Invariance, price indices and estimation in almost ideal demand systems

Two issues are addressed in this paper. First, we explore the issue of price index invariance in the linearized Almost Ideal demand system. We establish that the Stone index, which lacks invariance, and the recently proposed invariant Laspeyres, Paasche and Tornqvist indices all generate biased and inconsistent estimators. Monte Carlo evidence shows that invariance does not necessarily lead to better estimates of price and income elasticities insofar as the Stone and Paasche indices are unambiguously inferior to the Laspeyres and Tornqvist indices, especially if prices are not strongly positively correlated. Second, we examine the merits of the widely used conditional ML estimator of the non-linear Almost Ideal system in which a prior value is chosen for the "subsistence" parameter. We find that the bias and trace mean square error increases induced by conditional estimation are modest. The choice between the linearized and the non-linear models favors the latter although in some cases linear methods are as good as non-linear.