This article tests a simple consumption-based asset pricing model by a
pproximating the true asset pricing kernel using low-order orthonormal
polynomials based on the model's state variables. Approximated kernel
s based solely on next period's consumption growth are not rejected by
overall measures of model fit, but they produce statistically and eco
nomically large pricing errors. Approximated kernels based on two quar
ters of future consumption growth and technology shocks have substanti
ally improved overall fit. In particular, the best of these kernels ar
e capable of eliminating the small firm effect.