CREATES Research Paper 2008-46 Semiparametric Inference in a GARCH-in-Mean Model

A new semiparametric estimator for an empirical asset pricing model with general nonparametric risk-return tradeoff and a GARCH process for the underlying volatility is introduced. The estimator does not rely on any initial parametric estimator of the conditional mean function, and this feature facilitates the derivation of asymptotic theory under possible nonlinearity of unspecified form of the risk-return tradeoff. Besides the nonlinear GARCH-in-mean effect, our specification accommodates exogenous regressors that are typically used as conditioning variables entering linearly in the mean equation, such as the dividend yield. Using the profile likelihood approach, we show that our estimator under stated conditions is consistent, asymptotically normal, and efficient, i.e. it achieves the semiparametric lower bound. A sampling experiment provides evidence on finite sample properties as well as comparisons with the fully We are grateful to Valentina Corradi, Enno Mammen, Joon Y. Park and participants at the 2008 SETA Conference in Seoul and at the 2008 European Meeting of the Econometric Society in Milan for very useful comments. We also thank the Center for Research in Econometric Analysis of TimE Series (CREATES) funded by the Danish National Research Foundation, the Danish Social Science Research Council, and the MSU Intramural Research Grants Program for financial and research support. Address: School of Economics and Management and CREATES, University of Aarhus, Building 1322, DK-8000 Aarhus C. Phone: +45 8942 1547. E-mail: [email protected]. Address: School of Economics and Management and CREATES, University of Aarhus, Building 1322, DK-8000 Aarhus C. E-mail: [email protected]. Address: Department of Economics, Michigan State University, 101 Marshall-Adams Hall, East Lansing, MI 48824-1038, USA. E-mail: [email protected].