Testing Distributional Assumptions: A GMM Approach

• Activity Number: 48
• Type: Contributed
• Date/Time: Sunday, August 11, 2002 : 4:00 PM to 5:50 PM
• Sponsor: Business & Economics Statistics Section*
• Author(s): Nour Meddahi*+ and Christian Bontemps
• Affiliation(s): Montreal University and CENA-Toulouse
• Keywords: Distributional assumptions ; Parameter uncertainty ; GMM ; Stein-Hansen-Scheinkman equation ; Diffusions ; HAC

Abstract

In this paper, we consider testing marginal distributional assumptions. More precisely, we propose tests based on moment conditions implied by the marginal distribution assumption. This is a generalization of Bontemps and Meddahi (2002), who considered the Gaussian case. In this case, the moment condition is known as the Stein (1972) equation. In the general case, the moment conditions correspond to Hansen and Scheinkman (1995) moment conditions implied by the marginal distribution when one considers a diffusion process. Examples of distributions we consider are the Gamma, the Student, and the Beta ones in cross-sectional and time series cases. We treat in detail the parameter uncertainty problem when the variable of interest is not observable and depends on an estimated parameter. We provide moment conditions that are robust to the parameter uncertainty problem. We also consider the time series case which is unusual in this literature. We adopt a Heteroskedastic-Autocorrelation-Consistent approach to take into account the dependence. We apply our appraoch to the short term interest rates where the most popular model (CIR) implies that the marginal distribution is Gamma.