We use a Barro-Becker model of endogenous fertility, in which parents are subject to idiosyncratic shocks that are private information (either to labor productivity or taste for leisure), to study the efficient degree of consumption inequality in the long run. The planner uses the trade-off between family size and future consumption and leisure, to provide incentives for workers to reveal their shocks. We show that in this environment, the optimal dynamic contract no longer features immiseration in consumption. We also discuss the implications of the model on the long run properties of family size in the optimal contract and show that the long run trend in dynasty size can be either positive or negative depending on parameters.
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We are indebted to Alice Schoonbroodt for all of her helpful comments and suggestions at various stages of this project. We would also like to thank Laurence Ales, V.V. Chari, Bob Lucas, Mike Golosov, Greg Kaplan, Chris Phelan, Richard Rogerson, Maxim Troshkin, Aleh Tsyvinski, Ariel Zetlin-Jones and seminar participants at ASU, Columbia, Carnegie Mellon, Iowa, Ohio State, St. Louis Fed, Texas Austin, Western Ontario, Wharton, Yale, 2009 SED summer meeting, 2009 Minnesota Macro Workshop and 2010 Cowles Summer Conference for comments. We would like to also thank two anonymous referees and Christian Hellwig (the editor) for helpful comments and suggestions. Larry E. Jones thanks NSF for financial support, NSF Grant No. SES-0962432 .
- Endogenous fertility
- Long run inequality
- Private information
- Risk sharing