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We use Bayesian model averaging to analyze the sample evidence on return predictability in the presence of model uncertainty. The analysis reveals in-sample and out-of-sample predictability, and shows that the out-of-sample performance of the Bayesian approach is superior to that of model selection criteria. We find that term and market premia are robust predictors. Moreover, small-cap value stocks appear more predictable than large-cap growth stocks. We also investigate the implications of model uncertainty from investment management perspectives. We show that model uncertainty is more important than estimation risk, and investors who discard model uncertainty face large utility losses.

We develop a term structure model where the short interest rate and the market price of risks are subject to discrete regime shifts. Empirical evidence from efficient method of moments estimation provides considerable support for the regime shifts model. Standard models, which include affine specifications with up to three factors, are sharply rejected in the data. Our diagnostics show that only the regime shifts model can account for the well-documented violations of the expectations hypothesis, the observed conditional volatility, and the conditional correlation across yields. We find that regimes are intimately related to business cycles. MANY PAPERS DOCUMENT THAT THE UNIVARIATE short interest rate process can be reasonably well modeled in the time series as a regime switching process ~see Hamilton ~1988!, Garcia and Perron ~1996!!. In addition to this statistical evidence, there are economic reasons as well to believe that regime shifts are important to understanding the behavior of the entire yield curve. For example, business cycle expansion and contraction “regimes ” potentially

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This paper investigates nonlinear pricing kernels in which the risk factor is endogenously determined and preferences restrict the definition of the pricing kernel. These kernels potentially generate the empirical performance of nonlinear and multifactor models, while maintaining empirical power and avoiding ad hoc specifications of factors or functional form. Our test results indicate that preferencerestricted nonlinear pricing kernels are both admissible for the cross section of returns and are able to significantly improve upon linear single- and multifactor kernels. Further, the nonlinearities in the pricing kernel drive out the importance of the factors in the linear multi-factor model. A PRINCIPAL IMPLICATION OF THE Capital Asset Pricing Model ~CAPM! is that the pricing kernel is linear in a single factor, the portfolio of aggregate wealth. Numerous studies over the past two decades have documented violations of this restriction. 1 In response, researchers have examined the performance of alternative models of asset prices. These models have generally fallen into two classes: ~1! multifactor models such as Ross ’ APT or Merton’s ICAPM, in which factors in addition to the market return determine asset prices; or ~2! nonparametric models, such as Bansal et al. ~1993!, Bansal and Viswanathan ~1993!, and Chapman ~1997!, in which the pricing kernel is not

Often researchers find parametric models restrictive and sensitive to deviations from the parametric specifications; semi-nonparametric models are more flexible and robust, but lead to other complications such as introducing infinite dimensional parameter spaces that may not be compact. The method of sieves provides one way to tackle such complexities by optimizing an empirical criterion function over a sequence of approximating parameter spaces, called sieves, which are significantly less complex than the original parameter space. With different choices of criteria and sieves, the method of sieves is very flexible in estimating complicated econometric models. For example, it can simultaneously estimate the parametric and nonparametric components in semi-nonparametric models with or without constraints. It can easily incorporate prior information, often derived from economic theory, such as monotonicity, convexity, additivity, multiplicity, exclusion and non-negativity. This chapter describes estimation of semi-nonparametric econometric models via the method of sieves. We present some general results on the large sample properties of the sieve estimates, including consistency of the sieve extremum estimates, convergence rates of the sieve M-estimates, pointwise normality of series estimates of regression functions, root-n asymptotic normality and efficiency of sieve estimates of smooth functionals of infinite dimensional parameters. Examples are used to illustrate the general results.

This paper investigates the empirical characteristics of investor risk aversion over equity return states by estimating a time-varying pricing kernel, which we call the empirical pricing kernel (EPK). We estimate the EPK on a monthly basis from 1991 to 1995, using S&P 500 index option data and a stochastic volatility model for the S&P 500 return process. We find that the EPK exhibits countercyclical risk aversion over S&P 500 return states. We also find that hedging performance is significantly improved when we use hedge ratios based the EPK rather than a time-invariant pricing kernel.

In parametric models a sufficient condition for local identification is that the vector of momentconditionsisdifferentiable at the true parameter with full rank derivative matrix. We show that additional conditions are often needed in nonlinear, nonparametric models to avoid nonlinearities overwhelming linear effects. We give restrictions on a neighborhood of the true valuethataresufficient for local identification. We apply these results to obtain new, primitive identification conditions in several important models, including nonseparable quantile instrumental variable (IV) models, single-index IV models, and semiparametric consumption-based asset pricing models. JEL Classification: C12, C13, C23

In this paper we study the asset pricing implications of a parsimonious two-agent macroeconomic model with two key features: limited participation in the stock market and heterogeneity in the elasticity of intertemporal substitution. The parameter values for the model are taken from the business cycle literature and are not calibrated to match any financial statistic. Yet, with a risk aversion of two, the model is able to explain a large number of asset pricing phenomena including all the facts matched by the external habit model of Campbell and Cochrane (1999). Examples in this list include a high equity premium and a low risk-free rate; a counter-cyclical risk premium, volatility and Sharpe ratio; predictable stock returns with coefficients and R2 values of long-horizon regressions matching their empirical counterparts, among others. In addition the model generates a risk-free rate with low volatility (5.7 percent annually) and with high persistence. We also show that the similarity of our results to those from an external habit model is not a coincidence: the model has a reduced form representation which is remarkably similar to Campbell and Cochrane’s framework for asset pricing. However,themacroeconomic implications of the two models are quite different, favoring the limited participation model. Moreover, we show that policy analysis yields dramatically different conclusions in each framework.