Rational Factor Analysis

Abstract

In econometrics, phenomenologically modelling asset returns by an ad hoc low order polynomial in macroeconomic quantities is referred to as factor analysis. Here, we present a rational factor analysis for a weakly heterogeneous Lucas tree economy. The method is generally applicable.

We show that the equilibrium state price density process for a weakly heterogeneous economy is a 'globally' unique and smooth function of all relevant parameters. We explicitly compute the second order Taylor approximation and write it as a polynomial in macroeconomic quantities; e.g., aggregate consumption, cross-sectional variance of wealth, risk aversion and patience. The second order Taylor polynomial is an intrinsic and rigorous factor analysis of the economy.

The moral is: perturbation theory reveals the form of factor analysis one should look for in an econometric analysis.

Keywords: factor analysis, heterogeneity, perturbation theory, general equilibrium, existence, uniqueness

JEL Classification: C62, D58, G12, C78