Simultaneous Equation Systems with Heteroskedasticity: Identification, Estimation, and Stock Price Elasticities

Abstract

We give a set of identifying conditions for simultaneous equation systems (SES) with heteroskedasticity in the framework of the Gaussian quasi maximum likelihood (QML) approach. Our conditions rely on the presence of heteroskedasticity rather than exclusion restrictions. The QML estimators are shown to be consistent and asymptotically normal. Monte Carlo experiments show that the QML estimators perform well in finite samples in comparison to the GMM estimators even when volatility is mildly misspecified. In the framework of SES, we analyse the relationships between traded stock prices and volumes. Based on a sample of the Russell 3000 stocks, our estimation results provide new evidence against the homogeneous valuations hypothesis.

Keywords: Endogeneity, Multivariate Structural Models, Quasi Maximum Likelihood, Asymptotics, Stock Prices and Volumes

JEL Classification: C30, G14, C50, G12