Identification of Random Resource Shares in Collective Households Without Preference Similarity Restrictions

Abstract

Resource shares, defined as the fraction of total household spending going to each person in a household, are important for assessing individual material well-being, inequality and poverty. They are difficult to identify because consumption is measured typically at the household level, and many goods are jointly consumed, so that individual-level consumption in multi-person households is not directly observed. We consider random resource shares, which vary across observationally identical households. We provide theorems that identify the distribution of random resource shares across households, including children's shares. We also provide a new method of identifying the level of fixed or random resource shares that does not require previously needed preference similarity restrictions or marriage market assumptions. Our results can be applied to data with or without price variation. We apply our results to households in Malawi, estimating the distributions of child and female poverty across households.

Static and Intertemporal Household Decisions

“…Under independence of scale and the additional assumption that the parents’ preferences regarding their own consumption do not depend on the number of children, they obtain full identification. In Dunbar, Lewbel, and Pendakur (2014), the same authors show an even stronger result. They find that, in the presence of a distribution factor, independence of scale guarantees full identification even without assumptions on preferences.…”

Intertemporal Collective Household Models: Identification in Short Panels with Unobserved Heterogeneity in Resource Shares

“…Dunbar et al (2013) does not accommodate unobserved heterogeneity in resource shares. Two newer papers, Chiappori and Kim (2017) and Dunbar et al (2019) consider identification in cross-sectional data with unobserved household-level heterogeneity in resource shares. Like Chiappori and Kim (2017) and Theorem 1 in Dunbar et al (2019), our work investigates identification of the distribution of resource shares up to an unknown normalization.…”

Uniform Sharing

“…Such so-called distribution factors can improve estimates and even aid identification (e.g. in Browning et al, 1994;Dunbar et al, 2017). Under these and some additional technical conditions, BCL show that household demand for a good k can be written in budget share form as:…”