Heteroskedasticity-Consistent Estimation of the Variance-Covariance Matrix for the Almost Ideal Demand System

In this note I demonstrate the previously overlooked fact that if the AIDS aggregate demand model is constructed as the aggregation of individual consumer demands, then the error structure for any individual equation is necessarily heteroskedastic unless the distribution of income is constant across aggregates. Maximum likelihood estimation which ignores this heteroskedasticity yields inconsistent estimates of the variance-covariance matrix and renders likelihood ratio tests of the restrictions of consumer demand theory inappropriate. A heteroskedasticity-consistent estimator of the variance-covariance matrix is proposed by adopting the technique of White (1980) to the case at hand.