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How much income would a woman living alone require to attain the same standard of living that she would have if she were married? What percentage of a married couple's expenditures are controlled by the husband? How much money does a couple save on consumption goods by living together versus living apart? We propose and estimate a collective model of household behavior that permits identi cation and estimation of concepts such as these. We model households in terms of the utility functions of its members, a bargaining or social welfare function, and a consumption technology function. We demonstrate generic nonparametric identi cation of the model, and hence of a version of adult equivalence scales that we call "indifference scales," as well as consumption economies of scale, the household's resource sharing rule or members' bargaining power, and other related concepts.

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The share of household resources devoted to children is hard to identify because consumption is measured at the household level and goods can be shared. Using semiparametric restrictions on individual preferences within a collective model, we identify how total household resources are divided up among household members by observing how each family member's expenditures on a single private good like clothing vary with income and family size. Using data from Malawi we show how resources devoted to wives and children vary by family size and structure, and we find that standard poverty indices understate the incidence of child poverty. (JEL I31, I32, J12, J13, O12, O15)

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THE RANK O F DEMAND SYSTEMS: THEORY AND NONPARAMETRIC ESTIMATION' Gorman's (1981) concept of Engel curve "rank" is extended to apply to any demand system. Rank is shown to have implications for specification, separability, and aggregation of demands. A simple nonparametric test of rank using Engel curve data is described and applied to U.S. and U.K. consumer survey data. The test employs a new general method for testing the rank of estimated matrices. The results are used to assess theoretical and empirical aggregation error in representative consumer models, and to explain a representative consumer paradox.

We invent Implicit Marshallian Demands, a new type of demand function that combines desirable features of Hicksian and Marshallian demand functions. We propose and estimate the Exact Af ne Stone Index (EASI) Implicit Marshallian Demand system. Like the Almost Ideal Demand (AID) system, EASI budget shares are linear in parameters given real expenditures. However, unlike the AID, EASI demands can have any rank and its Engel curves can be polynomials or splines of any order in real expenditures. EASI error terms equal random utility parameters to account for unobserved preference heterogeneity. EASI demand functions can be estimated using GMM or three stage least squares, and, like AID, an approximate EASI model can be estimated by linear regression. JEL Codes: D11, D12, C31, C33, C51