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Seminonparametric Estimation of Conditionally Constrained Heterogeneous Processes: Asset Pricing Applications

A. Ronald Gallant
George Tauchen

Abstract

The overidentifying restrictions of the intertemporal capital asset pricing model are usually rejected when tested using data on consumption growth and asset returns, particularly when additively separable, constant relative risk utility is attributed to the representative agent. This article investigates the extent to which specification error can explain these rejections. The empirical strategy is limited information maximum likelihood in conjunction with seminonparametric (expanding parameter space) representations for both the law of motion and utility. We find that consumption growth and asset returns display conditional heterogeneity, but this fact does not account for rejection of the overidentifying restrictions as might be anticipated from the work of Hansen, Singleton, and others using generalized method of moments methods. We also find that expansion of the parameter space in the direction of nonseparable utility causes the overidentifying restrictions to be accepted. Our estimation strategy provides information on the manner in which the restrictions distort the law of motion. In particular, imposition of additively separable, constant relative risk aversion utility causes the conditional variance of consumption growth to be overpredicted, the conditional covariance of asset returns with consumption growth to be overpredicted, and an equity premium. Imposition of nonseparable seminonparametric utility causes distortion in these same directions, though the distortions are much smaller which is consistent with the outcomes of the tests of the restrictions.