Cross-Sectional Aggregation of Nonlinear Dynamic Models and Aggregate Consumption Dynamics

This paper considers the cross-sectional aggregation of nonlinear decision rules derived from intertemporal optimization problems under uncertainty, examining in particular (i) the role of aggregation across decision rules of heterogeneous decision makers as a source of variation and persistence in macroeconomic variables, and (ii) what may be learned about individual decision rules from observations on macroeconomic variables alone. A two-step methodology to deriving the macroeconomic model is proposed. In the first step, perturbation techniques are used to derive the micro decision rules from individual decision makers' intertemporal optimization problems. In the second step, the macroeconomic model is derived as the optimal forecast of the macroeconomic variables of interest given the micro decision rules as well as the econometrician's loss function and information set. The paper's proposed methodology and its main theoretical results are illustrated by examining whether some key properties of aggregate U.S. consumption data can be explained using a life-cycle model of consumption under uncertainty where individual consumers display heterogeneous, non-time separable preferences and face differential labor income dynamics.