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Nonlinear Income Variance Profile and Consumption Inequality over the Life Cycle*1

February 2006
Naohito Abe*2
Tomoaki Yamada*3


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  • *1 We are grateful to the Research and Statistics Department, Bank of Japan, for providing us with a very stimulating research environment. We have benefited from discussions with Hideo Hayakawa, Munehisa Kasuya, Miki Kohara, Isao Ohashi, Etsuro Shioji, Daiji Kawaguchi, Makoto Saito, and seminar participants at the Bank of Japan, Nagoya City University, and Hitotsubashi University. We are particularly thankful to Hiroshi Matsui for his assistance in obtaining the microdata. We also acknowledge financial support from the Ministry of Science and Education, the Japan Economic Research Foundation, COE-RES, and COE-Hi-Stat. We would like to thank the excellent research assistance of Yuko Sagara.
  • *2 Corresponding Author. The Institute of Economic Research, Hitotsubashi University.
  • *3 Graduate School of Economics, Hitotsubashi University.


In an economy with a seniority wage system, elderly workers are subject to greater income risks when they lose their jobs than young workers are. This paper investigates: (1) whether we can observe the age dependence of idiosyncratic income risks; and (2) the importance of age dependecne for the evolution of inequalities in consumption using Japanese micro data. Our estimation of the income process demonstrates a strong age dependence of income risks; at the age of 48, the variance of permanent income shocks begins to increase, which creates a nonlinear age?variance profile of income. This paper also uses structural estimation of a precautionary savings life cycle model to demonstrate that the nonlinearity in the income process is crucial for understanding the evolution of the consumption inequalities over age.

JEL Classification Number: D12, D31, D52, E21

Key words:
Income risk, buffer stock savings, consumption inequality, method of simulated moments.