Constrained Inefficiency and Optimal Taxation with Uninsurable Risks

Piero Gottardi, Atsushi Kajii, and Tomoyuki Nakajima
Working Paper 2014-25
November 2014

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When individuals' labor and capital income are subject to uninsurable idiosyncratic risks, should capital and labor be taxed, and if so, how? In a two-period general equilibrium model with production, we derive a decomposition formula of the welfare effects of these taxes into insurance and distribution effects. This method allows us to determine how the sign of the optimal taxes on capital and labor depends on the nature of the shocks, the degree of heterogeneity among consumers' income, and the way in which the tax revenue is used to provide lump sum transfers to consumers. When shocks affect primarily labor income and heterogeneity is small, the optimal tax on capital is positive. However, in other cases, a negative tax on capital improves welfare.

JEL classification: D52, H21


The authors thank Naoki Yoshihara for his valuable comments. Gottardi acknowledges financial support from the European University Institute. Kajii acknowledges financial support from the Inamori Foundation and Japan Society for the Promotion of Science Grant-in-Aid for Scientific Research No.(S)20223001. Nakajima acknowledges financial support from the Murata Science Foundation and the Japan Society for the Promotion of Science Grant-in-Aid for Scientific Research No. 23530218. Nakajima acknowledges the hospitality of the Federal Reserve Bank of Atlanta. The views expressed here are the authors' and not necessarily those of the Federal Reserve Bank of Atlanta or the Federal Reserve System. Any remaining errors are the authors' responsibility.
Please address questions regarding content to Piero Gottardi, Department of Economics, European University Institute, Villa San Paolo, Via della Piazzuola 43, 50133 Florence, Italy, 39-055-4685-919, piero.gottardi@eui.eu; Atsushi Kajii, Institute of Economic Research, Kyoto University, Yoshida-Honmachi, Sakyo-ku, Kyoto 606-8501, Japan, 81-75-753-7102, kajii@kier.kyoto-u.ac.jp; or Tomoyuki Nakajima, Kyoto University, the Canon Institute for Global Studies, and the Federal Reserve Bank of Atlanta, Research Department, 1000 Peachtree Street NE, Atlanta, GA 30309-4470, 404-498-8166, nakajima@kier.kyoto-u.ac.jp.