Estimation of the Indirect Translog Demand System with Binding Non-Negativity Constraints

摘要

During the past few years, several authors have studied the problem of estimating systems of demand equations if a significant proportion of the observations in the sample contains zero expenditures on one or more goods. Wales and Woodland (1983) formulate a model based on the Kuhn-Tucker approach, which is consistent with utility maximizing behavior and allows for stochastic preferences. Ransom (1987) comments on the relationship between the Wales and Woodland model and the 'simultaneous equation' Tobit model of Amemiya (1974) for the special case of a quadratic utility function. The paper addresses the issue of internal consistency, i.e. the question whether there is a one-to-one correspondence between all possible realizations of the random variables. In an earlier paper (Van Soest and Kooreman (1986)), it was shown with a simple example in the three goods case, that internal consistency can be severely violated for certain values of parameters of the indirect translog specification (which do not guarantee concavity of the direct utility function in a large enough region). In the paper, it is shown that, provided that the parameters satisfy certain conditions, internal consistency is guaranteed and, moreover, that the direct utility function behaves well in the feasible region of the quantity-space.