Parental Reputation and School Performance

Chao Fu, University of Wisconsin-Madison
Juan Pantano, Washington University in St. Louis

It is possible to model parent-child interactions with the tools of game theory. However, empirical work that takes these game-theoretic models to the data is in its infancy. We formulate and estimate a reputation game between a parent, who threatens punishment upon bad school performance, and her children who choose costly study effort to reduce their punishment chances. Parents have incentives to build reputations of severity and while children don't know parental type, they try to infer it by observing the history of play within the family. For given structural parameters, the game between a parent and her children is solved by backwards recursion. The solution to the game is embedded in an estimation routine that leverages longitudinal microdata from U.S. households, featuring histories of grades and punishments for each sibling. We use the estimated model to investigate the role parenting plays in determining the school performance of children.