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Income Effects and Indeterminacy in a Calibrated One-Sector Growth Model

Mar 2007
Working Paper
By  Nir Jaimovich

This paper analyzes how the indeterminacy of competitive equilibrium in one-sector growth models depends on the magnitude of the households' income effect on the demand for leisure. The paper first establishes that the presence of income effect is necessary for the existence of an indeterminate equilibrium. Because I am further interested in quantitatively characterizing regions of uniqueness and regions of indeterminacy of equilibria as a function of this income effect, I need a utility function that is capable of inducing varying degrees of such effects. The most widely used utility functions in the business cycle literature—King, Plosser, and Rebelo (1988) (KPR) and Greenwood, Hercowitz, and Huffman (1988) (GHH)—are not suitable for this task, because they induce two polar cases of constant income effect. Therefore, I incorporate into the analysis the Jaimovich and Rebelo (2006) preferences that nest the KPR and GHH utility functions and span the entire range of income effect that exists between the two. Having identified these regions of indeterminacy, I find a lower and an upper bound for the magnitude of income effect that leads to indeterminacy. Moreover, by allowing for variation in the degree of income effect, I find that indeterminacy can occur for levels of aggregate-returns-to-scale that are well within recent empirical estimates. Finally, for these regions of indeterminacy, I simulate the model driven solely by sunspot shocks. I find that the second-moment properties of this model are generally consistent with the U.S. data at the business cycle frequency.