A Theoretical and Empirical Comparison of Free Agent and Arbitration-Eligible Salaries Negotiated in Major League Baseball.

• Author: Miller, Phillip A.

Phillip A. Miller [*]

This paper presents a theoretical and empirical comparison of determination of negotiated salaries in baseball's free agent market to that in its final-offer arbitration (FOA) system. The theoretical bargaining model of each system is based on Nash (1950). It is argued that Farber's (1980) model of FOA is not fully applicable in explaining baseball's FOA process. The free agent market and the arbitration system each determine negotiated salaries that are dependent on the different disagreement outcomes of the negotiators in the respective systems. It is thus concluded theoretically that the two systems will determine salaries differently. The theoretical analysis also suggests that there may be selection bias present when one empirically analyzes only negotiated settlements. Using a straightforward regression model that controls for productivity, playing experience, and the potential selection bias, the empirical analysis substantiates the theory's results. A method is then developed to estimate the effect th at free agent salaries have on salaries for arbitration-eligible players. It is found that there is a significant positive relationship between them, but the systems do not determine equal salaries for comparable players.

1. Introduction

   Final-offer arbitration (FOA) is a dispute resolution system in which disputants give their final offers to a third party who then chooses one of the offers as the binding settlement. The most public example of FOA is that found in Major League Baseball.

   The labor market for major league baseball players is unique in that it is a three-tiered market. All players with fewer than six years of experience are subject to the reserve clause. However, 17% of two-year players and all players with at least three years of playing experience in the major leagues are eligible for salary arbitration. Players with six or more years of experience are eligible for free agency.

   As Vrooman (1996) has argued and others (e.g., Zimbalist 1992) have shown empirically, the free agent market, as structured, has given rise to player monopoly power. Zimbalist argues that this monopoly power may arise because each free agent may have unique abilities that the team that signs him needs (p. 93). Zimbalist argues that this, coupled with competitive pressures, may lead to additional risk taking by teams that results in free agents being paid above their marginal revenue product (p. 94).

   Conversely, the reserve clause has caused the labor market for players who are not arbitration eligible to be monopsonistic and, as Vrooman argued, allows teams to recoup their player development expenses. However, during the 1994-1995 players' strike, team owners proposed to allow players to move between teams after four years rather than six years in return for the removal of player rights to binding arbitration after three years. This proposal indicates that team owners believe that arbitration may raise player salaries such that teams in general are unable to recoup all their player development costs. This is most likely through the mechanism by which arbitrators make their decisions. In deciding a particular case, arbitrators are allowed to base their decisions on salaries of other players with comparable productivity to the particular player involved. This raises two interesting questions: (i) Is there a difference between the structures of negotiated salaries of free agents and arbitration eligibles? ( ii) What is the effect of the former on the latter?

   In economics, the literature on FOA is vast, as is that on Major League Baseball. This paper contributes to and complements both bodies of literature by providing a theoretical and empirical comparison of negotiated salaries determined in baseball's free agent system to those determined in its FOA system. To my knowledge, there is no research developing a formal model describing the bargaining behind free agency that also compares it to a formal bargaining model describing salaries negotiated in baseball's FOA system. The present paper does this.

   Moreover, it is argued that Farber's (1980) model of FOA is not fully applicable to explain baseball's arbitration system, and thus a more adequate model is described. In addition, the theoretical model of arbitration is used to explain how free agent salaries affect salaries negotiated within the arbitration system. Then, using a straightforward empirical model and readily available productivity and salary measures, the paper presents regression estimates of the relationship between player characteristics and the salaries of free agents and arbitration-eligible players and examines the effect the salaries of free agents have on those negotiated by arbitration eligibles.

   The paper is organized as follows. Section 2 presents the theoretical models. Section 3 describes the empirical models and methodology. Section 4 presents the variables used as regressors, the data, and the empirical results. Section 5 discusses and concludes.

2. The Theory

   This section presents theoretical models of bargaining that result in negotiated salaries in baseball's FOA system and in its free agent system. Note that I do not analyze the situations in which a particular case was decided by an arbitrator. We will return to this point later.

   Baseball's FOA system consists of two stages: a noncooperative initial stage of bargaining in which negotiators set final offers to be presented to an arbitrator in case a dispute ensues, and a cooperative second round of bargaining in which the negotiators bargain over the salary to be paid to the player (see Faurot and McAllister 1992; Miller 1998). If the negotiators do not arrive at a voluntary settlement in the second round, the parties go to arbitration. Even if they arrive at a negotiated salary, it is influenced by their final offers since these in part determine the disagreement outcome if a dispute occurs.

   There is no direct analogue to this initial noncooperative round in the free agent system. The bargaining in this system is essentially a one-stage cooperative process in which the player and the team bargain over the salary to be paid to the player. However, when a disagreement occurs in free agency between a particular player and team, the player may sign with another team or may leave the league, perhaps playing in another league (such as the minor leagues) or leaving baseball altogether. Since the disagreement outcome will affect negotiated salaries and because the disagreement outcomes are different, it is likely that the two systems will determine negotiated salaries differently.

   However, negotiated salaries in the two systems are interconnected. In deciding a particular case, the arbitrator can consider salaries of players with similar abilities and productivity to the player in question, including those of comparable free agents. Consequently, the disagreement outcome in FOA and, thus, salaries negotiated in the second stage of this system will be influenced by salaries negotiated for free agents. It is therefore important to formally analyze and compare negotiated salaries determined in the free agent system to those determined in the arbitration system.

   Bargaining and Salaries Negotiated in the Free Agent System

   As noted previously, the bargaining that occurs between teams and free agents is essentially cooperative. The bargaining model employed here is thus based on that of Nash (1950).

   For simplicity, consider a two-team league with teams 1 and 2. Let the free agent earn the team gross benefits of B. If the player receives a wage of W, the team receives a surplus of B -- w. Assume that each negotiator is risk averse [1] and has increasing preferences over the share of the benefits he receives. Let the preferences of the player and the two teams over shares of the pie be represented by, respectively, [U.sub.p] and [[U.sup.i].sub.t] (i = 1, 2), continuously differentiable, strictly increasing and concave von Neumann and Morgenstern utility functions. Note that for either team, [[U.sup.i].sub.t] is decreasing in w. Assume that the player and the team are utility maximizers and each negotiates in his own behalf. Assume that the player is negotiating with team 1.

   The Nash solution for free agents is characterized by

   [[w.sup.*].sub.FA] = [arg.sub.[w.sub.FA]] max [U.sub.p][[w.sub.FA] - [d.sub.p])([[U.sup.1].sub.t][B - [w.sub.FA]] - [[d.sup.1].sub.t]) (1)

   where [[w.sup.*].sub.FA] is the negotiated salary received by the free agent; [d.sub.p] and [[d.sup.1].sub.t] are the disagreement outcomes for the player and team 1 and the outcomes should the player not sign with this particular team, respectively.

   In free agency, the disagreement outcome for the player is the utility from not being signed by the team in question. This will include the utility of outside opportunities such as playing for another team or of leaving the league (perhaps signing a minor-league contract or playing in a foreign league). For the team, the disagreement outcome is the utility of not signing the player in question: the value of not having the player on the team. Essentially, it is the value to the team of signing another player to take the place of the unsigned player. We assume that the team's utility is not a function of having the other team signing the player in question.

   First consider the player's disagreement outcome, [d.sub.p]. If the player and team 1 do not reach an agreement, then the player can possibly sign with team 2 for [w.sub.2]. If he is unable to sign with team 2, then assume he will work outside the league for a salary of [[w.sup.p].sub.r]. The term [[w.sup.p].sub.r] can be interpreted as a reservation wage arising from playing in the minor leagues or in another independent league or by working outside of baseball. Consequently, [w.sub.2] [greater than] [[w.sup.p].sub.r].

   When the player is negotiating with team 1, he is not precluded from informally negotiating...