ARTICLE IN PRESS. European Economic Review

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1 European Economic Review 53 (2009) Contents lists available at ScienceDirect European Economic Review ournal omepage: Te response to incentives and contractual efficiency: Evidence from a field experiment Harry J. Paarsc a, Bruce S. Searer b, a Department of Economics, University of Melbourne and CIRANO, Canada b Département Économique, Université Laval; CIRPÉE; IZA; and CIRANO, Canada article info Article istory: Received 12 February 2008 Accepted 4 November 2008 Available online 21 November 2008 JEL classification: J33 C93 Keywords: Piece rates Incentives Contractual efficiency Field experiments abstract We use data from a field experiment to estimate worker reaction to incentives and te optimality of piece-rate contracts. Our estimate of te elasticity of output wit respect to piece rates is 0:39. Regression metods cannot predict performance under ypotetical contracts. Terefore, we apply structural econometric metods (witout imposing profit maximization) to evaluate observed-contract optimality. Using profit as a metric, we estimate te distance between observed and profit-maximizing contracts to be negligible. Tis suggests tat observed contracts closely approximate optimal contracts under asymmetric information about worker ability. Under complete information, te firm could increase expected profits by 14 percent keeping workers indifferent to te observed piece-rate contract. Profits could increase between 44 and 49 percent if te firm exploited information about ability to reduce worker utility to te outside alternative. & 2008 Elsevier B.V. All rigts reserved. 1. Introduction and motivation Worker performance under different contract forms plays a central role in te modern teory of te firm. Economic teorists ave modelled te ability of contracts to align te interests of workers and firms: see, for example, Hart and Holmström (1987), Holmström and Milgrom (1990), Milgrom and Roberts (1992) and Baker (1992). In te related and recently developed field of personnel economics (see, for example, Lazear, 1998), compensation systems are considered policy instruments of te firm tat can be used to improve te performance of workers and te profits of firms. Recently, researcers ave used data from payroll records to estimate te effects of contracts on worker and firm performance. 1 Structural econometrics as proven to be a powerful tool in tis respect, allowing researcers to evaluate te performance of contracts not observed in te actual data and to measure te importance of asymmetric information: examples of applications include Ferrall and Searer (1999), Paarsc and Searer (1999, 2000), Haley (2003), Searer (2004) and Copeland and Monnet (2003). Despite te growing number of data sets available for analysing incentive models, little is known about te efficiency of observed contracts witin firms. For example, do observed contracts maximize profits? At one level, te answer is obviously no. Optimal contracts will take into account all relevant information and will typically be complicated, nonlinear functions; see, for example, Holmström (1979). On te oter and, observed contracts are often simple, linear functions of Corresponding autor. Tel.: addresses: p@paarsc.ecom.unimelb.edu.au (H.J. Paarsc), Bruce.Searer@ecn.ulaval.ca (B.S. Searer). 1 For reviews of tis literature, see Prendergast (1999) as well as Ciappori and Salanié (2003). Oter autors ave investigated te effects of different organizational structures on firm decisions and performance; see, for example, Pencavel and Craig (1992) /$ - see front matter & 2008 Elsevier B.V. All rigts reserved. doi: /.euroecorev

2 482 H.J. Paarsc, B.S. Searer / European Economic Review 53 (2009) output; see, for example, Stiglitz (1991). Explanations of tese differences typically involve te added costs of implementing complicated contracts; see, for example, Holmström and Milgrom (1990) as well as Ferrall and Searer (1999). Peraps te relevant empirical question is: Do observed contracts maximize profits witin a subset of easily implemented local alternatives? However, even tis question can be difficult to answer reduced-form econometric metods cannot recover te structural parameters tat would permit one to compare te profit performance of different contracts, and structural econometric metods typically maintain te optimality of te observed contract. Evaluating te local optimality of observed contracts requires identifying structural parameters witout imposing profit maximization. One strategy is to obtain econometric identification using only a subset of te constraints implied by a complete economic model. In te standard principal agent model, te firm cooses a contract to maximize expected profits subect to incentive-compatibility and participation constraints. Below, we sow tat it is possible to identify te parameters of an empirical principal agent model using a subset of tese constraints, excluding expected-profit maximization on te part of te firm. Tis strategy allows us to calculate expected profits, conditional on te estimated parameters, and ten to compare te profits of te observed contracts wit oter, local alternatives. Our data are from a field experiment conducted witin a tree-planting firm operating in te province of Britis Columbia, Canada. Workers at tis firm are typically paid piece rates: daily earnings are strictly proportional to te number of trees a worker planted during a given day. During te experiment, te piece rate paid planters was exogenously increased over 20 percent. We exploit tis increase to identify worker reaction to incentives and to measure te performance of contracts witin tis firm. We begin our analysis of tese data using regression metods, estimating te elasticity of worker productivity wit respect to experimental canges in te piece rate to be 0:39. Tis regression estimate as no direct interpretation in terms of economic fundamentals. In fact, regression metods are limited in teir ability to predict beaviour under alternative contracts not observed in te experiment; see, for example, Wolpin (1995). To undertake suc a comparison, we ave turned to structural metods and used information gatered during extensive discussions wit firm managers to guide our modelling of worker and firm decision rules over effort expended and contract form. We model te coice of contract as satisfying a worker s participation constraint, subect to optimal effort coices on te part of workers. Tis allows us to capture te correlation between planting conditions and te piece rate, witout imposing expected-profit maximization. Incorporating tese decision rules into te econometric strategy admits identification of te model s parameters; we estimate te model using te metod of maximum likeliood. We ave evaluated contractual performance at te maximum-likeliood estimates of te structural model, comparing expected profits realized under te observed contract (a linear contract wit no base wage) wit tose attainable under alternative contracts. To test te optimality of tis contract, we ave derived te optimal, unconstrained, linear contract wic consists of a piece rate and a base wage. We ave found tat tis contract would ave only a negligible effect on te expected profits garnered by firms, suggesting tat te observed contract closely approximates te expectedprofit-maximizing contract, at least witin a set of local alternatives. Our results also suggest tat te firm foregoes large gains by failing to tailor its contracts to individual abilities, pointing to te likely importance of intertemporal commitment, once worker types are revealed. In particular, introducing an individual-specific base wage into te contract would increase te firm s expected profits by about 14 percent, leaving workers indifferent between te base-wage contract and te observed contract. Expected profits would increase between 44 and 49 percent were te firm to use te base-wage contract to capture all rents from te workers. Our paper is organized as follows: in te next section, we describe te tree-planting industry in Britis Columbia, wile in Section 3, we describe te compensation system in te firm in wic our experiment was conducted. In Section 4, we describe te design of our experiment, wile in Section 5, we describe te sample of data. In Section 6, we derive our structural model and present te estimation results; in Section 7, we perform policy analysis; in Section 8, we discuss some important caveats to our analysis; and in Section 9, we summarize and conclude. 2. Tree planting in Britis Columbia Britis Columbia is te largest producer of timber in Nort America; some 25 percent of Nort American softwood lumber is produced in tis province. Wile timber is a renewable resource, active reforestation can increase te speed at wic forests regenerate and also permits foresters to control for species composition, someting tat is difficult to do in te case of natural regeneration. Reforestation is central to a steady supply of timber to te Nort American market. In Britis Columbia, extensive reforestation is undertaken by bot te Ministry of Forests and Range and te maor timberarvesting firms. Prior to te arvest of any tract of coniferous timber, random samples of cones are taken from trees on te tract, and seedlings are grown from te seeds contained in tese cones. Tis ensures tat te seedlings to be replanted are compatible wit te local micro-climates and soil, and representative of te istorical species composition. Tree planting is a simple, yet pysically exausting, task. It involves digging a ole wit a special sovel, placing a seedling in tis ole, and ten covering its roots wit soil, ensuring tat te tree is uprigt and tat te roots are fully covered. A worker s productivity depends on effort expended as well as te terrain on wic te planting must be completed. In general, te terrain can vary a great deal from site to site. In some cases, after a tract as been arvested, te

3 H.J. Paarsc, B.S. Searer / European Economic Review 53 (2009) land is prepared for planting by removing te natural build-up of organic matter on te forest floor so tat te soil is exposed, also known as screefing. Because seedlings must be planted directly in te soil, screefing simplifies planting. Sites tat are relatively flat, tat are free of rocks, or tat ave been screefed are muc easier to plant tan sites tat are very steep or tat ave not been screefed. Te typical density of seedlings is between 1200 and 1800 stems per ectare, an intertree spacing of about 2:4 2.8 m. 2 Depending on conditions and effort, an average planter can plant between 700 and 1100 trees per day, about alf an ectare. Typically, tree-planting firms are cosen to plant seedlings on arvested tracts troug a process of competitive bidding. Depending on te land-tenure arrangement, eiter a timber-arvesting firm or te Ministry of Forests and Range will call for sealed-bid tenders concerning te cost per tree planted, wit te lowest bidder s being selected to perform te work; below, te price received by te firm per tree planted is referred to as te bid price. Bidding for contracts takes place in te late autumn of te year preceding te planting season, wic runs from early spring troug late summer. Before te bidding, te principals of te tree-planting firms typically view te land to be planted and estimate te cost at wic tey can complete te contract. Tis estimated cost depends on te expected number of trees tat a worker will be able to plant in a day wic, in turn, depends on te general conditions of te area to be planted. Planters are predominantly paid using piece-rate contracts, altoug fixed-wage contracts are sometimes used instead. Under piece-rate contracts, planters are paid in proportion to teir output. Generally, no explicit base wage or production standard exists, altoug firms are governed by minimum-wage laws. Output is typically measured as te number of trees planted per day, altoug area-based scemes are used, albeit infrequently. An area-based sceme is one under wic workers are paid in proportion to te area of land tey plant in a given day, assuming a particular seedling density. 3. Firm involved in te experiment Our data were collected at a medium-sized tree-planting company. Tis company is divided into four contracting units, eac under te control of a separate manager. Eac manager is responsible for bidding for contracts, iring workers, and setting piece rates. Essentially, eac manager runs an independent firm. Our data are from one of tese firms. At any time, eac manager employs between 10 and 20 planters. Te planters work under te supervision of foremen, approximately one foreman per 10 planters. Te foremen are responsible for supplying trees to te planters and monitoring planting quality. Poorly planted trees ave a lower survival rate tan tose tat are planted well. Depending on te landtenure arrangement, planting quality is evaluated by eiter te government or a timber-arvesting firm, once te contract as been completed. Lower-tan-acceptable quality exposes te firm to fines. Terefore, te firm monitors its planters closely; poorly planted trees must be replanted at te planter s expense. 3 Workers in tis firm are typically paid piece rates. Daily earnings are strictly proportional to te number of trees planted on a particular day; no base wage is included in te contract. Blocks to be planted are divided into plots, eac of wic is allocated to an individual worker for planting. For eac block, te firm decides on a piece rate. Tis rate takes into account te expected number of trees tat a worker can plant in a day and te expected wage te firm wants to pay. Steep, rocky, unprepared terrain slows planters, rendering planting more difficult tan in flat, prepared terrain. Consequently, for a given piece rate, workers prefer to plant in easy terrain since tey can earn more money for less effort. To induce workers to plant trees in difficult terrain, te firm increases te piece rate, tus satisfying a participation constraint. It is important to note tat under non-experimental conditions te piece rate is te same for all plots in a particular block. No systematic matcing of workers to planting conditions occurs in tis firm so, even toug planters may be eterogeneous, te piece rate received is independent of planter caracteristics. 4. Experimental design Te experiment took place on tree separate blocks over a tree-mont period. During te experiment, eac omogeneous block was divided into two parts. One of tese parts was ten randomly cosen to be planted under te regular piece rate, te oter to be planted under te treatment piece rate. Te treatment piece rate represented an increase of between 21 and 28 percent above te regular piece rate. Two limitations in te design of te experiment warrant discussion. First, in order to avoid any possible Hawtorne effects, te experimental cange in te piece rate was presented to te workers witin te context of te normal daily operations of te firm. To accomplis tis, te firm presented te control and treatment blocks as separate blocks, wit separate piece rates. 4 Note tat tis required spatial separation of te plots to be planted under eac piece rate. As suc, individual plots could not be randomly assigned to regular (control) and treatment piece rates, but rater alf of te block was randomly assigned to regular and alf to treatment piece rates. 2 One ectare is an area 100 metres square, or 10; 000 square metres. Tus, one ectare is approximately 2:4711 acres. 3 Incidents involving poor-quality planting are relatively rare; none is present in our experimental data. 4 A convincing explanation for te difference in piece rates was prepared, invoking te claim tat conditions on te treatment blocks ad canged since te original bidding. Tis sometimes appens wen te block as been unexpectedly prepared by te government or te timber arvester. In practice, owever, no explanation was required because none of te planters questioned te iger piece rates.

4 484 H.J. Paarsc, B.S. Searer / European Economic Review 53 (2009) Table 1 Summary statistics: full sample, 197 observations. Variable Mean St. dev. Minimum Maximum Number of trees Regular piece rate Piece rate paid Daily earnings ($CAD) Te need to present te experiment witin te natural workings of te firm also restricted te temporal design of te experiment. Blocks, large enoug to accommodate all workers at once, are typically planted sequentially. Tis ensures tat all workers are planting under similar conditions on te same day. Wary to be seen reducing te piece rate on similar ground, te firm insisted tat planting under te regular piece rate take place before planting under te treatment piece rate. 5. Sample data Our data set contains information on te regular piece rate set for eac block, wic we sall denote by r, and te piece rate received by eac planter, wic we sall denote by ( p4r for treatment group observations; p ¼ r for control group observations; as well as tat planter s daily productivity (trees planted), wic we sall denote by Y. In Table 1, we present summary statistics concerning all 197 observations from te experiment. A total of 21 planters were observed during te experiment, planting on tree different blocks, over a tree-mont period in te spring and summer of 2003, 109 on control plots and 88 on treatment plots. Te piece rates paid to planters during te experiment ranged from 18 to 28 cents per seedling, wit an average of 23 cents. Te regular (or control) piece rates ranged from 18 to 23 cents per seedling, wit an average of 21 cents. On average, workers planted around 944 seedlings per day and earned about $215 (Canadian) per day. Te endogeneity problems tat plague te identification of worker reactions to incentives in tese types of data are well known; see, for example, Paarsc and Searer (1999). Tey arise from te firm s determining te contract as a function of conditions unobserved by te econometrician. 5 Access to experimental data circumvents te endogeneity problem by providing exogenous variation in te piece rate for a given set of planting conditions. In Table 2, we present te data by block and treatment. Te numbers of observations differ across blocks because te blocks are different sizes. In fact, since te blocks were planted at different dates, not all of te planters were observed on eac block: some planters ad left te firm and oters were planting elsewere. Note, owever, tat if a planter is observed planting on a given block, ten tat worker is observed under bot te control and te treatment piece rate for tat block. Two piece rates were paid on eac block: 0:18 and 0:23 on Block 1 as well as 0:23 and 0:28 on Blocks 2 and 3. Correspondingly, te average number of trees planted and te average earnings are iger under te iger (treatment) piece rates for eac block. Tis reflects te reaction of planters to incentives. To consider te statistical significance of our results furter, we estimated te following regression equation: log Y i ¼ b 0;i þ b 1 log p þ U i, (1) were p represents te piece rate paid on block, so ( p ¼ p for treatment-group observations; r for control group observations: Here, b 0;i represents a constant term tat is individual and block specific. Note tat te exogenous variation in te piece rate directly identifies te elasticity of productivity wit respect to piece rates. Te results from estimating Eq. (1) are presented in Table 3; te estimated elasticity is positive, 0:39, and statistically significant. 6 5 As in Paarsc and Searer (1999), wen non-experimental data were used, te estimated elasticity of productivity wit respect to te piece rate is negative; see Paarsc and Searer (2007) for details. 6 Controlling for possible confounding factors (suc as weater, fatigue, and participation) ad little effect on tese estimates; te details are available from te autors on request, or in Paarsc and Searer (2007).

5 H.J. Paarsc, B.S. Searer / European Economic Review 53 (2009) Table 2 Sample means: by block. Variable Control group Treatment group Block 1: 76 observations Piece rate paid Number of trees Daily earnings ($CAD) Observations Block 2: 33 observations Piece rate paid Number of trees Daily earnings ($CAD) Observations Block 3: 88 observations Piece rate paid Number of trees Daily earnings ($CAD) Observations Table 3 Treatment/control regression results. Independent variable Estimate Constant (0.153) Logaritm of p (0.089) Maximum individual effect (0.083) Minimum individual effect (0.056) Maximum site effect (0.046) Minimum site effect (0.048) R 2 ¼ 0:881 Note: standard errors are in parenteses. Dependent variable: logaritm of daily production; sample size ¼ Structural model Above, we ave provided an estimate of te response of worker output to an experimental cange in te piece rate. Yet it may be of interest to consider te profit performance of te observed contract vis-à-vis alternative contracts. Tis presents two potential problems. First, beaviour may cange wen contracts cange: effort levels are sensitive to contracts and must be predicted as contracts cange. Second, any comparison must consider contracts tat are acceptable to bot te firm and te workers: a proposed contract must satisfy expected-utility constraints. Taking tese factors into account requires estimating a structural econometric model in wic te parameters determining worker utility and productivity are identified. In tis section, we develop and estimate a structural econometric model of worker and firm beaviour under te observed piece-rate contract. Our teoretical model and econometric strategy are similar to tose in Searer (2004); we exploit experimental variation in te contract to identify te empirical specification. But rater tan concentrate on piece rates versus fixed wages, we analyse worker response to variation in te piece rate. Te estimated parameters are used, in Section 7, to evaluate te relative performance of te observed contract, concentrating on te marginal benefit of introducing a base wage into te contract. Importantly, we estimate te structural model witout imposing te assumption of expected-profit maximization: to wit, contracts are only cosen to ensure te marginal worker s participation. 7 We ten test for te optimality of te observed contract by solving for te optimal base-wage contract (given te estimated structural parameters) and comparing would-be expected profits to tose earned under te observed contract. 7 Tis is consistent wit te manner in wic te firm cooses te piece rate; see Section 2.

6 486 H.J. Paarsc, B.S. Searer / European Economic Review 53 (2009) Productivity To begin, we assume tat daily productivity Y is determined by Y ¼ ES, were E represents te worker s effort level and S is a productivity sock representing planting conditions beyond te worker s control, suc as te ardness of te ground. We assume tat S follows a lognormal distribution wit parameters m and s 2. Planters are assumed to ave a utility function U defined over earnings I and effort E. For a given piece rate r, earnings I equal ry or res. We assume tat te cost of effort function for planter i as te following form: g C i ðeþ ¼ ðg þ 1Þ Eðgþ1Þ=g ; 40; g40, were denotes te planter-specific component of costs and g caracterizes te curvature of C i ðþ. We assume furter a utility function separable in I and E, aving te following form: g UðI; EÞ ¼½I C i ðeþš ¼ res ðg þ 1Þ Eðgþ1Þ=g. (2) Timing: For eac block, te sequence of events in te model is assumed to follow: 1. Nature cooses ðm ; s 2 Þ for block. 2. Te firm observes ðm ; s 2 Þ and ten selects a piece rate r. 3. Worker i observes ðm ; s 2 Þ for block, and is offered te contract r for planting on tat block; te planter eiter accepts or reects te contract. 4. Conditional on accepting te contract, worker i is ten randomly assigned to plant on a particular plot of block were tat planter draws a particular value of S denoted s. Planter i ten cooses an effort level E and produces Y i. 5. Te firm observes Y and pays earnings I Control-group observations Letting e i denote te optimal level of effort cosen by worker i, ten conditional on s, optimal effort is given by e i ¼ rs g, and observed productivity on block is y i ¼ rg k g s gþ1. (3) i In order for a worker to accept te contract offered, it must satisfy is expected-utility constraint. Te piece rate paid on block satisfies te participation constraint of te marginal (lowest-ability, igest k) worker in te firm. Substituting optimal effort into (2), taking expectations, and using te properties of te log-normal distribution yields r ðgþ1þ exp½ðg þ 1Þm þ 0:5ðg þ 1Þ 2 s 2 Š ðg þ 1Þk g ¼ ū, (4) were k ¼ maxðk 1 ; k 2 ;...; k n Þ. Taking logaritms of (3) and substituting from (4) yields log Y i ¼ logðg þ 1Þþlog ū log r þ g log k 0:5ðg þ 1Þ k 2 s 2 þ V i, (5) i were te error term V i equals ðg þ 1Þðlog S i m Þ is distributed normally wit mean zero and variance ðg þ 1Þ 2 s Treatment-group observations Under our experiment, te piece rate on block is exogenously increased from r to p for part of te block, cosen at random te treatment block. Worker productivity on te treatment plots is ten given by te following observedproductivity equation: y i ¼ pg k g s gþ1. (6) i

7 H.J. Paarsc, B.S. Searer / European Economic Review 53 (2009) Given tat conditions ave not canged, r still satisfies Eq. (4), yielding te following empirical specification in terms of random variables: log Y i ¼ logðg þ 1Þþlog ū log r þ g log k 0:5ðg þ 1Þ k 2 s 2 þ g log p þ V i r i. (7) 6.4. Identification results or To identify te parameters of te model, we combine Eqs. (5) and (7) to yield te following: log Y i ¼ logðg þ 1Þþlog ū log r þ g log k 0:5ðg þ 1Þ k 2 s 2 þ g log p þ V i r i (8) log Y i ¼ a 0 þ logðg þ 1Þ log r þ ga 1i 0:5ðg þ 1Þ 2 s 2 þ g log p þ V i, (9) were a 0 ¼ log ū þ g½logðk Þ logðk 1 ÞŠ and a 1i ¼ logðk 1 Þ logð Þ for k 1, te normalized individual in te sample. Identification Teorem. Part (a): If te marginal individual is in te experimental sample, ten te parameters g, s 8, ½logðk Þ logð ÞŠ, and log ū in Eq. (9) are identified and can be estimated by te metod of maximum likeliood. Part (b): If te marginal individual is not in te experimental sample, ten te parameters g, s 8, ½logðk 1 Þ logð ÞŠ, and log ū þ g½logðk Þ logðk 1 ÞŠ in Eq. (9) are identified and can be estimated by te metod of maximum likeliood. Te proofs of te above two parts of te teorem are collected in an appendix. Te marginal benefit of experimental data vis-à-vis non-experimental data for estimating te structural model is now clear. Experimental variation in te piece rate allows one to identify directly te elasticity of effort. 8 In te absence of suc variation, wen p equals r, identifying g requires a measure of alternative utility, ū; and te estimated value of g will be sensitive to any suc measure. 9 r 6.5. Empirical results We estimated Eq. (9) using te experimental data. Te results are presented in Table 4, column (a). Te estimate of te elasticity of effort wit respect to te piece rate g is 0:330, aving a standard error of 0:091. Te value of te logaritm of te likeliood function is 29:246. Te estimate of g using experimental data is statistically significant, altoug substantially smaller tan tat of Paarsc and Searer (1999) or Haley (2003). In addition, from te estimates of a 0 and g, one can recover an estimate of ū under te ypotesis tat te marginal individual was in te experimental sample. Tis yields an estimate of ū of $85:31, considerably larger tan tat imposed by Paarsc and Searer (1999) or Haley (2003), even accounting for inflation. Given te identification results, tis suggests tat te values of ū used by Paarsc and Searer as well as Haley to identify g were too low Correlated weater socks and perception errors Increased flexibility can be obtained in te structural model by introducing daily weater socks W and perception errors n. Perception errors capture te possibility tat te firm may misudge actual planting conditions on a given block. Let daily output be given by Y it ¼ E it S i W t were S and W are independent random variables, wit log S being distributed normally aving mean m and variance s 2 and log W t being distributed normally aving mean m W and variance s 2 W.10 Furtermore, we assume tat te value of W t is observed after participation decisions are made, but before effort is cosen. To account for perception errors on a given block, we assume tat at te beginning of te contract bot te firm and te worker observe m, an unbiased estimate of true conditions m,so m ¼ m þ n n Nð0; s 2 n Þ; Eðn m Þ¼0, 8 Note tat te restrictions embodied in Eq. (8) permit te interpretation of g as te elasticity of effort wit respect to te piece rate. In te absence of tese restrictions, te parameter on te experimental variation in te piece rate identifies te output elasticity, someting different. 9 Tis was te identification strategy adopted by Paarsc and Searer (1999) as well as Haley (2003). 10 We place a subscript on average daily weater socks m W to denote te fact tat te firm s expectations of daily weater socks may differ across contracts because tey take place at different times of te year. We do not allow tese expectations to cange daily since expected weater will affect te setting of te piece rate and te piece rate is constant for a given contract.

8 488 H.J. Paarsc, B.S. Searer / European Economic Review 53 (2009) Table 4 Maximum-likeliood estimates: structural model. Parameter (a) (b) (c) (d) g (0.091) (0.167) (0.043) (0.108) a (0.051) (0.054) (0.029) (0.072) s (0.008) (0.110) (0.071) (0.131) s (0.016) (0.112) (0.063) (0.131) s (0.015) (0.109) (0.072) (0.164) s W (0.034) (0.036) s n (0.045) (0.046) Logaritm of likeliood function Note: standard errors are in parenteses. Dependent variable: logaritm of daily production; sample size ¼ 197. were E denotes te expectation operator. Optimal effort is e it ¼ r s i w g t. Given decisions are based on m, te piece rate is cosen to satisfy r gþ1 exp½ðg þ 1Þ m þ 0:5ðg þ 1Þ 2 ðs 2 þ s 2 n ÞŠ exp½ðg þ 1Þm W þ 0:5ðg þ 1Þ2 s 2 W Š ðg þ 1Þk g ¼ ū (10) yielding log Y it ¼ logðg þ 1Þþlog ū log r þ g log k 0:5ðg þ 1Þ k 2 ðs 2 þ s 2 W þ s2 nþþglog p i were e it ¼ðg þ 1Þ½ðlog W t m W Þþðlog S i m Þþn Š. Under te above assumptions, te first- and second-moment structure of te error term e is given by Eðe it Þ¼0, Eðe it e it Þ¼ðg þ 1Þ 2 ðs 2 þ s 2 W þ s2 n Þ, Eðe it e i 0 0 t Þ¼ðg þ 1Þ2 s 2 W, Eðe it e i 0 t 0Þ¼ðg þ 1Þ2 s 2 n, Eðe it e i 0 t 0Þ¼0, Eðe it e i 0 t Þ¼ðg þ 1Þ2 ðs 2 W þ s2 n Þ, Eðe it e it 0Þ¼ðg þ 1Þ 2 s 2 n, Eðe it e i 0 tþ¼ðg þ 1Þ 2 s 2 W. r þ e it, (11) Estimates of different versions of Eq. (11) are presented in Table 4, columns (b) (d). In column (b), we admit weater socks, but no perception errors; i.e., s W is positive, wile s n is zero. Te estimate of g is 0:443 and te value of te logaritm of te likeliood function increases to 37:675. In column (c), we present estimates of te model witout weater socks, but admitting perception errors; i.e., s W is zero, wile s n is positive. Te estimate of g is 0:336 and te value of te logaritm of te likeliood is 41:069. Finally, in column (d), we present estimates of te model admitting bot daily weater socks and perception errors; i.e., s W and s n are bot positive. Here, te estimate of g is 0:366 and te value of te logaritm of te likeliood function increases to 44: Strictly speaking, we cannot compare models wit variances set to zero using te standard likeliood-ratio test as te variance parameters, wen set to zero, are on te boundary of te parameter space, so standard, first-order asymptotic metods are invalid. Here we do so simply to provide te reader wit some feeling for ow muc better te models fit wen daily weater socks and perception errors are included.

9 H.J. Paarsc, B.S. Searer / European Economic Review 53 (2009) In general, te individual variance parameters are not precisely estimated, altoug te value of te logaritm of te likeliood function increases substantially by teir inclusion. Note, too, tat te estimates of te effort elasticity are reasonably stable, ranging from 0:33 to 0: Goodness-of-fit In order to evaluate te performance of te structural model, we calculated 95-percent confidence intervals for te predicted values of te logaritm of daily productivity, for te model wit daily weater socks and perception errors. Te model fits quite well, altoug (in strict terms) it is reected by te data: in all, 90 percent of te observations fall witin te 95-percent confidence intervals. 12 Because te output and effort elasticities coincide in our model, we can compare te estimated output elasticity from te structural model wit tat from te regression model. We note tat tese parameters are very close, 0:37 for te structural model and 0:39 for te regression model; any mis-specification does not appear to affect te estimate of worker reaction to incentives. Tis is peraps not too surprising since identification of tis parameter derives mainly from te exogenous cange in te piece rate. Neverteless, tis igligts te benefits of field experiments. As always, tere is a trade-off in te application of structural models to data: structural models do not fit te data as well as teir unrestricted counterparts. However, structural models allow one to make beavioural interpretations of te results and to investigate alternative policies unobserved during te experiment. We develop tis latter point in te next section. 7. Policy analysis: alternative contract forms and firm profits Estimating te structural model allows us to predict te performance of alternative contract forms not observed during te experiment. Note tat te observed contract as only one instrument, te piece rate. Given canging planting conditions, te piece rate must accomplis two tasks to provide incentives for effort and to guarantee participation. A contract tat includes a base wage allows te firm to separate te tasks of two instruments, te piece rate providing incentives and te base wage ensuring participation. In tis section, we consider ow introducing a base wage into te contract would affect firm profits. Initially, we restrict te alternative contract to be independent of worker type (as is te observed contract), extending tis later to allow te firm to condition on worker ability. Information Assumption 1. Te firm can write contracts on te set fm; s 2 ; k ; f K ð Þ; gg. Here, f K ð Þ is te distribution of ability levels in te firm. Trougout, we assume tat a worker s type is independent of site-specific productivity and daily weater socks. Te base-wage contract includes a base wage B and a piece rate R and, for block, takes te following form: I ¼ B þ R Y. As wit te observed piece-rate contract, te base-wage contract is independent of worker type. Tis is consistent wit two scenarios: first, te firm cannot observe worker type ; and, second, te firm can observe worker type, but cannot write (or refrains from writing) a contract on it. To compare contracts, we denote te effort level under te observed piece-rate contract by EðrÞ ¼ rsw g, and te effort level under te alternative base-wage contracts by EðB; RÞ ¼ Rsw g. We solve for te base-wage contract tat would ensure te marginal worker continues to participate in tis firm. Tis ensures tat te distribution of types will not cange under te new contract. From Eq. (2), expected utility is given by EðU r i Þ¼ rgþ1 exp½ðg þ 1Þ m þ 0:5ðg þ 1Þ 2 ðs 2 þ s 2 n ÞŠ k g ðg i þ 1Þ exp½ ðg þ 1Þm W 0:5ðg þ 1Þ2 s 2 W Š. From Eq. (10), r gþ1 exp½ðg þ 1Þ m þ 0:5ðg þ 1Þ 2 ðs 2 þ s 2 n ÞŠ exp½ðg þ 1Þm W þ 0:5ðg þ 1Þ2 s 2 WŠ¼ðgþ1Þkg ū. Substitution yields expected utility under piece-rate contracts: EðU r i Þ¼ k g ū. 12 See Paarsc and Searer (2007) for graps of tese confidence intervals.

10 490 H.J. Paarsc, B.S. Searer / European Economic Review 53 (2009) Under te base-wage contract, expected utility is given by E½U ðb ;R Þ g i Š¼E B þ R EðB ; R ÞWS g þ 1 EðB ; R Þ ðgþ1þ=g ¼ B þ Rðgþ1Þ exp½ðg þ 1Þ m þ 0:5ðg þ 1Þ 2 ðs 2 þ s 2 n ÞŠ k g ðg i þ 1Þ exp½ ðg þ 1Þm W 0:5ðg þ 1Þ2 s 2 W Š ¼ B þ Rðgþ1Þ r ðgþ1þ k g ū. Solving for a B tat guarantees participation of te marginal worker yields 2 3 B ðr Þ¼ū41 Rðgþ1Þ 5. (12) r ðgþ1þ Given BðR Þ and R, we can write expected profits per worker under any base-wage contract as ðg R ÞR g ūe k g " ðg þ 1Þ ū 1 R # gþ1, (13) r r gþ1 were G is te bid price, te price te firm receives per tree planted on block. Maximizing Eq. (13) wit respect to R yields te following solution: ^R ¼ g ðg þ lþ G, were!! E 1 k g 1 k g i l ¼! E 1 o1 k g i given k equals maxfk 1 ; k 2 ;...; k n g. 13 Two special cases of te optimal contract imply tat incentives are independent of te distribution of worker type f K ð Þ. First, if workers are omogeneous (so is te same for all i), ten l is zero and ^R equals G, te bid price. Under tese circumstances, te firm s marginal return to increasing te piece rate is independent of worker type and te firm can use te base wage to recover te surplus generated by ig-powered incentives. Tis is te standard solution wit risk-neutral agents. Second, if te participation constraint does not bind (so k!1), ten l is one and te firm maximizes profits by setting ^R equal to ½G g=ðg þ 1ÞŠ, equating te firm s marginal revenue of increasing te piece rate to its marginal cost. 14 In te presence of eterogeneous workers, a common base wage and a binding participation constraint, te firm s marginal return to increasing te piece rate is type-dependent: te optimal contract must balance incentives across types. 13 If te firm can observe individual ability, but cannot write a contract on, ten te firm s expected profits are ðg RÞR g ðg þ 1Þ X n " k g ū nū 1 R # gþ1. r gþ1 k i¼1 i r Te optimal piece rate is ten given by ^R ¼ g ðg þ lþ G, were!! P n 1 i¼1 k g n 1 k g i l ¼!. P n 1 i¼1 k g i 14 More generally, tis solution satisfies te condition G ^R ¼ 1 ^R g wic is a variant of te monopolist s price-markup equation. Here, te firm controls te piece rate and sets te markup to be equal to te inverse elasticity of effort.

11 H.J. Paarsc, B.S. Searer / European Economic Review 53 (2009) Table 5 (a) Base-wage contract expected profits; (b) constant-utility base-wage contract expected profits; (c) alternative-utility base-wage contract expected profits. Block Rate paid Price Optimal rate Base wage p r p ðb;rþ Percent increase (a) I II III Block Rate paid Optimal rate Base wage p r p ðb;rþ Percent increase (b) I II III Block Rate paid Optimal rate Base wage p r p ðb;rþ Percent increase (c) I II III Te optimal base-wage is given by substituting ^R into Eq. (12), yielding expected profits per worker under te basewage contract p ðb ;R Þ ¼ðG ^R ^R g 2 Þ ðg þ 1ÞūE k g! 3 gþ1 ^R ū41 5. r r gþ1 Under te piece-rate contract, expected profits per worker are given by p r ¼ ðg r Þ E k g ðg þ 1Þū. r We calculated expected profits under te assumption tat te marginal individual is in te experiment. Tis assumption is reasonable given te structure of te firm. Recall tat te piece rate on a given contract is cosen by te manager responsible for tat contract. In effect, eac manager operates is own independent firm witin te company, setting piece rates and iring workers. Since te experiment was completed on one suc firm, it is not unreasonable to assume tat te marginal worker is present. 15 In Table 5a, we present a summary of contractual performance on eac experimental block, evaluated at te estimates from Table 4(d) i.e., admitting daily weater socks and perception errors. In te first column, we present te piece rate paid under te actual contract, wile in te second column we present te price per tree planted received by te firm. In te tird column we present te optimal piece rate under te base-wage contract; in te fourt, te base-wage paid under te base-wage contract; in te fift, expected profits under te actual piece-rate contract; in te sixt, expected profits under te base-wage contract; and, in te sevent, te percentage increase in expected profit by switcing to te basewage contract. We estimate te increase in expected profits to be less tan one percent in all tree cases. Tis suggests tat te actual contract, wic sets te base wage to zero on all blocks, is very close to being te optimal linear contract: te firm s coice of contracts gets close to maximizing expected profits. We now turn to evaluating te importance of information over worker type on contracts and profits Information over worker type To consider te importance of information to firm profits, we relax te restriction proibiting te firm from conditioning te contract on worker type. Information Assumption 2. Te firm can write contracts on te set fm ; s 2 ; k ; ; gg. If te firm can condition on worker type, ten te optimal contract is to sell te rigts to plant trees on a particular block to a worker. Since workers earn rents under te current contract, a base-wage contract will ave two effects: first, it will allow 15 If te marginal individual were not in te data set, ten te analysis would still go troug, wit a sligt cange in interpretation; viz., by redefining te base wage to satisfy te expected utility of te igest-cost individual in te sample, we can calculate te profits accruing from rendering tat individual indifferent between contracts.

12 492 H.J. Paarsc, B.S. Searer / European Economic Review 53 (2009) te firm to tailor te contract to eac worker; and, second, it will allow te firm to capture rents. To decompose te importance of eac element in te contract, we distinguis between two cases. First, we impose tat te base-wage contract ensures eac planter obtains tat worker s current level of utility, k g ū. We call tese contracts constant-utility contracts. Any increase in expected profits from te base-wage contract under tese conditions is attributed to conditioning on individual type. Second, we allow te firm to reduce te base wage to capture all of te rent from eac worker, ensuring tat eac worker earns te alternative utility level ū. We call tese contracts alternative-utility contracts. Case A: Constant-utility contracts. Te base wage tat keeps worker i indifferent between te piece-rate contract and te base-wage contract is given by B i ðr Þ¼ k 2 3 g ū41 Rðgþ1Þ 5. r ðgþ1þ Terefore, expected profits per worker are given by ðg R ÞR g k g ðg þ 1Þ ū k " g ū 1 R # gþ1. r gþ1 r Maximizing expected profits over R yields te standard solution ^R ¼ G, B i ¼ k " g ū 1 G # gþ1. r Te firm sells te rigts to plant on block to te workers. Eac planter pays a fee tat depends on tat worker s cost of effort. Since te piece rate is equal to te price te firm receives per tree planted, profits per worker are equal to B i. Te relative performance of te constant-utility base-wage contract is presented in Table 5(b). By introducing a base wage, expected profits would increase by approximately 14 percent. Case B: Alternative-utility contracts. Te firm can capture all of te rent tat eac worker earns by setting te base wage according to 2 3 B i ðrþ ¼ū 1 k g R ðgþ1þ 4 5. r ðgþ1þ Te optimal contract is ten given by ^R ¼ G ", B i ¼ ū 1 k g G # gþ1. r We calculated te expected profits associated wit eac of tese contracts in Table 5(c). If te firm were to capture all of te rents workers earn, ten expected profits would increase between 44 and 49 percent. 8. Discussion Our model as been derived under a number of assumptions tat warrant some discussion. First, under our identification strategy, we assumed tat te marginal worker s participation constraint is exactly satisfied across contracts. Tis allows us to identify te model witout imposing profit maximization, but rules out any selection effects of different contracts as were igligted in Lazear (2000). Tis strategy is similar to tat used in labour-supply models in wic labour-force participation constraints are imposed to identify reservation wages. Notice, owever, in contrast to structural searc models, we do not exploit order statistics to identify alternative utility, so measurement error sould be less of a concern in our model tan in tose models. 16 Our identification strategy also imposes restrictions on utility: most notably, peraps, alternative utility is omogeneous and workers are risk neutral. Allowing for eterogeneity in alternative utility only introduces a sligt cange in te interpretation of te coefficients. Since te piece rate is cosen to satisfy te participation constraint of te marginal worker, te alternative utility level of te marginal worker ū would be identified by te constant term in Eq. (9). 16 See Cristensen and Kiefer (1994) for a discussion of te importance of measurement error in searc models.

13 H.J. Paarsc, B.S. Searer / European Economic Review 53 (2009) Our policy analysis would go troug, wit te exception of alternative-utility contracts wic would not be identified in tis case. Ruling out risk preferences allows us to concentrate on te reaction to incentives, simplifying te analysis. Incorporating risk preferences would not affect effort levels in our model because effort is cosen after te sock S is observed. Hence, our estimate of te reaction to incentives would not be greatly affected by its introduction. Introducing risk preferences would, owever, affect te participation decisions of te marginal worker and, consequently, te estimates of te variance parameters. In tis case, te introduction of te base wage into te contract would provide insurance to risk-averse workers. Hence, to te extent tat workers are risk averse, te profits under te base-wage contract may be understated. Of course, tis depends on te extent to wic tese workers are risk averse. Bellemare and Searer (2006) exploited preference-revealing experiments to investigate te risk attitudes in a sample of tree planters. Tey found tat risk attitudes were eterogeneous, but tat many workers exibited risk-tolerant beaviour. Our calculations of te profits under a base-wage contract may also be sensitive to income effects: income effects may affect effort coices in te same way tat tey do oter labour-supply decisions. In general, it is difficult to identify an income effect as well as a substitution effect from canges in te piece rate alone. Experimental metods may be useful in tis regard, allowing researcers to vary bot te piece rate and a base wage independently. Dickens (1999) as provided an example witin a laboratory setting; field experiments would provide te opportunity to confirm is results witin te labour market. 9. Summary and conclusions Economists are increasingly turning to experiments to gater data concerning individual beaviour. Experiments allow for te exogenous allocation of treatments, simplifying identification and estimation. Field experiments extend te benefits of exogenous variation in treatments to real-world data, facilitating te generalization of statistical results; see, for example, Frenc (1953). Field experiments also provide a simple, yet powerful, tool for analysing te effects of different personnel policies witin te firm. We ave analysed data from one suc field experiment wic was designed to measure te reaction of workers to canges in piece-rate incentives. Experimental variation in te piece rate admitted direct measurement of reactions witin an unrestricted framework. Our results suggest tat workers do react to incentives. We estimate an output elasticity wit respect to canges in te piece rate of 0:39. At a general level, our results are consistent wit te literature devoted to investigating incentive effects. Specifically, as Paarsc and Searer (2000), Lazear (1998, 2000) and Searer (2004) ave also found, incentives do matter. More specifically, our results illustrate tat workers respond positively to increases in te piece rate. Tis is consistent wit previous results obtained Paarsc and Searer (1999) as well as Haley (2003). Furtermore, our results ave implications for researc on income targeting. Fer and Goette (2007) ave sown tat income targeting may be important among bicycle messengers wo are paid piece rates, rendering worker s productive reaction to te piece rate to be negligible or even negative. Our results suggest tat any influence of income targeting witin te tree-planting environment is overridden by incentives. We ave also considered te relative benefits of estimating structural econometric models using experimental data. In general, te ability to generalize experimental results to evaluate policies unobserved witin te experimental setting represents te maor advantage of structural estimation. In fact, experimental and structural-econometric metods are complementary: te experiments provide exogenous variation wic reduces te sensitivity of te results to functionalform assumptions. Our results point to te importance of worker eterogeneity in determining contractual performance witin te firm. Indeed, if eterogeneity is ignored, ten te observed contract is locally optimal; adding a base wage would ave only a negligible effect on expected profits. In contrast, conditioning te base wage on worker type would increase expected profits substantially. Tis raises te question of wy contracts are independent of worker type. One possible explanation is tat te firm does not know worker type. However, given te nature of te work and te fact tat te firm gaters worker productivity records for payroll purposes, tis does not seem to be plausible. An alternative explanation deals wit contracting costs. In particular, wereas te piece-rate contract is only block specific, te base-wage contract is individual and block specific. Te costs of negotiating suc a contract may outweig te benefits of its implementation. We find tat te firm forgoes a 14 percent increase in expected profits by ignoring eterogeneity. One interpretation is tat tese results provide a lower bound to te cost of implementing suc a contract. Furter benefits are predicted if te firm were to use te base wage to extract rents from eac worker. However, under suc circumstances, workers would ave an incentive to mis-represent teir abilities. Tis points to intertemporal commitment as an important determinant of observed contracts: te firm commits to refrain from using information over worker type in order to induce ig-ability workers to reveal teir type. Our results also suggest a number of directions for future researc. Incorporating more general preference functions, possibly wit te elp of experiments to acieve identification, would allow researcers to investigate te importance of risk and income effects in field settings. Dynamic elements are also igligted witin te contracting environment. We ave identified te firm s commitment to ignore worker type as important in implementing te observed contract. But, as