Title: GMM estimation of structural vector autoregressions
Authors: Markku Lanne - University of Helsinki (Finland) [presenting]
Jani Luoto - University of Helsinki (Finland)
Abstract: A structural vector autoregressive (SVAR) model with an independent non-Gaussian error vector is known to be locally identified without any further restrictions. However, its estimation by the method of maximum likelihood entertained in the previous literature requires the specification of a particular non-Gaussian error distribution. Moreover, for statistical inference, additional restrictions are needed to ensure global identification. We propose a generalized method of moments (GMM) estimator for the SVAR model that avoids explicit distributional assumptions by making use of independence and non-Gaussian features of the structural shocks. Independence implies no contemporaneous correlation and no lead-lag relations between the components of the error vector, while non-Gaussianity is captured by moment conditions related to their co-kurtosis. When the moment conditions only involve lead-lag relations in one direction, or co-kurtosis is defined using skewness terms, identification up to the signs of the structural shocks is achieved. Commonly used moment selection criteria are applicable in our setup, and tests of over-identifying restrictions can be used to assess the adequacy of identification. According to simulation results, two-step GMM estimation works well even in small samples, and is robust with respect to the moments selected. An empirical application to postwar U.S. macroeconomic data illustrates the methods.