In the U.S. Consumer Expenditure Interview Survey (CEQ), consumer units (roughly equivalent to households) are asked to provide month-by-month reports of the amounts of money spent on each of a large number of items. Reported expenditures are recorded at a relatively fine level of detail defined by the six-digit Universal Classification Code (UCC). For a given month, most consumer units report nonzero expenditures for a relatively small proportion of the possible UCC items. When no expenditure is reported, available data do not allow one to distinguish between cases of no expenditure for this item in the specified month ("true nonexpenditure") and cases of failure to report a true non zero expenditure ("nonidentified item nonresponse"). However, under specific models for relationships among true nonexpenditure, nonidentified item nonresponse and observable auxiliary variables, some important model parameters are estimable. This paper reviews the relevant models and available auxiliary information, discusses identifying restrictions for specific parameters, and presents related point estimators and variance estimators.