Aggregation with Log-Linear Models

Abstract

When economic theory suggests a log-linear specification for individual agents, e.g., CobbDouglas production, it is common to estimate the same log-linear model with aggregate data, invoking a representative agent assumption and thereby assuming away aggregation errors. This paper gives necessary and sufficient restrictions on the distribution of agents in an economy for log-linear agent models to aggregate into log-linear macro models, and discusses the aggregation bias resulting from violation of these restrictions. Theorems, tests, economic rationales, and empirical results are given. Included are connections to random walks and to cointegration. Analogous results for log-level models are derived.