Estimating Consumption Economies of Scale, Adult Equivalence Scales, and Household Bargaining Power

Abstract

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.

The economies of scale of living together and how they are shared: estimates based on a collective household model

“…Assuming that preferences do not change by living together, it is possible to identify the returns to scale and the sharing function from data on singles and couples. This identification result is one of the major contributions of Browning, Chiappori, and Lewbel (2008). In this setup, it is possible to identify so-called indifference scales which allow to make welfare comparisons between the same person in different living conditions.…”

“…This identification assumption has been made by Browning et al (2008), Lise and Seitz (2007), Lewbel and Pendakur (2008), Cherchye et al (2008), and Alessie et al (2006).…”

Allocation of Expenditures in Elderly Households and the Cost of Widowhood

“…The approach allows to estimate how household resources are divided between wives and husbands and to identify the returns to scale from joint consumption. The Lewbel and Pendakur (LP) model is related to the approach by BROWNING, CHIAPPORI, and LEWBEL (2013), which is less restrictive but comes at the cost of requiring data on price variation. 3 Since data on prices of the goods consumed are not available, this paper sticks to the LP model.…”

Sharing Rule Identification for General Collective Consumption Models

“…For example, we can see how much the bounds tighten if we treat each individual's leisure as an exclusive private good, or if we treat the aggregate Hicksian commodity as a private good without externalities. Lise and Seitz (2011) similarly use labor supply to identify resource shares, but for identi…cation their results depend on strong functional form assumptions, as well as restrictions across households like those in Browning, Chiappori, and Lewbel (2006). Some implementations of collective household models treat wages as distribution factors, thereby assuming they only a¤ect sharing rules and not preferences.…”

“…The sharing rule is also useful for recovering information about the economic well being of household members. For example, Lise and Seitz (2011) use sharing rule estimates to recover the population distribution of income across individuals rather than across households, Browning, Chiappori and Lewbel (2006) combine the sharing rule with other information to recover "indi¤erence scales" that measure the welfare implications of changes in household composition, and Dunbar, Lewbel, and Pendakur (2012) use sharing rule estimates to back out rates of child poverty. See, also Browning, Bourguignon, Chiappori and Lechene (1994), Chiappori, Fortin and Lacroix (2002), Blundell, Chiappori and Meghir (2005), Lewbel and Pendakur (2008), Bargain and Donni (2012), and Cherchye, De Rock and Vermeulen (2012a) for various applications of the collective consumption model that make use of the sharing rule concept.…”