Income effects and indeterminacy in a calibrated one-sector growth model

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 …rst establishes that the presence of income e¤ect 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 e¤ect, I need a utility function that is capable of inducing varying degrees of such e¤ects. The most widely used utility functions in the business cycle literature –King, Plosser, and Rebelo (1988) (KPR) and Greenwood, Hercowitz, and Hu¤man (1988) (GHH) –are not suitable for this task, because they induce two polar cases of constant income e¤ect. 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 identi…ed these regions of indeterminacy, I …nd a lower and an upper bound for the magnitude of income e¤ect that leads to indeterminacy. Moreover, by allowing for variation in the degree of income e¤ect, I …nd 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 …nd that the second-moment properties of this model are generally consistent with the U.S. data at the business cycle frequency.