Using an Empirically Estimated Production Function for Major League Baseball to Examine Worker Disincentives Associated with Multi-Year Contracts

Article excerpt

1. Introduction

As an industry, Major League Baseball can serve as a wonderful laboratory for economists. Few other industries are as conscientious in collecting production data and reporting them openly: production statistics, both on the input side (individual player statistics) and on the output side (team won/loss record), are available every day in every American newspaper from April to October. Furthermore, in few other industries is labor productivity so easily quantifiable. The number of games a team (a firm) wins in a season (a production run) is its output; individual player (employee) performance may be captured in uniquely objective statistics, such as batting average, home runs, and strikeouts.

The first part of this paper empirically estimates the production function, in a Cobb-Douglas format, of Major League Baseball. Cross-sectional data from the most recent complete season, the 1993 season, are used in a multiple regression analysis. A reliable estimate of the production function could assist the management of a team in determining which players should be hired (i.e., traded for, drafted or signed as free agents). Just as a manufacturing firm could use its production function to determine how much of each input to employ, a baseball team could use the information to decide whether, for example, to seek pitching help over power-hitting talent. Additionally, knowledge of Major League Baseball's production function could serve as the basis, along with team revenue information, for a salary structure in a regulatory scheme. Perhaps most interesting is the fact that we can easily find the marginal products of individual players once we specify a production function. These marginal products will be the most accurate measures available of an employee's contribution to output.

The second part of this paper uses the production function found earlier to derive the marginal products of players who signed multiyear contracts between the 1992 and 1993 seasons in hopes of resolving the debate over the existence of performance disincentives in response to long-term contracts [3, 4, and 6]. In addition to confirming the beliefs of many baseball insiders, verification that, on average, players shirk after signing multi-year contracts could have implications far beyond baseball, supporting arguments for one-year contracts and annual salary negotiations, and arguments against job security associated with, for example, government employees and tenured professors.

2. An Empirical Estimate of Major League Baseball's Production Function

The Model

To find Major League Baseball's production function, a cross-sectional regression will be run using data from the 1993 season, the last full season completed.(1) The Cobb-Douglas functional form of the production function will be used, as it is simple yet widely accepted and it straightforwardly relates information about relative factor shares and returns to scale.

The output measure chosen for this study is straightforward. The product of a baseball team is victories. Other considerations play a part in determining team revenue, such as stadium amenities, player popularity, and geographic location, but the major element in long-run profitability of a team is success on the playing field [7]. Because each team plays the same number of games in a season, using the winning percentage of a team (i.e., victories divided by games played) is analogous to using the absolute number of wins.

The inputs used to create a victory fall into three main categories. A team needs to score runs to win games, so offense must be included in a production function for Major league Baseball. Conversely, a team wins games by restricting the number of runs scored by the opponent, so pitching and defense are the other two general input categories. Team speed is a related characteristic, as it affects both offense and defense.

Offense is comprised of two components: hitting and speed. …