Here is the much awaited discussion about the theoretical underpinnings and empirical implications of intra-household resource allocation models. As noted in the previous two posts, the household is most appropriately treated as a “firm” which makes production and consumption decisions simultaneously. The next question is, then, how should we represent the preference of the whole household?

Take an analogy from the voting behavior models. By Arrow’s Impossibility Theorem, no rank order system can convert the ranked preferences of individuals into a community-wide (complete and transitive) ranking while meeting the following criteria:

1. Non-dictatorship, i.e. everyone’s preference needs to figure in.

2. Unrestricted domain, i.e. there exists a deterministic function linking constituencies to outcomes.

3. Pareto principle.

4. Independence of Irrelevant Alternatives (IIA for short).

5. Rationality, which is needed for utility function specification.

There are three approaches to analyze household resource allocations. Samuelson (1956) first points out a common preference model where household “consensus” can be seen as a single representative. Gary Becker, on the other hand, added altruism into the model and elaborates the “consensus” process. The other class of models are collective models by Chiappori, McElroy and Hearney, Lundberg and Pollak, etc. In particular, Chiappori’s general collective model address the violation of unrestricted domain by assuming outcome of household decisions to depend on income distributions and other factors affecting bargaining power (modeled as “lamda”).

Becker’s Rotten Kid Theorem generated quite a bit of discussion in class. The critical assumption here is that an altruist fully incorporates the utility function of the beneficiary into his own. Therefore, when he is faced with lower incomes, he “punishes” his beneficiary in a way that lowers his utility as well. Knowing this unfavorable consequence, the selfish beneficiary (the “rotten kid”) is induced to behave in a way that maximizes household’s welfare. This approach has been criticized as unrealistic and largely rejected by empirical evidence.

The empirical papers discussed were quite interesting. Udry’s paper on inefficient farming households in Burkina Faso is flawed because plots controlled by men and women are likely to differ in unobservable characteristics which also drives the productivity gap. Amar pointed out that by the same reasoning, since plot decile effects are quite significant, dividing a big plots into smaller ones should increase yields by a substantial margin, which does not make sense at all.

Lundberg, Pollak and Wales (1997) and Hotchkiss (2005) investigate the impacts of child subsidy on household expenditure on women’s and children’s clothing relative to men’s. Hotchkiss flunked LPW’s findings, but neither accounts for a potential “labeling effect” which results from the change in the *way* families receive the child subsidy.

My next post will be about marriage markets and investments in children.

References:

Becker, G. 1991. “A Treatise on the Family: Enlarged edition.” Chapter 8.

Browning, M., Chiappori, P., and Weiss, Y. 2011. “Cooperative Models: The collective approach.” Section 3.5 in *Family Economics*.

Lundberg, S and Pollak, R. 1996. “Bargaining and Distribution in Marriage.” Journal of Economic Perspectives 10(4): 139-158.

Hotchkiss, J. 2005. “Do Husbands and Wives Pool Their Resources? Further Evidence.” Journal of Human Resources 50(2): 519-531.

Udry, C. 1996. “Gender, Agricultural Production, and the Theory of the Household.” Journal of Political Economy 104(5): 1010-1046.