## Seminonparametric Estimation of Conditionally Constrained
Heterogeneous Processes: Asset Pricing Applications

A. Ronald Gallant, George Tauchen

*Econometrica*, Vol. 57, No. 5. (Sep., 1989),
pp. 1091-1120.

### 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.