Household economics
Eliana La Ferrara
May 11, 2016
Outline
How do families decide? Intra-hh allocation
1. Unitary model of the household
2. Intra-household bargaining
3. Testing the unitary model
4. Pareto e¢ ciency
1. Unitary model (neoclassical)
Household w/ N members
m goods
HH maximizes HH welfare s.t. budget constraint:
maxX W (u1 (X ) ; :::; uN (X ))
f
s:t: pX
=
N
X
yi
(1)
i=1
where X is m N matrix, with Xmi =cons. of mth good by ith member,
f is a m
X
1 vector of total cons. of good, yi is income of member i
(exogenous).
E.g. if individual i only cares about his own consumption, weight assigned
to Xmj , j 6= i is zero in ui (X ).
Solution to (1) gives HH demand for each good
Assumption:
* all members have exactly the same preferences
or
a dictator makes all the decisions (weight to other ui’s in W is 0)
HH acts as if it is one entity which pools all income:
0
Xm = g @p;
Key result: ......................
N
X
i=1
1
yiA
(2)
Key result: income pooling
– Note: In order to represent aggregate choices of individuals in HH as
if they were made by a single agent, pref’s must be characterized by
b 1; :::; u
b N ) s.t.
transferable utility: if (u1; :::; uN ) is feasible, then (u
P
P
b i also feasible
ui = u
) HH aggregate demand not in‡uenced by distribution of utility in
HH.
Ex: members have identical homothetic pref’s [x
y) x
y ].
2. Intra-HH bargaining
Manser-Brown (1980); McElroy - Horney (1981)
Assumption: Nash Bargaining among HH members.
Individuals bargain: either they agree on an allocation and they remain part of
the HH, or they disagree, the HH splits and each gets outside option.
Let Di (:) be disagreement outcome that i would have outside HH.
Nash solution has a simple characterization =) maximization of product of
utilities:
max [uM (XM )
DM (yM )] [uF (XF )
s:t: XM + XF = yM + yF
Demand functions
XM = g (yM ; yF )
XM = g (yM ; yF )
Key result: ...................................................
DF (yF )]
Key result: not only aggregate income, but source of income matters!
3. Empirics: tests of unitary model
Think of estimating the following equation:
Xm =
+ M YM + F YF + 0 Z + " m
where Xm = consumption of good m
What does the unitary model imply in terms of the coe¢ cients in (3)?
(3)
3.1 YM ;YF = labor income
Problems in interpreting M ; F ?
Problem: labor supply (leisure) jointly determined w/consumption of other
goods!
E.g.: if women work less in families that place high value on child health:
) corr(YW ; child health) < 0 even though HH is unitary!
3.2 YM ;YF = NONLABOR income
Thomas (1990)
no individual-level data on consumption of goods, except
– leisure (labor force participation)
– health & nutrition
Brazilian HH survey 1974-1975:
25; 000 HH’s
contains data on non-wage income (pensions, social sec., assets income,
gifts...)
Husband: 76% total HH income
Wife: 13%
6 "consumption" goods, or resource allocation outcomes:
– HH level nutrient intakes: calories
– HH level nutrient intakes: proteins
– Wife’s fertility
– Wife’s children’s survival rate
– Children 0-8 yrs:
weight for height (short run)
height for age (long run)
)
% of US median
* e¤ect on wife > e¤ect on husband ( 4 to 7 times more)
*
Nutrients:
signi…cant di¤erence:
proteins: linear
calories: quadratic
Survival rate: women’s income e¤ect > men’s (20 times)
Anthropometric measures:
Holds w/ asset income
*
mother =) weight
mother, father =) height
Gender e¤ects
Do parents have 6= preferences on boys & girls?
mother > father for boys and girls
di¤erence b/w mother & father greater for girls (weight: 5 times)
...any critique to this approach?
Critiques to Thomas (1990)
Correlation b/w asset ownership & child health can occur even in unitary
model if due to "third" factors
Ex: more traditional HH’s
(
do not allow women to own assets
have less healthy children
Can be solved by looking at assets’income at the time HH was formed.
Endog. HH formation may be the cause for corr (Yw ; child health) > 0
Ex: assume men’s child rearing ability " with YH . Then:
assortative matching: " YW )" YH
" YH )" child health
)
" YW )" child health
3.3 Short term variation in non-labor income
Considering unexpected changes in Y should solve the above problems, i.e.
use transitory variation in share of YW & YH
)but optimal HH consumption should not change w/ temporary Y ‡uctuations!
3.4 Permanent exogenous change in non-labor income
Du‡o (2003)
Consider a permanent shock to non-labor income of a HH member that was
not expected at the time of HH formation.
*
Unitary model: a¤ects cons. allocation only through HH income
Bargaining model: a¤ects cons. allocation also through bargaining power
Then: use gov’t transfer program as "quasi-natural" experiment
Ex: Lundberg, Pollak, Wales (1996) !child bene…ts in UK & cons. of clothes.
Program: South African Old Age Pensions
Initially was for whites
End of Apartheid (1989): move towards parity in pensions
Fully operative at beginning of ’93
Universal & non-contributory
Payments to
*
women >60
men >65
subject to means test on couple income:
couple resources divided by 2
income of other members not counted
)
no incentives to partition or stop
work
Focus on comparison by eligibility status, b/c getting the pension (conditional on eligibility) is endogenous: in‡uenced by current & past decisions
on labor supply, etc.
2 strategies:
1. E¤ect on weight for height (‡ow/short term)
+ w Ew + hEh + 0Z + "if
EW = 1 if 9 eligible woman in HH
Xif =
Controls include dummies for presence of old (not eligible) membes: e.g.
women 56-60, men 61-65, etc.
)Identi…cation assumption: no systematic di¤erence b/w eligible & non eligible HH’s who have an old member at home.
col. 6:
Ew = 1 )" weight by 0:6 std. dev.
Eh = 1 ) not signi…cant
col. 7:It could be that husbands are eligible but don’t claim pension b/c they
have worked & have private pensions.
)use P EN Sw = 1 if receives pension & instrument w/eligibility dummies.
Result: P EN Sw = 1 )"weight by 1:19 std. dev., P EN Sh = 1 )not
signi…cant.
1.
Caveats:
1.
presence of old member may be sign of healthy HH (survived!)
pension program may have changed HH composition
2 E¤ects on height for age (stock, long term)
)Identi…cation strategy: compare di¤erence b/w children in eligible vs. noneligible HH’s exposed to program for fraction of life vs. all life.
)Interpretation: even if HH’s eligible have worse characteristics, within these
HH’s children who are younger have been well nourished longer.
Non-parametric regression of height on age:
Compare children who live w/ eligible women and w/ no eligible member.
The former are
Xif =
(
shorter when old
taller when young (born after ’91)
+ w (young
Ew )+ h (young
Eh)+ w Ew + hEh + 0Z + "if
where young = 1 if child born from Jan ’92 on (full expansion of program)
Interaction term insigni…cant for boys, signi…cant for girls
young
Ew = 1 )"height by 0:71 std.dev.
(young
P EN Sw ) and (young
P EN Sh) instrumented w/ young
Conclusion: both strategies 1: and 2: lead to the same result!
Ej