03. household and intrahousehold models

7/29/2019 03. Household and Intrahousehold Models

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3 . HOUSEHOLD AND INTRAHOUSEHOLD MODELS

PPS603Microeconomics of International Development Policy


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Agricultural Households as Consumption and Production Units

Standard microeconomic theory relies on two fundamental, separate

agentsthe consumer and the producer.

But households in developing countries are often consumers andproducers of specific goods. This is especially true for staples

(e.g., rice, maize, wheat).

We focus on the agricultural household, which is both a productionand a consumption unit. Well talk of agricultural household

models (AHMs).


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Good 1

Good 2

IC0

IC1

*

1x

*

2x

21/pp

Direction of IncreasingUtility

Refresher: Consumer Theory


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pw/

*L

),(* AELF

Labor

Output

Refresher: Production Theory


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Basic Agricultural Household Model

}2,1{iTwo individuals:

Each individual has a level of consumption ci and a level of leisure

The price of the consumption good isp and the price of labor (and

thus leisure) is wThe household produces some of the consumption good according to

the production function F(L,A), whereL denotes labor used on the

farm andA denotes the amount of cultivable land

Endowments of time and land are andPrice of one unit of land is r

i

L

iEA

E


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The households maximization problem is thus

subject to),,,(max 2121,,, 2121

ccUcc

mmmhh

rALLwALpFrAwLccp )(),()( 2121

hffLLLL

21

hf AAA mfA

AAE

i

m

i

f

i

L

iLLE

0,,,,, mfm

i

f

iii AALLc Resource

Constraints

IncomeExpenditures


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The problem of the household is to maximize its utility subject to a

budget constraint (expenditures cannot exceed income) and

several resource constraints.

The above problem can be reduced by substituting the resource

constraints into the budget constraint: this yields the following

version of the households maximization problem.


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The households maximization problem is then

subject to

The new budget constraint is called the full-income constraint, andthe next equation represents farm profits.

),,,(max2121

,,, 2121

ccUcc

ALL

rEEEwwccp )()()( 212121

rAwLALpF ),(

0,,, ALc ii

Farm Profit

New Budget Constraint


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The new problem is recursive: ifUis characterized by non-satiation,

then the full-income constraint is binding and household utility is

increasing in farm profitthe higher the profits from the farm, the

better off the householdand the optimal choices ofL andA 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.

),,,(max2121

,,, 2121

ccUcc

ALL rEEEwrwpwccp )(),,()()( 21*

2121


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This setup allows to

1. Maximize profit; then

2. Maximize utility

In other words: with complete markets, production decisions onlydepend on prices and plot characteristics, and notonhousehold endowments or preferences.

This is called the Separation Property: production decisions areseparable from consumption choices (but not the other wayaround).


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LE

),( cu

pw/

),(A

ELF

Labor,

- Leisure

Output,

Consumption

Good

*L

),(* AELF

Profit),/(

AEpw

*c

*

LE

The Agricultural Household Model with Separability


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The Separation Property holds even if one market is missing (e.g., in

our example, either land or labor).

The Separation Property 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, theSeparation Property fails to hold, and household consumption is

constrained by household production, so to speak.


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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 longermaximizes profit, and production decisions depend on the

preferences of the household and its endowments.


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More specifically, and assuming for simplicity that there is only one

individual in the household, we have

subject to),(max,,,

cUfh

LLc

mhAhf wLwLELLpFpc ),(

Lmf ELL

MLm


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IfLm = 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).

),(max,

cUc

wMEMEpFpc AL ),(

L

c

FU

U


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M

),(A

ELF

wM

c

-Leisure

Labor

*q*c

),( cu

fL

MLf

A

B C

The Agricultural Household Model with Non-Separability


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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 ofrejecting the Separation Property.


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Benjamin (1992) tests for separation in Indonesia.

Idea:Holding everything else constant, supply-side (i.e., productionfactors) variables should not affect labor demand, and demand-

side variables (i.e., consumption factors) should not affect laborsupply.

Test: Household composition has no effect on the households labor

allocation at the margin.

Benjamin cannot reject the null hypothesis.


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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).


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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.

iii ebWaMPL


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Agricultural Household Models

What to remember from all this? The following points are key:

1. What happens when the Separation Property holds?

2. The Separation Property holds if there is only one market

failure.

3. When the Separation Property fails to hold, production decisions

depend on preferences and endowments.

4. The Separation Property has been largely rejected.


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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 ofeach individual of the household

(Gorman, 1953).


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Response to Aggregation Limitation

To overcome this, we can make strong assumptions about the

intra-household distribution of resources

For example, Beckers Rotten Kid Theorem assumes thehousehold includes a benevolent dictator who redistributes

resources efficiently, i.e., up to the point where everyones

marginal utility of income is the same.

In this case, the household is (analytically) indistinguishable from

a single individual.


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Intra-Household Modeling

There is no good reason, however, to believe that the unitary AHMis 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 gametheory (i.e., bargaining within the household).

In this case, resources are allocated efficiently, but the allocation isdetermined by threat points (i.e., the utility achieved by eachindividual in case of cooperation breakdown).


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Browning and Chiappori (1994), for their part, only assume that the

intra-household allocation is efficient.

If markets are complete, the households production decisions are

not a function of its preferences or endowments (this should be

familiar to you by now.)


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Browning and Chiapporis (1994) requirement that the households

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 households allocation of

resources to be efficient (but think of what could make the

efficiency assumption not hold)


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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 conceptual framework with which to study

households, based on four propositions.


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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.


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Empirical Evidence on Intra-Household Models

Thus, Folbres paper constitutes the 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.


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Similarly, Udry (1996) wishes to test the proposition that intra-household allocations are Pareto-efficient.

After developing a relatively simple theoretical model, he proceedsto test empirically that gender has no effect on yields, i.e.,whether a man or a woman exploits a given plot, the yieldremains the same, ceteris paribus.

Using data from Burkina Faso, he rejects the null hypothesis.


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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 Carrs (2011) qualitative evidence to

the contrary.

The evidence is thus damningto say the leastboth 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.


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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).


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Intrahousehold Allocation of Technology

In Lee and Bellemare (2011), we wanted to know whether owning amobile phone was associated with increased prices for a cashcrop.

Using data from a rural area of the Philippines, we find thathousehold mobile phone ownership is not associated with asignificant increase in the price of onions.

When controlling for who owns the mobile phone within thehousehold, however, we find that mobile phone ownership by thefarmer or his spouse is associated with price increases, but notownership by the farmers children. It thus looks as though theintrahousehold allocation of technology may also matter.

03. household and intrahousehold models

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