When a major league baseball player's contract has expired, he can either sign a new contract with his current team or become a free agent and sign a contract to play with a different team
If adverse selection is a problem in the market for major league ball players, who do you think are more likely to be injured the season after they sign a new contract: players who re-sign with their current team or players who sign with a new team? Explain.
A player's current team may know more about a player's health and the chances that he will be injured in the future than a new team would. That is to say, a player's health is (at least in part) private information. Teams will therefore want to re-sign healthy players but allow unhealthy players to sign with other teams. Unhealthy players are thus like lemons in used car markets. If this analogy is correct then we should expect players who re-sign with their current team to be less likely to be injured the year after they sign a new contract than players who sign with a new team. Kenneth Lehn found a fair amount of evidence to support this argument. He also found that as teams gained more experience with the market for free agents they learned that they would often be buying a lemon when they signed a free agent.
See Kenneth Lehn, "Information Asymmetries in Baseball's Free Agent Market," Economic Inquiry, January 1984, pp 37–44
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