Indeterminate Balanced Growth under Habit Persistence and Fiscal Policies

Abstract

This paper studies a dynamic general equilibrium model with habit persistence in preferences and fiscal policies of taxation and expenditures. Preference takes a subtractive form of habits (the marginal rate of substitution between the agent's own consumption and habit stocks is constant), and technology is linear in aggregate capital (the economy grows without a limit in the long run). We find a continuum of competitive equilibrium paths in conjunction with a unique balanced growth path in the growing economy, in which habits represent both envy/jealousy and altruism/admiration. In addition, in the social optimum under second-best fiscal policies, we show the existence of indeterminacy in transitional allocations along with a unique balanced growth path. Thus, we find that the introduction of habits influences the patterns of the transitional paths but has no impact on the balanced growth path in either competitive or social optimum allocations. The second-best fiscal policy, therefore, restores the socially optimal balanced growth rate but fails to select the unique transitional path among multiple competitive equilibrium paths in the imperfectly competitive economy.