Missing data from infrequency of purchase: Bayesian estimation of a linearexpenditure system

One of the problems associated with using household expenditure data in cro ss-sectional demand studies is that the data on expenditure that is collect ed for a short period of time does not necessarily correspond to consumptio n over that same period of time. Since it is consumption that typically app ears in utility-based demand equations, this problem can be viewed as one w here there are missing values on consumption. In particular, in a two-week interview period it is common to have zero expenditures on commodities such as clothing, although clothing is obviously being consumed. In this paper Bayesian methodology using latent variables, data augmentation, and a Metro polis within Gibbs sampling algorithm is developed to estimate a four-commo dity system involving food, clothing, housing, and "other" expenditure. In this system households with different demographic compositions have differe nt intercepts, but identical slope coefficients. The differing intercepts a re used to estimate household equivalence scales which reflect the differen t consumption needs of households with different demographic compositions. Observed expenditures are linked to unobserved consumption through unknown probability-of-purchase parameters. The methodology is applied to data from the 1988-1989 Household Expenditure Survey conducted by the Australian Bur eau of Statistics.