Working Paper

The simultaneous equations model with generalized autoregressive conditional heteroskedasticity: the SEM-GRACH model

Abstract: In this paper I generalize the standard simultaneous equations model by allowing the innovations of the structural equations to exhibit Generalized Autoregressive Conditional Heteroskedasticity (GARCH). I refer to this new specification as the SEM-GARCH model. I develop two estimation strategies: LIM-GARCH, a limited information estimator, and FIM-GARCH, a full information estimator. I show that these estimators are consistent and asymptotically normal. Following Weiss (1986) I show that when the errors in the SEM-GARCH process are incorrectly assumed to be conditionally normal the likelihood function is still maximized at the true parameters, given certain regularity conditions. This results in the asymptotic variance-covariance matrix being more complex than the usual inverse of the information matrix.

Keywords: Economics; Vector autoregression;

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Bibliographic Information

Provider: Board of Governors of the Federal Reserve System (U.S.)

Part of Series: International Finance Discussion Papers

Publication Date: 1988

Number: 322