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Efficient insurance contracts in environments with various frictions have been characterized in the literature (see, for example, Thomas and Worrall (1988)). In some environments, the first-order approach suggested by Rogerson (1985) is useful in their characterization. This paper shows that the first-order approach is not valid in an environment with one-sided no commitment and hidden savings under the assumption that the utility function is CRRA or CARA and the return on savings is equal to the inverse of the agent's discount factor. The result complements the numerical result by Ábrahám and Laczó (2014), which suggests that the first-order approach is valid when the return on savings is low.

I would like to thank Neil Wallace for his continuous support and advice. I also thank Edward Green and two anonymous referees for helpful comments. This article was a chapter of my dissertation at Pennsylvania State University. All errors are my own. Citation: Wataru Nozawa,(2016)''Failure of the first-order approach in an insurance problem with no commitment and hidden savings'', Economics Bulletin, Volume 36, Issue 4, pages 2422-2429