ESTIMATION OF CONSUMER DEMAND SYSTEMS WITH BINDING NON-NEGATIVITY CONSTRAINTS* T.J. WALES and A.D. WOODLAND

Although the economic and statistical theory underlying the estimation of systems of demand functions is well developed, very little attention has been paid to the problems which arise when the sample contains a significant proportion of observations in which expenditure on one or more goods is zero. For such a sample the econometric model should allow for zero expenditures to occur with positive probability. However, the econometric model used in most studies assumes that expenditures (or shares) follow a joint normal distribution and this does not allow for a positive probability of zero expenditures.’ Standard estimation methods for this model, such as Zellner’s two-stage estimator for seemingly unrelated regressions and the maximum likelihood estimator, do not take special account of zero expenditures, and consequently yield inconsistent estimates of the parameters. Indeed even if every observation containing zero expenditures on one or more goods was excluded for purposes of estimation, these standard estimators would be biased and inconsistent.’ Moreover, excluding these observations might significantly reduce the sample size. Regardless of whether or not the complete sample is used, the bias and inconsistency occur because the random disturbances have expectations which are not zero and which depend upon the exogenous variables.