Testing the consumption-based CAPM using the stochastic discount factor^*

Abstract

This article investigates the problem of optimal intertemporal consumption in the CCAPM setup from a new empirical perspective. The econometric analysis is based on use of the equality between the stochastic discount factor (SDF) and the marginal rate of intertemporal substitution of consumption, which in the CCAPM is equivalent to the Euler equation resulting from the intertemporal optimization problem of the representative individual. We start from an asset pricing equation to find the estimators of the SDF, without the need to make a parametric assumption about preferences, and then estimate the parameters of the consumption models. In our empirical exercise, the dataset covers income, aggregate consumption and return on financial assets in the quarterly period from 1996:1 to 2016:4. We also consider the existence of a portion of rule-of-thumb consumers and the utility functions CRRA and habit formation in consumer preferences. The empirical results suggest that the preferences that exhibit the formation of consumption habits combined with the stochastic discount factor originating from the hypotheses of Brownian motion are those that most closely correspond to the hypotheses related to the behavior of aggregate consumption.