Primal-Dual Estimation of a Linear Expenditure Demand System

Efficient estimates require the utilization of all the available theoretical and statistical information. This fact suggests that econometric models based on an explicit optimization theory might achieve more efficient estimates when all the primal and dual relations are used for a joint estimation of the model’s parameters. We present a discussion of this idea using a Linear Expenditure System (LES) of consumer demand. We assume that the risk-neutral household chooses its consumption plan on the basis of expected information. Some time after that decision, the econometrician attempts to measure quantities and prices and in so doing commits measurement errors. Hence, the econometric model is an errors-in-variables nonlinear system of equations for which there is no known consistent estimator. We propose an easy-to-implement estimator and analyze its empirical properties by a Monte Carlo simulation that shows a relatively small bias