The problem of not observing small expenditures in a consumer expenditure survey

In consumer expenditure surveys one often faces the problem that full information on small consumption expenditures is not available. Suppose a panel of households is available, which is divided into two subsamples, say, A and B. For subsample B all expenditures are registered, but from subsample A only expenditures above some fixed amount, say Z dollars. Suppose, furthermore, that in some economic analysis the use of the sum of all expenditures of each single observation in the sample is required. It is then evident that the use of the (observed) sum of expenditures above Z dollars instead of the (unobserved) sum of all expenditures in case of observations in subsample A will lead to underestimation of the sum of all expenditures. To correct for this underestimation one could, for instance, make use of blow-up factors, computed with subsample B, or one could construct a Tobit model explaining the sum of expenditures below Z dollars and use this model, after estimating it with subsample B, to predict the sum of expenditures below Z dollars in subsample A. In this paper we propose an alternative method to correct for the underestimation. The method consists of constructing a model, which explains the sum of expenditures below Z dollars, by explicitly taking into account that each one of these is below Z dollars. This model is estimated on the subsample B data and can then be used to compute the expected values of the sum of expenditures below Z dollars made by households in subsample A. We apply this and the other two methods to a Dutch panel where the above-mentioned situation actually occurred. The sample consists of two subsamples; for one subsample all expenditures are registered, but for the other subsample only expenditures above 10 Dutch guilders.