Structural estimation of rank-order tournament games with private information.

In most sporting events, prizes are awarded not on basis of absolute performance but based on relative performance, or tournaments. Besides sporting events, tournaments are also frequently used in labor contracts. The name "tournament" typically suggests a rank-order (ordinal) scheme such as is considered by Lazear and Rosen (1981), whereas a broader definition applies to any compensation scheme based on relative performance (e.g., Nalebuff and Stiglitz 1983; Tsoulouhas and Vukina 1999). Despite the sizeable theoretical literature on tournaments, empirical work related to these models remains rather limited. Most of the theoretical literature on tournaments (see McLaughlin 1988 for a survey) has been concerned primarily with the comparison of tournaments against various independent reward structures under various assumptions about risk preferences, the number of participants and prizes, specifications of production shocks, and the asymmetry of information. Previous empirical work has largely focused on testing the predictions of the theoretical models. This includes articles on executive compensation (e.g., Main, O'Reilly and Wade 1993; Ericksson 1999; Gibbons and Murphy 1990), professional sports (e.g., Ehrenberg and Bognanno 1990; Bronars and Oettinger 2001) and broiler production contracts (Knoeber and Thurman 1994; Levy and Vukina 2004; Leegomonchai and Vukina 2005).

Empirical articles on tournaments are all done with data sets from industries where performance measures for individual tournament contestants are available. In principle, this data feature enables researchers to measure the effects of changes in the incentive structure on the individual performances of tournament participants, even if the data set per se contains no incentive regime changes. This can be accomplished by using a structural econometrics approach where researchers estimate only the model primitives, such as densities of random shocks or parameters of the agents' utility or cost functions, which cannot be influenced by the quantitative or qualitative changes in the incentive structure. Somehow, this type of work has not been done for tournament-style labor contracts, but has been done in the context of individualized labor contracts. A good example is an article by Paarsch and Shearer (2000) who estimated a structural model with moral hazard in the context of tree-planting labor contracts and found that incentives caused a 22.6% increase in productivity, only a part of which represented valuable output because workers responded to incentives by reducing the quality of their work.

This article focuses on rank-order tournaments used to settle broiler production tournaments. The modern broiler industry in the United States represents a completely vertically integrated chain involving the production of hatching eggs, hatcheries, production of broilers, as well as slaughtering and further processing. The production of broilers is almost entirely organized via production contracts between firms, called integrators, and independent producers, most of them being small family farmers. At some point in the evolution of the contract design, the industry started using feed conversion or production cost tournaments. Some of those early tournaments were based on ordinal rankings of growers, whereas most modern contracts seem to be predominantly settled using cardinal tournaments where an individual grower's bonus or penalty depends on the distance between her performance and the group average performance.

In this article we propose a new gametheoretic model of a rank-order tournament with private information and characterize its equilibrium. Our model modifies the original Lazear and Rosen (1981) and Green and Stockey (1983) rank-order tournament models to capture the most important features of production contracts observed in the broiler industry. Using the data set of Knoeber and Thurman (1994), we estimate a fully structural model of a symmetric Nash equilibrium of this game. We show that growers' equilibrium effort depends on four factors: the spread in piece rates between the performance brackets, the number of players in each tournament, the number of performance brackets used, and the density of growers' private information. We use estimates of productivity shocks density to simulate how changes in the tournament characteristics that affect equilibrium effort impact total welfare and the distribution of welfare between the growers and the integrator. Considering the typical industry performance measures (cost of production, feed conversion) all obtained results look very reasonable.

Broiler Industry

The broiler industry represents an entirely vertically integrated chain, including all stages from breeding flocks, hatcheries and grow-out to feed mills, transportation divisions, and processing plants. The production of live birds is organized almost entirely through contracts with independent growers. Modern poultry production contracts are agreements between an integrator company and farmers (growers) that bind farmers to tend for the company's birds until they reach market weight in exchange for monetary compensation. Poultry contracts have two main components: the division of responsibility for providing inputs and the method used to determine grower compensation. Growers provide land and housing facilities, utilities (electricity and water), and labor. Operating expenses such as repairs and maintenance, clean up cost, manure, and mortality disposal are also the responsibility of the grower. An integrator provides animals to be grown to processing weight, feed, medications, and the services of field personnel and makes decisions about the frequency of flock rotations on any given farm. Most integrators nowadays require that houses be built according to strict specifications regarding construction and equipment.

Extensive but incomplete empirical evidence suggests that most broiler contracts are nowadays settled using a two-part cardinal tournament scheme consisting of a fixed base payment per pound of live meat produced and a variable bonus payment based on the grower's relative performance. However, some of the earlier broiler contracts used rank-order tournaments to compensate their growers. In our data set, growers that competed in the same tournament were ranked by performance from the smallest settlement cost (best performance) to the largest settlement cost, and this ranking was then divided into quartiles. The settlement cost was determined as the sum of two production input costs, that is, the number of chicks placed multiplied by 12 cents and the total feed intake (in kilocalories) multiplied by 6 cents, divided by the total live weight (in pounds) of birds produced. Growers received an incremental per pound compensation of 0.3 cents per pound of live weight as they moved to the next higher (lower cost per unit of output) quartile.

The data set includes production information for seventy-five contract growers that produced broilers from November 30, 1981 until December 17, 1985. For the period between November 1981 and June 1984 the minimum pay for growers ranked in the bottom quartile was 2.6 cents per pound, with the exception of late 1981 and early 1982 when the base payment was temporarily lowered and ranged from 1.98 cents to 2.45 cents per pound. The incremental pay for performance in higher quartiles remained 0.3 cents over the entire period through June 1984, when the contract form switched from the rank-order tournament to a cardinal tournament. Due to the infeasibility of figuring out which growers belong to which cardinal tournaments, this part of the data set (June 1984-December 1985) was not usable for the purposes of our article. The problem of exactly determining which growers belong to which tournament was present in the rank-order tournament part of the data set as well. However, this difficulty is considerably mitigated by the fact that the scheme uses quartiles; so it is only natural to believe that the number of participants has to be a multiple of four. Since, according to Knoeber and Thurman (1994), the tournaments were formed by putting together growers whose flocks were harvested within approximately ten-day periods, the obvious number of participants in each tournament turned out to be eight. (1)

In total, we have ninety-three tournaments and 744 observations. The variable settlement denotes the monetary value of inputs used (in cents) to grow a chick with the target weight. On average, the per chick settlement costs for the growers in the data is 20.94 cents, with a standard deviation of 0.71 and a range from 17.19 cents to 25.42 cents. (2) The variation in settlement costs is mainly caused by weather, fluctuations in quality of inputs supplied by the integrator (chicks and feed), and growers' idiosyncrasies.

Rank-Order Tournament with Private Information