David T. Frazier
Department of Economics
Maximization by Parts in Semiparametric Models (Slides from MEG 2013 conference),
In this paper we propose and examine a new algorithm for solving score equations within semiparametric Maximum Likelihood estimation. This new algorithm is particularly useful in situations where directly maximizing the log-likelihood function with respect to all occurrences of the parameter of interest is difficult or impossible. The proposed algorithm avoids direct optimization of the log-likelihood function by iteratively solving a sequence of much simpler estimation problems. Convergence of this iterative (fixed-point) algorithm is established under consistent and inconsistent starting values and an identification condition. Under additional regularity conditions we demonstrate that the estimators obtained upon convergence of this new algorithm are asymptotically equivalent to those obtained by Maximum Likelihood. This new estimation algorithm is applied to two examples: a semiparametric GARCH-in-mean model and a dynamic semiparametric model with latent variables. Simulation results demonstrate that this new algorithm provides estimators that are well behaved in finite samples and have better finite sample properties than some existing estimators.
Two-Stage Estimators Without Nuisance Parameters (with E. Renault)
We derive a unified strategy for consistent and efficient two-stage extremum estimation in non-adaptive models. A comparison between existing iterative estimators and our two-stage approach reveals that both methods have similar computational costs. However, unlike existing iterative estimators, the two-stage estimation strategy can deliver consistent estimators even if the identification conditions required by iterative estimators are not satisfied. Practical examples highlighting this two-stage estimation strategy are demonstrated within the confines of Gaussian copula models and the Merton credit risk model
The Shape of the Risk Premium Across Multiple Assets
We investigate the relationship between risk premium and conditional covariance with the market across a cross-section of asset returns using a new semiparametric GARCH-M model. This new model parameterizes the dynamics for the conditional covariances using a finite number of parameters but allows the conditional mean of expected returns to be an unknown function of the conditional covariances. We model the conditional mean using local-linear kernel methods. A backfitting algorithm is presented to estimate the conditional covariances and the conditional mean. Using this new model we analyze the shape of the risk premium across ten size, book-to-market, momentum and industry portfolios. Unlike existing studies that analyze the shape of the risk premium using nonparametric methods we find a linear relationship between risk premium and conditional covariance with the market across each portfolio.
Papers in Progress
Backfitting in Structural Economic Models with Nuisance Parameters.
Structural Credit Risk Models with Predictability.