SIEPR Discussion paper No. 07-012
Income Effects and Indeterminacy
in a Calibrated One-Sector Growth Model
Nir Jaimovich
March 2007
This paper analyzes how the indeterminacy of competitive equilibrium in one-sector growth models depends on the magnitude of the households.income e¤ect 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 e¤ect 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.