[Risk aversion functions extracted from observed stock and option prices can be negative, as shown by Aït-Sahalia and Lo (2000), Journal of Econometrics 94: 9-51; and Jackwerth (2000), The Review of Financial Studies 13(2), 433-51. We rationalize this puzzle by a lack of conditioning on latent state variables. Once properly conditioned, risk aversion functions and pricing kernels are consistent with economic theory. To differentiate between the various theoretical explanations in terms of heterogeneity of beliefs or preferences, market sentiment, state-dependent utility, or regimes in fundamentals, we calibrate several consumption-based asset pricing models to match the empirical pricing kernel and risk aversion functions at different dates and over several years.]

This paper proposes a test for common conditionally heteroskedastic (CH) features in asset returns. Following Engle and Kozicki (1993), the common CH features property is expressed in terms of testable overidentifying moment restrictions. However, as we show, these moment conditions have a degenerate Jacobian matrix at the true parameter value and therefore the standard asymptotic results of Hansen (1982) do not apply. We show in this context that Hansen's (1982) J-test statistic is asymptotically distributed as the minimum of the limit of a certain random process with a markedly nonstandard distribution. If two assets are considered, this asymptotic distribution is a fifty–fifty mixture of χ2H−1 and χ2H, where H is the number of moment conditions, as opposed to a χ2H−1. With more than two assets, this distribution lies between the χ2H−p and χ2H (p denotes the number of parameters). These results show that ignoring the lack of first-order identification of the moment condition model leads to oversized tests with a possibly increasing overrejection rate with the number of assets. A Monte Carlo study illustrates these findings.

Causality in Granger's sense is defined in terms of predictibility one period ahead. The notion of causality is generalized by considering causality at any given horizon 1

In this paper, we introduce the extended method of moments (XMM) estimator. This estimator accommodates a more general set of moment restrictions than the standard generalized method of moments (GMM) estimator. More specifically, the XMM differs from the GMM in that it can handle not only uniform conditional moment restrictions (i.e., valid for any value of the conditioning variable), but also local conditional moment restrictions valid for a given fixed value of the conditioning variable. The local conditional moment restrictions are of special relevance in derivative pricing to reconstruct the pricing operator on a given day by using the information in a few cross sections of observed traded derivative prices and a time series of underlying asset returns. The estimated derivative prices are consistent for a large time series dimension, but a fixed number of cross sectionally observed derivative prices. The asymptotic properties of the XMM estimator are nonstandard, since the combination of uniform and local conditional moment restrictions induces different rates of convergence (parametric and nonparametric) for the parameters.

Risk aversion functions extracted from observed stock and option prices can be negative, as shown by Aït-Sahalia and Lo (2000), Journal of Econometrics 94: 9–51; and Jackwerth (2000), The Review of Financial Studies 13(2), 433–51. We rationalize this puzzle by a lack of conditioning on latent state variables. Once properly conditioned, risk aversion functions and pricing kernels are consistent with economic theory. To differentiate between the various theoretical explanations in terms of heterogeneity of beliefs or preferences, market sentiment, state-dependent utility, or regimes in fundamentals, we calibrate several consumption-based asset pricing models to match the empirical pricing kernel and risk aversion functions at different dates and over several years.