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

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

If a nonlinear risk premium in a conditional asset pricing model is approximated with a linear function, as is commonly done in empirical research, the fitted model is misspecified. We use a generic reduced-form model economy with moderate risk premium nonlinearity to examine the size of the resulting misspecification-induced pricing errors. Pricing errors from moderate nonlinearity can be large, and a version of a test for nonlinearity based on risk premiums rather than pricing errors has reasonable power properties after properly controlling for the size of the test. We conclude by examining the importance of moderate nonlinearity in the context of the investment-specific technology shock models of Papanikolaou (2011) and Kogan and Papanikolaou (2014).

Do stocks bear a crash risk premium? We examine the empirical performance of the tail index measure from Kelly and Jiang (2014). We find that the tail index explains the cross-section of the discount rate component of returns, but not the cash-flow component. Moreover, in the time series the tail index is uncorrelated with theoretically motivated measures of aggregate uncertainty and systemic risk. In contrast, the tail index Granger causes and is Granger caused by the level of the term structure, and the slope of the term structure Granger causes tail risk. Received June 22, 2016; editorial decision December 23, 2017 by Editor Raman Uppal.

We examine the form, adoption rates, and economic rationale for various mutual fund investment restrictions. A sample of U.S. domestic equity funds from 1994 to 2000 reveals systematic patterns in investment constraints, consistent with an optimal contracting equilibrium in the fund industry. Restrictions are more common when (i) boards contain a higher proportion of inside directors, (ii) the portfolio manager is more experienced, (iii) the fund is managed by a team rather than an individual, and (iv) the fund does not belong to a large organizational complex. Low- and high-constraint funds produce similar risk-adjusted returns, also consistent with an optimal contracting equilibrium.

Aït‐Sahalia (1996) and Stanton (1997) use nonparametric estimators applied to short‐term interest rate data to conclude that the drift function contains important nonlinearities. We study the finite‐sample properties of their estimators by applying them to simulated sample paths of a square‐root diffusion. Although the drift function is linear, both estimators suggest nonlinearities of the type and magnitude reported in Aït‐Sahalia (1996) and Stanton (1997) . Combined with the results of a weighted least squares estimator, this evidence implies that nonlinearity of the short rate drift is not a robust stylized fact.