Economics of the Family (2): Defining “Family”

Family clip art
Blogging has been light for the past few days, partly because I was preparing for an academic presentation and partly because I was a bit lazy as the Lunar New Year approached. Now that celebrations are over, I am back to my normal blog schedule.

This is the second post in my “family economics” series. Following our last discussion, we talked about how to define “family” or “household” in economics.

The US Census defines the family as “a group of two people or more (one of whom is the householder) related by birth, marriage, or adoption and residing together”. This definition differs from that of a “household” because the latter only requires joint residence. Relative to households, families not only share public goods (e.g. heating) but also pool their resources and make consumption choices together.

The economic theory of the family was established most notably by Gary Becker in his book A Treatise on the Family. For a long time, economists treated the family as a single consumption unit which maximizes its utility given a budget constraint. However, a family contains individuals of different objectives and incomes sharing certain public goods yet retaining some degree of autonomy. In addition, there are production-type activities within a family, ranging from household chores to raising a kid. These distinct features of the family require us to model it like a firm where production and consumption choices are jointly made.

Gary Becker incorporated the production component of the family in the so-called “Z” goods, which are produced using a combination of market goods (X) and time devoted by family members (t). In a single-person household, the individual (household head) maximizes his own utility subject to an income constraint (with respect to market goods), a time constraint (he only has 24 hours a day), and a home production function describing how X and t are transformed into Z. These constraints can be condensed into one equation which says the total amount of income spent on market goods plus the forgone wages cannot exceed the individual’s full income (if he spends all his time working) and unearned income. Optimal allocations equalize the marginal utility from purchasing each market good and the that from devoting time to home goods production. The key insight is that market goods must be purchased such that they are equally “productive” given individual’s preferences over Z goods. Marginal utilities are now determined by production as well as inputs. Being in a family, where individuals can complement each others’ skills and enjoy economies of scale, might change the production function of the Z goods.

Parallel to the advances in theoretical work, applied economists have explored how different definitions of the family affect individuals’ response in household surveys. Beaman and Dillon (2011) carried out a randomized control trial in Mali where they surveyed villagers about household composition, assets and consumption using four different definitions of the household. They found additional keywords in definition, such as joint food preparation and cooperation in agricultural production, tend to increase rather than decrease household size. Definitions emphasizing joint consumption or production increases the levels of household assets and consumption statistics, but not on per adult equivalence terms. Their findings suggest that household survey questions should be carefully framed to address the purpose of the specific study. Moreover, a consistent household definition is essential for comparisons over time and across populations.

Next week we will dive deeper into the decision-making process within the family, and explore the merits and flaws of different household bargaining models with empirical examples. Highlights include Gary Becker’s Rotten Kid Theorem, Christopher Udry’s agricultural production model, and empirical evidence from West Africa.

References:
Beaman, L and Dillon, A. (2011) “Do Household Definitions Matter in Survey Design? Results from a randomized survey experiment in Mali” Journal of Development Economics 98(1):124-135.
Becker, GS.(1991). “A Treatise on the Family: Enlarged edition,” Chapter 1.
Becker, GS.(1965). “A Theory on the Allocation of Time” Economic Journal 75(299):493-517.
World Bank. (2000). “Designing Household Survey Questionnaires for Developing Countries: Lessons from 15 years of the Living Standards Measurement Study,” vol 1, chapter 6, section 1 (Pp.135-137).

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