This paper solves a real business cycle model with heterogeneous agents and uninsurable income risk using perturbation methods. A second order accurate characterization of agent's optimal decision rules is given, which renders the implications of aggregation for macroeconomic dynamics transparent. The role of cross-sectional holdings of capital in determining equilibrium dynamics can be directly assessed. Analysis discloses that an individual's optimal saving decisions are almost linear in their own capital stock giving rise to permanent income consumption behavior. This provides an explanation for the approximate aggregation properties of this model documented by Krusell and Smith (1998): the distribution of capital does not affect aggregate dynamics. While the variance-covariance properties of endogenous variables are almost entirely determined by first order dynamics, the second order dynamics, which capture properties of the wealth distribution, are nonetheless important for an individual's mean consumption and saving decisions and therefore the mean equilibrium capital stock. Policy evaluation exercises therefore need to take account of these higher order terms.
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Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number
13260.
Length: Date of creation: Jul 2007 Date of revision: Handle: RePEc:nbr:nberwo:13260
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Find related papers by JEL classification: C6 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming D52 - Microeconomics - - General Equilibrium and Disequilibrium - - - Incomplete Markets E21 - Macroeconomics and Monetary Economics - - Macroeconomics: Consumption, Saving, Production, Employment, and Investment - - - Consumption; Saving; Wealth E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles
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