hens’ age, which is consistent with the evidence in Figure 1. Coefficient estimates are significant at the 1% level and confirm the existence of a concave relationship between hens’ age and productivity.24 In this quadratic specification, together with day fixed effects, hens’ age explains 0.41 of the variability in the dependent variable. The same number rises to 0.43 when we include lags of the amount of food distributed in Column 2. In Column 3, we include the full set of shed-week dummies. The age variables still induce meaningful variation in productivity: coefficients are almost unchanged with respect with those in Column 2. Table 2 Own and coworkers’ hens’ age and productivity Daily number of eggs per hen, $\(y_i\)$ (1) (2) (3) (4) (5) $\(age_i\)$ 0.04073*** 0.03903*** 0.03860*** 0.03822*** 0.03249*** (0.0024) (0.0022) (0.0059) (0.0058) (0.0056) $\(age^2_i\)$ –0.00040*** –0.00038*** –0.00038*** –0.00038*** –0.00032*** (0.0000) (0.0000) (0.0001) (0.0001) (0.0001) $\(\overline{age}_{-i}\)$ –0.00339* –0.00660** (0.0019) (0.0028) $\(\overline{age^2}_{-i}\)$ 0.00002 0.00005 (0.0000) (0.0000) $\(food_{t-1}\)$ 0.00197** 0.00137*** 0.00139*** 0.00452*** (0.0009) (0.0005) (0.0004) (0.0012) $\(food_{t-2}\)$ 0.00088* 0.00078** 0.00080*** 0.00298*** (0.0005) (0.0003) (0.0003) (0.0011) $\(food_{t-3}\)$ 0.00063 –0.00001 –0.00003 0.00313** (0.0010) (0.0004) (0.0004) (0.0012) Day FEs Y Y Y Y Y Shed-week FEs N N Y Y Y Worker FEs N N N N Y Observations 21,213 21,213 21,206 21,206 21,206 $\(R^2\)$ 0.409 0.431 0.859 0.860 0.886 Daily number of eggs per hen, $\(y_i\)$ (1) (2) (3) (4) (5) $\(age_i\)$ 0.04073*** 0.03903*** 0.03860*** 0.03822*** 0.03249*** (0.0024) (0.0022) (0.0059) (0.0058) (0.0056) $\(age^2_i\)$ –0.00040*** –0.00038*** –0.00038*** –0.00038*** –0.00032*** (0.0000) (0.0000) (0.0001) (0.0001) (0.0001) $\(\overline{age}_{-i}\)$ –0.00339* –0.00660** (0.0019) (0.0028) $\(\overline{age^2}_{-i}\)$ 0.00002 0.00005 (0.0000) (0.0000) $\(food_{t-1}\)$ 0.00197** 0.00137*** 0.00139*** 0.00452*** (0.0009) (0.0005) (0.0004) (0.0012) $\(food_{t-2}\)$ 0.00088* 0.00078** 0.00080*** 0.00298*** (0.0005) (0.0003) (0.0003) (0.0011) $\(food_{t-3}\)$ 0.00063 –0.00001 –0.00003 0.00313** (0.0010) (0.0004) (0.0004) (0.0012) Day FEs Y Y Y Y Y Shed-week FEs N N Y Y Y Worker FEs N N N N Y Observations 21,213 21,213 21,206 21,206 21,206 $\(R^2\)$ 0.409 0.431 0.859 0.860 0.886 Notes: (*$$p < 0.1$$; **$$p < 0.05$$; ***$$p < 0.01$$) Ordinary Least Square estimates. Sample is restricted to all production units in sheds with at least one other production unit. Two-way clustered standard errors, with residuals grouped along both shed and day. Dependent variable is the average number of eggs per hen collected by the worker. $\(age_i\)$ is own hens’ age in weeks, while $\(\overline{age}_{-i}\)$ is average age of coworkers’ hens in neighbouring production units. $\(food_{t-s}\)$ are lags of amount of food distributed as measured by 50 kg sacks employed. Table 2 Own and coworkers’ hens’ age and productivity Daily number of eggs per hen, $\(y_i\)$ (1) (2) (3) (4) (5) $\(age_i\)$ 0.04073*** 0.03903*** 0.03860*** 0.03822*** 0.03249*** (0.0024) (0.0022) (0.0059) (0.0058) (0.0056) $\(age^2_i\)$ –0.00040*** –0.00038*** –0.00038*** –0.00038*** –0.00032*** (0.0000) (0.0000) (0.0001) (0.0001) (0.0001) $\(\overline{age}_{-i}\)$ –0.00339* –0.00660** (0.0019) (0.0028) $\(\overline{age^2}_{-i}\)$ 0.00002 0.00005 (0.0000) (0.0000) $\(food_{t-1}\)$ 0.00197** 0.00137*** 0.00139*** 0.00452*** (0.0009) (0.0005) (0.0004) (0.0012) $\(food_{t-2}\)$ 0.00088* 0.00078** 0.00080*** 0.00298*** (0.0005) (0.0003) (0.0003) (0.0011) $\(food_{t-3}\)$ 0.00063 –0.00001 –0.00003 0.00313** (0.0010) (0.0004) (0.0004) (0.0012) Day FEs Y Y Y Y Y Shed-week FEs N N Y Y Y Worker FEs N N N N Y Observations 21,213 21,213 21,206 21,206 21,206 $\(R^2\)$ 0.409 0.431 0.859 0.860 0.886 Daily number of eggs per hen, $\(y_i\)$ (1) (2) (3) (4) (5) $\(age_i\)$ 0.04073*** 0.03903*** 0.03860*** 0.03822*** 0.03249*** (0.0024) (0.0022) (0.0059) (0.0058) (0.0056) $\(age^2_i\)$ –0.00040*** –0.00038*** –0.00038*** –0.00038*** –0.00032*** (0.0000) (0.0000) (0.0001) (0.0001) (0.0001) $\(\overline{age}_{-i}\)$ –0.00339* –0.00660** (0.0019) (0.0028) $\(\overline{age^2}_{-i}\)$ 0.00002 0.00005 (0.0000) (0.0000) $\(food_{t-1}\)$ 0.00197** 0.00137*** 0.00139*** 0.00452*** (0.0009) (0.0005) (0.0004) (0.0012) $\(food_{t-2}\)$ 0.00088* 0.00078** 0.00080*** 0.00298*** (0.0005) (0.0003) (0.0003) (0.0011) $\(food_{t-3}\)$ 0.00063 –0.00001 –0.00003 0.00313** (0.0010) (0.0004) (0.0004) (0.0012) Day FEs Y Y Y Y Y Shed-week FEs N N Y Y Y Worker FEs N N N N Y Observations 21,213 21,213 21,206 21,206 21,206 $\(R^2\)$ 0.409 0.431 0.859 0.860 0.886 Notes: (*$$p < 0.1$$; **$$p < 0.05$$; ***$$p < 0.01$$) Ordinary Least Square estimates. Sample is restricted to all production units in sheds with at least one other production unit. Two-way clustered standard errors, with residuals grouped along both shed and day. Dependent variable is the average number of eggs per hen collected by the worker. $\(age_i\)$ is own hens’ age in weeks, while $\(\overline{age}_{-i}\)$ is average age of coworkers’ hens in neighbouring production units. $\(food_{t-s}\)$ are lags of amount of food distributed as measured by 50 kg sacks employed. In Column 4 of Table 2, we include both averages of the age of hens assigned to coworkers in neighbouring production units and its square as additional regressors. The magnitude of coefficients of the own hen’s age variables experience does not change, confirming the absence of any systematic relationship between own and coworkers’ hens’ age within each shed-week group.25 Any systematic relationship between the average age of coworkers’ hens and own productivity can thus be interpreted as reduced-form evidence of productivity spillovers. The corresponding coefficients are opposite in sign with respect to the ones of own hens’ age. This result is confirmed in Column 5 of Table 2, which also includes worker fixed effects. The latter eliminate any bias in the coefficients of own hens’ age that could arise if batches with specific characteristics are systematically assigned to specific workers. This specification allows to detect systematic differences in the outcome of the same worker according to differences in the age of hens assigned to coworkers. Consistent with these results, Figure 2 shows how, once own hens’ age, day and shed-week fixed effects are controlled for, the relationship between residual productivity and the age of coworkers’ hens is U-shaped: the opposite with respect to the one between productivity and own hens’ age. Conditional on own input quality, workers’ productivity is systematically lower (higher) when coworkers are assigned inputs of higher (lower) quality. We interpret this result as reduced-form evidence of negative productivity spillovers. Figure 2 View largeDownload slide Residual productivity and age of coworkers’ hens. Notes: Once own hens’ age, day and shed-week fixed effects are controlled for, residual productivity is plotted against the age of coworkers’ hens in weeks. Productivity is measured as the average daily number of eggs per hen collected by the worker. Recall that hens in a given batch are all of the same age. The graph shows the smoothed average and its 95% confidence interval, together with the quadratic fit. Conditional on own hens’ age, day and shed-week fixed, workers’ residual productivity is higher (lower) when coworkers are assigned hens of low (high) productivity. Figure 2 View largeDownload slide Residual productivity and age of coworkers’ hens. Notes: Once own hens’ age, day and shed-week fixed effects are controlled for, residual productivity is plotted against the age of coworkers’ hens in weeks. Productivity is measured as the average daily number of eggs per hen collected by the worker. Recall that hens in a given batch are all of the same age. The graph shows the smoothed average and its 95% confidence interval, together with the quadratic fit. Conditional on own hens’ age, day and shed-week fixed, workers’ residual productivity is higher (lower) when coworkers are assigned hens of low (high) productivity. Using the age of coworkers’ hens as a source of variation, we can estimate the effect of coworkers’ productivity $\(\gamma\)$ in our main regression specification by means of 2SLS.26 The first column in Table 3 reports OLS estimates of the parameters from the main regression specification. Column 2 provides the 2SLS estimate of the coefficient of interest. When using both averages of the age of hens assigned to coworkers and its square as instruments for coworkers’ productivity, the value of the F-statistic of a joint test of significance of the instruments in the first-stage regression is equal to 103.31. The 2SLS estimate of $\(\gamma\)$ is negative and significant at the 1% level. The OLS estimate is lower but similar to the 2SLS one. This is because the full set of day, shed-week and worker fixed effects capture the variation in unobserved common shocks and sorting to a large extent, thus eliminating the sources of positive bias. The small downward bias in the OLS estimate can be attributed to the mechanical exclusion bias discussed in Caeyers and Fafchamps (2016), although the relatively high large number of observations per group makes the issue less salient. Table 3 Coworkers’ and own productivity Daily number of eggs per hen, $\(y_i\)$ (1) (2) (3) (4) OLS 2SLS 2SLS 2SLS Coworkers’ –0.29338*** –0.21792*** –0.28778*** –0.29040*** eggs per hen, $\(\bar{y}_{-i}\)$ (0.0764) (0.0651) (0.0705) (0.1004) $\(age_i\)$ 0.03052*** 0.03135*** (0.0057) (0.0057) $\(age^2_i\)$ –0.00030*** –0.00031*** (0.0001) (0.0001) $\(food_{t-1}\)$ 0.00431*** 0.00432*** 0.00404*** 0.00411*** (0.0012) (0.0012) (0.0011) (0.0012) $\(food_{t-2}\)$ 0.00274*** 0.00277*** 0.00249*** 0.00262*** (0.0011) (0.0011) (0.0009) (0.0010) $\(food_{t-3}\)$ 0.00268** 0.00277** 0.00217** 0.00221** (0.0011) (0.0011) (0.0010) (0.0011) 1st Stage F-stat n.a. 103.31 46.90 60.12 Shed-week FEs Y Y Y Y Age dummies N N Y Y Day FEs Y Y Y Y Worker FEs Y Y Y Y Batch FEs N N N Y Observations 21,206 21,206 21,206 21,206 $\(R^2\)$ 0.892 0.889 0.919 0.928 Daily number of eggs per hen, $\(y_i\)$ (1) (2) (3) (4) OLS 2SLS 2SLS 2SLS Coworkers’ –0.29338*** –0.21792*** –0.28778*** –0.29040*** eggs per hen, $\(\bar{y}_{-i}\)$ (0.0764) (0.0651) (0.0705) (0.1004) $\(age_i\)$ 0.03052*** 0.03135*** (0.0057) (0.0057) $\(age^2_i\)$ –0.00030*** –0.00031*** (0.0001) (0.0001) $\(food_{t-1}\)$ 0.00431*** 0.00432*** 0.00404*** 0.00411*** (0.0012) (0.0012) (0.0011) (0.0012) $\(food_{t-2}\)$ 0.00274*** 0.00277*** 0.00249*** 0.00262*** (0.0011) (0.0011) (0.0009) (0.0010) $\(food_{t-3}\)$ 0.00268** 0.00277** 0.00217** 0.00221** (0.0011) (0.0011) (0.0010) (0.0011) 1st Stage F-stat n.a. 103.31 46.90 60.12 Shed-week FEs Y Y Y Y Age dummies N N Y Y Day FEs Y Y Y Y Worker FEs Y Y Y Y Batch FEs N N N Y Observations 21,206 21,206 21,206 21,206 $\(R^2\)$ 0.892 0.889 0.919 0.928 Notes: (*$$p < 0.1$$; **$$p < 0.05$$; ***$$p< 0.01$$) (1), OLS estimates; (2)–(4) 2SLS estimates. Sample is restricted to all production units in sheds with at least one other production unit. Two-way clustered standard errors, with residuals grouped along both shed and day. Dependent variable is the average number of eggs per hen collected by the worker. Main variable of interest is average daily number of eggs per hen collected by coworkers in neighbouring production units, $\(\bar{y}_{-i}\)$. $\(age_i\)$ is own hens’ age in weeks. In (2) average age of coworkers’ hens and the average of its square $\((\overline{age}_{-i},\overline{age^2}_{-i})\)$ are used as instruments in the first stage. The full set of coworkers’ hens’ age dummies is used in the first stage in (3) and (4). $\(food_{t-s}\)$ are lags of amount of food distributed as measured by 50 kg sacks employed. Table 3 Coworkers’ and own productivity Daily number of eggs per hen, $\(y_i\)$ (1) (2) (3) (4) OLS 2SLS 2SLS 2SLS Coworkers’ –0.29338*** –0.21792*** –0.28778*** –0.29040*** eggs per hen, $\(\bar{y}_{-i}\)$ (0.0764) (0.0651) (0.0705) (0.1004) $\(age_i\)$ 0.03052*** 0.03135*** (0.0057) (0.0057) $\(age^2_i\)$ –0.00030*** –0.00031*** (0.0001) (0.0001) $\(food_{t-1}\)$ 0.00431*** 0.00432*** 0.00404*** 0.00411*** (0.0012) (0.0012) (0.0011) (0.0012) $\(food_{t-2}\)$ 0.00274*** 0.00277*** 0.00249*** 0.00262*** (0.0011) (0.0011) (0.0009) (0.0010) $\(food_{t-3}\)$ 0.00268** 0.00277** 0.00217** 0.00221** (0.0011) (0.0011) (0.0010) (0.0011) 1st Stage F-stat n.a. 103.31 46.90 60.12 Shed-week FEs Y Y Y Y Age dummies N N Y Y Day FEs Y Y Y Y Worker FEs Y Y Y Y Batch FEs N N N Y Observations 21,206 21,206 21,206 21,206 $\(R^2\)$ 0.892 0.889 0.919 0.928 Daily number of eggs per hen, $\(y_i\)$ (1) (2) (3) (4) OLS 2SLS 2SLS 2SLS Coworkers’ –0.29338*** –0.21792*** –0.28778*** –0.29040*** eggs per hen, $\(\bar{y}_{-i}\)$ (0.0764) (0.0651) (0.0705) (0.1004) $\(age_i\)$ 0.03052*** 0.03135*** (0.0057) (0.0057) $\(age^2_i\)$ –0.00030*** –0.00031*** (0.0001) (0.0001) $\(food_{t-1}\)$ 0.00431*** 0.00432*** 0.00404*** 0.00411*** (0.0012) (0.0012) (0.0011) (0.0012) $\(food_{t-2}\)$ 0.00274*** 0.00277*** 0.00249*** 0.00262*** (0.0011) (0.0011) (0.0009) (0.0010) $\(food_{t-3}\)$ 0.00268** 0.00277** 0.00217** 0.00221** (0.0011) (0.0011) (0.0010) (0.0011) 1st Stage F-stat n.a. 103.31 46.90 60.12 Shed-week FEs Y Y Y Y Age dummies N N Y Y Day FEs Y Y Y Y Worker FEs Y Y Y Y Batch FEs N N N Y Observations 21,206 21,206 21,206 21,206 $\(R^2\)$ 0.892 0.889 0.919 0.928 Notes: (*$$p < 0.1$$; **$$p < 0.05$$; ***$$p< 0.01$$) (1), OLS estimates; (2)–(4) 2SLS estimates. Sample is restricted to all production units in sheds with at least one other production unit. Two-way clustered standard errors, with residuals grouped along both shed and day. Dependent variable is the average number of eggs per hen collected by the worker. Main variable of interest is average daily number of eggs per hen collected by coworkers in neighbouring production units, $\(\bar{y}_{-i}\)$. $\(age_i\)$ is own hens’ age in weeks. In (2) average age of coworkers’ hens and the average of its square $\((\overline{age}_{-i},\overline{age^2}_{-i})\)$ are used as instruments in the first stage. The full set of coworkers’ hens’ age dummies is used in the first stage in (3) and (4). $\(food_{t-s}\)$ are lags of amount of food distributed as measured by 50 kg sacks employed. The use of hens’ age and its square as predictors of daily output imposes a precise functional form to the relationship between the two variables. The parameter of interest can be identified more accurately using the full set of own and coworkers’ hens week-of-age dummies respectively as regressors and instruments. Column 3 of Table 3 shows the corresponding results. The F-statistic of a joint test of significance of all the instrument dummies in the first stage is equal to 46.90, and the 2SLS parameter estimate is comparable to the previous one. Finally, in Column 4, we include the full set of hen batch fixed effects. This allows to exploit variation in hens’ age over time within each assigned batch, netting out time-invariant batch characteristics which can be correlated with productivity. The first-stage F-statistic is now equal to 60.12, and the estimate of the coefficient of interest remains unchanged and significant at the 1% level. According to these estimates, one standard deviation increase in average coworkers’ daily output is associated with a decrease in own daily output of almost a third of its standard deviation. If all workers are assigned the same number of hens, an increase of average coworkers’ output of 500 eggs causes the number of own collected eggs to fall by 150. Evidence supports the hypothesis of negative productivity spillovers among coworkers in neighbouring production units. 5.2.1. Sources of identifying variation As explained in Section 5.1, hen batches are not replaced on the same day. Such differences in the exact day of replacement constitute the primary source of variation in the age of hens assigned to coworkers. One first concern with the previous results is that the exact day of coworkers’ batch replacement could be correlated with pre-existing trends in individual productivity. Table A.5 in Supplementary Appendix A.1 shows the coefficient estimates from a regression of a dummy equal to one if the batch assigned to neighbouring coworkers was replaced in a given day over lags of individual productivity. Evidence shows the absence of any systematic relationship between past productivity and the probability of a batch replacement in neighbouring production units. Second, Section 3 explains that the technology of production and storage is independent among production units. Still, coworkers’ batch replacement may have a direct effect of individual productivity. This could be the case if new, young hens are more noisy, or if the process of batch replacement generates any kind of disruption in worker’s operations. The productivity of workers operating older hens would thus be lower on the days following coworkers’ batch replacement. Our conversations with the firm suggest that this is not the case.27 This is also consistent with the available evidence. Figure A.4 in Supplementary Appendix A.1 plots worker’s residual productivity around the day of coworkers’ batch replacement. We find no evidence of discontinuity. If anything, the arrival of new hens in the shed increases the productivity of those workers who are still assigned old hens, but the increase is not statistically distinguishable from zero.28 The results in Table A.6 in Supplementary Appendix A.1 further address these issues in a regression framework. We report 2SLS coefficient estimates from our main regression specification across different subsamples. In Column 1, we exclude those observations belonging to production units with very old hens (more than 80 weeks old) and surrounded by production units with very young hens (less than 22 weeks old on average). The estimate of our coefficient of interest is still equal to $$-$$0.31 and significant at the 5% level. In Column 2, we exclude all production units with very old or very young hens altogether: the estimated coefficient is equal to $$-$$0.25 and still significant at the 5% level. In Columns 3 to 6, we progressively exclude all observations within 1, 2, 3, and 4 weeks respectively from the date of own or coworkers’ batch replacement. The decreasing value of the F-statistic for the joint test of significance of the instruments in the first stage reveals that the instruments lose strength when we exclude those observations where most of the variation in age comes from. Still, even when excluding observations within one month from coworkers’ batch replacement, the value of the F-statistic is above 10 and the estimated coefficient of interest is equal to $$-$$0.40 and significant at the 5% level. In Column 7, we exclude those observations belonging to weeks in which any of the workers in the shed was replaced by a new one, with little consequences on both the magnitude and significance of our estimates.29 We interpret these results altogether as showing that the variation we exploit for identification does not belong only to those periods where the match between workers and hen batches is disrupted, but also to periods where the match is stable. Differences in the exact day of batch replacement map into initial differences in the age of hens assigned to coworkers. These differences persist through the productive life of hens, shaping differences in workers’ output non-linearly over time as hens get old.30 5.2.2. The size of spillovers Above and beyond the specific sources of variation, one may wonder whether the effect we find is plausible. First, the variation in the productivity of coworkers induced by changes in their hens’ age is detectable. The average difference between own and coworkers’ hens’ age is 3.22 weeks, corresponding to an average productivity difference of 0.06 daily eggs per hen. Figure 1 suggests that the same three-weeks difference in age can amount to large or small productivity differences, depending on the hens’ stage of life. For example, the average daily number of eggs per hen is 0.06 when hens are 19 weeks old, but is more than eight times larger at age 22, being equal to 0.50: a 0.44 productivity difference, equal to 4,400 eggs more for a batch of 10,000 hens. A similar but opposite pattern holds when productivity starts to decrease in the last stages of a hen’s life. This means that even a small variation in hen’s age can have a sizable and observable impact on daily output, at least when hens are far from their productivity peak age. Although opposite in sign, the magnitude of our estimates is comparable with the one found in previous studies of productivity spillovers (Gould and Winter, 2009; Bandiera et al., 2010; Herbst and Mas, 2015). Perhaps more importantly, the negative sign makes the aggregate implications for overall productivity smaller. When a given worker is assigned inputs of higher quality his productivity increases. Because of negative spillovers, coworkers’ productivity decreases. These effects reverberate through the system. It follows that, although the individual response is positive and higher than in isolation, the decrease in coworkers’ productivity makes the aggregate response of the system lower than what it would be in the absence of spillovers. This is not the case when spillovers are positive and the aggregate response is higher than in the absence of externalities.31 5.3. Feeding effort and output quality The previous results show that, conditional on own input quality, workers’ productivity is systematically lower (higher) when inputs make neighbouring coworkers more (less) productive. We claim that such negative spillover effect occurs through changes in the level of effort exerted by the worker. Hens’ feeding is one observable dimension of effort. We replace the average amount of food per hen distributed by the worker as outcome in the main specification. The first column of Table 4 shows the corresponding 2SLS estimates. The estimated coefficient of coworkers’ productivity is negative, consistent with our interpretation of previous results. However, the estimate is not significantly different from zero. This indicates that the effect of coworkers’ productivity operates through changes in other dimensions of effort. Table 4 Feeding effort and output quality Food (gr) Good/total Broken/total Dirty/total Deaths/hens (1) (2) (3) (4) (5) Coworkers’ –34.88524 –0.15403*** 0.00948 0.06619** –0.01624 eggs per hen, $\(\bar{y}_{-i}\)$ (60.7982) (0.0416) (0.0131) (0.0323) (0.0167) $\(food_{t-1}\)$ 0.38861 0.00176*** –0.00031*** –0.00096*** 0.00003 (0.6388) (0.0005) (0.0001) (0.0003) (0.0001) $\(food_{t-2}\)$ 1.09963** 0.00109** –0.00011 –0.00070** –0.00020** (0.5424) (0.0005) (0.0001) (0.0003) (0.0001) $\(food_{t-3}\)$ 0.33709 0.00002 –0.00005 –0.00018 –0.00003 (0.2755) (0.0005) (0.0001) (0.0003) (0.0001) 1st Stage F-stat 60.12 23.74 23.74 23.74 116.79 Shed-week FEs Y Y Y Y Y Age dummies Y Y Y Y Y Day FEs Y Y Y Y Y Worker FEs Y Y Y Y Y Batch FEs Y Y Y Y Y Outcome mean 22.351 0.857 0.024 0.059 0.001 Observations 21,206 21,035 21,035 21,035 19,679 $\(R^2\)$ 0.235 0.846 0.907 0.714 0.270 Food (gr) Good/total Broken/total Dirty/total Deaths/hens (1) (2) (3) (4) (5) Coworkers’ –34.88524 –0.15403*** 0.00948 0.06619** –0.01624 eggs per hen, $\(\bar{y}_{-i}\)$ (60.7982) (0.0416) (0.0131) (0.0323) (0.0167) $\(food_{t-1}\)$ 0.38861 0.00176*** –0.00031*** –0.00096*** 0.00003 (0.6388) (0.0005) (0.0001) (0.0003) (0.0001) $\(food_{t-2}\)$ 1.09963** 0.00109** –0.00011 –0.00070** –0.00020** (0.5424) (0.0005) (0.0001) (0.0003) (0.0001) $\(food_{t-3}\)$ 0.33709 0.00002 –0.00005 –0.00018 –0.00003 (0.2755) (0.0005) (0.0001) (0.0003) (0.0001) 1st Stage F-stat 60.12 23.74 23.74 23.74 116.79 Shed-week FEs Y Y Y Y Y Age dummies Y Y Y Y Y Day FEs Y Y Y Y Y Worker FEs Y Y Y Y Y Batch FEs Y Y Y Y Y Outcome mean 22.351 0.857 0.024 0.059 0.001 Observations 21,206 21,035 21,035 21,035 19,679 $\(R^2\)$ 0.235 0.846 0.907 0.714 0.270 Notes: (*$$p < 0.1$$; **$$p < 0.05$$; ***$$p <$$0.01) 2SLS estimates. Sample is restricted to all production units in sheds with at least one other production unit. Two-way clustered standard errors, with residuals grouped along both shed and day. Dependent variable are: average daily amount of food in grams distributed (1), fraction of good eggs over the total (2), fraction of broken eggs over the total (3), fraction of dirty eggs over the total (4), fraction of hens dying in the day (5). Main variable of interest is average daily number of eggs per hen collected by coworkers in neighbouring production units, $\(\bar{y}_{-i}\)$. The full set of own hens’ age dummies are included as controls, while the full set of coworkers’ hens’ age dummies is used in the first stage in all specifications. $\(food_{t-s}\)$ are lags of amount of food distributed as measured by 50 kg sacks employed. Table 4 Feeding effort and output quality Food (gr) Good/total Broken/total Dirty/total Deaths/hens (1) (2) (3) (4) (5) Coworkers’ –34.88524 –0.15403*** 0.00948 0.06619** –0.01624 eggs per hen, $\(\bar{y}_{-i}\)$ (60.7982) (0.0416) (0.0131) (0.0323) (0.0167) $\(food_{t-1}\)$ 0.38861 0.00176*** –0.00031*** –0.00096*** 0.00003 (0.6388) (0.0005) (0.0001) (0.0003) (0.0001) $\(food_{t-2}\)$ 1.09963** 0.00109** –0.00011 –0.00070** –0.00020** (0.5424) (0.0005) (0.0001) (0.0003) (0.0001) $\(food_{t-3}\)$ 0.33709 0.00002 –0.00005 –0.00018 –0.00003 (0.2755) (0.0005) (0.0001) (0.0003) (0.0001) 1st Stage F-stat 60.12 23.74 23.74 23.74 116.79 Shed-week FEs Y Y Y Y Y Age dummies Y Y Y Y Y Day FEs Y Y Y Y Y Worker FEs Y Y Y Y Y Batch FEs Y Y Y Y Y Outcome mean 22.351 0.857 0.024 0.059 0.001 Observations 21,206 21,035 21,035 21,035 19,679 $\(R^2\)$ 0.235 0.846 0.907 0.714 0.270 Food (gr) Good/total Broken/total Dirty/total Deaths/hens (1) (2) (3) (4) (5) Coworkers’ –34.88524 –0.15403*** 0.00948 0.06619** –0.01624 eggs per hen, $\(\bar{y}_{-i}\)$ (60.7982) (0.0416) (0.0131) (0.0323) (0.0167) $\(food_{t-1}\)$ 0.38861 0.00176*** –0.00031*** –0.00096*** 0.00003 (0.6388) (0.0005) (0.0001) (0.0003) (0.0001) $\(food_{t-2}\)$ 1.09963** 0.00109** –0.00011 –0.00070** –0.00020** (0.5424) (0.0005) (0.0001) (0.0003) (0.0001) $\(food_{t-3}\)$ 0.33709 0.00002 –0.00005 –0.00018 –0.00003 (0.2755) (0.0005) (0.0001) (0.0003) (0.0001) 1st Stage F-stat 60.12 23.74 23.74 23.74 116.79 Shed-week FEs Y Y Y Y Y Age dummies Y Y Y Y Y Day FEs Y Y Y Y Y Worker FEs Y Y Y Y Y Batch FEs Y Y Y Y Y Outcome mean 22.351 0.857 0.024 0.059 0.001 Observations 21,206 21,035 21,035 21,035 19,679 $\(R^2\)$ 0.235 0.846 0.907 0.714 0.270 Notes: (*$$p < 0.1$$; **$$p < 0.05$$; ***$$p <$$0.01) 2SLS estimates. Sample is restricted to all production units in sheds with at least one other production unit. Two-way clustered standard errors, with residuals grouped along both shed and day. Dependent variable are: average daily amount of food in grams distributed (1), fraction of good eggs over the total (2), fraction of broken eggs over the total (3), fraction of dirty eggs over the total (4), fraction of hens dying in the day (5). Main variable of interest is average daily number of eggs per hen collected by coworkers in neighbouring production units, $\(\bar{y}_{-i}\)$. The full set of own hens’ age dummies are included as controls, while the full set of coworkers’ hens’ age dummies is used in the first stage in all specifications. $\(food_{t-s}\)$ are lags of amount of food distributed as measured by 50 kg sacks employed. Column 2 to 5 of Table 4 show 2SLS estimates of the effect of coworkers’ productivity on output quality. Coworkers’ productivity is negatively and systematically correlated with the own fraction of good eggs over the total. A one standard deviation increase in coworkers’ productivity causes a 3 percentage points decrease in the fraction of good eggs. Column 3 shows a positive correlation between coworkers’ productivity and the fraction of broken eggs, although the estimate is not statistically significant. This is not the case for the estimate in Column 4 which shows that coworkers’ productivity increases the fraction of dirty eggs. Workers can turn dirty eggs into good ones: the results in Column 2 and 4 together indicate that workers exert less effort in cleaning dirty eggs when coworkers are more productive. Finally, Column 5 shows that coworkers’ productivity negatively affects the hens’ mortality rate, but the corresponding estimate is insignificant. This is particularly important, as the number of living hens on a given day may be itself endogenous to worker’s effort. The absence of a systematic relationship between hens’ death and coworkers’ productivity lead us to conclude that our estimates of productivity spillovers are not the result of a strategic decision of workers to adjust the number of living hens to coworkers’ input quality and productivity. Overall, estimates in Table 4 show that coworkers’ productivity negatively affects not only own output but its quality as well. These results suggest that coworkers’ productivity does not affect all the dimensions of worker’s effort in the same way. The effect of coworkers’ productivity on own productivity appears to work through changes in effort along dimensions other than total food distribution, such as those related to egg collection and uniform feeding discussed in Section 3. Egg cleaning effort is also negatively affected, while coworkers’ productivity does not seem to affect those components of effort which map into hens’ survival probabilities, such as cleaning and maintenance of the facilities. These results can be explained by the level of heterogeneity in the observability of each one of these different effort categories, which in turn determine the scope for free riding. Indeed, while it is easier for a worker to detect if a coworker is shirking on the amount of food distributed to the hens or the maintenance of facilities, it is supposedly harder to detect the effort exerted by coworkers while walking along cages within the unit or smoothing the same amount of food across the hens. 5.4. Additional results and effect heterogeneity Workers in non-neighbouring production units can hardly interact or observe each other. In Column 1 and 2 of Table 5, we replace as main regressor the average productivity of coworkers in the adjacent shed and non-neighbouring production units respectively.32 2SLS point estimates are negligible in magnitude and not significantly different from zero. We interpret these findings as evidence that observability between workers plays a crucial role. Table 5 Robustness checks and effect heterogeneity Daily number of eggs per hen, $\(y_i\)$ (1) (2) (3) (4) (5) (6) $\(\ln y_i\)$ High ability Low ability Other shed workers’ 0.00680 eggs per hen, $\(\tilde{y}_{-i}\)$ (0.0402) Non-neighbouring workers’ –0.01734 eggs per hen, $\(\tilde{y}_{-i}\)$ (0.0567) Coworkers’ –1.47172*** –0.28373*** –0.01841 –0.25628*** Eggs per hen, $\(\bar{y}_{-i}\)$ (0.3734) (0.0661) (0.0601) (0.0891) $\(food_{t-1}\)$ 0.00414*** 0.00458*** 0.01271*** 0.00411*** 0.00305*** 0.00543*** (0.0012) (0.00122) (0.0043) (0.0012) (0.0012) (0.0020) $\(food_{t-2}\)$ 0.00276*** 0.00298*** 0.01125*** 0.00263*** 0.00205*** 0.00275** (0.0010) (0.00080) (0.0038) (0.0010) (0.0007) (0.0013) $\(food_{t-3}\)$ 0.00240** 0.00218*** 0.00986** 0.00222** 0.00154** 0.00395** (0.0011) (0.00080) (0.0040) (0.0011) (0.0006) (0.0017) 1st Stage F-stat 11.01 40.71 60.12 29.56 22.27 232.50 Shed-week FEs Y Y Y Y Y Y Age dummies Y Y Y Y Y Y Day FEs Y Y Y Y Y Y Worker FEs Y Y Y Y Y Y Batch FEs Y Y Y Y Y Y Observations 20,223 8,294 21,206 21,206 10,024 11,168 $\(R^2\)$ 0.926 0.887 0.900 0.928 0.960 0.953 Daily number of eggs per hen, $\(y_i\)$ (1) (2) (3) (4) (5) (6) $\(\ln y_i\)$ High ability Low ability Other shed workers’ 0.00680 eggs per hen, $\(\tilde{y}_{-i}\)$ (0.0402) Non-neighbouring workers’ –0.01734 eggs per hen, $\(\tilde{y}_{-i}\)$ (0.0567) Coworkers’ –1.47172*** –0.28373*** –0.01841 –0.25628*** Eggs per hen, $\(\bar{y}_{-i}\)$ (0.3734) (0.0661) (0.0601) (0.0891) $\(food_{t-1}\)$ 0.00414*** 0.00458*** 0.01271*** 0.00411*** 0.00305*** 0.00543*** (0.0012) (0.00122) (0.0043) (0.0012) (0.0012) (0.0020) $\(food_{t-2}\)$ 0.00276*** 0.00298*** 0.01125*** 0.00263*** 0.00205*** 0.00275** (0.0010) (0.00080) (0.0038) (0.0010) (0.0007) (0.0013) $\(food_{t-3}\)$ 0.00240** 0.00218*** 0.00986** 0.00222** 0.00154** 0.00395** (0.0011) (0.00080) (0.0040) (0.0011) (0.0006) (0.0017) 1st Stage F-stat 11.01 40.71 60.12 29.56 22.27 232.50 Shed-week FEs Y Y Y Y Y Y Age dummies Y Y Y Y Y Y Day FEs Y Y Y Y Y Y Worker FEs Y Y Y Y Y Y Batch FEs Y Y Y Y Y Y Observations 20,223 8,294 21,206 21,206 10,024 11,168 $\(R^2\)$ 0.926 0.887 0.900 0.928 0.960 0.953 Notes: (*$$p < 0.1$$; **$$p < 0.05$$; ***$$p < 0.01$$) 2SLS estimates. Sample is restricted to all production units in sheds with at least one other production unit. Subsamples in (5) and (6) are derived as discussed in Section 5.4. Two-way clustered standard errors, with residuals grouped along both shed and day. Dependent variable is average number of eggs per hen collected by the worker in all columns but (3), where the log of its value augmented by 0.01 is considered. Main variable of interest in (1) is average daily number of eggs per hen collected by coworkers in adjacent shed; in (2) is average daily number of eggs per hen collected by coworkers in the same shed, but in non-neighbouring production units; in (3) to (6) is average daily number of eggs per hen collected by coworkers in neighbouring production units, $\(\bar{y}_{-i}\)$. The full set of own hens’ age dummies are included as controls. The full set of coworkers’ hens’ age dummies is used in the first stage in all columns but (4), where expected hens’ productivity per week of age as reported by bird producer is used as instrument. $\(food_{t-s}\)$ are lags of amount of food distributed as measured by 50 kg sacks employed. Table 5 Robustness checks and effect heterogeneity Daily number of eggs per hen, $\(y_i\)$ (1) (2) (3) (4) (5) (6) $\(\ln y_i\)$ High ability Low ability Other shed workers’ 0.00680 eggs per hen, $\(\tilde{y}_{-i}\)$ (0.0402) Non-neighbouring workers’ –0.01734 eggs per hen, $\(\tilde{y}_{-i}\)$ (0.0567) Coworkers’ –1.47172*** –0.28373*** –0.01841 –0.25628*** Eggs per hen, $\(\bar{y}_{-i}\)$ (0.3734) (0.0661) (0.0601) (0.0891) $\(food_{t-1}\)$ 0.00414*** 0.00458*** 0.01271*** 0.00411*** 0.00305*** 0.00543*** (0.0012) (0.00122) (0.0043) (0.0012) (0.0012) (0.0020) $\(food_{t-2}\)$ 0.00276*** 0.00298*** 0.01125*** 0.00263*** 0.00205*** 0.00275** (0.0010) (0.00080) (0.0038) (0.0010) (0.0007) (0.0013) $\(food_{t-3}\)$ 0.00240** 0.00218*** 0.00986** 0.00222** 0.00154** 0.00395** (0.0011) (0.00080) (0.0040) (0.0011) (0.0006) (0.0017) 1st Stage F-stat 11.01 40.71 60.12 29.56 22.27 232.50 Shed-week FEs Y Y Y Y Y Y Age dummies Y Y Y Y Y Y Day FEs Y Y Y Y Y Y Worker FEs Y Y Y Y Y Y Batch FEs Y Y Y Y Y Y Observations 20,223 8,294 21,206 21,206 10,024 11,168 $\(R^2\)$ 0.926 0.887 0.900 0.928 0.960 0.953 Daily number of eggs per hen, $\(y_i\)$ (1) (2) (3) (4) (5) (6) $\(\ln y_i\)$ High ability Low ability Other shed workers’ 0.00680 eggs per hen, $\(\tilde{y}_{-i}\)$ (0.0402) Non-neighbouring workers’ –0.01734 eggs per hen, $\(\tilde{y}_{-i}\)$ (0.0567) Coworkers’ –1.47172*** –0.28373*** –0.01841 –0.25628*** Eggs per hen, $\(\bar{y}_{-i}\)$ (0.3734) (0.0661) (0.0601) (0.0891) $\(food_{t-1}\)$ 0.00414*** 0.00458*** 0.01271*** 0.00411*** 0.00305*** 0.00543*** (0.0012) (0.00122) (0.0043) (0.0012) (0.0012) (0.0020) $\(food_{t-2}\)$ 0.00276*** 0.00298*** 0.01125*** 0.00263*** 0.00205*** 0.00275** (0.0010) (0.00080) (0.0038) (0.0010) (0.0007) (0.0013) $\(food_{t-3}\)$ 0.00240** 0.00218*** 0.00986** 0.00222** 0.00154** 0.00395** (0.0011) (0.00080) (0.0040) (0.0011) (0.0006) (0.0017) 1st Stage F-stat 11.01 40.71 60.12 29.56 22.27 232.50 Shed-week FEs Y Y Y Y Y Y Age dummies Y Y Y Y Y Y Day FEs Y Y Y Y Y Y Worker FEs Y Y Y Y Y Y Batch FEs Y Y Y Y Y Y Observations 20,223 8,294 21,206 21,206 10,024 11,168 $\(R^2\)$ 0.926 0.887 0.900 0.928 0.960 0.953 Notes: (*$$p < 0.1$$; **$$p < 0.05$$; ***$$p < 0.01$$) 2SLS estimates. Sample is restricted to all production units in sheds with at least one other production unit. Subsamples in (5) and (6) are derived as discussed in Section 5.4. Two-way clustered standard errors, with residuals grouped along both shed and day. Dependent variable is average number of eggs per hen collected by the worker in all columns but (3), where the log of its value augmented by 0.01 is considered. Main variable of interest in (1) is average daily number of eggs per hen collected by coworkers in adjacent shed; in (2) is average daily number of eggs per hen collected by coworkers in the same shed, but in non-neighbouring production units; in (3) to (6) is average daily number of eggs per hen collected by coworkers in neighbouring production units, $\(\bar{y}_{-i}\)$. The full set of own hens’ age dummies are included as controls. The full set of coworkers’ hens’ age dummies is used in the first stage in all columns but (4), where expected hens’ productivity per week of age as reported by bird producer is used as instrument. $\(food_{t-s}\)$ are lags of amount of food distributed as measured by 50 kg sacks employed. In Column 3 of Table 5, we replace the natural logarithm of the daily average number of eggs per hen collected as outcome.33 The estimated coefficient of interest is still significant at the 1% level, and equal to $$-$$1.47. This implies that an increase in coworkers’ average output of one standard deviation is associated with a 29% decrease in own output, consistent with previous results. In Column 4 of Table 5, we implement an alternative identification strategy where we use as instrument for coworkers’ productivity the expected hens’ productivity measure in the data. Such measure is elaborated by the supplier company that sells hen batches to the firm we investigate. It measures the average number of eggs per week each hen is expected to produce at every week of its age. This measure is thus predetermined and exogenous to anything specific to the egg production phase, including workers’ characteristics and their actual effort choice. When used as instrument, the first-stage F-statistic is equal to 29.56. The estimated coefficient of coworkers’ productivity is highly significant and remarkably similar to the ones derived before.34 We have so far abstracted from dynamic considerations. The actions taken by the worker in a given day (especially those related to hen feeding and cleaning of facilities) may affect output not only on that same day, but also in the following period. We have already partially taken into account this possibility by including the lags of food distributed by the worker. To address these concerns further, we include in the baseline regression specification the lags of own and coworkers’ productivity. Given the high correlation between the output levels of a given production unit in subsequent days, we consider one and two-week lags. Including the lag of the dependent variable as regressor in a specification with unit fixed effects can lead to biased coefficient estimates (Nickell, 1981). We address this issue by instrumenting the lag of own productivity with the two-week lag of own hens’ age and its square in all specifications. Similarly, we instrument both the contemporaneous and the lag of coworkers’ productivity with the two-week lag of coworkers’ hens’ age and its square.35Table A.9 in Supplementary Appendix A.1 shows the corresponding results. The coefficient of coworkers’ average productivity on the same day remains negative and significant at least at the 10% level across all specifications. This indicates that the estimated negative spillovers are not explained by own or coworkers’ productivity trends or the dynamic features of the production process. To conclude, we explore heterogeneity in the size of spillovers according to workers’ ability. Similarly to Bandiera et al. (2005) and Mas and Moretti (2009), we estimate the full set of worker fixed effects in a regression specification that also includes as regressors hens’ week-of-age dummies, batch and day fixed effects.36 We then split the workers into high and low ability according to their position relative to the median in the estimated fixed effect distribution, and assign observations belonging to the worker’s assigned production unit to the two corresponding subsamples. The parameter of interest is estimated separately and results reported in Columns 5 and 6 of Table 5. The estimated coefficient is negative and significant only for low ability workers, suggesting that high ability do not respond to changes in coworkers’ productivity. As we discuss in Section 7, this is consistent with high ability workers being more likely to hit the bonus threshold and thus be exposed to piece rate incentives. 6. The Mechanism The conceptual framework identifies the termination policy implemented by the management as the source of free riding and negative productivity spillovers among workers. In evaluating workers, the management attaches a positive weight on the average productivity of all workers on the same day. When average productivity increases, the evaluation of each given worker increases, and so does the probability of keeping the job. It follows that workers free ride on each other, decreasing their supply of effort when coworkers are more productive. A close inspection of the data reveals that turnover is exceptionally high at this firm. Throughout the nine months of observations in our sample, we observe 23 terminations of employment relationship over a workforce of 97 workers. The firm we are studying is close to have monopsony power in the local labour market. It is located in rural Peru, the average wage over the sampling period is more than 50% higher than the legally established minimum wage in the country, and close to the nationwide average.37 The firm is the biggest employer in the three closest small towns. Although the data we have do not allow to distinguish between dismissals and voluntary quits, evidence is in favour of an efficiency wage argument, where the firm pays high wages while using the threat of dismissal as an incentive device (Shapiro and Stiglitz, 1984). 6.1. Termination policy: empirics The goal of this section is to provide evidence that supports our formalization of the mechanism in Section 2 by showing that (1) individual termination probabilities are negatively correlated with both own and average productivity, and (2) marginal returns from own productivity in terms of increased probability of keeping the job decrease with coworkers’ productivity. We implement a logistic hazard model and study the relative odds of the probability $\(1-q(\cdot)\)$ of losing the job after $\(t\)$ days as defined by \begin{equation}\label{eq:term} \frac{1-q(t)}{q(t)}=\frac{h(t)}{1-h(t)}=\exp\{\gamma_{t} + \alpha \ y_{igt}+ \beta \ \bar{y}_{t}\}, \end{equation} (13) where $\(y_{igt}\)$ is the productivity of worker $\(i\)$ operating in shed $\(g\)$ on day $\(t\)$, and $\(\bar{y}_{t}\)$ is the average productivity among all workers on the same day. $\(t\)$ measures tenure on the job and is defined as days since the worker first appears in the data and is assigned to a given production unit. $\(\gamma_{t}\)$ accounts for the relative odds of baseline hazard on day $\(t\)$. Specifically, we let $\(\gamma_{t}=\delta \ln t\)$, and we estimate $\(\delta\)$ together with $\(\alpha\)$ and $\(\beta\)$. This approach allows the baseline hazard of losing the job to increase or decrease monotonically with tenure at different rates depending on the value of $\(\delta\)$.38 We report maximum likelihood estimates of the coefficients in the first three columns of Table 6. The estimated $\(\delta\)$ is negative across all specifications, indicating that the relative odds of the baseline probability of losing the job decrease with tenure, although not significantly so. Column 1 shows that an increase in own productivity is associated with a decrease in the odds of employment termination, but not significantly so. Conditional on own productivity, an increase in average productivity is highly significantly associated with a decrease in the odds of termination. Coefficient signs and predicted probabilities are such that returns from own productivity in terms of retention probability are always lower at the margin when coworkers’ productivity increases.39 Table 6 Termination policy Logit of termination probability (Coefficients) (1) (2) (3) (4) (5) (6) $\(y_{igt}\)$ –1.0147 –0.3751 –1.2737 (0.7377) (2.5079) (1.9843) $\(\bar{y}_{t}\)$ –6.6506*** –6.5854*** –6.0210*** (1.0439) (1.0650) (2.2966) $\(\bar{y}_{gt}\)$ –0.7095 (2.6394) $\(Y_{igt}\)$ –0.0865 –0.0560 –0.0970 (0.0530) 0.1750) ( 0.1503) $\(\bar{Y}_{t}\)$ –0.0006*** –0.0006*** –0.0006*** (0.0001) (0.0001) (0.0002) $\(\bar{Y}_{gt}\)$ –0.0000 (0.0002) $\(\ln t\)$ –0.2191 –0.2185 –0.2740 –0.1742 –0.1740 –0.2303 (0.1588) (0.1587) (0.1749) (0.1654) (0.1653) (0.1716) Observations 19496 19496 19496 19496 19496 19496 Logit of termination probability (Coefficients) (1) (2) (3) (4) (5) (6) $\(y_{igt}\)$ –1.0147 –0.3751 –1.2737 (0.7377) (2.5079) (1.9843) $\(\bar{y}_{t}\)$ –6.6506*** –6.5854*** –6.0210*** (1.0439) (1.0650) (2.2966) $\(\bar{y}_{gt}\)$ –0.7095 (2.6394) $\(Y_{igt}\)$ –0.0865 –0.0560 –0.0970 (0.0530) 0.1750) ( 0.1503) $\(\bar{Y}_{t}\)$ –0.0006*** –0.0006*** –0.0006*** (0.0001) (0.0001) (0.0002) $\(\bar{Y}_{gt}\)$ –0.0000 (0.0002) $\(\ln t\)$ –0.2191 –0.2185 –0.2740 –0.1742 –0.1740 –0.2303 (0.1588) (0.1587) (0.1749) (0.1654) (0.1653) (0.1716) Observations 19496 19496 19496 19496 19496 19496 Notes: (*$$p < 0.1$$; **$$p < 0.05$$; ***$$p < 0.01$$) Logit estimates. Sample is restricted to all production units in sheds with at least one other production unit. Dependent variable is dummy equal to 1 if employment relationship terminates on day $\(t\)$. $\(y_{igt}\)$ is own daily number of eggs per hen collected by worker $\(i\)$ in shed $\(g\)$ on day $\(t\)$, $\(\bar{y}_{gt}\)$ is the corresponding average for all workers in shed $\(g\)$ on day $\(t\)$, and $\(\bar{y}_{t}\)$ is the average among all workers on day $\(t\)$; $\(Y_{igt}\)$ is own daily number of total eggs collected by worker $\(i\)$ in shed $\(g\)$ on day $\(t\)$, $\(\bar{Y}_{gt}\)$ is the corresponding average for all workers in shed $\(g\)$ on day $\(t\)$, and $\(\bar{Y}_{t}\)$ is the average among all workers on day $\(t\)$. (3) and (6) are Two-stage residual inclusion estimates with bootstrapped standard errors from 200 repetitions (Terza et al., 2008). Table 6 Termination policy Logit of termination probability (Coefficients) (1) (2) (3) (4) (5) (6) $\(y_{igt}\)$ –1.0147 –0.3751 –1.2737 (0.7377) (2.5079) (1.9843) $\(\bar{y}_{t}\)$ –6.6506*** –6.5854*** –6.0210*** (1.0439) (1.0650) (2.2966) $\(\bar{y}_{gt}\)$ –0.7095 (2.6394) $\(Y_{igt}\)$ –0.0865 –0.0560 –0.0970 (0.0530) 0.1750) ( 0.1503) $\(\bar{Y}_{t}\)$ –0.0006*** –0.0006*** –0.0006*** (0.0001) (0.0001) (0.0002) $\(\bar{Y}_{gt}\)$ –0.0000 (0.0002) $\(\ln t\)$ –0.2191 –0.2185 –0.2740 –0.1742 –0.1740 –0.2303 (0.1588) (0.1587) (0.1749) (0.1654) (0.1653) (0.1716) Observations 19496 19496 19496 19496 19496 19496 Logit of termination probability (Coefficients) (1) (2) (3) (4) (5) (6) $\(y_{igt}\)$ –1.0147 –0.3751 –1.2737 (0.7377) (2.5079) (1.9843) $\(\bar{y}_{t}\)$ –6.6506*** –6.5854*** –6.0210*** (1.0439) (1.0650) (2.2966) $\(\bar{y}_{gt}\)$ –0.7095 (2.6394) $\(Y_{igt}\)$ –0.0865 –0.0560 –0.0970 (0.0530) 0.1750) ( 0.1503) $\(\bar{Y}_{t}\)$ –0.0006*** –0.0006*** –0.0006*** (0.0001) (0.0001) (0.0002) $\(\bar{Y}_{gt}\)$ –0.0000 (0.0002) $\(\ln t\)$ –0.2191 –0.2185 –0.2740 –0.1742 –0.1740 –0.2303 (0.1588) (0.1587) (0.1749) (0.1654) (0.1653) (0.1716) Observations 19496 19496 19496 19496 19496 19496 Notes: (*$$p < 0.1$$; **$$p < 0.05$$; ***$$p < 0.01$$) Logit estimates. Sample is restricted to all production units in sheds with at least one other production unit. Dependent variable is dummy equal to 1 if employment relationship terminates on day $\(t\)$. $\(y_{igt}\)$ is own daily number of eggs per hen collected by worker $\(i\)$ in shed $\(g\)$ on day $\(t\)$, $\(\bar{y}_{gt}\)$ is the corresponding average for all workers in shed $\(g\)$ on day $\(t\)$, and $\(\bar{y}_{t}\)$ is the average among all workers on day $\(t\)$; $\(Y_{igt}\)$ is own daily number of total eggs collected by worker $\(i\)$ in shed $\(g\)$ on day $\(t\)$, $\(\bar{Y}_{gt}\)$ is the corresponding average for all workers in shed $\(g\)$ on day $\(t\)$, and $\(\bar{Y}_{t}\)$ is the average among all workers on day $\(t\)$. (3) and (6) are Two-stage residual inclusion estimates with bootstrapped standard errors from 200 repetitions (Terza et al., 2008). Another implication of the theory is that, in guessing worker’s type, the management uses the average productivity of all workers, and not just the productivity of coworkers in the same shed. We directly test for this hypothesis in Column 2 of Table 6. We include as additional regressor the average productivity $\(\bar{y}_{gt}\)$ of all workers in the same shed of worker $\(i\)$. We find no systematic correlation of the latter with the probability of termination. These results show that the relevant metric for worker’s evaluation and dismissal is the average productivity of all workers, and not only those in the same shed. In Column 3 of Table 6, we rely again on hens’ age as an exogenous source of variation for productivity to estimate the parameters of the model. We do this for two reasons. First, our claim is that externalities in worker’s evaluation and dismissal are the mechanism responsible for the negative productivity spillovers we have identified in the previous section. In showing evidence of the former, we therefore need to rely on the same source of variation that we exploited in the analysis of the latter. That is, we want to provide evidence that the mechanism of interest is set in motion by the same source of variation that we exploit for identification in reduced form. Second, the identification of the coefficients of average productivity in equation (13) could be problematic. One possible concern is that worker’s effort may respond to expectations regarding coworkers’ termination probabilities. Reverse causality would therefore bias the estimates of the coefficient of average productivity. The use of average hens’ age as an exogenous source of variation for average productivity rules out such endogenous effort responses and identification concerns. Given the non-linear nature of the second stage, we follow Terza et al. (2008) and adopt a two-stage residual inclusion (2SRI) control function approach (Wooldridge, 2015). We use the average age of hens $\(\overline{age}_{t}\)$ and the average of squares $\(\overline{age^2}_{t}\)$ as instruments for average productivity $\(\bar{y}_{t}\)$. The magnitude of coefficients in Column 3 is very similar to the previous estimates. We interpret this as further evidence that individual termination decisions are informed by the average productivity of all workers and their inputs. 6.1.1. Additional evidence Even if the management were using the total number of eggs as performance metric rather than the number of eggs per hen, results would not change. The coefficient estimates in Columns 4 to 6 of Table 6 show that the relationship between own output, average output and own probability of keeping the job has the same sign and is still significant if we use own total number of eggs and the average number of eggs among all workers as regressors in specification 13.40 The empirical analysis of termination probabilities so far has matched the first case in our conceptual framework, where we assume that the management does not hold any information on input quality. This is motivated by our conversations with the management, as the data we use in our analysis are collected by the veterinary unit and are not processed by the human resource department. Nonetheless, we cannot exclude that the management uses other available information. We evaluate the robustness of results by matching the second case in our conceptual framework, where the management holds partial information on input quality. We use the information on the expected productivity of hens as elaborated by the bird supplier company and that we have use as instrument in Column 4 of Table 5. This measure provides a point estimate of the number of eggs each hen in a the batch is expected to lay in each week of age. As such, the measure maps from the $\(a_i\)$ variable of our conceptual framework. We divide daily productivity of eggs per hen $\(y_i\)$ by the expected productivity measure $\(a_i\)$ to derive signal $\(z_i\)$ of worker’s effort. We then estimate a logistic hazard model of termination probability where own and average signal are included as regressors. Table A.13 in Supplementary Appendix A.1 reports the corresponding coefficient estimates. Results are in line with those in our main analysis, showing that, conditional on the value of own signal, an increase in the average signal is systematically and negatively correlated with own termination probability. Notice in particular that the 2SRI estimates in Column 3 suggest that the hens’ age variables are still informative of productivity signals $\(z_i\)$. This means that expected productivity $\(a_i\)$ does not capture the full extent of variation in input quality, which therefore remains partially unobservable to the management. 6.2. Alternative explanations The evidence presented above could be consistent with other mechanisms. First, workers may get discouraged and quit the job when their productivity is lower than the one of neighbouring peers. However, evidence shows that, conditional on individual and average productivity, the difference between own and neighbouring coworkers’ productivity is not systematically correlated with termination probabilities. This rules out that voluntary quits from discouragement are driving the empirical regularities described above.41 A second alternative explanation is related to workers’ monitoring. Suppose that the management monitor workers, and that these monitoring efforts target disproportionally more workers handling highly productive hens. The negative causal effect of an increase in coworkers’ productivity on own productivity could then be attributed to a higher level of shirking which follows a reallocation of monitoring efforts towards highly productive coworkers. However, if this was the case, we should have found a negative effect of coworkers’ productivity also considering coworkers in non-neighbouring production units in the same shed. Results from Column 2 of Table 5 show that this is not the case. A third possibility is that workers steal eggs from each other. If this was the case, though, we should expect an increase in coworkers’ input quality to increase own productivity, as stealing opportunities would increase with coworkers’ productivity. More in general, this is what we would expect if other possible sources of positive productivity spillovers were present. Other examples are knowledge spillovers from social learning when hens are highly productive, or a situation where young or old hens are more prone to experience transmittable diseases and these spread to neighbouring production units. All these explanations would bias our baseline results in the opposite direction with respect to what we find: if these were present, the magnitude of our negative estimates would be a lower bound for the true effect. Finally, our conceptual framework and analysis are built upon the assumption that workers are evaluated each day on the basis on their productivity on that day, and not on their history on the job, or since the assignment of the last batch of hens. It could be the case that workers are more likely to be fired when hen batches they are assigned to are close to be dismissed. If so, the results on our termination policy regression could be capturing changes in own and coworkers’ productivity close to the end of the hens’ productive life cycle, with no role played by worker evaluation. Figure A.7 in Supplementary Appendix A.1 plots the distribution of worker terminations over the entire hens’ age support based on the age of assigned hens on the day of termination. The Figure shows that employment terminations are almost uniformly distributed over the entire support. This rules out the concern that our results are only capturing changes in productivity and termination probabilities that materialize when batches are about to be dismissed. 7. Monetary and Social Incentives Workers are paid every two weeks. Their wage is equal to a base salary plus a variable amount which depends on number of boxes of eggs collected by the worker in a randomly chosen day within the two weeks. Specifically, wage is equal to \begin{equation} \omega_i=\alpha \ + \ \max \ \{ \ 0 \ , \ \delta \times [ \ 2Y_i - r \ ] \ \}, \end{equation} (14) where $\(\alpha\)$ is the base pay and $\(Y_i\)$ is the amount of boxes of eggs collected by the worker in the randomly chosen day. This quantity is multiplied by 2 and, if the resulting quantity exceeds a given threshold $\(r\)$, a piece rate $\(\delta\)$ is awarded for each unit above the threshold.42 Despite its strong relationship with productivity, no component of worker’s pay is adjusted by the age of hens the worker is assigned during the pay period. This confirms that the human resource department does not process any information on inputs. It also implies that the probability for each worker of earning extra pay is a function of hens’ age. Figure 3 plots the distribution of the average number of daily egg boxes collected by the worker within each pay period per quartiles of the hens’ age distribution. For each quartile, the boundaries of each box indicate the 10th and 90th percentile of the egg boxes distribution, while the horizontal lines within each box correspond to the mean. The ends of the vertical lines indicate the 1st and 99th percentile. The straight horizontal line corresponds to the normalized bonus threshold $\(r/2\)$. First, notice that the inverted U-shaped relationship between hens’ age and productivity can be still observed when considering egg boxes as a measure of productivity. Second, the probability of reaching the threshold and be exposed to incentive pay is higher for those workers whose hens are of high productivity, meaning they belong to the second and third quartiles of the hens’ age distribution. On the contrary, the average worker whose hens belong to the first or fourth quartile of the hens’ age distribution does not reach the bonus threshold.43 Figure 3 View largeDownload slide Hens’ age and number of egg boxes. Notes: The figure plots the distribution of the average number of boxes collected by the worker in each two-weeks pay period. Within each age quartile, the bottom and top of the box correspond to the 10th and 90th percentile respectively, while the horizontal line corresponds to the mean. The ends of the vertical lines indicate the 1st and 99th percentile. The probability of reaching the bonus threshold is higher for workers whose assigned hens belong to the 2nd or 4th quartile of the age distribution, meaning of high productivity. Figure 3 View largeDownload slide Hens’ age and number of egg boxes. Notes: The figure plots the distribution of the average number of boxes collected by the worker in each two-weeks pay period. Within each age quartile, the bottom and top of the box correspond to the 10th and 90th percentile respectively, while the horizontal line corresponds to the mean. The ends of the vertical lines indicate the 1st and 99th percentile. The probability of reaching the bonus threshold is higher for workers whose assigned hens belong to the 2nd or 4th quartile of the age distribution, meaning of high productivity. We provide suggestive evidence on the role of monetary and social incentives by implementing following regression specification \begin{equation} \begin{array}{l c l} y_{igwt}&=& \varphi_{gw} + \ \sum_d \ \left\{\psi_d \ +\ \gamma_d \ \bar{y}_{-igwt} \ + \ \alpha_d \ age_{igwt} \ + \ \beta_d \ age^2_{igwt} \right\} \times \ D_{digwt} \\ &&\\ &&+ \ \sum^{t-1}_{s=t-3}\lambda_{s} \ {\it{food}}_{igsw} \ + \ \mu_{igwt}, \end{array} \end{equation} (15) where $\(\varphi_{gw}\)$ are shed-week fixed effects and $\(D_{d}\)$ are dummy variables which identify the heterogeneous categories of interest. We interact the latter with both own hens’ age variables and coworkers’ productivity. We estimate the parameters $\(\gamma_d\)$ using both $\(\overline{age}_{-i}\)$ and $\(\overline{age^2}_{-i}\)$ multiplied by $\(D_d\)$ as instruments for the endogenous interaction variables $\(\bar{y}_{-igwt} \times D_d\)$. We first focus on monetary incentives and exploit the heterogeneity in piece rate exposure summarized in Figure 3. We define a low productivity age subsample of production units whose assigned hens’ age is in the first or the fourth quartile of the age distribution, and group the rest of observations in a second high productivity age subsample. Column 1 of Table 7 provides the corresponding 2SLS estimates from the above specification, with $\(D_{d}\)$ identifying these two subsamples. The Table reports the F-statistic from the Sanderson–Windmeijer multivariate $\(F\)$ test of excluded instruments, which confirms that first stage relationships are strong. We find no significant effect of coworkers’ productivity when the worker is assigned highly productive hens and is more likely to be exposed to piece rate pay. The effect is instead negative and highly significant for the same worker when assigned hens are less productive. This evidence is consistent with our extended conceptual framework as it shows that incentive pay smooths the negative externalities generated by the termination policy. However, we interpret this with caution as the low productivity age subsample is also the one that carries most of the variation in productivity. Table 7 Incentive heterogeneity Daily number of eggs per hen, $\(y_i\)$ (1) (2) (3) High prod. age Low prod. age $\(\bar{y}_{-i} \ \times \ \text{High productivity age}\)$ –0.13365 (0.2554) $\(\bar{y}_{-i} \ \times \ \text{Low productivity age}\)$ –0.20819*** (0.0791) $\(\bar{y}_{-i} \ \times \ \text{Friend}\)$ 0.26949 (0.2022) $\(\bar{y}_{-i} \ \times \ \text{No friend}\)$ –0.42802** (0.2101) $\(\bar{y}_{-i} \ \times \ \text{Experienced}\)$ –0.57512*** (0.1179) $\(\bar{y}_{-i} \ \times \ \text{Not experienced}\)$ 0.22580 (0.1548) $\(\bar{y}_{-i} \ \times \ \text{Low age difference}\)$ –0.21894 –0.19540 (0.4577) (0.3512) $\(\bar{y}_{-i} \ \times \ \text{High age difference}\)$ –0.02754 –0.27601 (0.0968) (0.1786) $\(food_{t-1}\)$ 0.00487*** 0.00577*** 0.00468** 0.00073*** 0.00412*** (0.0014) (0.0018) (0.0019) (0.0003) (0.0012) $\(food_{t-2}\)$ 0.00319** 0.00354** 0.00293** –0.00009 0.00287*** (0.0013) (0.0016) (0.0015) (0.0001) (0.0009) $\(food_{t-3}\)$ 0.00316** 0.00387** 0.00310** –0.00026 0.00220* (0.0013) (0.0016) (0.0015) (0.0002) (0.0011) Sanderson–Windmeijer F-stat 66.55 60.01 50.63 9.52 5.23 61.69 37.60 47.30 12.91 7.98 Shed-week FEs Y Y Y Y Y Day FEs Y Y Y Y Y Worker FEs Y Y Y Y Y Batch FEs Y Y Y Y Y Observations 21,206 16,590 16,590 11,030 10,169 $\(R^2\)$ 0.904 0.918 0.935 0.842 0.927 Daily number of eggs per hen, $\(y_i\)$ (1) (2) (3) High prod. age Low prod. age $\(\bar{y}_{-i} \ \times \ \text{High productivity age}\)$ –0.13365 (0.2554) $\(\bar{y}_{-i} \ \times \ \text{Low productivity age}\)$ –0.20819*** (0.0791) $\(\bar{y}_{-i} \ \times \ \text{Friend}\)$ 0.26949 (0.2022) $\(\bar{y}_{-i} \ \times \ \text{No friend}\)$ –0.42802** (0.2101) $\(\bar{y}_{-i} \ \times \ \text{Experienced}\)$ –0.57512*** (0.1179) $\(\bar{y}_{-i} \ \times \ \text{Not experienced}\)$ 0.22580 (0.1548) $\(\bar{y}_{-i} \ \times \ \text{Low age difference}\)$ –0.21894 –0.19540 (0.4577) (0.3512) $\(\bar{y}_{-i} \ \times \ \text{High age difference}\)$ –0.02754 –0.27601 (0.0968) (0.1786) $\(food_{t-1}\)$ 0.00487*** 0.00577*** 0.00468** 0.00073*** 0.00412*** (0.0014) (0.0018) (0.0019) (0.0003) (0.0012) $\(food_{t-2}\)$ 0.00319** 0.00354** 0.00293** –0.00009 0.00287*** (0.0013) (0.0016) (0.0015) (0.0001) (0.0009) $\(food_{t-3}\)$ 0.00316** 0.00387** 0.00310** –0.00026 0.00220* (0.0013) (0.0016) (0.0015) (0.0002) (0.0011) Sanderson–Windmeijer F-stat 66.55 60.01 50.63 9.52 5.23 61.69 37.60 47.30 12.91 7.98 Shed-week FEs Y Y Y Y Y Day FEs Y Y Y Y Y Worker FEs Y Y Y Y Y Batch FEs Y Y Y Y Y Observations 21,206 16,590 16,590 11,030 10,169 $\(R^2\)$ 0.904 0.918 0.935 0.842 0.927 Notes: (*$$p < 0.1$$; **$$p< 0.05$$; ***$$p < 0.01$$) 2SLS estimates. Sample is restricted to all production units in sheds with at least one other production unit. Two-way clustered standard errors, with residuals grouped along both shed and day. Dependent variable is the average number of eggs per hen collected by the worker. Main variable of interest is average daily number of eggs per hen collected by coworkers in neighbouring production units $\(\bar{y}_{-i}\)$ and its interactions. In all specifications, the average age of coworkers’ hens and the average of $\((\overline{age}_{-i},\overline{age^2}_{-i})\)$ are interacted with dummy categories and used as instruments for the corresponding endogenous interaction regressor in the first stage. $\(food_{t-s}\)$ are lags of amount of food distributed as measured by 50 kg sacks employed. Table 7 Incentive heterogeneity Daily number of eggs per hen, $\(y_i\)$ (1) (2) (3) High prod. age Low prod. age $\(\bar{y}_{-i} \ \times \ \text{High productivity age}\)$ –0.13365 (0.2554) $\(\bar{y}_{-i} \ \times \ \text{Low productivity age}\)$ –0.20819*** (0.0791) $\(\bar{y}_{-i} \ \times \ \text{Friend}\)$ 0.26949 (0.2022) $\(\bar{y}_{-i} \ \times \ \text{No friend}\)$ –0.42802** (0.2101) $\(\bar{y}_{-i} \ \times \ \text{Experienced}\)$ –0.57512*** (0.1179) $\(\bar{y}_{-i} \ \times \ \text{Not experienced}\)$ 0.22580 (0.1548) $\(\bar{y}_{-i} \ \times \ \text{Low age difference}\)$ –0.21894 –0.19540 (0.4577) (0.3512) $\(\bar{y}_{-i} \ \times \ \text{High age difference}\)$ –0.02754 –0.27601 (0.0968) (0.1786) $\(food_{t-1}\)$ 0.00487*** 0.00577*** 0.00468** 0.00073*** 0.00412*** (0.0014) (0.0018) (0.0019) (0.0003) (0.0012) $\(food_{t-2}\)$ 0.00319** 0.00354** 0.00293** –0.00009 0.00287*** (0.0013) (0.0016) (0.0015) (0.0001) (0.0009) $\(food_{t-3}\)$ 0.00316** 0.00387** 0.00310** –0.00026 0.00220* (0.0013) (0.0016) (0.0015) (0.0002) (0.0011) Sanderson–Windmeijer F-stat 66.55 60.01 50.63 9.52 5.23 61.69 37.60 47.30 12.91 7.98 Shed-week FEs Y Y Y Y Y Day FEs Y Y Y Y Y Worker FEs Y Y Y Y Y Batch FEs Y Y Y Y Y Observations 21,206 16,590 16,590 11,030 10,169 $\(R^2\)$ 0.904 0.918 0.935 0.842 0.927 Daily number of eggs per hen, $\(y_i\)$ (1) (2) (3) High prod. age Low prod. age $\(\bar{y}_{-i} \ \times \ \text{High productivity age}\)$ –0.13365 (0.2554) $\(\bar{y}_{-i} \ \times \ \text{Low productivity age}\)$ –0.20819*** (0.0791) $\(\bar{y}_{-i} \ \times \ \text{Friend}\)$ 0.26949 (0.2022) $\(\bar{y}_{-i} \ \times \ \text{No friend}\)$ –0.42802** (0.2101) $\(\bar{y}_{-i} \ \times \ \text{Experienced}\)$ –0.57512*** (0.1179) $\(\bar{y}_{-i} \ \times \ \text{Not experienced}\)$ 0.22580 (0.1548) $\(\bar{y}_{-i} \ \times \ \text{Low age difference}\)$ –0.21894 –0.19540 (0.4577) (0.3512) $\(\bar{y}_{-i} \ \times \ \text{High age difference}\)$ –0.02754 –0.27601 (0.0968) (0.1786) $\(food_{t-1}\)$ 0.00487*** 0.00577*** 0.00468** 0.00073*** 0.00412*** (0.0014) (0.0018) (0.0019) (0.0003) (0.0012) $\(food_{t-2}\)$ 0.00319** 0.00354** 0.00293** –0.00009 0.00287*** (0.0013) (0.0016) (0.0015) (0.0001) (0.0009) $\(food_{t-3}\)$ 0.00316** 0.00387** 0.00310** –0.00026 0.00220* (0.0013) (0.0016) (0.0015) (0.0002) (0.0011) Sanderson–Windmeijer F-stat 66.55 60.01 50.63 9.52 5.23 61.69 37.60 47.30 12.91 7.98 Shed-week FEs Y Y Y Y Y Day FEs Y Y Y Y Y Worker FEs Y Y Y Y Y Batch FEs Y Y Y Y Y Observations 21,206 16,590 16,590 11,030 10,169 $\(R^2\)$ 0.904 0.918 0.935 0.842 0.927 Notes: (*$$p < 0.1$$; **$$p< 0.05$$; ***$$p < 0.01$$) 2SLS estimates. Sample is restricted to all production units in sheds with at least one other production unit. Two-way clustered standard errors, with residuals grouped along both shed and day. Dependent variable is the average number of eggs per hen collected by the worker. Main variable of interest is average daily number of eggs per hen collected by coworkers in neighbouring production units $\(\bar{y}_{-i}\)$ and its interactions. In all specifications, the average age of coworkers’ hens and the average of $\((\overline{age}_{-i},\overline{age^2}_{-i})\)$ are interacted with dummy categories and used as instruments for the corresponding endogenous interaction regressor in the first stage. $\(food_{t-s}\)$ are lags of amount of food distributed as measured by 50 kg sacks employed. To explore the role of social incentives, we rely instead on the information on social relationship among workers. We identify those workers working along someone they recognize as a friend, and let the dummy variables $\(D_{d}\)$ identify the two resulting subsamples. Column 2 of Table 7 reports the corresponding 2SLS estimates.44 We estimate negative and significant productivity spillovers only for those workers who do not work along friends. The same estimate is instead positive but insignificant when the worker recognizes any of his neighbouring coworkers as a friend. This evidence is consistent with the peer pressure argument outlined in our extended conceptual framework. It also rules out the possibility that the negative spillover effect we find is capturing cooperative behaviour among workers. For example, workers handling highly productive hens could benefit from the help of neighbouring coworkers, with negative productivity spillovers on the latter. Such cooperative strategy would be sustainable in a repeated interaction framework. However, we would expect such strategy to be differentially more sustainable among friends in light of the possibility of social punishment and increased cost of deviation from the cooperative path. The absence of any significant negative spillover effect among friends does not support this hypothesis.45 We also identify spillovers separately according to worker’s experience. We distinguish whether the worker’s tenure at the firm is above or below the median, and implement the same specification above. Column 3 of Table 7 shows that spillovers are negative and significant for more experienced workers, and positive but insignificant for less experienced ones. We interpret this result as suggestive evidence that experienced workers are more aware of management policies and therefore more prone to free riding, while the opposite holds for newly hired workers. Finally, we explore heterogeneity according to the difference (in absolute value) between the age of own and coworkers’ hens. We identify two subsamples depending on whether such difference is higher or lower than the mean difference in the sample, equal to 3.22 weeks. We estimate the corresponding equation for the low productivity age and the high productivity age subsamples separately, defined as in Column 1. If the free riding mechanism in the absence of piece rate incentives is responsible for the average effect we find, we should expect the negative effect of coworkers’ productivity to be the highest in magnitude when the scope of free riding is widest. This corresponds to the situation in which a given worker is assigned lowly productive hens while coworkers are assigned highly productive ones. We instead expect the magnitude to be the lowest when the worker is assigned highly productive hens and his coworkers are assigned lowly productive ones. The evidence in Column 4 and 5 is supportive of this hypothesis, although none of the estimates is statistically significant. 8. Counterfactual Policy Analysis 8.1. Termination policy The evidence gathered so far shows that the worker evaluation and termination policy implemented at this firm generates externalities among coworkers and negative productivity spillovers. Our conceptual framework shows that the scope for such policy originates in the asymmetry of information between the worker and the management, and the impossibility for the latter to observe input quality and perfectly disentangle the effort and input contribution to output. The purpose of this Section is to illustrate the productivity consequences of changes in the amount of information available to the management. We make the extreme but simplifying assumption that the age of hens carries all relevant information regarding input quality, and we hypothesize a scenario in which this information is fully available to the management. The latter can therefore fully net out the input contribution to output and derive the level of effort exerted by the worker as residual. In this case, the management faces no inferential problem and the probability for the worker to keep the job is an increasing and concave function of his effort $\(e_i\)$. This shuts down the externalities among coworkers generated by and built into the actual policy. Let the termination policy in this case be given by \begin{equation} \tilde{q}(e_{it})=\alpha_{0} + \alpha_{1} \ e_{it} + \alpha_{2} \ e^2_{it} \end{equation} (16) with $\(\alpha_{1}\)$ and $\(\alpha_{2}\)$ being such that $\(\tilde{q}_{1}(\cdot)>0\)$ and $\(\tilde{q}_{11}(\cdot)< 0\)$ for every $\(e_i\)$. The first-order condition of the worker’s effort maximization problem becomes \begin{equation} \label{eqcount} e_i=\frac{U(\omega)}{c} \ (\alpha_{1}+2\alpha_{2} \ e_{it}). \end{equation} (17) We structurally estimate the unobserved components of the above equation, and derive daily effort $\(e_{it}\)$ and productivity $\(y_{it}\)$ for all workers in this counterfactual scenario. Supplementary Appendix A.6 describes the details of the procedure. Table 8 shows the corresponding results, and reports counterfactual productivity gains and losses. For each parameter values in the corresponding row and column, each entry shows the simulated percentage change in productivity as measured by average daily number of eggs per hen collected by workers over the period. The table also reports 95% confidence intervals as computed by repeating the estimation procedure 100 times using bootstrapped samples. Evidence show that, for sufficiently high values of $\(\alpha_{1}\)$, eliminating the asymmetry of information between the worker and the management can bring about significant productivity gains. Table 8 Termination policy counterfactual: results $\(\alpha_2\)$ $$-$$0.60 $$-$$0.70 $$-$$0.80 $$-$$0.90 $$-$$1.00 $\(\alpha_1\)$ 0.06 $$-$$5.58 $$-$$12.38 $$-$$18.31 $$-$$23.25 $$-$$27.99 [$$-$$5.72;$$-$$5.43] [$$-$$12.48;$$-$$12.28] [$$-$$18.47;$$-$$18.16] [$$-$$23.44;$$-$$23.06] [$$-$$28.27;$$-$$27.71] 0.07 9.91 2.1 $$-$$4.87 $$-$$10.7 $$-$$15.81 [9.7;10.12] [1.99;2.21] [$$-$$5.1;$$-$$4.64] [$$-$$10.95;$$-$$10.45] [$$-$$16.11;$$-$$15.5] 0.08 25.5 16.73 9.06 2.03 $$-$$3.88 [25.22;25.78] [16.59;16.87] [8.91;9.22] [1.74;2.32] [$$-$$4.19;$$-$$3.56] 0.09 41.23 31.28 22.62 14.87 8.15 [40.97;41.5] [31.14;31.41] [22.43;22.81] [14.53;15.21] [7.75;8.55] 0.10 56.23 45.8 36.26 27.85 19.93 [55.8;56.67] [45.59;46.01] [36.02;36.5] [27.54;28.16] [19.43;20.43] $\(\alpha_2\)$ $$-$$0.60 $$-$$0.70 $$-$$0.80 $$-$$0.90 $$-$$1.00 $\(\alpha_1\)$ 0.06 $$-$$5.58 $$-$$12.38 $$-$$18.31 $$-$$23.25 $$-$$27.99 [$$-$$5.72;$$-$$5.43] [$$-$$12.48;$$-$$12.28] [$$-$$18.47;$$-$$18.16] [$$-$$23.44;$$-$$23.06] [$$-$$28.27;$$-$$27.71] 0.07 9.91 2.1 $$-$$4.87 $$-$$10.7 $$-$$15.81 [9.7;10.12] [1.99;2.21] [$$-$$5.1;$$-$$4.64] [$$-$$10.95;$$-$$10.45] [$$-$$16.11;$$-$$15.5] 0.08 25.5 16.73 9.06 2.03 $$-$$3.88 [25.22;25.78] [16.59;16.87] [8.91;9.22] [1.74;2.32] [$$-$$4.19;$$-$$3.56] 0.09 41.23 31.28 22.62 14.87 8.15 [40.97;41.5] [31.14;31.41] [22.43;22.81] [14.53;15.21] [7.75;8.55] 0.10 56.23 45.8 36.26 27.85 19.93 [55.8;56.67] [45.59;46.01] [36.02;36.5] [27.54;28.16] [19.43;20.43] Notes: The Table shows productivity gains and losses from counterfactual termination policy as discussed and implemented in Section 8.1. 95% confidence intervals in square brackets, computed using bootstrapped samples from 100 repetitions. Productivity is measured as average daily number of eggs per hen over the period. Entries are percentage change with respect to actual data, with counterfactual productivity being derived using the parameter values indicated in the corresponding row and column. Table 8 Termination policy counterfactual: results $\(\alpha_2\)$ $$-$$0.60 $$-$$0.70 $$-$$0.80 $$-$$0.90 $$-$$1.00 $\(\alpha_1\)$ 0.06 $$-$$5.58 $$-$$12.38 $$-$$18.31 $$-$$23.25 $$-$$27.99 [$$-$$5.72;$$-$$5.43] [$$-$$12.48;$$-$$12.28] [$$-$$18.47;$$-$$18.16] [$$-$$23.44;$$-$$23.06] [$$-$$28.27;$$-$$27.71] 0.07 9.91 2.1 $$-$$4.87 $$-$$10.7 $$-$$15.81 [9.7;10.12] [1.99;2.21] [$$-$$5.1;$$-$$4.64] [$$-$$10.95;$$-$$10.45] [$$-$$16.11;$$-$$15.5] 0.08 25.5 16.73 9.06 2.03 $$-$$3.88 [25.22;25.78] [16.59;16.87] [8.91;9.22] [1.74;2.32] [$$-$$4.19;$$-$$3.56] 0.09 41.23 31.28 22.62 14.87 8.15 [40.97;41.5] [31.14;31.41] [22.43;22.81] [14.53;15.21] [7.75;8.55] 0.10 56.23 45.8 36.26 27.85 19.93 [55.8;56.67] [45.59;46.01] [36.02;36.5] [27.54;28.16] [19.43;20.43] $\(\alpha_2\)$ $$-$$0.60 $$-$$0.70 $$-$$0.80 $$-$$0.90 $$-$$1.00 $\(\alpha_1\)$ 0.06 $$-$$5.58 $$-$$12.38 $$-$$18.31 $$-$$23.25 $$-$$27.99 [$$-$$5.72;$$-$$5.43] [$$-$$12.48;$$-$$12.28] [$$-$$18.47;$$-$$18.16] [$$-$$23.44;$$-$$23.06] [$$-$$28.27;$$-$$27.71] 0.07 9.91 2.1 $$-$$4.87 $$-$$10.7 $$-$$15.81 [9.7;10.12] [1.99;2.21] [$$-$$5.1;$$-$$4.64] [$$-$$10.95;$$-$$10.45] [$$-$$16.11;$$-$$15.5] 0.08 25.5 16.73 9.06 2.03 $$-$$3.88 [25.22;25.78] [16.59;16.87] [8.91;9.22] [1.74;2.32] [$$-$$4.19;$$-$$3.56] 0.09 41.23 31.28 22.62 14.87 8.15 [40.97;41.5] [31.14;31.41] [22.43;22.81] [14.53;15.21] [7.75;8.55] 0.10 56.23 45.8 36.26 27.85 19.93 [55.8;56.67] [45.59;46.01] [36.02;36.5] [27.54;28.16] [19.43;20.43] Notes: The Table shows productivity gains and losses from counterfactual termination policy as discussed and implemented in Section 8.1. 95% confidence intervals in square brackets, computed using bootstrapped samples from 100 repetitions. Productivity is measured as average daily number of eggs per hen over the period. Entries are percentage change with respect to actual data, with counterfactual productivity being derived using the parameter values indicated in the corresponding row and column. 8.2. Input allocation The presence of productivity spillovers from heterogeneous inputs implies that changing the way the same set of inputs is allocated among workers can affect the total size of externalities and aggregate productivity. In our basic regression specification, coworkers’ productivity enters linearly in the equation defining worker’s productivity. As a result, the impact of input reallocation on overall productivity can only materialize through pairwise exchanges between production units both within and across sheds of different size.46 We evaluate the impact of input reallocation in our setting by means of a counterfactual simulation exercise. As a first step, we regress the daily average number of eggs per hen $\(y_{it}\)$ over the full sets of own and coworkers’ hens’ week-of-age dummies, together with shed-week fixed effects. We then consider the set of hen batches in production in the first week of the sample, and simulate their age profiles over the sampling period assuming hens are replaced after the 86th week of life. Using the parameter estimates from the former regression specification, we then predict the daily productivity of workers in each production unit. Not surprisingly, Figure 4 shows that predicted and actual average productivity match closely, except for some weeks in the second half of the sampling period, when, according to the management, some sheds were affected by bird disease. Figure 4 View largeDownload slide Input allocation and productivity. Notes: The figure plots the true, predicted and counterfactual average worker’s productivity over time in the period under investigation. Predictions are derived starting with the batches in production in the first week of the sample, and simulating their age profiles over the period, assuming that hens were replaced after the 86th week of life. Reduced-form estimates from a fully specified model where the full sets of own and coworkers’ hen’s week-of-age dummies and shed-week fixed effects are included are then used to predict average daily productivity. Counterfactual productivity is derived using the same estimates, but reallocating hen batches in production in the first week of the sample among production units following a hierarchical clustering procedure which minimizes the variance of the age of hens within sheds. Average counterfactual productivity is higher than the actual one, and up to 20% higher than the predicted one. Figure 4 View largeDownload slide Input allocation and productivity. Notes: The figure plots the true, predicted and counterfactual average worker’s productivity over time in the period under investigation. Predictions are derived starting with the batches in production in the first week of the sample, and simulating their age profiles over the period, assuming that hens were replaced after the 86th week of life. Reduced-form estimates from a fully specified model where the full sets of own and coworkers’ hen’s week-of-age dummies and shed-week fixed effects are included are then used to predict average daily productivity. Counterfactual productivity is derived using the same estimates, but reallocating hen batches in production in the first week of the sample among production units following a hierarchical clustering procedure which minimizes the variance of the age of hens within sheds. Average counterfactual productivity is higher than the actual one, and up to 20% higher than the predicted one. The same parameter estimates that we just used to predict daily productivity of workers under the actual input allocation can be used to predict productivity under alternative input allocations. Taking the batches in production in the first week of the sample, we reallocate them among production units following a hierarchical clustering procedure which minimizes the variance of the age of hens within the same shed. This is consistent with the implicitly stated goal of the management. We simulate hens’ age profiles over the period under the alternative allocation (assuming the same replacement policy as before), and predict worker’s daily productivity using the same parameter estimates derived at the beginning. The dashed line in Figure 4 shows the smoothed average of counterfactual productivity. Productivity gains are substantial, up to 20% in a given day, even though counterfactual average productivity is more volatile than actual one. When averaged throughout the period, the difference between the counterfactual and actual productivity is equal to 0.08, which corresponds to a 10% increase. The counterfactual productivity estimates in this section suffer from one important limitation: they are based upon the assumption that the termination policy implemented by the management remains unchanged. This is because we want to isolate and illustrate the productivity gains from implementing alternative input allocation schedules, and abstract from the possibility that the management revises its termination policy in conjunction. In fact, the decrease in the variance of input quality within sheds brings about information gains for the management, which may thus find optimal to revise its policy in a way to put additional weight on individual productivity signals. The results from the previous section suggest that productivity gains would be even higher in this case. 8.3. Discussion Results from the counterfactual policy analyses suggest that productivity would be higher if the firm implemented either of the two policies above, meaning process information on input quality or fully segregate batches into sheds according to hens’ age. A natural question is why the firm has not implemented these changes already. First, the results in Section 8.1 are based upon the assumption that the age of hens carries all relevant information regarding input quality. This may not be the case. Our conceptual framework shows how, as long as input quality remains partially unobservable to the management, worker’s evaluation will depend positively on coworkers’ signals, generating free-riding and negative productivity spillovers. Second, the costs of resolving the asymmetry of information by processing information on input quality on a daily basis may exceed the benefits of doing so. Even if this was not the case, managers lacked precise estimates of the magnitude of negative spillovers and their impact on productivity. Therefore, they had incorrect information on the cost-benefit calculation. This is not surprising in the context of a large firm operating in a developing country (Bloom et al., 2013). As for the input allocation schedule, in the last paragraph of Section 8.2 we point out that our analysis ignores the possibility that the management revises its termination policy together with its input allocation schedule. Still, we hypothesize that this would bring about even higher productivity gains. Importantly, the cost of reallocation only needs to be paid once, as co-movements in hens’ age over time will ensure that the latter keeps being synchronized among neighbouring production units. However, this also means that, once hens get old enough and need to be discarded, all batches belonging to production units within a given shed need to be substituted simultaneously. This is simply not feasible using the current technology for batch replacement.47 The cost of investing in a new technology may offset the net present value of increased revenues from higher productivity. Finally, Section 8.2 also shows that the counterfactual productivity under a fully segregated allocation of input batches is more volatile than the actual one. To the extent to which volatility in production enters negatively the objective function of the firm, the management may not be willing to implement this alternative allocation schedule despite its positive impact on average productivity. 9. Conclusion In many workplaces, workers produce output combining effort with inputs of heterogeneous quality. This article shows that input heterogeneity and information on input quality contribute to shape human resource management practices and can trigger productivity spillovers among workers. Using data from an egg production plant, we show that workers exert less effort when their coworkers are assigned high-quality inputs. Our conceptual framework and the analysis of workforce turnover data reveal that the effect captures free riding among workers, which originates from the way the management evaluates workers and makes dismissal decisions in a setting where input quality is not fully observable. Our study illustrates how the analysis of relatively more complex production environments may reveal non-trivial interactions between different areas of management. Indeed, inputs can also trigger productivity spillovers of alternative origins. In a companion article still work in progress, we investigate both theoretically and empirically how workers influence each other in their choice of inputs while updating information on the productivity of the latter from own and coworkers’ experience. The editor in charge of this paper was Aureo de Paula. Acknowledgements We are especially grateful to Albrecht Glitz and Alessandro Tarozzi for their advice, guidance and support. We would like to thank the Editor Aureo de Paula and three anonymous referees for their insightful comments. We are also thankful to the following people for helpful comments and discussion: Nava Ashraf, Ghazala Azmat, Paula Bustos, David Card, Vasco Carvalho, Matteo Cervellati, Giacomo De Giorgi, Rohan Dutta, Jan Eeckhout, Ruben Enikolopov, Gabrielle Fack, Rosa Ferrer, Maria Paula Gerardino, Sílvia Gonçalves, Libertad González, Marc Goñi, Stephen Hansen, Jonas Hjort, Andrea Ichino, Fabian Lange, Stephan Litschig, Rocco Macchiavello, Karen Macours, Marco Manacorda, Rohini Pande, Michele Pellizzari, Nicola Persico, Steve Pischke, Imran Rasul, Pedro Rey-Biel, Mark Rosenzweig, Tetyana Surovtseva, Chris Woodruff, and all seminar participants at Universitat Pompeu Fabra, Yale School of Management, University College London, European University Institute, University of Zurich, University of Warwick, CEMFI, IZA, Indiana University, McGill University, UNC Greensboro, Universidad de Piura, Universidad de Los Andes, Universitat de Barcelona, Università di Bologna, 2016 LACEA-LAMES, 21st SOLE Annual Meeting, COPE2016, 2015 NBER/BREAD Conference on Economic Development, 2015 Annual Congress of the Peruvian Economic Association, 2014 Ascea Summer School in Development Economics, 2014 Petralia Job Market Boot Camp, and 2014 EALE Conference. Errors remain our own. Footnotes 1. In our empirical setting, this is a plausible assumption. We explain later how variation in input quality across workers at a given point in time is given by heterogeneity in the age of assigned hens, which in turn is determined by heterogeneity in the timing of hen batch replacement and its technology. Input quality at a given point in time is therefore unrelated to worker’s characteristics. The evidence in Table A.1 of Supplementary Appendix A.1 supports this claim by showing that that observable worker’s characteristics do not differ systematically across quartiles of the assigned hens’ age distribution. 2. More precisely, this is an example of “false moral hazard” (Laffont and Martimort, 2002). Supplementary Appendix A.2 shows how, differently from the standard models of moral hazard, the worker’s effort choice is a deterministic function of his type and input quality, and a complete mapping exists between the latter and output. This category of models is therefore closely related to the standard models of adverse selection. 3. Notice that it is possible to interpret $\(U(\omega)\)$ as capturing the utility associated with the future stream of income associated with the job and not just the utility derived at one point in time. 4. We show in Supplementary Appendix A.2 that the linear projection $\({P}(\tilde{\theta}_i| \tilde{y}_i,\bar{\tilde{y}})\)$ used by the management is an approximation of the best linear projection of $\(\tilde{\theta}_i\)$ on $\(\tilde{y}_i\)$, in the spirit of Mas and Moretti (2009). The equilibrium values of $\(b_0,b_1,b_2\)$ are such that (1) the management takes workers’ choices (the data generating process) as given and uses $\({P}(\tilde{\theta}_i| \tilde{y}_i,\bar{\tilde{y}})\)$ to guess workers’ type, and (2) workers take the evaluation policy function $\({P}(\tilde{\theta}_i| \tilde{y}_i,\bar{\tilde{y}})\)$ as given and choose the level of effort that maximizes their utility. 5. Indeed, we have $$q_{1}(y_i,y_{-i})=f'(\cdot)\left(\frac{b_1}{y_i}+\frac{b_2}{Ny_i}\right)>0$$ $$q_{2}(y_i,y_{-i})=f'(\cdot)\frac{b_2}{Ny_{-i}}>0$$ $$q_{11}(y_i,y_{-i})=f''(\cdot)\left(\frac{b_1}{y_i}+\frac{b_2}{Ny_i}\right)^2+f'(\cdot)\left(-\frac{b_1}{y^2_i}-\frac{b_2}{Ny^2_i}\right)<0$$ $$q_{12}(y_i,y_{-i})=f''(\cdot)\left(\frac{b_1}{y_i}+\frac{b_2}{Ny_i}\right)\frac{b_2}{Ny_{-i}}<0$$ 6. Notice that, first, utility functions are quasi-concave with respect to $\(e_i\)$. Second, the strategy space of workers is convex and compact. Indeed, with $\(0\le q(\cdot)\le1\)$, in order for worker’s utility to be non-negative it must be that $\(e_i\in[0,\left(2\theta_iU(\omega)\right)^{\frac{1}{2}}]\)$. Finally, the continuous differentiability of $\(q_{1}(\cdot)>0\)$ ensures best-reply function to exist and be continuous. Hence, the Kakutani fixed-point theorem applies and an equilibrium exists. Under specific functional forms for $\(q(\cdot)\)$, it is possible to solve for the equilibrium of the non-cooperative game workers play and derive closed-form solutions. At equilibrium, the sign of the relationship between own effort and coworkers’ input quality is still informed by the sign of the cross derivative $\(q_{12}(\cdot)\)$. The intuition for this result goes as follows. An increase in coworkers’ input quality increases their output. With $\(q_{12}(\cdot)<0\)$, own effort simultaneously decreases, decreasing own output and inducing coworkers’ effort to increase even more, etc. That is, the negative relationship between coworkers’ input quality and own effort self-reinforces itself at equilibrium. This can be seen more clearly in equation (18) of Supplementary Appendix A.2. 7. The conceptual framework in Falk and Ichino (2006) and Mas and Moretti (2009) builds on the same argument. 8. Supplementary Appendix A.3 shows the corresponding theoretical results for both social and monetary incentives. 9. Also in this case it is possible to interpret $\(F\)$ not only as the fixed component of wage in the current period, but as incorporating the utility associated with the future stream of income associated with the job. 10. The worker’s typical daily schedule is reported in Table A.2 of Supplementary Appendix A.1. Egg production establishments in developed countries are typically endowed with automatic feeders and automated gathering belts for egg handling and collection. The production technology in the plant under investigation is thus more labor intensive relative to the frontier (see American Egg Board, Factors that Influence Egg Production, http://www.aeb.org, accessed on 27, December 2013) 11. Figure A.3 in the Supplementary Appendix shows the distribution of the estimated worker fixed effects as derived as described at the end of Section 5. The variance of the distribution is indicative that, conditional on input quality, workers can have a substantial impact on productivity. 12. Given the focus on productivity spillovers, we exclude those observations belonging to sheds hosting a single production. 13. The number of living hens on a given day may be by itself endogenous to worker’s effort. We discuss this possibility in greater details in Section 5. In particular, results from Table 4 show that the fraction of hens dying on each day does not change systematically with coworkers’ productivity. We thus conclude that our estimates of productivity spillovers are not sensitive to the adjustment by the number of living hens. One other option is to use total output as measure of productivity, and control for the number of living hens in the regression specifications that we implement in our empirical analysis. When we control for the number of hens in a flexible way, we still find evidence of negative productivity spillovers. These additional results are available from the authors upon request. 14. This quantity is computed by dividing the number of 50 kg sacks of food opened by the worker by the number of living hens on each day. Once the sack is opened, the food it contains does not need to be all distributed to the hens. This results in measurement error, and can explain why the maximum quantity of food per chicken in the data is almost 6 kg. 15. We directly test for this hypothesis by estimating worker fixed effects in a subsample of our data, and then focusing on the remaining sample and regressing individual productivity over the estimated worker fixed effects, a proxy for input quality, and the interaction between the two. The estimated coefficient of the interaction variable is positive and highly significant. This means that an increase in input quality is associated with a differential productivity increase for high ability workers, thus showing evidence of complementarity between workers and input quality. We explain the details of this test in Supplementary Appendix A.4. We thank one anonymous referee for suggesting the procedure. 16. These time intervals together account for around 40% of the overall productive life span. 17. In Supplementary Appendix A.5, we show explicitly how the linearized first-order condition of the worker’s maximization problem maps into the proposed regression specification. We there show that the sign of the parameter $\(\gamma\)$ is informative of the sign of the cross-derivative $\(q_{12}(\cdot)\)$ of the termination policy function. 18. In Section 5.2, we also use a kinked regression specification and week-of-age dummies to better fit the productivity-age profile shown in Figure 1. Parameter estimates are highly comparable across specifications. In our baseline analysis, we prefer to adopt a quadratic functional form to avoid the many-weak-instruments problems that would arise by using the full set of week-of-age dummies as instruments for coworkers’ productivity. 19. The suggested specification differs from the basic treatment in Manski (1993) along two important dimensions. First, it adopts a leave-out mean formulation, as the average productivity regressor is computed excluding worker $\(i\)$. Second, peer groups overlap, as peers in this context are coworkers in neighbouring production units and some sheds count more than two units (Bramoullé et al., 2009; De Giorgi et al., 2010; Blume et al., 2011; Angrist, 2014). 20. The technology is such that the old batch is typically loaded on a truck, which then travels to the main operation centre to be unloaded. Maintenance is then carried on the production unit for the next few days. When ready, the new batch is then loaded on a truck in the raising sector and taken to the production unit, where the new batch is unloaded and positioned. 21. Table A.3 in Supplementary Appendix A.1 reports the estimates of the conditional correlation coefficients. Since every hen batch in the sample is neighbour of some other batch, within-group correlation estimates using the whole sample suffer from mechanical downward bias (Bayer et al., 2008; Guryan et al., 2009; Caeyers and Fafchamps, 2016). This bias is relatively larger for smaller peer groups. To overcome this problem, we follow Bayer et al. (2008) and randomly select one production unit per group as defined by the shed-week interaction $\((g,w)\)$. Estimates are computed using the same resulting subsample. 22. The orthogonality hypothesis can be further tested using the regression specification proposed by Guryan et al. (2009), which in this case becomes $$ age_{igwt}=\pi_1 \ \overline{age}_{-igwt}+\pi_2 \ \overline{age}_{-igw}+\psi_{gw}+\delta_{t}+u_{igwt}, $$ where $\(age_{igwt}\)$ is the age in weeks of hens assigned to worker $\(i\)$ in shed $\(g\)$ in week $\(w\)$ on day $\(t\)$. $\(\overline{age}_{-igwt}\)$ is the corresponding average value for coworkers in neighbouring production units on the same day, while $\(\overline{age}_{-igw}\)$ is the average value for peers in the same shed in all days of the week. The hypothesis of daily random assignment of age of coworkers’ hens within each shed-week group is equivalent to the null $\(H_0: \pi_1=0\)$. Regression results are reported in the bottom panel of Table A.3 in Supplementary Appendix A.1, showing that $\(H_0\)$ cannot be rejected. 23. We discuss the validity of both assumptions in detail in the next Section and in evaluating the robustness of results. Several contributions in the literature exploit within-group random variation in peer characteristics to identify peer effects (see for instance Sacerdote, 2001; Ammermueller and Pischke, 2009; Guryan et al., 2009). In our case, the variation we exploit for identification is meaningful. Conditional on day fixed effects, within-shed-week variation accounts for 5.4% of the total variation in the age of coworkers’ hens in the sample, measured in weeks. The same fraction goes up to 35% for observations belonging to those weeks in which any batch replacement took place in the shed. 24. Standard errors are clustered along the two dimensions of shed and day in all specifications. Idiosyncratic residual determinants of productivity are thus allowed to be correlated both in time and space, specifically among all observations belonging to the same working day and all observations belonging to the same shed. 25. The coefficients of the own hen’s age variables do not change also when coworkers’ hens’ age variables are included separately as controls one by one, as shown in Table A.4 of Supplementary Appendix A.1. 26. Notice that that hens’ age is a linear function of time and is therefore predictable by the workers. It follow that workers may directly respond to changes in the quality of inputs assigned to coworkers, and not to the resulting changes in their observed productivity. This would not invalidate the reduced-form estimates in Table 2 and their interpretation of negative productivity spillovers, but it would affect the interpretation of the 2SLS estimates of the $\(\gamma\)$ parameter. Deriving these estimates is nonetheless useful to pin down the exact magnitude of productivity spillovers. 27. We specifically asked whether batch replacement may affect neighbouring workers in any way, and the answer was that it does not affect them. 28. Nonetheless, Figure A.4 in Supplementary Appendix A.1 also shows that there is substantial variation in productivity across days. This raises the issue of whether the inclusion of shed-week fixed effects is sufficient to net out other determinants of individual productivity, possibly negatively correlated with the age of coworkers’ hens. We address this concern by restricting our sample to those observations within 4, 5, and 6 weeks from coworkers’ batch replacement and including the full set of shed-day fixed effects. Columns 1 to 3 of Table A.7 in Supplementary Appendix A.1 report the corresponding coefficient estimates. These are still negative and bigger in magnitude than previous ones, and significant at the 5% level. We therefore conclude that confounders at the shed-day level cannot be responsible for our baseline results. A related concern is that our measurement of hens’ age in weeks may be driving the result. We thus implement the main regression specification, but measuring both own and coworkers’ hens age in days, and including shed-day fixed effects. Column 4 of Table A.7 in Supplementary Appendix A.1 reports the corresponding coefficient estimate, which are consistent in magnitude with the previous ones and significant at the 5% level. 29. This result is in line with the evidence from Figure A.5 in Supplementary Appendix A.1 showing that coworkers’ replacement brings no discontinuous changes in individual productivity. 30. To validate this claim further, we also fit the relationship between hens’ age and productivity using a kinked regression with three kinks, as shown by Figure A.6 in Supplementary Appendix A.1. We choose the values of hens’ age at the kinks that maximize the $\(R^2\)$ of the kinked regression of productivity over hens’ age. We then estimate the parameters from the main regression specification using as instrument for coworkers’ productivity its value as predicted by the kinked regression estimates. Column 1 of Table A.8 in Supplementary Appendix A.1 shows the corresponding results. Columns 2 to 5 show that estimates are insignificant when implementing this regression on different subsamples as defined by the kinked regression interval the age of coworkers’ hens belongs to. This confirms that the variation that we exploit for identification does not belong to any specific segment of the productivity-age profile. 31. This can be easily shown in the case of two peer workers. Let $\(\tilde{y}_i=\tilde{s}_i+\gamma \tilde{y}_j\)$, with $\(\gamma<0\)$. As $\(\tilde{s}_i\)$ increases by one, its impact on own productivity reverberates through the system and is equal to $\(\frac{1}{1-\gamma^2}>1\)$. At the same time, the impact on coworkers’ productivity is negative and equal to $\(\frac{\gamma}{1-\gamma^2}<\gamma<0\)$. The aggregate productivity response would thus be equal to $\(\frac{1+\gamma}{1-\gamma^2}=\frac{1}{1-\gamma}<1\)$. 32. In Column 1, coworkers’ variables are the same for all workers in a shed, so there is no daily within-shed variation left to exploit. This explains why the strength of the first stage relationship is lower, although the corresponding F-statistic of a joint test of significance of the instruments is still equal to 11.01. In Column 2, the sample is restricted to workers located in sheds with more than two production units. 33. Variable values are augmented by 0.01 before taking the log. Implementing a log–log specification we can also estimate the elasticity of own productivity with respect to coworkers’ productivity, equal to 0.35, with the estimate being significant at the 1% level. 34. We also perform two additional robustness checks. First, we address the identification concerns in Angrist (2014) by explicitly separating the subjects who are object of the study from their peers. Specifically, we randomly select one production unit per each shed-week and run the main identifying regression over the restricted sample only. Second, we drop out all observations belonging to those days in which the worker assigned to a given production unit was listed as absent. Results are in line with the previous estimates in both cases, and are available from the authors upon request. 35. Given the high correlation between contemporaneous hens’ age and its one and two-week lag, we drop contemporaneous own hens’ age and its square from the set of regressors and use the two-week lag of coworkers’ hens’ age and its square as set of instruments for both contemporaneous and the lag of coworkers’ productivity. 36. Figure A.3 in Supplementary Appendix A.1 shows the distribution of workers’ ability. Notice that we estimate worker fixed effects in a regression framework without modelling productivity spillovers explicitly. We therefore incur the risk that the estimated worker fixed effects are confounded by the productivity of neighbouring coworkers and their hens. However, as explained in Section 3, once a batch is assigned to a given production unit it maintains its position until the end of its productive life. This rules out the possibility that workers are systematically assigned hens of particular age (and productivity), and diminishes the concerns that the estimated worker fixed effects are confounded by the age and productivity of neighbouring hens. 37. See Section 7 and Table A.15 in Supplementary Appendix A.1 for more detailed information on the wage schedule of workers at the firm. Average and minimum wage data are from the World Bank. 38. Specifically, we let $\(\frac{h_0(t)}{1-h_0(t)}=\exp\{\gamma_{t}\}\)$ which implies $\(\text{logit } h_0(t)=\ln \frac{h_0(t)}{1-h_0(t)}=\gamma_{t}\)$. With $\(\gamma_{t}=\delta \ln t\)$ we let $\(\frac{h_0(t)}{1-h_0(t)}=t^\delta\)$ and $\(h_0(t)=\frac{t^\delta}{1+t^\delta}\)$. 39. Notice that $$q(t)=\frac{1}{1+\exp\{\ \gamma_{t} + \alpha \ y_{igt}+ \beta \ \bar{y}_{t} \ \}}$$ $$\frac{\partial q(\cdot)}{\partial y_{igt}}=-\frac{\exp\{\ \gamma_{t} + \alpha \ y_{igt}+ \beta \ \bar{y}_{t} \ \}}{(1+\exp\{\ \gamma_{t} + \alpha \ y_{igt}+ \beta \ \bar{y}_{t} \ \})^2}\left(\alpha+\frac{\beta}{N}\right)$$ $$\frac{\partial^2 q(\cdot)}{\partial y_{igt}{y}_{jgt}}=-\frac{\exp\{\ \gamma_{t} + \alpha \ y_{igt}+ \beta \ \bar{y}_{t} \ \}(1-\exp\{\ \gamma_{t} + \alpha \ y_{igt}+ \beta \ \bar{y}_{t} \ \})}{(1+\exp\{\ \gamma_{t} + \alpha \ y_{igt}+ \beta \ \bar{y}_{t} \ \})^3}\left(\alpha+\frac{\beta}{N}\right)\frac{\beta}{N},$$ Where the latter is negative if $\(\gamma_{t} + \alpha y_{igt}+ \beta \bar{y}_{t}<0\)$ and $\(\alpha, \beta<0\)$. This is always the case in our sample. 40. Table A.10 in Supplementary Appendix A.1 shows the corresponding results when replacing average productivity with the average number of eggs per hen across all workers, and the average number of eggs with the total number of eggs collected on the day. In Tables A.11 and A.12 of Supplementary Appendix A.1, we replace instead the regressors of interest with their seven-days moving averages. The magnitude and significance of the estimated coefficients are largely consistent with the ones in Table 6. 41. Table A.14 in Supplementary Appendix A.1 reports the parameter estimates from the corresponding logistic hazard model specifications. 42. The average total pay in the two-weeks period is equal to the equivalent of 220 USD, with the bonus component being 15% of the base pay on average. Table A.15 in Supplementary Appendix A.1 shows the corresponding summary statistics for the base pay, the bonus component and total pay. Average base pay is equal to 505 PEN (Peruvian Nuevo Sol), equal to around 190 USD. The average of the bonus component of pay is instead equal to 82 PEN, around 30 USD ($\(\delta\)$=40 PEN). 43. Table A.16 in Supplementary Appendix A.1 shows the average base pay, bonus pay, and total pay for the average worker across the assigned hens’ age distribution, confirming the existence of a strong relationship between hens’ age and bonus pay. Notice that small variations in base pay are observed across productivity categories. Base pay can indeed still vary with workers’ age, tenure, and base contract. Nonetheless, most of the variation in total pay is due to variation in the bonus pay component. 44. As reported in Table 1, 25% of the observations in the overall sample correspond to workers who recognize at least one of their coworkers in neighbouring production units as friend. Notice that the number of observation is reduced because the sample is restricted to those 80% of observations that we can merge with the information on workers elicited in March 2013. 45. Notice that the possible endogeneity of friendship relationship to the implementation of cooperative strategies makes this point even stronger. Indeed, we should find even more of a negative effect of coworkers’ productivity in this case for those workers who are working along friends. 46. Graham (2011) provides a formal discussion of this result. To understand this, it is useful to think about the case of a given number of sheds each hosting two production units. In this case, the quality of inputs assigned to each worker only affects the productivity of one neighbouring worker. Reallocating inputs does not change that, and the total amount of externalities in the system does not change. 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Published: Oct 1, 2018