Statistical models for zero expenditures in household budgets

Household budget surveys are an important source of data on consumer’s expenditure, not just for individual consumers, but also for estimating national aggregates. However, it is a widespread finding that for certain commodities, most notably tobacco and alcohol, the estimate from the household survey falls short of the known consumption total calculated (with some confidence) from data on production, imports, exports and excise duties. For example, in the British Family Expenditure Survey (with which we shall largely be concerned) total tobacco expenditure was underestimated in 1976 by 21 percent [see Kemsley, Redpath and Holmes (1980, p. 51)]. Much of this understatement, together with that on alcohol, is thought to occur because of the design of the survey which excludes many persons amongst whom consumption of such items is thought to be atypically high (e.g. prisoners, hoteliers and their residents, merchant seamen). Even so, the possibility remains that some of the understatement is due to various types of misreporting by households included in the survey. In this paper we consider a model in which the standard tobit specification [Tobin (1958)] is supplemented by the operation of a simple binary censor. The tobit model is essentially a linear regression model in which non-positive observations of the dependent variable are replaced by zero. We take this specification as our starting point but add a second censoring process that randomly replaces a fraction of the observations generated by the tobit model bv zeroes. The combined model can serve as a representation of several types of

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