Reconciling Jaimovich-Rebello Preferences, Habit in Consumption and Labor Supply

This note studies two forms of a utility function of consumption with habit and leisure that are (a) compatible with long-run balanced growth, (b) hit a steady state observed target for hours worked and (c) are consistent with micro-econometric evidence for the inter-temporal elasticity of substitution and the Frisch elasticity of labor supply. For Jaimovich-Rebello pref- erences our Theorems 1 and 2 highlight a constraint on the preference parameter needed to target the Frisch elasticity leading to a lower bound for the latter that cannot be reconciled empirically with external habit. Even with internal or no habit, the range of possible values of the Frisch elasticity lie outside empirical results unless we allow for a modest wealth e ect. In Theorem 3 we propose a generalized JR utility function that in conjunction with a labor wedge solves the problem.