# PPS232S.01 Microeconomics of International Development Policy

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PPS232S.01 Microeconomics of International Development Policy
3. Household and Intrahousehold Models

Agricultural Households as Consumption and Production Units
Standard microeconomic theory relies on two fundamental, separate agents – the consumer and the producer. But households in developing countries are often consumers and producers of specific goods. This is especially true for staples (e.g., rice, maize, teff, etc.) We thus focus on the agricultural household, which is both a production and a consumption unit. We’ll talk of agricultural household models (AHMs).

Refresher: Consumer Theory
Good 2 Direction of Increasing Utility IC1 IC0 Good 1

Refresher: Production Theory
Output Labor

Basic Agricultural Household Model
Two individuals: Each individual has a level of consumption ci and a level of leisure The price of the consumption good is p and the price of labor (and thus leisure) is w The household produces some of the consumption good according to the production function F(L,A), where L denotes labor used on the farm and A denotes the amount of cultivable land Endowments of time and land are and Price of one unit of land is r

Basic Agricultural Household Model
The household’s maximization problem is thus subject to Expenditures Income Resource Constraints

Basic Agricultural Household Model
The problem of the household is thus to maximize its utility subject to a budget constraint (expenditures must not exceed income) and several resource constraints. The above problem, however, can be reduced by substituting the resource constraints into the budget constraint: this yields the following version of the household’s maximization problem.

Basic Agricultural Household Model
The household’s maximization problem is then subject to The new budget constraint is called the full-income constraint, and the next equation represents farm profits. New Budget Constraint Farm Profit

Basic Agricultural Household Model
The new problem is recursive: if U is characterized by non-satiation, then the full-income constraint is binding and household utility is increasing in farm profit – the higher the profits from the farm, the better off the household – and the optimal choices of L and A do not appear in the objective function. The problem can then be rewritten as subject to where * is the profit function, which only depends on prices.

Basic Agricultural Household Model
This setup allows to 1. Maximize profit; then 2. Maximize utility In other words: with complete markets, production decisions only depend on prices and plot characteristics, and not on household endowments or preferences. This is called the Separation Property: production decisions are separable from consumption choices (but not the other way around).

The Agricultural Household Model with Separability
Output, Consumption Good Profit Labor, - Leisure

Basic Agricultural Household Model
Additionally, the Separation Property holds even if one market is missing (e.g., in our example, either land or labor). The Separation Property, however, rarely ever holds in practice, as it is quite likely that more than one market goes missing. When there are multiple (i.e., two or more) market failures, the Separation Property fails to hold, and household consumption is constrained by household production, so to speak.

Basic Agricultural Household Model: Multiple Missing Markets
Suppose now that both markets (land and labor) are missing. The Separation Property does not hold: the household no longer maximizes profit, and production decisions depend on the preferences of the household and its endowments.

Basic Agricultural Household Model
More specifically, and assuming for simplicity that there is only one individual in the household, we have subject to

Basic Agricultural Household Model
If Lm = M, the problem becomes subject to But then, the first-order conditions yield and the production decision now depends on preferences and endowments (see graph).

The Agricultural Household Model with Non-Separability
Labor -Leisure

Empirical Evidence on Agricultural Household Models
Knowing what we know about market failures, we come to the crux of this section: What do the data have to say? In other words, does the Separation Property hold in practice? The short answer is that the bulk of the empirical evidence is in favor of rejecting the Separation Property.

Empirical Evidence on Agricultural Household Models
Benjamin (1992) tests for separation in Indonesia. Idea: Holding everything else constant, supply-side (i.e., production factors) variables should not affect labor demand, and demand-side variables (i.e., consumption factors) should not affect labor supply. Test: Household composition has no effect on the household’s labor allocation at the margin. Benjamin cannot reject the null hypothesis.

Empirical Evidence on Agricultural Household Models
Problem: The test is not very powerful, since the bulk of the probability mass lies with non-rejection, i.e., a “nonresult.” Even though Pitt and Rosenzweig (1986) also cannot reject separation in an earlier round of the same Indonesian data, these results should be taken with a grain of salt. The vast majority of empirical studies reject the Separation Property (Collier, 1983; Carter, 1984; Jacoby, 1993; Kevane, 1994; Barrett, 1996; Udry, 1999).

Empirical Evidence on Agricultural Household Models
For example, Jacoby rejects that the Separation Property holds in Peru. Idea: Households set their marginal productivity of labor equal to the market wage. Test: a = 0 and b = 1 in the regression Jacoby rejects the null hypothesis of separation.

Agricultural Household Models
What to remember from all this? The following points are key: What happens when the Separation Property holds? The Separation Property holds if there is only one market failure. When the Separation Property fails to hold, production decisions depend on preferences and endowments. The Separation Property has been largely rejected.

Intrahousehold Models: A Technical Aside
In the AHM, we assume that one utility function can represent the preferences of many individuals. This is inconsistent with the methodological individualism of economic theory. For such aggregation to be possible, a lot of structure needs to be imposed on the preferences of each individual of the household (Gorman, 1953).

Response to Aggregation Limitation
To overcome this, we can make strong assumptions about the intra-household distribution of resources For example, Becker’s “Rotten Kid” Theorem assumes the household includes a benevolent dictator who redistributes resources efficiently, i.e., up to the point where everyone’s marginal utility of income is the same. In this case, the household is (analytically) indistinguishable from a single individual.

Intra-Household Modeling
There is no good reason, however, to believe that the unitary AHM is a good representation of reality. In fact, evidence points to the fact it is not (Alderman et al., 1995). Manser and Brown (1980) and McElroy and Horney (1981) develop models of the household based on cooperative game theory (i.e., bargaining within the household). In this case, resources are allocated efficiently, but the allocation is determined by “threat points” (i.e., the utility achieved by each individual in case of cooperation breakdown).

Intra-Household Modeling
Browning and Chiappori (1994), for their part, only assume that the intra-household allocation is efficient. If markets are complete, the household’s production decisions are not a function of its preferences or endowments (this should be familiar to you by now.)

Intra-Household Modeling
Browning and Chiappori’s (1994) requirement that the household’s allocation efficient is much weaker than the requirements of the unitary AHM. Why is that? As a result, these “efficient household models” are more realistic and true to form than the unitary AHM. Additionally, it makes a lot of sense for a household’s allocation of resources to be efficient (but think of what could make the efficiency assumption not hold)

Empirical Evidence on Intrahousehold Models
Folbre (1984) originally asked why development microeconomists aggregate a number of individual preferences into a single utility function and offered a solid critique of the AHM. She then develops a non-mathematical framework with which to study households, based on four propositions.

Empirical Evidence on Intrahousehold Models
1. Altruism coexists with conflicts over distribution of goods and leisure time 2. Individual income shares are partly determined by bargaining power. 3. The relative bargaining power of men, women, and children changes over the development process. 4. Changes in bargaining power lead to changes in the distribution of goods and leisure time and affects the price of goods (including children) produced in the household.

Empirical Evidence on Intra-Household Models
Thus, Folbre’s paper constitutes the very first pass at empirically studying intra-household models. Her empirical results contradict the “benevolent dictator” argument put forth by Becker, by and large, and indicate that the unitary household model might not be the best way to model households.

Empirical Evidence on Intra-Household Models
Similarly, Udry (1996) wishes to test the proposition that intra-household allocations are Pareto-efficient. After developing a relatively simple theoretical model, he proceeds to test empirically that gender has no effect on yields, i.e., whether a man or a woman exploits a given plot, the yield remains the same, ceteris paribus. Using data from Burkina Faso, he rejects the null hypothesis.

Empirical Evidence on Intra-Household Models
At the end of the day, he estimates that the output loss due to this inefficiency is about 6%, i.e., households operate at about 94% of their efficient level. Contrast this with Carr’s (2011) qualitative evidence to the contrary. The evidence is thus damning – to say the least – both for the AHM and the efficient household model. Still, those models are often retained in the literature in order to study microeconomic phenomena that are external to the household.

Consequences for Policy
If households do not behave in a unitary fashion, then transfer programs may not reach their intended recipients (e.g., food distribution programs and children). Depending on our goals, we may need a good understanding of how resources are allocated within the household (e.g., it is often preferable to give cash or food to women rather than men).

Intrahousehold Allocation of Technology
In Lee and Bellemare (2011), we wanted to know whether owning a mobile phone was associated with increased prices for a cash crop. Using data from a rural area of the Philippines, we found that mobile phone ownership was not associated with a significant increase in the price of onions. When controlling for who owns the mobile phone within the household, however, we find that mobile phone ownership by the farmer or his spouse is associated with price increases, but not ownership by the farmer’s children. It thus looks as though the intrahousehold allocation of technology may also matter.

Summary It is very unlikely that we can aggregate over each individual’s utility function so as to have one utility function for the household. A much weaker requirement is that of efficiency: intra-household allocations should at least be Pareto-efficient. The unitary household model has been rejected pretty convincingly in empirical studies (see, for example, Folbre, 1984, and Browning and Chiappori, 1998).

Summary The weaker requirement of Pareto-efficiency has also been rejected quite convincingly in empirical studies (for example, Udry, 1996). Udry also rejects the cooperative bargaining approaches of Brown and Manser (1980) and of McElroy and Horney (1981). This points to the need for non-cooperative models of the household as well as for models in which control over the land is individualized.

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