The Econometric SocietyEdited by: Guido W. Imbens • Print ISSN: 0012-9682 • Online ISSN: 1468-0262
August 15, 2022
Econometrica: Jul, 2012, Volume 80, Issue 4
https://doi.org/10.3982/ECTA9042
p. 1505-1531
Debraj Ray, Arthur Robson
This paper studies endogenous risk‐taking by embedding a concern for status (relative consumption) into an otherwise conventional model of economic growth. We prove that if the intertemporal production function is strictly concave, an equilibrium must converge to a unique steady state in which there is recurrent endogenous risk‐taking. (The role played by concavity is clarified by considering a special case in which the production function is instead convex, in which there is no persistent risk‐taking.) The steady state is fully characterized. It displays features that are consistent with the stylized facts that individuals both insure downside risk and gamble over upside risk, and it generates similar patterns of risk‐taking and avoidance across environments with quite different overall wealth levels. Endogenous risk‐taking here is generally Pareto‐inefficient. A concern for status thus implies that persistent and inefficient risk‐taking hinders the attainment of full equality.
This online appendix contains the proofs of all the lemmas that do not appear in the printed appendix to the paper. It also contains the statements of all these lemmas and details of the intervening arguments in the proofs of the propositions. It also contains a proof of existence for a more general model that implies Proposition 3 (ii).
