David T. Frazier
Department of Economics
Maximization by Parts in Semiparametric Models (Slides for an earlier version of the paper),
In this paper I propose and examine a new algorithm for solving score equations within semiparametric Maximum Likelihood estimation. This new algorithm is particularly useful in situations where solving the score equations using the Newton-Raphson algorithm is difficult or impossible. While the Newton-Raphson algorithm uses the entire Hessian matrix within estimation, which may be difficult to evaluate, this new algorithm only uses the portions that are easier to compute. Convergence and asymptotic properties of this iterative (fixed-point) algorithm are established under regularity conditions and an identification condition. Two simulation studies demonstrate this new estimation algorithm.
The Shape of the Risk Premium Across Multiple Assets
We investigate the relationship between the risk premium for a cross-section of assets (portfolios) and the assets conditional covariance with the market portfolio. We propose a new semiparametric model where the conditional variances and covariances for the assets are parametric, and the conditional mean is as an arbitrary function of the conditional covariances between the assets and the market portfolio. We use this model to analyze the shape of the risk premium across ten size, book-to-market, momentum and industry portfolios. For these portfolios the relationship between the conditional covariances and the risk premium is nonlinear and, in most cases, nonmonotonic.
Efficicent Sequential Extremum Estimators (with E. Renault)
We derive a unified strategy for consistent and efficient sequential extremum estimation in structural non-adaptive models. A comparison between existing iterative estimators and our sequential approach reveals that both methods have similar computational costs. However, unlike existing iterative estimators the sequential estimation strategy can deliver consistent estimators even if the identification conditions required by iterative estimators are not satisfied. Similar to existing iterative estimators, this sequential estimation strategy can alleviate potential singularity issues within estimation. Practical examples highlighting this sequential strategy are demonstrated within the confines of stochastic volatility models and affine term structure model with latent factors.
A Comparison of Several Popular Asymmetric GARCH-in-Mean Models
The statistical properties of four popular GARCH-in-mean (GARCH-M) models capable of capturing leverage effects are compared and analyzed: namely the EGARCH-M, APARCH-M, GJR-M and TGARCH-M models. Simulation studies compare the quasi-maximum likelihood (QML) parameter estimates for these models across two different specifications for the ``in-mean'' effect. We demonstrate that the sometimes puzzling results obtained from QML estimates of GARCH-M model parameters could be caused by two, non-exclusive, factors. One, the poor finite sample properties of QML estimates for GARCH-M model parameters of sample sizes often encountered in practice and two, the existence, or more specifically the non-existence of fourth moments for the innovation of GARCH-M models. In particular, for the GARCH-M models studied in this research I demonstrate that the fourth moments of the innovations do not exist for large portions of the parameter space. Empirical examples also demonstrate that the TARCH-M, GJR-M and APARCH-M models yield similar estimates while the estimates obtained from the EGARCH-M model differs substantially from other GARCH-M models.
Papers in Progress
Evidence for a Nonlinear Relationship Between Risk and Return in the ICAPM.
Is the Risk-Return Tradeoff Constant Across Assets?