Demand Systems with Heteroscedastic Disturbances

by Serletis, Apostolos and Xu, Libo

We address the estimation of singular demand systems with heteroscedastic disturbances. We relax the homoscedasticity assumption and instead assume that the covariance matrix of the errors of the demand system is time-varying. In doing so, we consider the VECH and BEKK parameterizations of the variance model. We analytically prove the invariance of the maximum likelihood estimator with respect to the choice of the good deleted from a singular demand system, and also prove a number of important practical results regarding how to recover the mean and variance equation parameters (and their standard errors) of the full demand system from those of any subsystem obtained by deleting an arbitrary good.

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