Dynamic Matching and Evolving Reputations

Abstract

This paper introduces a general model of matching that includes evolving public Bayesian reputations and stochastic production. Despite productive complementarity, assortative matching robustly fails for high discount factors, unlike in (Becker 1973). This failure holds around the highest (lowest) reputation agents for 'high skill' ('low skill') technologies.We find that matches of likes eventually dissolve. In another life-cycle finding, young workers are paid less than their marginal product, and old workers more. Also, wages rise with tenure but need not reflect marginal products: Information rents produce non-monotone and discontinuous wage profiles.

Sorting through Search and Matching Models in Economics

“…their continuation payoffs in future matches. Anderson and Smith (2010) explore the trade-off between these two goals. They show that despite production complementarities, PAM generally fails at high discount factors due to the importance of information.…”

“…To pin down the expected continuation payoff for an agent with current type x , Anderson and Smith (2010) notice that if he matches with y , then after observing output q i in the first period x , he updates his belief that his type is high to z i (x, y) = p i (1, y)x/ p i (x, y) .…”

“…We illustrate this finding in their simpler motivational two-period partnership model. Anderson and Smith (2010) assume a continuum of agents of two underlying true types, high or low, i.e., θ ∈ { θ ℓ , θ h } . No one knows his own type, but merely the probability x ∈ [0, 1] of a high true type-called his reputation.…”

Job Matching Within and Across Firms

“…My paper is also related to the learning models of MacDonald (1982), Felli and Harris (2004), Eeckhout and Xi (2009), and Anderson and Smith (2010). MacDonald (1982) analyzes equilibrium assignment in a competitive economy with task complementarities in which workers' abilities are unobserved, but assumes that the jobs of all firms are equally informative about ability and that ability is purely general.…”

“…They focus on the case in which ability is firm specific and do not characterize equilibrium assignment. Eeckhout and Xi (2009) and Anderson and Smith (2010) examine matching in the labor market with two-sided heterogeneity and learning. Whereas Anderson and Smith (2010) focus on limiting conditions under which assortative matching may or may not arise, Eeckhout and Xi (2009) characterize equilibrium assignment when firms consists of two jobs and ability is purely general across jobs and firms.…”