Truncated Hedonic Equilibrium

Workers and firms in a bilateral matching market choose wages and human capital investments then match assortatively. This paper studies Bayesian equilibria of finite matching games and shows that as the matching market becomes large, Bayesian equilibria can be approximated by a truncated hedonic equilibrium in the continuous matching market. We use the truncated hedonic equilibrium concept to study these limits. Under some conditions the worst types of workers and firms pool their investments at a level that exceeds the competitive level, while higher types choose bilaterally efficient wages and investments providing a potential explanation for the persistent skewed appearance of wage distributions. In these cases, we show that the lowest workers over invest in human capital. In particular, this means that under these conditions, Bayesian Nash equilibria of large finite investment matching games do not approximate simple hedonic equilibria, though they do approximate truncated hedonic equilibria. The workhorse model for understanding endogenous characteristics in the labour market is something called the hedonic pricing equilibrium. The paper that formalized this idea was Rosen (1974). In his paper, the characteristics of firms are fixed exogenously, but their wages vary to compensate workers for different levels of education. In a recent paper, Peters and Siow (2002) showed how hedonic pricing equilibria could be used to explain the characteristics of firms as well even if wages aren’t flexible, and even if both sides characteristics are endogenous. A very general existence theorem for hedonic equilibria with endogenous characteristics on both sides of the market, and with quasi linear utility is given by Ekeland (2003). The question this paper addresses is whether hedonic equilibrium can be supported as the limit of a sequence of Bayesian equilibria in Date: March 3, 2009. For a formal definition of hedonic equilibrium in the absence of quasi-linearity, see Peters (2004a). Similar competitive arguments have been proposed by Cole, Mailath, and Postlewaite (2001b), and Han (2006).