Research Database

This paper develops the Parameterized Expectations Approach (PEA) for solving nonlinear dynamic stochastic models with rational expectations. The method can be applied to a variety of models, including models with strong nonlinearities, sub-optimal equilibria, and many continuous state variables. In this approach, the conditional expectations in the equilibrium conditions are approximated by finite-dimensional classes of functional forms. The approach is highly efficient computationally because it incorporates endogenous oversampling and Monte-Carlo integration, and it does not impost a discrete grid on the state variables or the stochastic shocks. We prove that PEA can approximate the correct solution with arbitrary accuracy on the ergodic set by increasing the size of the Monte-Carlo simulations and the dimensionality of the approximating family of functions.

Macroeconomics has made tremendous advances following the introduction of labor supply into the field. Today, it is widely acknowledged that labor supply matters for many key economic issues, particularly for business cycles and tax policy analysis. However, the extent to which labor supply matters for such questions depends on the aggregate labor supply elasticity—that is, the sensitivity of the time allocation between market and nonmarket activities. For several decades, the magnitude of the aggregate labor supply elasticity has been the subject of much debate. In this article, we review the debate and conclude that the elasticity of labor supply of the aggregate household is much higher than the elasticity of the identical households being aggregated. The aggregate household utility function differs from the individuals’ utility functions for the same reason that the aggregate production function differs from the individual firms’ production functions being aggregated. The differences in individual and aggregate supply elasticities are what aggregation theory predicts.