Input Allocation, Workforce Management and ProductivitySpillovers: Evidence from Personnel Data∗

Francesco Amodio† Miguel A. Martinez-Carrasco‡

January 14, 2018

AbstractThis paper shows how input heterogeneity triggers productivity spillovers at the work-place. In an egg production plant in rural Peru, workers produce output combining effortwith inputs of heterogeneous quality. Exploiting variation in the productivity of inputsassigned to workers, we find evidence of a negative causal effect of an increase in cowork-ers’ daily output on own output and its quality. We show theoretically and suggest em-pirically that the effect captures free riding among workers, which originates from theway the management informs its dismissal decisions. Our study and results show thatinput heterogeneity and information on input quality contribute to determine the shape ofincentives and have implications for human resource management, production manage-ment, and the interaction between the two. Counterfactual analyses show that processinginformation on inputs or changing their allocation among workers can generate significantproductivity gains.

Keywords: spillovers, productivity, input heterogeneity, incentives, termination.JEL Codes: D22, D24, J24, J33, M11, M52, M54, O12.

∗We are especially grateful to Albrecht Glitz and Alessandro Tarozzi for their advice, guidance and sup-port. We would like to thank the Editor Aureo de Paula and three anonymous referees for their insightfulcomments. 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, Ro-han Dutta, Jan Eeckhout, Ruben Enikolopov, Gabrielle Fack, Rosa Ferrer, Maria Paula Gerardino, SılviaGoncalves, Libertad Gonzalez, Marc Goni, Stephen Hansen, Jonas Hjort, Andrea Ichino, Fabian Lange,Stephan Litschig, Rocco Macchiavello, Karen Macours, Marco Manacorda, Rohini Pande, Michele Pelliz-zari, 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, Universidadde Los Andes, Universitat de Barcelona, Universita di Bologna, 2016 LACEA-LAMES, 21st SOLE AnnualMeeting, COPE2016, 2015 NBER/BREAD Conference on Economic Development, 2015 Annual Congressof the Peruvian Economic Association, 2014 Ascea Summer School in Development Economics, 2014 Pe-tralia Job Market Boot Camp, and 2014 EALE Conference. Errors remain our own.†francesco.amodio@mcgill.ca, Department of Economics and Institute for the Study of International

Development, McGill University, Leacock Building 514, 855 Sherbrooke St. West, Montreal, QC H3A 2T7.‡ma.martinezc1@uniandes.edu.co, School of Management, Universidad de Los Andes, Calle 21 No. 1-

20, Bogota, Colombia and Department of Economics, Universidad de Piura, Calle Martir Jose Olaya 162,Lima, Peru.

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1 Introduction

The productivity of workers is affected by coworkers’ productivity. A number of stud-ies analyzing a highly diverse set of occupations provide evidence of these productivityspillovers. Herbst and Mas (2015) show how productivity spillovers are typically positiveand 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 sub-stitutes in the workplace production function, the effort of one worker affects the marginalproduct of effort for another worker. Sport teams are a clear example of this kind (Gouldand Winter 2009; Arcidiacono, Kinsler, and Price 2017). Second, workers may learn fromeach other, and therefore become more productive when working along highly productivepeers (Jackson and Bruegmann 2009; Nix 2015; Menzel 2016). Third, behavioral con-siderations may play a role, as workers may find effort less costly to exert at the marginif coworkers’ effort increases (Kandel and Lazear 1992; Falk and Ichino 2006). Fourth,the pay scheme, dismissal policy, or human resource management in general can generateexternalities among workers. For example, relative performance or team-based evaluationmake the effort choices of coworkers interdependent even in the absence of other sourcesof externalities (Bandiera, Barankay, and Rasul 2005; Mas and Moretti 2009).

All existing studies explore these issues in settings where output is a (noisy) function ofworker’s effort only. However, in many workplaces, workers produce output by combiningeffort with inputs of heterogeneous quality. In Bangladeshi garment factories, for instance,the quality of textiles affects productivity as measured by the number of items processedper unit of time. The speed at which warehouse workers fill trucks is affected by theshape and weight of the parcels they handle. The amount of time it takes for a judge toclose a case depends on his own effort as well as on both observable and unobservablecharacteristics or complexity of the case itself (Coviello, Ichino, and Persico 2014).

This paper investigates whether input heterogeneity triggers productivity spillovers atthe workplace. The characteristics of inputs individually assigned to workers directly affecttheir productivity. The amount of information on input quality and the extent to which it isshared by the worker and the management contribute to determine the shape of incentives.When incentives generate externalities among workers, heterogeneous inputs can triggerproductivity spillovers. Is there any evidence of productivity spillovers of this origin? Doesinput allocation matter for aggregate productivity at the workplace?

Measuring productivity spillovers from heterogeneous inputs is challenging for threemain reasons. First, firms often do not maintain records on the productivity of individualworkers. Second, even when such data exist, input quality is usually not recorded or hard tomeasure. Finally, in order to credibly identify productivity spillovers from heterogeneous

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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 itsplant are particularly suitable for our analysis. Workers operate in production units locatednext to the each other and grouped in several sheds. Each worker is assigned a given batchof laying hens as input in the production process. Hens’ characteristics and worker’s effortjointly determine individual productivity as measured by the daily number of collectedeggs. In particular, variation in the age of hens assigned to the worker induces variationin productivity. Using daily personnel data, we exploit quasi-random variation in the ageof 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 qual-ity, workers’ productivity is systematically lower when the productivity of neighboringcoworkers is exogenously raised by the assignment of higher quality inputs. A positiveshift in average coworkers’ input quality inducing a one standard deviation increase intheir daily output causes a given worker’s output to drop by almost a third of a standarddeviation. We also find output quality to decrease significantly, with the effect in standarddeviation units being similar in magnitude to the effect on quantity. We attribute theseeffects to a change in the level of effort exerted by the worker, which varies systematicallywith coworkers’ productivity.

We argue that the specific source of externalities in this setting lies in human resourcemanagement practices, and the worker evaluation and dismissal policy implemented bythe firm. Our conceptual framework builds upon the one in Mas and Moretti (2009), thatwe extend in order to accommodate input heterogeneity. Output is a function of effort andinput quality. The latter is observable to the worker, but not to the management, which can-not disentangle the separate contribution of effort and input to output. To solve the moralhazard problem, the management combines the available information on the productivityof all workers to guess their type and make dismissal decisions accordingly. Average pro-ductivity positively affects worker evaluation. An increase in the productivity of coworkersincreases a given worker’s probability of keeping the job. As a result, workers free rideon each other: when coworkers’ productivity increases, individual marginal returns fromeffort decrease for a given worker. His optimal effort supply falls accordingly. We useworkforce turnover information in the data to investigate how employment terminationprobabilities correlate with individual and average productivity, and provide suggestiveevidence of the mechanism identified by theory.

In the second part of the paper, we study whether and how the provision of social andmonetary incentives can mitigate free riding and offset negative spillovers at the work-place. On the one hand, monetary incentives provide extra marginal benefits from effort,

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leveraged by the probability of keeping the job. On the other hand, working along friendsinduces 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 neg-ative externalities generated by the termination policy. We test these hypotheses by ex-ploiting the specific features of the pay regime, and elicited information on the friendshipnetwork among workers. Workers receive extra pay for every egg box they produce abovea given threshold. Exposure to piece rate incentives therefore varies with input qualityand the age of assigned hens. We find no effect of coworkers’ productivity when hens arehighly productive and workers are more likely to hit the piece rate threshold. We also findno significant spillover effects when the worker identifies any of his neighboring cowork-ers as friends. Both findings are consistent with the theory. The second result also rulesout the possibility that the estimated average negative effect of coworkers’ productivity onown 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 implicationsof input heterogeneity at the workplace. We show how the presence of heterogeneousinputs and information on such heterogeneity matter for several different aspects of bothhuman resource and production management, ranging from incentive design and workerdismissal to input assignment and replacement schedule. To shed light on the individualrole of these practices, we perform a structural estimation exercise grounded in our con-ceptual framework. We estimate the unobserved exogenous parameters of the model, andconduct counterfactual policy analyses. We first quantify the productivity gains of process-ing all information on input quality, thus providing the management with a precise signalof worker’s effort. In this environment, termination probabilities are a function of individ-ual outcomes only, and no externalities arise. We show that, holding fixed the allocation ofinputs, processing information on their quality can generate significant productivity gains.Second, we quantify the extent to which input allocation affects productivity. Holding ev-erything else constant, we simulate alternative input assignment schedules and find thatdaily productivity could increase by up to 20%. We discuss the limitations of our analy-sis, and explain what informational or technological constraints may prevent the firm fromimplementing these alternative policies.

Our findings contribute to the literature on human resource management practices andthe externalities they generate among coworkers. Bandiera, Barankay, and Rasul (2005)explore the role played by social ties in the internalization of negative externalities un-der relative performance evaluation, and their impact on productivity under individualperformance pay (Bandiera, Barankay, and Rasul 2010). Bandiera, Barankay, and Rasul(2007, 2008, 2009) provide evidence of the impact of managerial incentives on productiv-ity, and their consequences for lower-tier workers who are socially connected to managers.

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Bandiera, Barankay, and Rasul (2013) study instead the effectiveness of team-based in-centives and their relationship with social connections. Mas and Moretti (2009) study peereffects among cashiers in a large US supermarket chain. They show how social pressurefrom observing high-ability peers is strong enough to more than offset the incentives tofree ride generated by the dismissal policy. Using daily personnel data from a flower pro-cessing plant in Kenya, Hjort (2014) shows that the ethnic composition of working teamsaffects productivity at the workplace, with the negative effect of ethnic diversity beinglarger when political conflict between ethnic blocs intensifies. He also shows how thiseffect is mitigated by the introduction of team-based pay.

Our results generalize to those settings that share the same technological and informa-tional assumptions of our conceptual framework. By technological assumptions we referto the shape of the production function and its inputs, and the presence of heterogeneityin input quality. By informational assumptions we refer to the information available to themanagement and its inability to perfectly disentangle the separate contributions of effortand input to output. More broadly, our findings generalize to those settings where humanresource management practices generate spillovers among coworkers, and the latter handleinputs of heterogeneous quality. In particular, the firm under investigation employs a rela-tively more labor intensive technology compared to firms in the same sector, but operatingin 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, Mahajan, McKenzie, and Roberts 2010; Bloom, Eifert, Mahajan, McKenzie,and Roberts 2013). In this respect, this paper is close to Hjort (2014) in that it highlightsthe efficiency cost of input misallocation among workers, and explores how properly de-signed incentives may partially eliminate these costs. In the context of an Indian garmentfactory, Adhvaryu, Kala, and Nyshadham (2016) show how the management can reducethe extent of negative productivity shocks by reallocating workers to tasks.

2 Conceptual Framework

This section illustrates how input heterogeneity contributes to shape human resource man-agement practices and triggers productivity spillovers among workers.N workers independently produce output yi > 0 combining effort ei ≥ 0 with a given

input of quality si > 0, with i ∈ {1, 2, ., N}. Inputs of higher quality raise the marginalproduct of effort. Output at a moment in time is given by

yi = siei (1)

Effort cost is positive and convex, with C(ei) = e2i /2θi and θi > 0. The marginal cost of

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effort is decreasing in θi, which defines worker’s type. θi is heterogeneous across work-ers, independently drawn from the same distribution. Input quality si is identically andindependently distributed across workers, and independent of θi.1 Each worker knows histype, perfectly observes input quality and exerts effort. The management observes output,but cannot observe and thus disentangle the separate contributions of effort and input tooutput. The asymmetry of information between the worker and the management generatesmoral hazard.2

To solve the moral hazard problem, the management uses the information on output toguess worker’s type and attach to each worker a given probability Qi of keeping the job.While on the job, the worker earns a fixed salary ω from which he derives utility U(ω).In case the employment relationship terminates, the worker does not earn any salary andderives zero utility. The threat of dismissal works as an incentive device.3

Let si = ln si, yi = ln yi, and θi = ln θi. We assume that E(si) = 0, V ar(si) andV ar(θi) are known to the management, but E(θi) is not. This means that the managementknows only specific features of the input quality and worker’s type distributions. It hasperfect information on the mean and variance of the (log of) input quality distribution, andthe variance of (log of) worker’s type. But, it lacks information on where the transformedtype distribution is centered. In this environment, the management estimates the log ofworker’s type using a linear projection of the form

P (θi|yi, ¯y) = b0 + b1yi + b2¯y (2)

where ¯y is the average of yi among all workers. Let the retention probability Qi be anincreasing and concave function of P (θi|yi, ¯y), i.e.

Qi = f (b0 + b1yi + b2¯y) (3)

with f ′(·) > 0 and f ′′(·) < 0. It can be shown that if f ′′(0)/f ′(0) > −1 then b1, b2 > 0.Under this condition, output is a positive signal of worker’s type. Unobserved heterogene-ity in input quality makes these signals individually imprecise. Their average provides

1In our empirical setting, this is a plausible assumption. We explain later how variation in input qualityacross workers at a given point in time is given by heterogeneity in the age of assigned hens, which in turnis determined by heterogeneity in the timing of hen batch replacement and its technology. Input quality at agiven point in time is therefore unrelated to worker’s characteristics. The evidence in Table A.1 of AppendixA.1 supports this claim by showing that that observable worker’s characteristics do not differ systematicallyacross quartiles of the assigned hens’ age distribution.

2More precisely, this is an example of “false moral hazard” (Laffont and Martimort 2002). Appendix A.2shows how, differently from the standard models of moral hazard, the worker’s effort choice is a deterministicfunction of his type and input quality, and a complete mapping exists between the latter and output. Thiscategory of models is therefore closely related to the standard models of adverse selection.

3Notice that it is possible to interpret U(ω) as capturing the utility associated with the future stream ofincome associated with the job and not just the utility derived at one point in time.

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the management with valuable information on the mean of the type distribution. To guessworker’s type, the management uses own and average output, attaching to the latter a pos-itive weight that increases with the extent of input heterogeneity. In Appendix A.2, weillustrate the signal extraction problem of the management, derive the equilibrium valuesof b0, b1, b2, and find the sufficient condition for b1, b2 > 0.4

From equation 3 it follows that Qi is increasing in both own output yi and any ofcoworkers’ output y−i. Moreover, the concavity of the f(·) function implies that the crossderivative is negative: marginal returns from own output in terms of increased retentionprobability decrease with coworker’s output. It is therefore possible to express Qi as afunction of own and any given coworker’s output q(yi, y−i), with q1(·) > 0 and continu-ously differentiable, q11(·) < 0, and q12(·) < 0.5

Each worker chooses the effort level ei ≥ 0 which maximizes his expected utility

maxei

U(ω) q(yi, y−i)−e2i

2θi(4)

Taking the corresponding first order condition we get

U(ω) q1(yi, y−i) siθi = ei (5)

We can apply the implicit function theorem to derive how the worker’s optimal effort levelchanges with coworkers’ output. We get

∂e∗i∂y−i

=U(ω) q12(yi, y−i) siθi

1− U(ω) q11(yi, y−i) s2i θi

< 0 (6)

Notice that the denominator is always positive, and the sign of the above derivative isuniquely determined by the sign of q12(·). As coworker’s output increases, the worker’soptimal effort level decreases. Workers free ride on each other. This is because marginal

4We show in Appendix A.2 that the linear projection P (θi|yi, ¯y) used by the management is an approx-imation of the best linear projection of θi on yi, in the spirit of Mas and Moretti (2009). The equilibriumvalues of b0, b1, b2 are such that (i) the management takes workers’ choices (the data generating process)as given and uses P (θi|yi, ¯y) to guess workers’ type, and (ii) workers take the evaluation policy functionP (θi|yi, ¯y) as given and choose the level of effort that maximizes their utility.

5Indeed, we have

q1(yi, y−i) = f ′(·)(b1yi

+b2Nyi

)> 0

q2(yi, y−i) = f ′(·) b2Ny−i

> 0

q11(yi, y−i) = f ′′(·)(b1yi

+b2Nyi

)2

+ f ′(·)(− b1y2i− b2Ny2i

)< 0

q12(yi, y−i) = f ′′(·)(b1yi

+b2Nyi

)b2

Ny−i< 0

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returns from own output in terms of increased probability of keeping the job decrease withcoworkers’ output, as captured by the sign of q12(·). Workers best-respond to each other inequilibrium.6

Consider now the case in which input quality is partially observed by the management.Let si = aiεi, with ai > 0 being observable to both the worker and the management, andεi > 0 observable to the worker only. Output at a moment in time is given by

yi = aiεiei (7)

The management uses the available information on input quality to mitigate the asymmetryof information and derive a more precise signal of worker’s type as given by

zi =yiai

= εiei (8)

Let εi = ln εi and zi = ln zi. Let also E(εi) = 0 and V ar(εi) be known to the manage-ment, which computes

P (θi|zi, ¯z) = b0 + b1zi + b2¯z (9)

where ¯z is the average of zi among workers. If the retention probability for a given workeris an increasing and concave function of P (θi|zi, ¯z), the same conditions specified aboveimply that b1, b2 > 0. Even after netting out the observable component of input quality,the residual unobserved heterogeneity εi does not allow the management to perfectly dis-entangle the separate contributions of effort and input to output. The management stillrelies on the average of all signals to derive an estimate of the mean of the worker’s typedistribution. The retention probability increases with both the individual signal zi and anyof coworkers’ signal z−i. Furthermore, marginal returns from own signal in terms of in-creased retention probability decrease with coworkers’ signal, generating free riding andnegative productivity spillovers.

Monetary and Social Incentives We now illustrate how incentives other than the threatof 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 operates6Notice that, first, utility functions are quasi-concave with respect to ei. Second, the strategy space of

workers is convex and compact. Indeed, with 0 ≤ q(·) ≤ 1, in order for worker’s utility to be non-negativeit must be that ei ∈ [0, (2θiU(ω))

12 ]. Finally, the continuous differentiability of q1(·) > 0 ensures best-reply

function to exist and be continuous. Hence, the Kakutani fixed-point theorem applies and an equilibrium ex-ists. Under specific functional forms for q(·), it is possible to solve for the equilibrium of the non-cooperativegame workers play and derive closed-form solutions. At equilibrium, the sign of the relationship betweenown effort and coworkers’ input quality is still informed by the sign of the cross derivative q12(·). The in-tuition for this result goes as follows. An increase in coworkers’ input quality increases their output. Withq12(·) < 0, own effort simultaneously decreases, decreasing own output and inducing coworkers’ effort toincrease even more, etc. That is, the negative relationship between coworkers’ input quality and own effortself-reinforces itself at equilibrium. This can be seen more clearly in equation 18 of Appendix A.2.

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through the effort cost function: coworkers’ effort diminishes the marginal cost of effortfor the worker.7 In the environment described here, output is a function of both worker’seffort and input quality. We thus model peer pressure as operating through a decrease inthe cost of effort that follows an increase in coworker’s output y−i. The worker’s problembecomes choosing effort level ei ≥ 0 that maximizes his expected utility

maxei

U(ω) q(yi, y−i)−ei2θi

(ei − λ y−i) (10)

where λ > 0 is a generic parameter capturing the intensity of peer pressure mecha-nisms. It can be shown that, while the firm’s implemented termination policy still generatesteamwork-type externalities, peer pressure pushes them in the opposite direction, possiblychanging 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 ω = F+κyi

with κ > 0.9 The worker chooses the level of effort ei ≥ 0 that maximizes his expectedutility

maxei

U(F + κyi)q(yi, y−i)−e2i

2θi(11)

Piece rate incentives provide extra motivation for effort. Notice also that monetaryincentives are leveraged by the probability q(·) of keeping the job. The sign of productiv-ity spillovers is no longer uniquely determined by the sign of the cross derivative q12(·),and own optimal effort may still increase with coworkers’ productivity. This is becausecoworkers’ productivity increases the probability of keeping the job. Even if marginal re-turns 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, suchas social learning, monitoring on behalf of supervisors, discouragement from highly pro-ductive peers, or the possibility that workers engage in cooperative strategies. These maypotentially be incorporated in the model without changing its basic intuition on the role ofthe termination policy. We will discuss these other sources of spillovers and the empiricalsalience of alternative explanations to our findings in Section 6.

7The conceptual framework in Falk and Ichino (2006) and Mas and Moretti (2009) builds on the sameargument.

8Appendix A.3 shows the corresponding theoretical results for both social and monetary incentives.9Also 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.

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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. Inthe plant under investigation, production takes place in several sectors, one of them beingshown in Figure A.1 of Appendix A.1. Each sector comprises several sheds. Each shedhosts one to four production units. As an example, Figure A.2 of Appendix A.1 shows ashed that hosts four production units.

Each production unit is defined by one worker and a given batch of laying hens assignedto him. Hens within a given batch have homogeneous characteristics. In particular, theyare all of the same age. This is because the bird batch is treated as a single input. The entirebatch is bought from an independent bird supplier company. After birth, hens are raisedin a dedicated sector. The batch is then moved to production when hens are around 20weeks old, and discarded altogether at age 80 to 90 weeks. While in production, the batchis always located in the same production unit and assigned to the same worker. Worker’smain tasks are: (i) to collect and store the eggs, (ii) to feed the hens and (iii) to maintainand clean the facilities.10

Output is collected eggs. These are classified into good, dirty, broken and porous, sothat measures of output quality can be derived accordingly. The batch of laying hens asa whole is the main production input. High quality hens increase the marginal productof effort for the worker. Two specific dimensions of worker’s effort directly map fromits conceptualization in the previous section. The first one relates to the logistics of eggcollection. The worker walks within the production unit along cages and fills a basket ofa given size with the newly laid eggs. Once the basket is full, the worker walks to thesmall warehouse in front of the production unit, visible in Figure A.2. There he emptiesthe basket, then goes back to the production unit and repeats. The number of times andspeed at which the worker goes back and forth from the production unit to the warehousedetermines how many eggs will be counted at the end of the day. Their quality is affectedas well, as eggs may break if the worker overloads the basket or is not careful in emptyingit. Importantly, effort in this task is complementary to input quality as the more hens areproductive the higher is the scope for going back and forth from the production unit to thestorage and repeat this operation multiple times. The second relevant dimension of effortis feeding. According to the veterinary at the firm, the extent to which the same amount offood is evenly distributed across hens matters greatly for productivity, and differentially so

10The worker’s typical daily schedule is reported in Table A.2 of Appendix A.1. Egg production establish-ments in developed countries are typically endowed with automatic feeders and automated gathering beltsfor egg handling and collection. The production technology in the plant under investigation is thus morelabor intensive relative to the frontier (see American Egg Board, Factors that Influence Egg Production,http://www.aeb.org, accessed on December 27, 2013)

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when hens are more productive.11

Production units are independent from each other and no technological complementar-ities nor substitutabilities arise among them. Each worker independently produces eggs asoutput combining effort and the hens assigned to him as input. Egg storage and manipu-lation is also independent across production units, as each one of them is endowed withan independent warehouse for egg and food storage. Nonetheless, workers in neighboringproduction units can interact and observe each other. The productivity of working peerscan be easily monitored as they take boxes of collected eggs to the warehouse. On thecontrary, 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 awardedwhen their productivity on a randomly chosen day within the same two weeks exceeds agiven threshold. In that case the worker is paid an additional piece rate for each egg boxexceeding the threshold. For simplicity, the first part of the analysis abstracts from thepiece rate component of pay. Section 7 explores in detail the consequences of incentivepay 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 March 11 to December 17of 2012. This information is collected by the veterinary unit at the firm with the purposeof monitoring hens’ health. The unit of observation is one production unit as observed oneach 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 productionunits. A total of 97 workers are at work in the sector for at least one day, and we canidentify 186 different hen batches in production throughout the period.

Table 1 shows the summary statistics for all the variables we use in the empirical anal-ysis. 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 batchassigned 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 10,000hens. There is substantial heterogeneity in the number of living hens per production uniton a given day, ranging from a minimum of 44 to a maximum of over 17,000. There aretwo reasons for this. First, hen batches are heterogeneous to begin with and already on theday they are moved to production. Second, within a given batch, hens die as time goes by

11Figure A.3 in the Appendix shows the distribution of the estimated worker fixed effects as derived asdescribed at the end of Section 5. The variance of the distribution is indicative that, conditional on inputquality, workers can have a substantial impact on productivity.

12Given the focus on productivity spillovers, we exclude those observations belonging to sheds hosting asingle production.

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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. Thisalso explains why, at each point in time, all hens within a given batch have the same age.

The data provide information on the total number of eggs collected in each productionunit on each day. We divide this number by the number of hens to compute the averagenumber 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 ininput quality. In other words, it allows to focus on differences across batches along dimen-sions other than their numerosity, since the latter would be a trivial source of variation fortotal output.13 We thus label the worker as more productive if he collects a higher numberof eggs while operating the same number of hens. This is not conceptually different fromwhat we would say of a firm that is capable of achieving higher output levels while usingthe same inputs. Perhaps more importantly, this measure is the one that the firm consid-ers relevant. When specifically asked how they would evaluate workers’ productivity, themanagement says that they would look at the total number of collected eggs and divide itby the number of assigned hens. Table 1 shows that the average productivity in the sampleis equal to 0.785 with a standard deviation of 0.2.

The data also provide information on the number of good, dirty, broken, and porouseggs, that we use to derive output quality measures. On average, 86% of eggs produced bya production unit in a day are labeled as good, and are thus ready to go through packaging.6% of eggs on average are classified as dirty. Workers can turn a dirty egg into a goodegg by cleaning it. Finally, we have information on the daily amount of food handled anddistributed among the hens by the worker as measured by the number of 50kg sacks offood employed. Workers distribute an average daily amount of 112g of food per hen.14

We personally collected information on the spatial arrangement of production unitswithin the sector, and their grouping into sheds. For each production unit, we can thuscompute the average daily output of coworkers in neighboring production units in the sameshed, and the average age of their assigned hens. In March 2013, we also administered toall workers an original survey to elicit demographic and personal information about themand their social relationships. Specifically, we asked the workers to list those coworkers

13The number of living hens on a given day may be by itself endogenous to worker’s effort. We discussthis possibility in greater details in Section 5. In particular, results from Table 4 show that the fraction ofhens dying on each day does not change systematically with coworkers’ productivity. We thus conclude thatour estimates of productivity spillovers are not sensitive to the adjustment by the number of living hens. Oneother option is to use total output as measure of productivity, and control for the number of living hens in theregression specifications that we implement in our empirical analysis. When we control for the number ofhens in a flexible way, we still find evidence of negative productivity spillovers. These additional results areavailable from the authors upon request.

14This quantity is computed by dividing the number of 50kg sacks of food opened by the worker by thenumber of living hens on each day. Once the sack is opened, the food it contains does not need to be alldistributed to the hens. This results in measurement error, and can explain why the maximum quantity offood per chicken in the data is almost 6kg.

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whom they identify as friends, with whom they would discuss personal issues, or go tolunch with. We say that worker i recognizes worker j as a friend if the latter appears inany of worker i’s above lists. 63 of the interviewed workers were already employed inthe period for which production data are available, so that this information can be mergedaccordingly 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 thesame batch of equally aged hens from the moment they are moved to production untilthey are discarded. Hens’ productivity varies with age, and changes the marginal productof effort.15 Figure 1 plots daily productivity against hens’ age in weeks. For all givenweek of age, each bin in the scatterplot shows productivity values as averaged across allobservations belonging to production units hosting hens of that given age. The Figure alsoshows the smoothed average of productivity and a one standard deviation interval aroundit. Productivity is typically low when hens are young and recently moved to production, butstarts to increase thereafter. It reaches its peak when hens are around 40 weeks old. Fromthat age onwards, productivity starts to decrease first slowly and then more rapidly oncehens are over 70 weeks old. Hens’ age induces meaningful variation in productivity. Thisis especially the case through the beginning and the end of the hens’ life cycle, meaningfrom week 16 to week 32 and from week 75 to 86.16

The first goal of the empirical analysis is to identify productivity spillovers. Our con-ceptual framework shows how the individual effort choice changes with coworkers’ pro-ductivity. Workers in neighboring production units can observe each other, while this ishardly the case for workers located farther away. We therefore hypothesize that workers’productivity changes with the one of coworkers in neighboring production units, as theyuse information on the latter to estimate the overall average productivity.17 To identify pro-

15We directly test for this hypothesis by estimating worker fixed effects in a subsample of our data, andthen focusing on the remaining sample and regressing individual productivity over the estimated workerfixed effects, a proxy for input quality, and the interaction between the two. The estimated coefficient ofthe interaction variable is positive and highly significant. This means that an increase in input quality isassociated with a differential productivity increase for high ability workers, thus showing evidence of com-plementarity between workers and input quality. We explain the details of this test in Appendix A.4. Wethank one anonymous referee for suggesting the procedure.

16These time intervals together account for around 40% of the overall productive life span.17In Appendix A.5, we show explicitly how the linearized first order condition of the worker’s maximiza-

tion problem maps into the proposed regression specification. We there show that the sign of the parameterγ is informative of the sign of the cross-derivative q12(·) of the termination policy function.

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ductivity spillovers, we estimate the parameters of the following regression specification

yigt = ϕ+ γ y−igt + α ageigt + β age2igt +

t−1∑s=t−3

λs foodigs + εigt (12)

where yigt is the daily number of eggs per hen collected by worker i in shed g on day t.y−igt captures the corresponding average value for coworkers in neighboring productionunits on the same day. Based on Figure 1, we include as regressors the age of hens as-signed to the worker, ageigt, and its square.18 We also include three lags of total amount offood distributed foodigs as controls. This is because we want to investigate the relationshipbetween the variables of interest at time t and conditional on one relevant and observabledimension of effort exerted by the worker on previous days. Finally, εigt captures idiosyn-cratic 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 betweencoworkers’ productivity and individual unobserved effort as captured by γ.

OLS estimates of γ are likely to be biased. First, the above equation defines productivitysimultaneously for all workers, leading to the so-called reflection problem first identifiedby Manski (1993).19 Second, sorting into sheds of hens or workers with the same un-observed characteristics, or idiosyncratic shed-level shocks may push the productivity ofneighboring workers in the same direction, generating a spurious correlation between theiroutcomes (Manski 1993; Blume, Brock, Durlauf, and Ioannides 2011). Nonetheless, hens’age represents a powerful source of variation. Changes in the age of hens assigned to work-ers induce exogenous variation in their productivity that we can exploit for identification.Still, in order to identify a causal effect, the age of coworkers’ hens needs to be orthogonalto other determinants of own productivity, and have no effect on own outcomes other thanthrough changes in coworkers’ productivity.

Coworkers’ and own hens’ age in weeks are both a function of time. Even conditionalon the full set of day fixed effects, residuals of hens’ age are still positively correlatedamong neighboring coworkers, with the estimated correlation coefficient being equal to0.89. This is because, for logistical reasons, the management allocates batches to produc-tion units in a way to replace those in the same shed approximately at the same time.20

18In Section 5.2, we also use a kinked regression specification and week-of-age dummies in order tobetter fit the productivity-age profile shown in Figure 1. Parameter estimates are highly comparable acrossspecifications. In our baseline analysis, we prefer to adopt a quadratic functional form in oder to avoidthe many-weak-instruments problems that would arise by using the full set of week-of-age dummies asinstruments for coworkers’ productivity.

19The suggested specification differs from the basic treatment in Manski (1993) along two importantdimensions. First, it adopts a leave-out mean formulation, as the average productivity regressor is computedexcluding worker i. Second, peer groups overlap, as peers in this context are coworkers in neighboringproduction units and some sheds count more than two units (Bramoulle, Djebbari, and Fortin 2009; DeGiorgi, Pellizzari, and Redaelli 2010; Blume, Brock, Durlauf, and Ioannides 2011; Angrist 2014).

20The technology is such that the old batch is typically loaded on a truck, which then travels to the main

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However, the exact day in which batch replacement occurs is not the same, so that there isresidual variation to exploit. The correlation between coworkers’ and own hens’ age fallsto 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 equalto 0.45. This means that daily deviations in the age of hens in each production unit fromthe corresponding shed-week and day averages are orthogonal to each other.2122

Evidence does not to reject the hypothesis that, conditioning on the full set of day δt andshed-week fixed effects ψgw, the age of hens assigned to coworkers is orthogonal to ownhens’ age. Proposition 2 of Manski (1993) demonstrates how, in the absence of contextualand correlated effects, linear independence between own and peers’ characteristics is asufficient condition to identify composite endogenous peer effects parameters. It followsthat if the age of coworkers’ hens has no direct effect of own productivity, and the full setof day and shed-week fixed effects absorb all the variation in unobservables due to sortingand idiosyncratic shed-level shocks, the age of coworkers’ hens can be used as a source ofexogenous variation to identify the causal effect of an increase in coworkers’ productivityon own productivity.23

operation center 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.

21Table A.3 in Appendix A.1 reports the estimates of the conditional correlation coefficients. Since ev-ery hen batch in the sample is neighbor of some other batch, within-group correlation estimates using thewhole sample suffer from mechanical downward bias (Bayer, Ross, and Topa 2008; Guryan, Kroft, and No-towidigdo 2009; Caeyers and Fafchamps 2016). This bias is relatively larger for smaller peer groups. Inorder to overcome this problem, we follow Bayer, Ross, and Topa (2008) and randomly select one produc-tion unit per group as defined by the shed-week interaction (g, w). Estimates are computed using the sameresulting subsample.

22The orthogonality hypothesis can be further tested using the regression specification proposed byGuryan, Kroft, and Notowidigdo (2009), which in this case becomes

ageigwt = π1 age−igwt + π2 age−igw + ψgw + δt + uigwt

where ageigwt is the age in weeks of hens assigned to worker i in shed g in week w on day t. age−igwt is thecorresponding average value for coworkers in neighboring production units on the same day, while age−igwis the average value for peers in the same shed in all days of the week. The hypothesis of daily randomassignment of age of coworkers’ hens within each shed-week group is equivalent to the null H0 : π1 = 0.Regression results are reported in the bottom panel of Table A.3 in Appendix A.1, showing that H0 cannotbe rejected.

23We discuss the validity of both assumptions in detail in the next Section and in evaluating the robustnessof results. Several contributions in the literature exploit within-group random variation in peer characteristicsin order to identify peer effects (see for instance Sacerdote 2001; Ammermueller and Pischke 2009; Guryan,Kroft, and Notowidigdo 2009). In our case, the variation we exploit for identification is meaningful. Con-ditional on day fixed effects, within-shed-week variation accounts for 5.4% of the total variation in the ageof coworkers’ hens in the sample, measured in weeks. The same fraction goes up to 35% for observationsbelonging to those weeks in which any batch replacement took place in the shed.

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5.2 Baseline Results

Table 2 presents the first set of results. In the first column, we regress the daily aver-age number of eggs per hen collected by the worker over the age of hens in weeks andits square. We also include the full set of day fixed effects. This specification yields aquadratic fit of the dependent variable as a function of hens’ age, which is consistent withthe evidence in Figure 1. Coefficient estimates are significant at the 1% level and con-firm the existence of a concave relationship between hens’ age and productivity.24 In thisquadratic specification, together with day fixed effects, hens’ age explains 0.41 of the vari-ability in the dependent variable. The same number rises to 0.43 when we include lagsof the amount of food distributed in Column 2. In Column 3, we include the full set ofshed-week dummies. The age variables still induce meaningful variation in productivity:coefficients are almost unchanged with respect with those in Column 2.

In Column 4 of Table 2, we include both averages of the age of hens assigned to cowork-ers in neighboring production units and its square as additional regressors. The magnitudeof coefficients of the own hen’s age variables experience does not change, confirming theabsence of any systematic relationship between own and coworkers’ hens’ age within eachshed-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 productiv-ity spillovers. The corresponding coefficients are opposite in sign with respect to the onesof own hens’ age. This result is confirmed in Column 5 of Table 2, which also includesworker fixed effects. The latter eliminate any bias in the coefficients of own hens’ age thatcould arise if batches with specific characteristics are systematically assigned to specificworkers. This specification allows to detect systematic differences in the outcome of thesame worker according to differences in the age of hens assigned to coworkers. Consis-tent with these results, Figure 2 shows how, once own hens’ age, day and shed-week fixedeffects are controlled for, the relationship between residual productivity and the age ofcoworkers’ hens is U-shaped: the opposite with respect to the one between productivityand own hens’ age. Conditional on own input quality, workers’ productivity is systemat-ically lower (higher) when coworkers are assigned inputs of higher (lower) quality. Weinterpret this result as reduced-form evidence of negative productivity spillovers.

Using the age of coworkers’ hens as a source of variation, we can estimate the effect ofcoworkers’ productivity γ in our main regression specification by means of 2SLS.26 The

24Standard errors are clustered along the two dimensions of shed and day in all specifications. Idiosyn-cratic residual determinants of productivity are thus allowed to be correlated both in time and space, specifi-cally among all observations belonging to the same working day and all observations belonging to the sameshed.

25The coefficients of the own hen’s age variables do not change also when coworkers’ hens’ age variablesare included separately as controls one by one, as shown in Table A.4 of Appendix A.1.

26Notice that that hens’ age is a linear function of time and is therefore predictable by the workers. Itfollow that workers may directly respond to changes in the quality of inputs assigned to coworkers, and not

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first column in Table 3 reports OLS estimates of the parameters from the main regressionspecification. Column 2 provides the 2SLS estimate of the coefficient of interest. Whenusing both averages of the age of hens assigned to coworkers and its square as instrumentsfor coworkers’ productivity, the value of the F-statistic of a joint test of significance ofthe instruments in the first stage regression is equal to 103.31. The 2SLS estimate of γ isnegative and significant at the 1% level. The OLS estimate is lower but similar to the 2SLSone. This is because the full set of day, shed-week and worker fixed effects capture thevariation in unobserved common shocks and sorting to a large extent, thus eliminating thesources of positive bias. The small downward bias in the OLS estimate can be attributedto the mechanical exclusion bias discussed in Caeyers and Fafchamps (2016), although therelatively high large number of observations per group makes the issue less salient.

The use of hens’ age and its square as predictors of daily output imposes a precisefunctional form to the relationship between the two variables. The parameter of interestcan 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 thecorresponding results. The F-statistic of a joint test of significance of all the instrumentdummies in the first stage is equal to 46.90, and the 2SLS parameter estimate is comparableto the previous one. Finally, in Column 4, we include the full set of hen batch fixedeffects. 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 ofinterest remains unchanged and significant at the 1% level. According to these estimates,one standard deviation increase in average coworkers’ daily output is associated with adecrease in own daily output of almost a third of its standard deviation. If all workers areassigned the same number of hens, an increase of average coworkers’ output of 500 eggscauses the number of own collected eggs to fall by 150. Evidence supports the hypothesisof negative productivity spillovers among coworkers in neighboring 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 differ-ences in the exact day of replacement constitute the primary source of variation in the ageof hens assigned to coworkers. One first concern with the previous results is that the ex-act day of coworkers’ batch replacement could be correlated with pre-existing trends inindividual productivity. Table A.5 in Appendix A.1 shows the coefficient estimates froma regression of a dummy equal to one if the batch assigned to neighboring coworkers was

to the resulting changes in their observed productivity. This would not invalidate the reduced-form estimatesin Table 2 and their interpretation of negative productivity spillovers, but it would affect the interpretation ofthe 2SLS estimates of the γ parameter. Deriving these estimates is nonetheless useful in order to pin downthe exact magnitude of productivity spillovers.

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replaced in a given day over lags of individual productivity. Evidence shows the absenceof any systematic relationship between past productivity and the probability of a batchreplacement in neighboring production units.

Second, Section 3 explains that the technology of production and storage is independentamong production units. Still, coworkers’ batch replacement may have a direct effect ofindividual productivity. This could be the case if new, young hens are more noisy, or if theprocess of batch replacement generates any kind of disruption in worker’s operations. Theproductivity of workers operating older hens would thus be lower on the days followingcoworkers’ batch replacement. Our conversations with the firm suggest that this is not thecase.27 This is also consistent with the available evidence. Figure A.4 in Appendix A.1plots worker’s residual productivity around the day of coworkers’ batch replacement. Wefind no evidence of discontinuity. If anything, the arrival of new hens in the shed increasesthe productivity of those workers who are still assigned old hens, but the increase is notstatistically distinguishable from zero.28

The results in Table A.6 in Appendix A.1 further address these issues in a regressionframework. We report 2SLS coefficient estimates from our main regression specificationacross different subsamples. In Column 1, we exclude those observations belonging toproduction units with very old hens (more than 80 weeks old) and surrounded by produc-tion units with very young hens (less than 22 weeks old on average). The estimate of ourcoefficient 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 estimatedcoefficient is equal to -0.25 and still significant at the 5% level. In Columns 3 to 6, weprogressively exclude all observations within 1, 2, 3, and 4 weeks respectively from thedate of own or coworkers’ batch replacement. The decreasing value of the F-statistic forthe joint test of significance of the instruments in the first stage reveals that the instrumentslose strength when we exclude those observations where most of the variation in age comesfrom. Still, even when excluding observations within one month from coworkers’ batch re-placement, the value of the F-statistic is above 10 and the estimated coefficient of interest

27We specifically asked whether batch replacement may affect neighboring workers in any way, and theanswer was that it does not affect them.

28Nonetheless, Figure A.4 in Appendix A.1 also shows that there is substantial variation in productivityacross days. This raises the issue of whether the inclusion of shed-week fixed effects is sufficient to netout 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 fromcoworkers’ batch replacement and including the full set of shed-day fixed effects. Columns 1 to 3 of TableA.7 in Appendix A.1 report the corresponding coefficient estimates. These are still negative and bigger inmagnitude than previous ones, and significant at the 5% level. We therefore conclude that confounders atthe shed-day level cannot be responsible for our baseline results. A related concern is that our measurementof hens’ age in weeks may be driving the result. We thus implement the main regression specification, butmeasuring both own and coworkers’ hens age in days, and including shed-day fixed effects. Column 4 ofTable A.7 in Appendix A.1 reports the corresponding coefficient estimate, which are consistent in magnitudewith the previous ones and significant at the 5% level.

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is equal to -0.40 and significant at the 5% level. In Column 7, we exclude those observa-tions belonging to weeks in which any of the workers in the shed was replaced by a newone, 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 identi-fication does not belong only to those periods where the match between workers and henbatches is disrupted, but also to periods where the match is stable. Differences in the exactday of batch replacement map into initial differences in the age of hens assigned to cowork-ers. These differences persist through the productive life of hens, shaping differences inworkers’ 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 wefind is plausible. First, the variation in the productivity of coworkers induced by changesin 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 eggsper hen. Figure 1 suggests that the same 3-weeks difference in age can amount to largeor small productivity differences, depending on the hens’ stage of life. For example, theaverage daily number of eggs per hen is 0.06 when hens are 19 weeks old, but is morethan 8 times larger at age 22, being equal to 0.50: a 0.44 productivity difference, equal to4,400 eggs more for a batch of 10,000 hens. A similar but opposite pattern holds whenproductivity starts to decrease in the last stages of a hen’s life. This means that even asmall variation in hen’s age can have a sizable and observable impact on daily output, atleast when hens are far from their productivity peak age.

Although opposite in sign, the magnitude of our estimates is comparable with the onefound in previous studies of productivity spillovers (Gould and Winter 2009; Bandiera,Barankay, and Rasul 2010; Herbst and Mas 2015). Perhaps more importantly, the nega-tive sign makes the aggregate implications for overall productivity smaller. When a givenworker is assigned inputs of higher quality his productivity increases. Because of nega-tive spillovers, coworkers’ productivity decreases. These effects reverberate through thesystem. It follows that, although the individual response is positive and higher than in

29This result is in line with the evidence from Figure A.5 in Appendix A.1 showing that coworkers’replacement brings no discontinuous changes in individual productivity.

30To validate this claim further, we also fit the relationship between hens’ age and productivity using akinked regression with three kinks, as shown by Figure A.6 in Appendix A.1. We choose the values of hens’age at the kinks that maximize the R2 of the kinked regression of productivity over hens’ age. We then esti-mate the parameters from the main regression specification using as instrument for coworkers’ productivityits value as predicted by the kinked regression estimates. Column 1 of Table A.8 in Appendix A.1 showsthe corresponding results. Columns 2 to 5 show that estimates are insignificant when implementing thisregression on different subsamples as defined by the kinked regression interval the age of coworkers’ hensbelongs to. This confirms that the variation that we exploit for identification does not belong to any specificsegment of the productivity-age profile.

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isolation, the decrease in coworkers’ productivity makes the aggregate response of the sys-tem lower than what it would be in the absence of spillovers. This is not the case whenspillovers are positive and the aggregate response is higher than in the absence of external-ities.31

5.3 Feeding Effort and Output Quality

The previous results show that, conditional on own input quality, workers’ productivity issystematically lower (higher) when inputs make neighboring coworkers more (less) pro-ductive. We claim that such negative spillover effect occurs through changes in the levelof effort exerted by the worker. Hens’ feeding is one observable dimension of effort. Wereplace the average amount of food per hen distributed by the worker as outcome in themain specification. The first column of Table 4 shows the corresponding 2SLS estimates.The estimated coefficient of coworkers’ productivity is negative, consistent with our inter-pretation of previous results. However, the estimate is not significantly different from zero.This indicates that the effect of coworkers’ productivity operates through changes in otherdimensions of effort.

Column 2 to 5 of Table 4 show 2SLS estimates of the effect of coworkers’ productivityon output quality. Coworkers’ productivity is negatively and systematically correlatedwith the own fraction of good eggs over the total. A one standard deviation increasein coworkers’ productivity causes a 3 percentage points decrease in the fraction of goodeggs. Column 3 shows a positive correlation between coworkers’ productivity and thefraction of broken eggs, although the estimate is not statistically significant. This is notthe case for the estimate in Column 4 which shows that coworkers’ productivity increasesthe fraction of dirty eggs. Workers can turn dirty eggs into good ones: the results inColumn 2 and 4 together indicate that workers exert less effort in cleaning dirty eggs whencoworkers are more productive. Finally, Column 5 shows that coworkers’ productivitynegatively 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 itselfendogenous to worker’s effort. The absence of a systematic relationship between hens’death and coworkers’ productivity lead us to conclude that our estimates of productivityspillovers are not the result of a strategic decision of workers to adjust the number of livinghens to coworkers’ input quality and productivity. Overall, estimates in Table 4 show thatcoworkers’ 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

31This can be easily shown in the case of two peer workers. Let yi = si+γyj , with γ < 0. As si increasesby one, its impact on own productivity reverberates through the system and is equal to 1

1−γ2 > 1. At thesame time, the impact on coworkers’ productivity is negative and equal to γ

1−γ2 < γ < 0. The aggregateproductivity response would thus be equal to 1+γ

1−γ2 = 11−γ < 1.

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worker’s effort in the same way. The effect of coworkers’ productivity on own productivityappears to work through changes in effort along dimensions other than total food distri-bution, such as those related to egg collection and uniform feeding discussed in Section3. Egg cleaning effort is also negatively affected, while coworkers’ productivity does notseem to affect those components of effort which map into hens’ survival probabilities, suchas cleaning and maintenance of the facilities. These results can be explained by the levelof heterogeneity in the observability of each one of these different effort categories, whichin turn determine the scope for free riding. Indeed, while it is easier for a worker to detectif a coworker is shirking on the amount of food distributed to the hens or the maintenanceof facilities, it is supposedly harder to detect the effort exerted by coworkers while walkingalong cages within the unit or smoothing the same amount of food across the hens.

5.4 Additional Results and Effect Heterogeneity

Workers in non-neighboring 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 ofcoworkers in the adjacent shed and non-neighboring production units respectively.32 2SLSpoint estimates are negligible in magnitude and not significantly different from zero. Weinterpret these findings as evidence that observability between workers plays a crucial role.

In Column 3 of Table 5, we replace the natural logarithm of the daily average number ofeggs per hen collected as outcome.33 The estimated coefficient of interest is still significantat the 1% level, and equal to -1.47. This implies that an increase in coworkers’ average out-put of one standard deviation is associated with a 29% decrease in own output, consistentwith previous results. In Column 4 of Table 5, we implement an alternative identifica-tion strategy where we use as instrument for coworkers’ productivity the expected hens’productivity measure in the data. Such measure is elaborated by the supplier companythat sells hen batches to the firm we investigate. It measures the average number of eggsper week each hen is expected to produce at every week of its age. This measure is thuspredetermined and exogenous to anything specific to the egg production phase, includingworkers’ 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 ishighly significant and remarkably similar to the ones derived before.34

32In Column 1, coworkers’ variables are the same for all workers in a shed, so there is no daily within-shedvariation left to exploit. This explains why the strength of the first stage relationship is lower, although thecorresponding F-statistic of a joint test of significance of the instruments is still equal to 11.01. In Column2, the sample is restricted to workers located in sheds with more than two production units.

33Variable values are augmented by 0.01 before taking the log. Implementing a log-log specification wecan 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.

34We also perform two additional robustness checks. First, we address the identification concerns inAngrist (2014) by explicitly separating the subjects who are object of the study from their peers. Specifically,

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We have so far abstracted from dynamic considerations. The actions taken by theworker 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 al-ready partially taken into account this possibility by including the lags of food distributedby the worker. To address these concerns further, we include in the baseline regressionspecification the lags of own and coworkers’ productivity. Given the high correlation be-tween the output levels of a given production unit in subsequent days, we consider one andtwo-week lags. Including the lag of the dependent variable as regressor in a specificationwith unit fixed effects can lead to biased coefficient estimates (Nickell 1981). We addressthis 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 contemporane-ous and the lag of coworkers’ productivity with the two-week lag of coworkers’ hens’ ageand its square.35 Table A.9 in Appendix A.1 shows the corresponding results. The coeffi-cient of coworkers’ average productivity on the same day remains negative and significantat least at the 10% level across all specifications. This indicates that the estimated nega-tive spillovers are not explained by own or coworkers’ productivity trends or the dynamicfeatures of the production process.

To conclude, we explore heterogeneity in the size of spillovers according to workers’ability. Similarly to Bandiera, Barankay, and Rasul (2005) and Mas and Moretti (2009), weestimate the full set of worker fixed effects in a regression specification that also includesas regressors hens’ week-of-age dummies, batch and day fixed effects.36 We then splitthe workers into high and low ability according to their position relative to the median inthe estimated fixed effect distribution, and assign observations belonging to the worker’sassigned production unit to the two corresponding subsamples. The parameter of interestis estimated separately and results reported in Columns 5 and 6 of Table 5. The estimatedcoefficient is negative and significant only for low ability workers, suggesting that highability 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

we randomly select one production unit per each shed-week and run the main identifying regression over therestricted sample only. Second, we drop out all observations belonging to those days in which the workerassigned to a given production unit was listed as absent. Results are in line with previous estimates in bothcases, and are available from the authors upon request.

35Given the high correlation between contemporaneous hens’ age and its one and two-week lag, we dropcontemporaneous own hens’ age and its square from the set of regressors and use the two-week lag ofcoworkers’ hens’ age and its square as set of instruments for both contemporaneous and the lag of coworkers’productivity.

36Figure A.3 in Appendix A.1 shows the distribution of workers’ ability. Notice that we estimate workerfixed effects in a regression framework without modeling productivity spillovers explicitly. We thereforeincur the risk that the estimated worker fixed effects are confounded by the productivity of neighboringcoworkers and their hens. However, as explained in Section 3, once a batch is assigned to a given productionunit it maintains its position until the end of its productive life. This rules out the possibility that workersare systematically assigned hens of particular age (and productivity), and diminishes the concerns that theestimated worker fixed effects are confounded by the age and productivity of neighboring hens.

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thus be exposed to piece rate incentives.

6 The Mechanism

The conceptual framework identifies the termination policy implemented by the manage-ment as the source of free riding and negative productivity spillovers among workers. Inevaluating workers, the management attaches a positive weight on the average productiv-ity of all workers on the same day. When average productivity increases, the evaluation ofeach given worker increases, and so does the probability of keeping the job. It follows thatworkers free ride on each other, decreasing their supply of effort when coworkers are moreproductive.

A close inspection of the data reveals that turnover is exceptionally high at this firm.Throughout the 9 months of observations in our sample, we observe 23 terminations ofemployment relationship over a workforce of 97 workers. The firm we are studying isclose to have monopsony power in the local labor market. It is located in rural Peru, theaverage wage over the sampling period is more than 50% higher than the legally estab-lished minimum wage in the country, and close to the nationwide average.37 The firm isthe biggest employer in the three closest small towns. Although the data we have do notallow to distinguish between dismissals and voluntary quits, evidence is in favor of an effi-ciency wage argument, where the firm pays high wages while using the threat of dismissalas 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 mech-anism in Section 2 by showing that (i) individual termination probabilities are negativelycorrelated with both own and average productivity, and (ii) marginal returns from ownproductivity 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 probability1− q(·) of losing the job after t days as defined by

1− q(t)q(t)

=h(t)

1− h(t)= exp{γt + α yigt + β yt} (13)

where yigt is the productivity of worker i operating in shed g on day t, and yt is the aver-age productivity among all workers on the same day. t measures tenure on the job and isdefined as days since the worker first appears in the data and is assigned to a given produc-

37See Section 7 and Table A.15 in Appendix A.1 for more detailed information on the wage schedule ofworkers at the firm. Average and minimum wage data are from the World Bank.

23

tion unit. γt accounts for the relative odds of baseline hazard on day t. Specifically, we letγt = δ ln t, and we estimate δ together with α and β. This approach allows the baselinehazard of losing the job to increase or decrease monotonically with tenure at different ratesdepending on the value of δ.38

We report maximum likelihood estimates of the coefficients in the first three columnsof Table 6. The estimated δ is negative across all specifications, indicating that the rela-tive odds of the baseline probability of losing the job decrease with tenure, although notsignificantly so. Column 1 shows that an increase in own productivity is associated witha decrease in the odds of employment termination, but not significantly so. Conditionalon own productivity, an increase in average productivity is highly significantly associatedwith a decrease in the odds of termination. Coefficient signs and predicted probabilitiesare such that returns from own productivity in terms of retention probability are alwayslower at the margin when coworkers’ productivity increases.39

Another implication of the theory is that, in guessing worker’s type, the managementuses the average productivity of all workers, and not just the productivity of coworkers inthe same shed. We directly test for this hypothesis in Column 2 of Table 6. We include asadditional regressor the average productivity ygt of all workers in the same shed of workeri. We find no systematic correlation of the latter with the probability of termination. Theseresults show that the relevant metric for worker’s evaluation and dismissal is the averageproductivity 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 varia-tion 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 mecha-nism responsible for the negative productivity spillovers we have identified in the previoussection. In showing evidence of the former, we therefore need to rely on the same sourceof variation that we exploited in the analysis of the latter. That is, we want to provide ev-idence that the mechanism of interest is set in motion by the same source of variation thatwe exploit for identification in reduced form. Second, the identification of the coefficientsof average productivity in equation 13 could be problematic. One possible concern is thatworker’s effort may respond to expectations regarding coworkers’ termination probabil-

38Specifically, we let h0(t)1−h0(t)

= exp{γt} which implies logit h0(t) = ln h0(t)1−h0(t)

= γt. With γt = δ ln t

we let h0(t)1−h0(t)

= tδ and h0(t) = tδ

1+tδ.

39Notice thatq(t) =

1

1 + exp{ γt + α yigt + β yt }

∂q(·)∂yigt

= − exp{ γt + α yigt + β yt }(1 + exp{ γt + α yigt + β yt })2

(α+

β

N

)∂2q(·)∂yigtyjgt

= −exp{ γt + α yigt + β yt }(1− exp{ γt + α yigt + β yt })(1 + exp{ γt + α yigt + β yt })3

(α+

β

N

)β

N

Where the latter is negative if γt + αyigt + βyt < 0 and α, β < 0. This is always the case in our sample.

24

ities. Reverse causality would therefore bias the estimates of the coefficient of averageproductivity. The use of average hens’ age as an exogenous source of variation for averageproductivity rules out such endogenous effort responses and identification concerns. Giventhe non-linear nature of the second stage, we follow Terza, Basu, and Rathouz (2008) andadopt a two-stage residual inclusion (2SRI) control function approach (Wooldridge 2015).We use the average age of hens aget and the average of squares age2

t as instruments foraverage productivity yt. The magnitude of coefficients in Column 3 is very similar tothe previous estimates. We interpret this as further evidence that individual terminationdecisions 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 ratherthan the number of eggs per hen, results would not change. The coefficient estimates inColumns 4 to 6 of Table 6 show that the relationship between own output, average outputand own probability of keeping the job has the same sign and is still significant if we useown total number of eggs and the average number of eggs among all workers as regressorsin specification 13.40

The empirical analysis of termination probabilities so far has matched the first casein our conceptual framework, where we assume that the management does not hold anyinformation 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 processedby the human resource department. Nonetheless, we cannot exclude that the managementuses other available information. We evaluate the robustness of results by matching thesecond case in our conceptual framework, where the management holds partial informationon input quality. We use the information on the expected productivity of hens as elaboratedby 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 isexpected to lay in each week of age. As such, the measure maps from the ai variable ofour conceptual framework. We divide daily productivity of eggs per hen yi by the expectedproductivity measure ai to derive signal zi of worker’s effort. We then estimate a logistichazard model of termination probability where own and average signal are included asregressors. Table A.13 in Appendix A.1 reports the corresponding coefficient estimates.Results are in line with those in our main analysis, showing that, conditional on the valueof own signal, an increase in the average signal is systematically and negatively correlated

40Table A.10 in Appendix A.1 shows the corresponding results when replacing average productivity withthe average number of eggs per hen across all workers, and the average number of eggs with the total numberof eggs collected on the day. In Tables A.11 and A.12 of Appendix A.1, we replace instead the regressors ofinterest with their 7-days moving averages. The magnitude and significance of the estimated coefficients arelargely consistent with the ones in Table 6.

25

with own termination probability. Notice in particular that the 2SRI estimates in Column3 suggest that the hens’ age variables are still informative of productivity signals zi. Thismeans that expected productivity ai does not capture the full extent of variation in inputquality, which therefore remains partially unobservable to the management.

6.2 Alternative Explanations

The evidence presented above could be consistent with other mechanisms. First, workersmay get discouraged and quit the job when their productivity is lower than the one ofneighboring peers. However, evidence shows that, conditional on individual and averageproductivity, the difference between own and neighboring coworkers’ productivity is notsystematically correlated with termination probabilities. This rules out that voluntary quitsfrom discouragement are driving the empirical regularities described above.41

A second alternative explanation is related to workers’ monitoring. Suppose that themanagement monitor workers, and that these monitoring efforts target disproportionallymore workers handling highly productive hens. The negative causal effect of an increasein coworkers’ productivity on own productivity could then be attributed to a higher levelof shirking which follows a reallocation of monitoring efforts towards highly productivecoworkers. However, if this was the case, we should have found a negative effect ofcoworkers’ productivity also considering coworkers in non-neighboring production unitsin 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 pro-ductivity, as stealing opportunities would increase with coworkers’ productivity. More ingeneral, this is what we would expect if other possible sources of positive productivityspillovers were present. Other examples are knowledge spillovers from social learningwhen hens are highly productive, or a situation where young or old hens are more proneto experience transmittable diseases and these spread to neighboring production units. Allthese explanations would bias our baseline results in the opposite direction with respect towhat we find: if these were present, the magnitude of our negative estimates would be alower bound for the true effect.

Finally, our conceptual framework and analysis are built upon the assumption that work-ers are evaluated each day on the basis on their productivity on that day, and not on theirhistory on the job, or since the assignment of the last batch of hens. It could be the casethat workers are more likely to be fired when hen batches they are assigned to are closeto be dismissed. If so, the results on our termination policy regression could be capturingchanges in own and coworkers’ productivity close to the end of the hens’ productive life

41Table A.14 in Appendix A.1 reports the parameter estimates from the corresponding logistic hazardmodel specifications.

26

cycle, with no role played by worker evaluation. Figure A.7 in Appendix A.1 plots thedistribution of worker terminations over the entire hens’ age support based on the age ofassigned hens on the day of termination. The Figure shows that employment terminationsare almost uniformly distributed over the entire support. This rules out the concern thatour results are only capturing changes in productivity and termination probabilities thatmaterialize 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 variableamount which depends on number of boxes of eggs collected by the worker in a randomlychosen day within the two weeks. Specifically, wage is equal to

ωi = α + max { 0 , δ × [ 2Yi − r ] } (14)

where α is the base pay and Yi is the amount of boxes of eggs collected by the worker inthe randomly chosen day. This quantity is multiplied by 2 and, if the resulting quantityexceeds a given threshold r, a piece rate δ is awarded for each unit above the threshold.42

Despite its strong relationship with productivity, no component of worker’s pay is ad-justed by the age of hens the worker is assigned during the pay period. This confirms thatthe human resource department does not process any information on inputs. It also impliesthat the probability for each worker of earning extra pay is a function of hens’ age. Figure3 plots the distribution of the average number of daily egg boxes collected by the workerwithin each pay period per quartiles of the hens’ age distribution. For each quartile, theboundaries 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 verti-cal lines indicate the 1st and 99th percentile. The straight horizontal line corresponds tothe normalized bonus threshold r/2. First, notice that the inverted U-shaped relationshipbetween hens’ age and productivity can be still observed when considering egg boxes as ameasure of productivity. Second, the probability of reaching the threshold and be exposedto incentive pay is higher for those workers whose hens are of high productivity, meaningthey belong to the second and third quartiles of the hens’ age distribution. On the con-trary, the average worker whose hens belong to the first or fourth quartile of the hens’ agedistribution does not reach the bonus threshold.43

42The average total pay in the two-weeks period is equal to the equivalent of 220 USD, with the bonuscomponent being 15% of the base pay on average. Table A.15 in Appendix A.1 shows the correspondingsummary statistics for the base pay, the bonus component and total pay. Average base pay is equal to 505PEN (Peruvian Nuevo Sol), equal to around 190 USD. The average of the bonus component of pay is insteadequal to 82 PEN, around 30 USD (δ=40 PEN).

43Table A.16 in Appendix A.1 shows the average base pay, bonus pay and total pay for the average worker

27

We provide suggestive evidence on the role of monetary and social incentives by imple-menting following regression specification

yigwt = ϕgw +∑

d

{ψd + γd y−igwt + αd ageigwt + βd age

2igwt

}× Ddigwt

+∑t−1

s=t−3 λs foodigsw + µigwt

(15)where ϕgw are shed-week fixed effects andDd are dummy variables which identify the het-erogeneous categories of interest. We interact the latter with both own hens’ age variablesand coworkers’ productivity. We estimate the parameters γd using both age−i and age2

−i

multiplied by Dd as instruments for the endogenous interaction variables y−igwt ×Dd.We first focus on monetary incentives and exploit the heterogeneity in piece rate expo-

sure summarized in Figure 3. We define a low productivity age subsample of productionunits 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 1of Table 7 provides the corresponding 2SLS estimates from the above specification, withDd identifying these two subsamples. The Table reports the F-statistic from the Sanderson-Windmeijer multivariate F test of excluded instruments, which confirms that first stagerelationships are strong. We find no significant effect of coworkers’ productivity when theworker is assigned highly productive hens and is more likely to be exposed to piece ratepay. The effect is instead negative and highly significant for the same worker when as-signed hens are less productive. This evidence is consistent with our extended conceptualframework as it shows that incentive pay smooths the negative externalities generated bythe termination policy. However, we interpret this with caution as the low productivity agesubsample is also the one that carries most of the variation in productivity.

To explore the role of social incentives, we rely instead on the information on socialrelationship among workers. We identify those workers working along someone they rec-ognize as a friend, and let the dummy variables Dd identify the two resulting subsamples.Column 2 of Table 7 reports the corresponding 2SLS estimates.44 We estimate negative andsignificant 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 ofhis neighboring coworkers as a friend. This evidence is consistent with the peer pressureargument outlined in our extended conceptual framework. It also rules out the possibility

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. Basepay can indeed still vary with workers’ age, tenure and base contract. Nonetheless, most of the variation intotal pay is due to variation in the bonus pay component.

44As reported in Table 1, 25% of the observations in the overall sample correspond to workers who rec-ognize at least one of their coworkers in neighboring production units as friend. Notice that the number ofobservation is reduced because the sample is restricted to those 80% of observations that we can merge withthe information on workers elicited in March 2013.

28

that the negative spillover effect we find is capturing cooperative behavior among work-ers. For example, workers handling highly productive hens could benefit from the helpof neighboring coworkers, with negative productivity spillovers on the latter. Such coop-erative strategy would be sustainable in a repeated interaction framework. However, wewould expect such strategy to be differentially more sustainable among friends in lightof the possibility of social punishment and increased cost of deviation from the coopera-tive path. The absence of any significant negative spillover effect among friends does notsupport this hypothesis.45

We also identify spillovers separately according to worker’s experience. We distinguishwhether the worker’s tenure at the firm is above or below the median, and implement thesame specification above. Column 3 of Table 7 shows that spillovers are negative and sig-nificant for more experienced workers, and positive but insignificant for less experiencedones. We interpret this result as suggestive evidence that experienced workers are moreaware of management policies and therefore more prone to free riding, while the oppositeholds for newly hired workers.

Finally, we explore heterogeneity according to the difference (in absolute value) be-tween the age of own and coworkers’ hens. We identify two subsamples depending onwhether such difference is higher or lower than the mean difference in the sample, equalto 3.22 weeks. We estimate the corresponding equation for the low productivity age andthe high productivity age subsamples separately, defined as in Column 1. If the free rid-ing mechanism in the absence of piece rate incentives is responsible for the average effectwe find, we should expect the negative effect of coworkers’ productivity to be the highestin magnitude when the scope of free riding is widest. This corresponds to the situationin which a given worker is assigned lowly productive hens while coworkers are assignedhighly productive ones. We instead expect the magnitude to be the lowest when the workeris 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 theestimates is statistically significant.

8 Counterfactual Policy Analysis

8.1 Termination Policy

The evidence gathered so far shows that the worker evaluation and termination policy im-plemented at this firm generates externalities among coworkers and negative productivityspillovers. Our conceptual framework shows that the scope for such policy originates in the

45Notice that the possible endogeneity of friendship relationship to the implementation of cooperativestrategies 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.

29

asymmetry of information between the worker and the management, and the impossibilityfor the latter to observe input quality and perfectly disentangle the effort and input contri-bution to output. The purpose of this Section is to illustrate the productivity consequencesof changes in the amount of information available to the management.

We make the extreme but simplifying assumption that the age of hens carries all relevantinformation regarding input quality, and we hypothesize a scenario in which this informa-tion is fully available to the management. The latter can therefore fully net out the inputcontribution to output and derive the level of effort exerted by the worker as residual. Inthis case, the management faces no inferential problem and the probability for the workerto keep the job is an increasing and concave function of his effort ei. This shuts down theexternalities among coworkers generated by and built into the actual policy.

Let the termination policy in this case be given by

q(eit) = α0 + α1 eit + α2 e2it (16)

with α1 and α2 being such that q1(·) > 0 and q11(·) < 0 for every ei. The first ordercondition of the worker’s effort maximization problem becomes

ei =U(ω)

c(α1 + 2α2 eit) (17)

We structurally estimate the unobserved components of the above equation, and de-rive daily effort eit and productivity yit for all workers in this counterfactual scenario.Appendix A.6 describes the details of the procedure. Table 8 shows the corresponding re-sults, and reports counterfactual productivity gains and losses. For each parameter valuesin the corresponding row and column, each entry shows the simulated percentage changein productivity as measured by average daily number of eggs per hen collected by workersover the period. The table also reports 95% confidence intervals as computed by repeat-ing the estimation procedure 100 times using bootstrapped samples. Evidence show that,for sufficiently high values of α1, eliminating the asymmetry of information between theworker and the management can bring about significant productivity gains.

8.2 Input Allocation

The presence of productivity spillovers from heterogeneous inputs implies that changingthe way the same set of inputs is allocated among workers can affect the total size ofexternalities and aggregate productivity. In our basic regression specification, coworkers’productivity enters linearly in the equation defining worker’s productivity. As a result, theimpact of input reallocation on overall productivity can only materialize through pairwise

30

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 henyit over the full sets of own and coworkers’ hens’ week-of-age dummies, together withshed-week fixed effects. We then consider the set of hen batches in production in the firstweek of the sample, and simulate their age profiles over the sampling period assuming hensare replaced after the 86th week of life. Using the parameter estimates from the formerregression specification, we then predict the daily productivity of workers in each produc-tion unit. Not surprisingly, Figure 4 shows that predicted and actual average productivitymatch 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.

The same parameter estimates that we just used to predict daily productivity of work-ers under the actual input allocation can be used to predict productivity under alternativeinput allocations. Taking the batches in production in the first week of the sample, we real-locate them among production units following a hierarchical clustering procedure whichminimizes the variance of the age of hens within the same shed. This is consistent withthe implicitly stated goal of the management. We simulate hens’ age profiles over theperiod under the alternative allocation (assuming the same replacement policy as before),and predict worker’s daily productivity using the same parameter estimates derived at thebeginning. The dashed green line in Figure 4 shows the smoothed average of counter-factual productivity. Productivity gains are substantial, up to 20% in a given day, eventhough counterfactual average productivity is more volatile than actual one. When aver-aged throughout the period, the difference between the counterfactual and actual produc-tivity is equal to 0.08, which corresponds to a 10% increase.

The counterfactual productivity estimates in this section suffer from one important lim-itation: they are based upon the assumption that the termination policy implemented bythe management remains unchanged. This is because we want to isolate and illustrate theproductivity gains from implementing alternative input allocation schedules, and abstractfrom the possibility that the management revises its termination policy in conjunction. Infact, the decrease in the variance of input quality within sheds brings about informationgains for the management, which may thus find optimal to revise its policy in a way to putadditional weight on individual productivity signals. The results from the previous sectionsuggest that productivity gains would be even higher in this case.

46Graham (2011) provides a formal discussion of this result. In order to understand this, it is useful tothink about the case of a given number of sheds each hosting two production units. In this case, the qualityof inputs assigned to each worker only affects the productivity of one neighboring worker. Reallocatinginputs does not change that, and the total amount of externalities in the system does not change. If insteadsome sheds host one or more than two production units, input reallocation within and between sheds leadsto changes in the number of neighbors affected. This changes the total amount of externalities in the systemand aggregate productivity

31

8.3 Discussion

Results from the counterfactual policy analyses suggest that productivity would be higherif the firm implemented either of the two policies above, meaning process information oninput quality or fully segregate batches into sheds according to hens’ age. A natural ques-tion is why the firm has not implemented these changes already. First, the results in Section8.1 are based upon the assumption that the age of hens carries all relevant information re-garding 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 eval-uation will depend positively on coworkers’ signals, generating free-riding and negativeproductivity spillovers. Second, the costs of resolving the asymmetry of information byprocessing information on input quality on a daily basis may exceed the benefits of doingso. Even if this was not the case, managers lacked precise estimates of the magnitude ofnegative spillovers and their impact on productivity. Therefore, they had incorrect infor-mation on the cost-benefit calculation. This is not surprising in the context of a large firmoperating in a developing country (Bloom, Eifert, Mahajan, McKenzie, and Roberts 2013).

As for the input allocation schedule, in the last paragraph of Section 8.2 we point outthat our analysis ignores the possibility that the management revises its termination pol-icy together with its input allocation schedule. Still, we hypothesize that this would bringabout even higher productivity gains. Importantly, the cost of reallocation only needs to bepaid once, as co-movements in hens’ age over time will ensure that the latter keeps beingsynchronized among neighboring production units. However, this also means that, oncehens get old enough and need to be discarded, all batches belonging to production unitswithin a given shed need to be substituted simultaneously. This is simply not feasible usingthe current technology for batch replacement.47 The cost of investing in a new technologymay 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 alloca-tion of input batches is more volatile than the actual one. To the extent to which volatilityin production enters negatively the objective function of the firm, the management may notbe willing to implement this alternative allocation schedule despite its positive impact onaverage productivity.

9 Conclusion

In many workplaces, workers produce output combining effort with inputs of heteroge-neous quality. This paper shows that input heterogeneity and information on input qualitycontribute to shape human resource management practices and can trigger productivity

47This is indeed where the residual variation in hens’ age we exploit for identification in the empiricalanalysis comes from.

32

spillovers among workers. Using data from an egg production plant, we show that workersexert less effort when their coworkers are assigned high quality inputs. Our conceptualframework and the analysis of workforce turnover data reveal that the effect captures freeriding among workers, which originates from the way the management evaluates workersand makes dismissal decisions in a setting where input quality is not fully observable.

Our study illustrates how the analysis of relatively more complex production environ-ments may reveal non-trivial interactions between different areas of management. Indeed,inputs can also trigger productivity spillovers of alternative origins. In a companion paperstill work in progress, we investigate both theoretically and empirically how workers in-fluence each other in their choice of inputs while updating information on the productivityof the latter from own and coworkers’ experience.

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Tables and Figures

TABLE 1: SUMMARY STATISTICS

Variable Obs. Mean St. Dev. Min Max

Hens’ Age (weeks) 21,213 45.327 17.016 19 86No. of Hens 21,213 9,947.792 3,869.995 44 17,559

Daily Eggs per Hen, yi 21,213 0.785 0.2 0 1

Good/Total 21,044 0.857 0.093 0 1Broken/Total 21,044 0.024 0.037 0 0.357Dirty/Total 21,044 0.059 0.048 0 1Porous/Total 21,044 0.052 0.058 0 1Deaths/No. of Hens 19,623 0.001 0.017 0 0.782

Food (50kg sacks) 21,213 22.351 8.936 0 40Food per Chicken (g) 21,213 112.029 50.154 0 5,947.137

Neighboring Coworkers 21,213 1.223 0.435 1 3

Daily Eggs per Hen 21,213 0.784 0.197 0 0.999Coworkers’ Average, y−i

Hens’ Age 21,213 45.248 16.604 19 86Coworkers’ Average (weeks)

Dummies:Working Along Friend 16,595 0.246 0.431 0 1Experience 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. Theunit of observation is the production unit in the sector under investigation in each day from March 11 to December17 of 2012. Sheds hosting only one production units are excluded from the sample.

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TABLE 2: OWN AND COWORKERS’ HENS’ AGE AND PRODUCTIVITY

Daily Number of Eggs per Hen, yi

(1) (2) (3) (4) (5)

agei 0.04073*** 0.03903*** 0.03860*** 0.03822*** 0.03249***(0.0024) (0.0022) (0.0059) (0.0058) (0.0056)

age2i -0.00040*** -0.00038*** -0.00038*** -0.00038*** -0.00032***

(0.0000) (0.0000) (0.0001) (0.0001) (0.0001)

age−i -0.00339* -0.00660**(0.0019) (0.0028)

age2−i 0.00002 0.00005

(0.0000) (0.0000)

foodt−1 0.00197** 0.00137*** 0.00139*** 0.00452***(0.0009) (0.0005) (0.0004) (0.0012)

foodt−2 0.00088* 0.00078** 0.00080*** 0.00298***(0.0005) (0.0003) (0.0003) (0.0011)

foodt−3 0.00063 -0.00001 -0.00003 0.00313**(0.0010) (0.0004) (0.0004) (0.0012)

Day FEs Y Y Y Y YShed-Week FEs N N Y Y YWorker FEs N N N N Y

Observations 21213 21213 21206 21206 21206R2 0.409 0.431 0.859 0.860 0.886

Notes. (* p-value<0.1; ** p-value<0.05; *** p-value<0.01) Ordinary Least Square estimates. Sample is restricted to allproduction units in sheds with at least one other production unit. Two-way clustered standard errors, with residuals groupedalong both shed and day. Dependent variable is the average number of eggs per hen collected by the worker. agei is own hens’age in weeks, while age−i is average age of coworkers’ hens in neighboring production units. foodt−s are lags of amount offood distributed as measured by 50kg sacks employed.

38

TABLE 3: COWORKERS’ AND OWN PRODUCTIVITY

Daily Number of Eggs per Hen, yi

(1) (2) (3) (4)OLS 2SLS 2SLS 2SLS

Coworkers’ -0.29338*** -0.21792*** -0.28778*** -0.29040***Eggs per Hen, y−i (0.0764) (0.0651) (0.0705) (0.1004)

agei 0.03052*** 0.03135***(0.0057) (0.0057)

age2i -0.00030*** -0.00031***

(0.0001) (0.0001)

foodt−1 0.00431*** 0.00432*** 0.00404*** 0.00411***(0.0012) (0.0012) (0.0011) (0.0012)

foodt−2 0.00274*** 0.00277*** 0.00249*** 0.00262***(0.0011) (0.0011) (0.0009) (0.0010)

foodt−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 YWorker FEs Y Y Y YBatch FEs N N N Y

Observations 21206 21206 21206 21206R2 0.892 0.889 0.919 0.928

Notes. (* p-value<0.1; ** p-value<0.05; *** p-value<0.01) (1), OLS estimates; (2)-(4) 2SLS estimates. Sampleis restricted to all production units in sheds with at least one other production unit. Two-way clustered standarderrors, with residuals grouped along both shed and day. Dependent variable is the average number of eggs per hencollected by the worker. Main variable of interest is average daily number of eggs per hen collected by coworkers inneighboring production units, y−i. agei is own hens’ age in weeks. In (2) average age of coworkers’ hens and theaverage of its square (age−i, 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). foodt−s are lags of amount of food distributed as measuredby 50kg sacks employed.

39

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** -0.01624Eggs per Hen, y−i (60.7982) (0.0416) (0.0131) (0.0323) (0.0167)

foodt−1 0.38861 0.00176*** -0.00031*** -0.00096*** 0.00003(0.6388) (0.0005) (0.0001) (0.0003) (0.0001)

foodt−2 1.09963** 0.00109** -0.00011 -0.00070** -0.00020**(0.5424) (0.0005) (0.0001) (0.0003) (0.0001)

foodt−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 YWorker FEs Y Y Y Y YBatch FEs Y Y Y Y Y

Outcome Mean 22.351 0.857 0.024 0.059 0.001Observations 21206 21035 21035 21035 19679R2 0.235 0.846 0.907 0.714 0.270

Notes. (* p-value<0.1; ** p-value<0.05; *** p-value<0.01) 2SLS estimates. Sample is restricted to all production units insheds with at least one other production unit. Two-way clustered standard errors, with residuals grouped along both shed andday. 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). Mainvariable of interest is average daily number of eggs per hen collected by coworkers in neighboring production units, y−i. Thefull set of own hens’ age dummies are included as controls, while the full set of coworkers’ hens’ age dummies is used in thefirst stage in all specifications. foodt−s are lags of amount of food distributed as measured by 50kg sacks employed.

40

TABLE 5: ROBUSTNESS CHECKS AND EFFECT HETEROGENEITY

Daily Number of Eggs per Hen, yi

(1) (2) (3) (4) (5) (6)ln yi High Ability Low Ability

Other Shed Workers’ 0.00680Eggs per Hen, y−i (0.0402)

Non-neighboring Workers’ -0.01734Eggs per Hen, y−i (0.0567)

Coworkers’ -1.47172*** -0.28373*** -0.01841 -0.25628***Eggs per Hen, y−i (0.3734) (0.0661) (0.0601) (0.0891)

foodt−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)

foodt−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)

foodt−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 YWorker FEs Y Y Y Y Y YBatch FEs Y Y Y Y Y Y

Observations 20223 8294 21206 21206 10024 11168R2 0.926 0.887 0.900 0.928 0.960 0.953

Notes. (* p-value<0.1; ** p-value<0.05; *** p-value<0.01) 2SLS estimates. Sample is restricted to all production units in sheds with atleast one other production unit. Subsamples in (5) and (6) are derived as discussed in Section 5.4. Two-way clustered standard errors, withresiduals grouped along both shed and day. Dependent variable is average number of eggs per hen collected by the worker in all columnsbut (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 perhen collected by coworkers in adjacent shed; in (2) is average daily number of eggs per hen collected by coworkers in the same shed, but innon-neighboring production units; in (3) to (6) is average daily number of eggs per hen collected by coworkers in neighboring productionunits, 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 firststage in all columns but (4), where expected hens’ productivity per week of age as reported by bird producer is used as instrument. foodt−s

are lags of amount of food distributed as measured by 50kg sacks employed.

41

TABLE 6: TERMINATION POLICY

Logit of Termination Probability(Coefficients)

(1) (2) (3) (4) (5) (6)

yigt -1.0147 -0.3751 -1.2737(0.7377) (2.5079) (1.9843)

yt -6.6506*** -6.5854*** -6.0210***(1.0439) (1.0650) (2.2966)

ygt -0.7095(2.6394)

Yigt -0.0865 -0.0560 -0.0970(0.0530) 0.1750) ( 0.1503)

Yt -0.0006*** -0.0006*** -0.0006***(0.0001) (0.0001) (0.0002)

Ygt -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-value<0.1; ** p-value<0.05; *** p-value<0.01) Logit estimates. Sample is restricted to all production units insheds with at least one other production unit. Dependent variable is dummy equal to 1 if employment relationship terminateson day t. yigt is own daily number of eggs per hen collected by worker i in shed g on day t, ygt is the corresponding averagefor all workers in shed g on day t, and yt is the average among all workers on day t; Yigt is own daily number of total eggscollected by worker i in shed g on day t, Ygt is the corresponding average for all workers in shed g on day t, and Yt is theaverage among all workers on day t. (3) and (6) are Two-stage residual inclusion estimates with bootstrapped standard errorsfrom 200 repetitions (Terza, Basu, and Rathouz 2008)

42

TABLE 7: INCENTIVE HETEROGENEITY

Daily Number of Eggs per Hen, yi

(1) (2) (3) High LowProd. Age Prod. age

y−i × High Productivity Age -0.13365(0.2554)

y−i × Low Productivity Age -0.20819***(0.0791)

y−i × Friend 0.26949(0.2022)

y−i × No Friend -0.42802**(0.2101)

y−i × Experienced -0.57512***(0.1179)

y−i × Not Experienced 0.22580(0.1548)

y−i × Low Age Difference -0.21894 -0.19540(0.4577) (0.3512)

y−i × High Age Difference -0.02754 -0.27601(0.0968) (0.1786)

foodt−1 0.00487*** 0.00577*** 0.00468** 0.00073*** 0.00412***(0.0014) (0.0018) (0.0019) (0.0003) (0.0012)

foodt−2 0.00319** 0.00354** 0.00293** -0.00009 0.00287***(0.0013) (0.0016) (0.0015) (0.0001) (0.0009)

foodt−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 5.2361.69 37.60 47.30 12.91 7.98

Shed-Week FEs Y Y Y Y Y

Day FEs Y Y Y Y YWorker FEs Y Y Y Y YBatch FEs Y Y Y Y Y

Observations 21206 16590 16590 11030 10169R2 0.904 0.918 0.935 0.842 0.927

Notes. (* p-value<0.1; ** p-value<0.05; *** p-value<0.01) 2SLS estimates. Sample is restricted to all production units in shedswith at least one other production unit. Two-way clustered standard errors, with residuals grouped along both shed and day. Dependentvariable is the average number of eggs per hen collected by the worker. Main variable of interest is average daily number of eggs per hencollected by coworkers in neighboring production units y−i and its interactions. In all specifications, the average age of coworkers’ hensand the average of (age−i, age

2−i) are interacted with dummy categories and used as instruments for the corresponding endogenous

interaction regressor in the first stage. foodt−s are lags of amount of food distributed as measured by 50kg sacks employed.

43

TABLE 8: TERMINATION POLICY COUNTERFACTUAL: RESULTS

α2

-0.60 -0.70 -0.80 -0.90 -1.00

α1

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 implementedin 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 respectto actual data, with counterfactual productivity being derived using the parameter values indicated in the corresponding rowand column.

44

FIGURE 1: HENS’ AGE AND PRODUCTIVITY

0.2

.4.6

.81

Avera

ge D

aily

No

. of E

ggs p

er

Hen

15 30 45 60 75 90

Hens' Age in Weeks

+/- One Standard Deviation Smoothed Average Average per Week of Age

kernel = epanechnikov, degree = 0, bandwidth = 3

Notes. The average daily number of eggs per hen collected by the worker is plotted against the age of hensin weeks. Recall that hens in a given batch are all of the same age. The graph shows the smoothed averagetogether 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 eggsper 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, andthen decreases thereafter until hens are old enough and the batch is discarded.

45

FIGURE 2: RESIDUAL PRODUCTIVITY AND AGE OF COWORKERS’ HENS

-.02

0.0

2.0

4.0

6.0

8

Resid

ual P

roductv

itiy

15 30 45 60 75 90

Age of Coworker's Hens in Weeks

95% CI Smoothed Average Quadratic Fit

kernel = epanechnikov, degree = 0, bandwidth = 2, pwidth = 3.11

Notes. Once own hens’ age, day and shed-week fixed effects are controlled for, residual pro-ductivity is plotted against the age of coworkers’ hens in weeks. Productivity is measured asthe average daily number of eggs per hen collected by the worker. Recall that hens in a givenbatch are all of the same age. The graph shows the smoothed average and its 95% confidenceinterval, 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.

46

FIGURE 3: HENS’ AGE AND NUMBER OF EGG BOXES

02

04

06

08

0

1 2 3 4

Hens' Age Quartile

Notes. The figure plots the distribution of the average number of boxes collected by theworker in each two-weeks pay period. Within each age quartile, the bottom and top ofthe box correspond to the 10th and 90th percentile respectively, while the horizontal linecorresponds 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 hensbelong to the 2nd or 4th quartile of the age distribution, meaning of high productivity.

47

FIGURE 4: INPUT ALLOCATION AND PRODUCTIVITY

.6.7

.8.9

1

Ave

rag

e D

aily

No

. o

f E

gg

s p

er

He

n

19050 19100 19150 19200 19250 19300 19350Date

Actual Data Predicted Values

Hierarchically Clustered Allocation

Notes. The figure plots the true, predicted and counterfactual average worker’s productivityover time in the period under investigation. Predictions are derived starting with the batchesin production in the first week of the sample, and simulating their age profiles over the pe-riod, assuming that hens were replaced after the 86th week of life. Reduced-form estimatesfrom a fully specified model where the full sets of own and coworkers’ hen’s week-of-agedummies and shed-week fixed effects are included are then used to predict average dailyproductivity. Counterfactual productivity is derived using the same estimates, but reallo-cating hen batches in production in the first week of the sample among production unitsfollowing a hierarchical clustering procedure which minimizes the variance of the age ofhens within sheds. Average counterfactual productivity is higher than the actual one, andup to 20% higher than the predicted one.

48