Intrahousehold Resource AllocationinCôte d’Ivoire: Social ...cru2/econ731_files/ivoireslides.pdf · ucts’ (e.g., yam) are under the control of the household head for feeding

Intrahousehold ResourceAllocation in Côte

d’Ivoire:Social Norms, Separate

Accounts andConsumption Choices

Esther Duflo and Christopher Udry

1

There is a huge literature on householdprovisioning in West Africa:Non-unified budgets:Men control their own cash income, andthe kinds of legitimate demands a wife canmake can be quite limited. (...) Beti wivesremain farmers throughout their lives.Before the recent expansion of food salesthey used to depend on their husbandsfor all major cash expenses, but neither intheory nor in day-to day life is a wife’sright to her own share of her husband’scash income guaranteed (..) Familywelfare and risk avoidance are probablyimproved by the family labor force havinga variety of occupations which cater todifferent markets, but the need in bad timesand the opportunity in good times for awoman to earn an independent incomeoriginate in a domestic organization withlimited income sharing... (Guyer 1987)

2

Separate Accounts: ‘Appreciated prod-ucts’ (e.g., yam) are under the control of thehousehold head for feeding the entire house-hold. But the control of cash crops and foodproducts belongs to its producer. Cash cropsand food crops, even when they are cultivatedby the same individual, and even when foodcrops are sold on the market, are not put to thesame use:“...as we have seen, most [yam] comesback to producers in the form of food. Therest is incorporated into particular goods(...). These goods cannot be diverted topersonal uses. Nor are they investmentgoods, used for the reproduction ofmaterial goods. Everything changes whenthe products of agriculture are cash crops,which can be put to other uses (...). Agreater part of this income disappears intoprestige expenditures...” (Meillassoux).

3

• Accounts contradict conventional eco-nomic models: No unified b.c. contradictsPE. Discrete ‘accounts’?

• If proceeds of different crops generallyused to buy different goods does notimply separate accounts. Could just bebargaining. Haddad and Hoddinott (1994).

• Common response: don’t deny realityof the norms which underlie these de-scriptions, but hh must have flexibility onmargin to undue any binding constraints.Money is sufficiently fungible to get PE.

•We show: C.I. expenditure patterns violaterestrictions implied by PE, and do so in away consistent with descriptive literature.

• Description of tests: If hh is PE, it fullyinsures. But short-run fluctuations inparticular kinds of income associated withvariations in consumption of particulargoods

4

• Ideal test: two identical shocks, one to(say) wife, other to husband. Do they havethe same effect on expenditure on (say)consumption of beer?

•We construct an overidentification testwhich assumes particular functional formbut can deal with mismeasurement andendogeneity of expenditure

• Plan: Model/derivation of tests; Côted’Ivoire; Results

5

1 Deriving a test of efficientrisk poolingIdea: rainfall realization should affect theconsumption of each good only to the extentthat they affect total consumption. Withtwo types of rain (“male rain” and “femalerain”), check if male rain affects (say) foodexpenditure only to the extent that it affectstotal expenditures (overid test).

6

Chris

Brief discussion of household models: unitary, bargaining, collective

1.1 Theory1.1.1 One period model:

household with 2 individuals and rainfallrisk. i ∈ {m, f} consumes a vector ofprivate goods ci: ui(ci) (easy to generalizeto non-selfish prefs, not easy to generalize toui(ci, li))

fi(Li, r), where r ≡µr1r2

¶. Li traded

on a competitive market at wage w.Any efficient allocation of resources in

the household can be characterized as thesolution to the program

maxci,Li

Euf(cf) + λEum(cm)

subject top·(cm+cf) ≤ ff(Lf, r)+fm(Lm, r)−w(Lf+Lm).

7

This problem is separable and equivalentto

maxci

Euf(cf) + λEum(cm)

subject top · (cm + cf) ≤ π∗f(r) + π∗m(r)

where π∗i ≡ maxLifi(r, Li)− wLi.

Note how r enters the problem - that’s thewhole story. λ indep of realization of r.

8

Denoting x = p · (cm + cf), we have:ci = ci(λ, p, x)

for i ∈ {m, f}. Conditional on expen-ditures, prices, and the preference and Paretoweight parameters, consumption of any par-ticular good is independent of the rainfallrealizations r1 and r2.

So r effects ci only through p and x.Forget about p for now. For any i inm, f andj in 1, 2:

dckidrj

=∂cki∂x∗ ∂x∂rj

.

PE implies that the ratio between the ef-fect of rainfall in quarter j on consumptionof good i and its effect on total expenditureshould be equal across all rainfall realiza-tions:

dckidr1∂x∂r1

=

dckidr2∂x∂r2

. (1)

9

Could use cm+ cf . We do NOT needto observe πi, hence avoid Rosenzweig andWolpin (2000) critique of Paxson (1992).• dri affects decisions only via its influenceon the household’s resource constraint.If ui(ci, r), restriction fails to hold (childhealth example?).

• Labor market generalizes easily. Butwe need leisure not to influence MRSconditional on x.

10

1.1.2 Dynamics

T periods, history of rainfall realizationswt ≡ {r1, r2, ..., rt}. E

Pt β

tiUi(ciwt

).The budget constraint in period t after wt

(wt includes rt)p·(cfwt

+cmwt)+Awt

≤ RAwt−1+π∗mwt+π∗fwt

,

where Awtis the amount invested after history

wt by the household in a safe asset that earnsa return R (easy to generalize).

Efficient allocation solves:max{ciwt}

EXt

βtfUf(cfwt

)+λEXt

βtmUm(cmwt

)

(2)for some value of λ, subject to bc and a periodT constraint on AwT

.

11

Efficient continuations after wt, so inperiod tmaxciwt,Awt

EUf(cfwt)+λEUm(cmwt

)+Vwt(Awt

;λ)

subject top·(cfwt

+cmwt)+Awt

≤ RAwt−1+π∗mwt+π∗fwt

.

Let A∗wtbe the efficient level of assets held

after wt. Then efficient consumption is{c∗iwt

} = argmaxciwt

EUf(cfwt) + λEUm(cmwt

)

subject top·(cfwt

+cmwt) ≤ RAwt−1+π

∗mwt+π∗fwt

−A∗wt.

Since xwt≡ RAwt−1 + π∗mwt

+ π∗fwt−A∗wt

, wehave ciwt

= ci(λ, p, xwt).

Again, the crucial restriction of thecollective model is risk pooling: rainfallvariation influences the allocation of currentconsumption only through its affect on currentexpenditure. Again we also have:

∂ckiwt∂r1∂xwt∂r1

=

∂ckiwt∂r2∂xwt∂r2

12

2 Empirical implementationWe assume (but will test)

log(cit) = α log(xit)+f(λi)+Xitδ+υi+νit,

First, we are assuming that commoditydemands are multiplicatively separablebetween the Pareto weight λ and householdexpenditure x. Second, we are assumingthat commodity demands are log-linear inexpenditure.

log(xt) = Ritα +Xitδx + it.

Taking first differences of equation (??) and(??), we obtain the reduced form system:

log(xi2)−log(xi1) = (Ri2−Ri1)α+(Xi2−Xi1)δx+( i2− i1),

log(ci2)−log(ci1) = (Ri2−Ri1)π+(Xi2−Xi1)δ+(νi2−νi1),The overidentification test is:

π = κα

for some scalar κ.

13

We can do better by testing against aspecific alternative. The overid restrictionmust hold for any linear combination of theelements of (Ri2 −Ri1):

log(xi2)−log(xi1) =SXs=1

DRisαs+(Xi2−Xi1)δx+( i2− i1)

and

log(ci2)−log(ci1) =SXs=1

DRisπs+(Xi2−Xi1)δ+(νwi2−νwi1)

and we test whether πsαs= πs0

αs0for any s, s0 ∈

{f,m, y}.

14

Where we are stuck:

We want commodity demands that are multiplicatively separable between thePareto weight and expenditure. Is that coherent? Here’s the second stage ofthe two stage problem:

maxci

EUi(ci)

subject to:p · ci ≤ xi(x(wt))

Suppose each individual has common beliefs and HARA preferences with iden-tical curvature parameters, so

Ui(ci) =[vi(ci)]

1−γ

1− γ, (1)

where vi(ci) is any function that is increasing, concave and homogeneous ofdegree one and γ > 0, γ 6= 1. For example, suppose that

vi(ci) =³c1i

´β1i · ³c2i ´β2i · ... · (cki )βki · ... · (cKi )(1−β1i−β2i−...−βki−...−βK−1i ).

Let ui(xi) = maxci vi(ci) subject to p · ci = xi. Then ui(xi) = ζixi, {andwithout loss of generality we can set ζi = 1 — this is wrong}. To make itexplicit, with these prefs we have

ζit = Πk

Ãβkipkt

!βki.

The pt in the denominator is a killer.. The first stage of the households’problem in any period in which its total expenditure is x is to find

maxxf

(ζftxf)1−γ

1− γ+ λ

(ζmt(x− xf))1−γ

1− γ,

the solution to which is:

xf(wt) =ζft

λ−1γζmt + ζft

x(wt) (2)

and similarly for the male.

This all ends up giving us a demand equation for a particular good k that looks

like

ckt =xt

pkth(λ, pt, {βki })

so that

ln ckt = lnxt − ln pkt + ln(h(λ, pt))

(the preference parameters don’t matter much here for now). First differencesdon’t get rid of the λ any more, because the optimal sharing rule depends onchanges in relative prices. If we had ζmt = ζft = 1, then aggregate householdconsumption of good k is

ck =x

pk1

1 + λ1γ

∙βkf + βkmλ

1γ

¸. (3)

This demand function has two properties that are useful for estimation. First,it is multiplicatively separable between the Pareto weight λ and householdexpenditure x. Second, it is log-linear in expenditure (and, indeed, with a

coefficient of 1 on expenditure). It is possible to test these properties, and wedo so in section ??.

Households differ in various respects: they face different prices, have differentλ, and the preferences of their members may also vary. Indexing household byh, goods by k and time by t and taking logs, we obtain the following demandfunction for good k,for household t at time k:

log(ckht) = log(xht) + fkh(λh) + log pkht. (4)

A variety of factors, including most importantly the distribution of rainfall andunobserved preference parameters, affect λh and f

kh(.), and this function re-

mains unobserved. This could induce a spurious correlation between rainfall

realizations rht and log(ckht), even conditional on log(xht). Therefore, we

take the difference between period 1 and period 2:

log(ckh2)− log(ckh1) = log(xh2)− log(xh1) + log(pkh2)− log(pkh1) (5)

Under our assumption that rainfall realizations do not affect preferences directly(that is: they do not affect the form of fkh(.)), the difference rh2− rh1 shouldnot enter

2.1 Data• Cote D’Ivoire Living Standard Measure-ment survey (LSMS)

• 3 waves of a two-year panel (1985/86-1986/87-1987/88).

• Data on value sold, home consumption andexpenditure by crops.

• Data on expenditures on various goods,education, health, etc...

• Rainfall data can be linked to the panel (14weather stations)

•We keep in the data set only agriculturalhouseholds, for whom agriculture is themain source of income.

15

2.2 Agriculture in Cote d’Ivoire• Rainfed• Individuals control plots• Men and women tend to grow differentcrops. From the anthropological literature(plus evidence from Ghana). Doss (2001)story.– Men: cocoa, coffee, wood, yam–Women: coconut, plantain, oil, palm,taro, sweet potato, banana, vegetables,fruits trees.– Variable by ethnic groups: cotton, rice,millet, sorghum, fonio– Unknown: cassava, maize, tobacco,sugar.

•We do not know who produces what inthe households we look at, so we take thispartition as given (reduced form).

16

TABLE 1: Descriptive statisticsMean, year 1 Difference in logs1000's FCFA Year2-Year1 Observations

Standard errors in parentheses(1) (2) (3)

Income from male crops 553.78 -0.07 1025(26.22) (.06)

Income from female crops 103.46 0.00 1025(9.28) (0.10)

Total "male income" 593.89 -0.08 1025(26.17) (0.06)

Total "female income" 143.58 0.06 1025(10.21) (0.09)

Unattributed income 144.85 0.17 1025(6.24) (0.12)

Total expenditure 1111.45 -0.10 1008(28.41) (0.02)

Food consumption 639.37 -0.06 973(12.68) (0.02)

Adult goods 45.67 -0.32 1025(2.61) (0.12)

Clothing 263.92 -0.17 1025(9.41) (0.06)

Prestige goods 218.11 -0.17 1025(8.06) (0.07)

Staples 442.58 -0.03 1025(12.32) (0.03)

Meat 142.72 -0.12 1025(7.62) (0.04)

Vegetables 51.21 -0.07 1025(2.67) (0.08)

Processed foods 41.15 -0.25 1025(1.74) (0.04)

All purchased foods 309.86 -0.17 1020(9.09) (0.03)

All food consumed at home 424.49 -0.06 1025(13.78) (0.05)

3 Results3.1 Rainfall and Income - Table 2• Rainfall affects income• Rainfall affects male crops differently thanfemale crops

17

Table 2: First stage summary statistics

Male cash Yam Femalecrop income Income

(1) (2) (3)F statistics(p value)

All rainfall variables 1.99 3.50 2.53are significant (0.014) (0.000) (0.000)Current year rainfall variables 1.18 3.38 2.43significant (0.315) (0.000) (0.005)Past year rainfall variables 2.79 4.64 2.64significant (0.005) (0.000) (0.001)

Rainfall variables significantly different from:

Male cash crop NA

2.10Yam income (0.010) NAFemale income 2.10 2.38 NA

(0.009) (0.002)

Note(1) The full results are presented in Appendix, table 1(2) The specification include year dummies, region dummies, and their interactions

Dependent variablesCurrent

Appendix Table A1: First stage regression results

Forest Savannah Forest Savannah Forest Savannahcoefficients interaction coefficients interaction coefficients interaction

(1) (2) (3) (4) (5) (6)Difference (year 2 - year 1) in:

Aggregate rainfall current year, season 1 -0.0015175 0.0040317 0.0004811 -0.003153 -0.010761(0.001) (0.003) (0.002) (0.002) (0.006)

Aggregate rainfall current year, season 2 0.0007268 0.0013814 -0.001099 0.0015603 0.0015827(0.000) (0.002) (0.001) (0.001) (0.004)

Aggregate rainfall current year, season 3 -0.0006134 0.0038313 0.0001552 -0.002321 -0.003099(0.001) (0.001) (0.001) (0.001) (0.002)

Aggregate rainfall current year, season 4 0.0007069 -0.0042 -0.000169 0.0005378 -0.006442(0.001) (0.005) (0.001) (0.001) (0.006)

Aggregate rainfall past year, season 1 -0.0003565 0.0068233 -0.004016 -0.00618 -0.010605(0.002) (0.008) (0.003) (0.003) (0.011)

Aggregate rainfall past year, season 2 0.0000808 -0.006707 0.0008669 0.0023795 -0.000265(0.000) (0.005) (0.001) (0.001) (0.006)

Aggregate rainfall past year, season 3 -0.00138 0.0033809 -9.57E-05 -0.00226 0.0027378(0.001) (0.001) (0.001) (0.001) (0.001)

Aggregate rainfall past year, season 4 -0.0007686 -0.003408 0.0014161 0.0007269 0.0053683(0.001) (0.005) (0.001) (0.001) (0.006)

Dummy for shock, current year, season 1 -0.476418 -0.093278 -0.894238(0.233) (0.364) (0.439)

Dummy for shock, current year, season 2 0.4592265 0.3583756 0.127267 0.4623188 -2.75326(0.193) (0.485) (0.300) (0.283) (0.828)

Dummy for shock, current year, season 3

Dummy for shock, current year, season 4 -0.4114966 0.6722299 -2.134331(0.378) (0.654) (0.520)

Dummy for shock, past year, season 1 0.2208379 -0.023197 0.1107528 0.2016122 3.537023(0.208) (0.531) (0.362) (0.262) 1.107312

Dummy for shock, past year, season 2 -0.0744996 0.1403303 -0.037784 -0.133787 -2.962664(0.119) (0.429) (0.183) (0.204) 0.9110861

Dummy for shock, past year, season 3 -0.3152398 0.5705816 -1.324416 -0.124188 -3.387585(0.245) (1.027) (0.384) (0.386) 1.388615

Dummy for shock, past year, season 4 -0.7206122 0.4587139 0.7792504 -1.748257 1.238107(0.267) (1.366) (0.437) (0.408) 1.274639

Number of observations 976 614 607Note: the specifications also include year dummies, region dummies, and their interactionsStandard errors in parentheses

Male cashcrop

Dependent variablesFemale

crop incomeYam

income

3.2 Overidentification tests• Table 3: Unconstrained tests: Rainfallmatters, but can’t reject ratio restrictions.Cannot reject PE.

18

Table 3: unconstrained overidentification tests

Food consumption Adult goods Clothing Prestige

goods Education Staples Meat Vegetables Processed foods

Purchased foods

Food consumed at home

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11)

F test (p value) 3.16 2.21 3.22 3.25 1.56 3.04 1.90 1.92 3.33 5.95 2.04Rainfall variables (0.000) (0.000) (0.000) (0.000) (0.039) (0.000) (0.003) (0.003) (0.000) (0.000) (0.001)jointly significantF test (p value) 0.59 0.85 1.02 1.01 0.59 0.75 0.40 0.74 0.94 1.29 0.94Test of overidentification (0.955) (0.681) (0.443) (0.453) (0.942) (0.823) (0.997) (0.833) (0.551) (0.150) (0.549)restrictions

Note: The second row presents the F statistics for a non-linear Wald Test of overidentification restriction that all year to year differences in rainfall variables affect year to yeardifferences in expenditures only through their impact on year to year difference in total expenditure (see text, equation 19). The p value is shown in parentheses.The regressions include year dummies, region dummies, and their interactions.

Dependent variable: Change in log(item consumption)

• Table 4: Overid rejected for prestige goods,adult goods, staples, vegetables, purchasedfoods, education.a. While yam is typically cultivated bymen, its effect is often different fromthat of other male crops

b. Adult Goods & Prestige Goodsc. Education & Purchased Foodsd. Staples & vegetables – discuss possibleprice effects, however, note that yamincome associated with increased pur-chases of food, and (not shown) femaleincome associated with purchases ofstaples.

e. Chop money + interpretation of femaleincome effects

f. Look again at size of effects

19

Table 4: Restricted overidentification tests

Total expenditure

Food consumption

Adult goods Clothing Prestige


Purchased foods


(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12)

PANEL AOLS coefficients:Predicted change in male non-yam 0.126 0.062 0.870 -0.164 0.683 -0.101 0.113 0.002 0.345 0.004 -0.029 0.098income (0.049) (0.054) (0.425) (0.334) (0.209) (0.128) (0.072) (0.126) (0.210) (0.139) (0.078) (0.119)Predicted change in yam 0.207 0.227 -0.473 0.296 -0.272 0.320 0.345 0.135 0.023 0.122 0.087 0.444income (0.037) (0.041) (0.320) (0.252) (0.158) (0.108) (0.054) (0.096) (0.159) (0.105) (0.059) (0.090)Predicted change in female 0.309 0.235 1.537 0.535 0.993 -0.098 0.193 0.492 0.995 0.474 0.412 0.313income (0.056) (0.061) (0.490) (0.382) (0.239) (0.159) (0.082) (0.144) (0.239) (0.159) (0.089) (0.136)

F tests (p value) : 0.934 5.064 0.514 7.595 2.260 5.870 1.824 3.277 1.397 4.777 1.912Overidentification (0.393) (0.007) (0.598) (0.001) (0.106) (0.003) (0.162) (0.038) (0.248) (0.009) (0.148)Restriction test

PANEL B: LAGGED RAINFALLOLS coefficients: Predicted change in lagged male 0.073 0.039 0.350 0.044 0.047 0.091 0.038 0.150 0.039 0.115 0.155 -0.007non-yam income (0.020) (0.022) (0.169) (0.133) (0.082) (0.056) (0.029) (0.050) (0.083) (0.055) (0.031) (0.047)Predicted change in lagged yam -0.003 0.004 0.008 -0.125 -0.076 -0.031 -0.021 0.015 0.011 0.027 0.024 -0.018income (0.009) (0.009) (0.073) (0.059) (0.036) (0.029) (0.013) (0.022) (0.036) (0.024) (0.013) (0.021)Predicted change in lagged female -0.001 0.018 -0.024 -0.251 -0.289 0.093 0.044 0.023 -0.054 -0.010 0.062 -0.035income (0.026) (0.028) (0.220) (0.173) (0.107) (0.079) (0.038) (0.064) (0.107) (0.071) (0.040) (0.061)

F tests (p value) : 0.105 0.128 0.254 0.043 0.016 0.049 0.052 0.024 0.058 0.054 0.057Overidentification (0.900) (0.880) (0.776) (0.958) (0.984) (0.952) (0.949) (0.976) (0.943) (0.948) (0.945)Restriction testNote: The table presents the OLS coefficient of the difference in log consumption of each item on the difference in predicted log income (obtained from the equation presented in table A1). Standard errors are shown in parentheses. The regressions include year dummies, region dummies, and their interactions.The overidentification test is a non-linear wald test for the hypothesis that the coefficients in each regression are proportionalto their coefficients in column (1)

Dependent variable: Change in log (item consumption)

• Table 5: No price effects

20

Table 5 : Relationship between predicted income shocks and local prices

beef imported local rice onion salt tomato peanut palm oil local maize local milletrice paste butter

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)predicted change in male non-yam 0.09 -0.19 -0.04 0.32 -0.23 -0.07 0.23 0.44 0.36 -0.01income (0.126) (0.134) (0.157) (0.189) (0.195) (0.064) (0.288) (0.246) (0.214) (0.103)predicted change in yam income 0.00 0.01 -0.07 0.04 -0.05 -0.01 0.01 -0.14 0.00 0.09

(0.047) (0.050) (0.058) (0.070) (0.073) (0.024) (0.107) (0.091) (0.079) (0.038)predicted change in female income 0.13 0.12 0.04 0.02 -0.23 0.10 -0.50 0.53 -0.06 -0.01

(0.158) (0.168) (0.197) (0.237) (0.245) (0.080) (0.362) (0.308) (0.268) (0.129)F statistics: predicted income variables jointly 0.33 1.04 0.46 1.04 0.71 1.23 1.05 2.80 1.08 1.76significant (p-value) (0.80) (0.38) (0.71) (0.39) (0.55) (0.31) (0.38) (0.05) (0.36) (0.17)

cassava yams plantain oil palm peanuts eggs cloth fish sandals enamelnuts bowl

(11) (12) (13) (14) (15) (16) (17) (18) (19) (20)predicted change male non-yam income -0.27 0.40 0.26 -0.14 0.34 -0.15 0.34 0.05 -0.04 0.18

(0.250) (0.225) (0.320) (0.213) (0.192) (0.220) (0.212) (0.147) (0.141) (0.222)predicted change in yam income -0.03 0.04 -0.07 0.01 -0.03 0.03 0.08 -0.04 -0.06 0.07

(0.093) (0.084) (0.119) (0.079) (0.071) (0.082) (0.079) (0.055) (0.052) (0.082)predicted change in female income -0.10 -0.05 -0.31 0.09 -0.12 -0.46 0.23 -0.19 0.40 0.19

(0.314) (0.283) (0.402) (0.267) (0.240) (0.276) (0.266) (0.185) (0.176) (0.278)

F statistics: predicted 0.41 1.18 0.65 0.23 1.40 1.06 1.20 0.58 2.53 0.50income variables jointly (0.75) (0.33) (0.58) (0.87) (0.26) (0.38) (0.32) (0.63) (0.07) (0.69)significant (p-value)

Note: item prices are obtained in the market for each enumeration area. The regressions include year dummies, region dummies, and their interactions.Standard errors in parentheses

Dependent variable: change in log(item price)

3.3 Robustness Checks3.3.1 Testing for Separability andLinearity in Commodity Demand

Consider a more general functional form

log(cit) = Φ(log(xit), λi) +Xitδ + υi + νit.

For group G (e.g., ethnicity, or relativeriskiness) defineΦG(log(x)) ≡ E(Φ(log(xit), λi)|xit = x, i ∈ G).

ΦG(log(x)) and ΦH(log(x)) are identical (upto a constant) for all arbitrary groupsG andHonly if Φ(log(x), λ) = φ(log(x)) + f(λ).

21

So for households in G, we considerestimating ΦG(x) inlog(cit) = ΦG(log(xit))+Xitδ+υi+ νit+ ηitFirst difference to find

log(ci2)− log(ci1) =ΦG(log(xi2))− ΦG(log(xi1))

+(Xi2 −Xi1)δ + νi2 − νi1 + ηi2 − ηi1,

which we re-write as

log(ci2)− log(ci1) =g(log(xi2), log(xi1)) + (Xi2 −Xi1)δ

+νi2 − νi1 + ηi2 − ηi1.

22

To simplify notation, let y be the vectorlog(c2) − log(c1), z1 be the vector log(x1),z2 be the vector log(x2), m be the matrix[(Xi2 −Xi1)]. The estimator of δ conditionalon membership in groupG is:

δG =

"NXi=1

(mi − E[m|z1i, z2i, G])(mi − E[m|z1i, z2i, G])0#

"NXi=1

(mi − E[m|z1i, z2i, G])(yi − E[y|z1i, z2i, G])0#

23

To calculate ΦG(x), we first obtain theestimate of g(z1, z2) by partialling out thecoefficient ofm:

gG(z1, z2) = E[y|z1, z2, G]−E[m|z1, z2, G]δG.We then apply the partial means method

to recover the shape of ΦG(.) (up to anunidentified constant term) in equation (??):

ΦG(z) = 0.5 ∗ 1

N

NXj=1

E[y|(z, z2j, G)]

−0.5 ∗ 1

N

NXj=1

E[y|(z1j, z,G)] .

Check figures 1&2:

24

___________ Akan Households --+--+--+-- Non-Akan Households

Figs. 1a-d: Partial Linear Expenditure Functions+/- 2 std. dev. pointwise confidence intervals

Food Expenditure

Total Expenditures12.5 13 13.5 14 14.5

-1

0

1

Adult Goods


-1

0

1

Child Clothing


-2

-1

0

1

Prestige Goods


-4

-2

0

2


Figs. 1e-h: Partial Linear Expenditure Functions+/- 2 std. dev. pointwise confidence intervals

Education


-1

-.5

0

.5

Staples


-1

0

1

2

Meat


-2

-1

0

1

Vegetables


-4

-2

0

2


Figs. 1i-k: Partial Linear Expenditure Functions+/- 2 std. dev. pointwise confidence intervals

Processed Foods


-2

-1

0

1

Purchased Foods


-1

0

1

Food From Own Farm


-2

0

2

___________ High Female Variance --+--+--+-- High Male Variance

Figs. 2a-d: Partial Linear Expenditure Functions+/- 2 std. dev. pointwise confidence intervals

Food Expenditure


-1

0

1

Adult Goods


-1

-.5

0

.5

1

Child Clothing


-1

-.5

0

.5

1

Prestige Goods


-4

-2

0

2


Figs. 2e-h: Partial Linear Expenditure Functions+/- 2 std. dev. pointwise confidence intervals

Education


-2

-1

0

1

Staples


-1

0

1

2

Meat


-2

-1

0

1

Vegetables


-4

-2

0

2

4


Figs. 2i-k: Partial Linear Expenditure Functions+/- 2 std. dev. pointwise confidence intervals

Processed Foods


-1

0

1

Purchased Foods


-1

0

1

Food From Own Farm


-4

-2

0

2

4

Labor Supply and Commodity DemandSource of the worry: potential nutrition-

productivity linkages, combined with imper-fect labor markets.

Table 6 shows:• Rainfall shocks not strongly associatedwith changes in labor demand

• To the extent that it is, it does not explainour results: shocks to female & maleincome associated with higher labordemand, which nutrition links would implyincreased demand for calories (not prestigeor adult goods).

Other worry is endogenous households:if households grow with total expenditure,doesn’t challenge validity of test. But ifhh size responds to different compositionof income (e.g., nephews come when wifedoes well), this could be a problem. Table 7provides no evidence of such a problem.

25

Table 6: Restricted overidentification tests, labor supply

Total expenditure

hours worked, men

hours worked, women

hours worked in agriculture, men

hours worked in agriculture,

women

hours work, non agriculture, men

hours work, non agriculture,

women

amount spent on

paid labor (1) (1) (2) (3) (4) (5) (6)

Predicted male non-yam 0.126 0.187 0.070 0.160 0.085 0.315 0.177 -0.927income (0.049) (0.140) (0.142) (0.177) (0.186) (0.207) (0.204) (0.586)Predicted yam 0.207 0.167 0.163 0.076 0.181 -0.119 -0.089 -0.341income (0.037) (0.106) (0.108) (0.134) (0.140) (0.157) (0.154) (0.444)Predicted female 0.309 0.200 0.239 0.413 0.280 0.307 -0.031 -1.205income (0.056) (0.160) (0.162) (0.202) (0.212) (0.236) (0.233) (0.669)

F tests (p value): 0.228 0.020 0.486 0.013 1.422 0.483 0.467Overidentification (0.797) (0.980) (0.615) (0.988) (0.242) (0.617) (0.627)Restriction test

Note: The table presents the OLS coefficient of difference in log(hours) for each type of labor supply on difference in predicted log income (obtained from the equation presented in table A1). Standard errors are shown in parentheses. The regressions include year dummies, regions dummies, and their interactions.The overidentification test is a non-linear wald test for the hypothesis that the coefficients in each regression are proportionalto their coefficient in column (1)

Dependent variable: Change in log (labor supply)

Table 7: Restricted overidentification tests: family composition

total Family expenditure size male female male female male female male female male female

(1) (2) (3) (4) (5) (6) (7) (8) (9) (9) (10) (11)

male non yams 0.126 0.311 0.174 -0.192 0.129 0.316 -0.144 -0.050 0.070 0.118 0.034 0.080(0.049) (0.243) (0.125) (0.131) (0.171) (0.217) (0.156) (0.138) (0.083) (0.089) (0.095) (0.116)

Yam 0.207 0.504 0.190 0.058 -0.010 0.212 0.106 -0.099 0.210 0.110 -0.004 -0.152(0.037) (0.184) (0.094) (0.100) (0.134) (0.170) (0.117) (0.115) (0.063) (0.067) (0.067) (0.088)

female 0.309 0.843 0.106 -0.005 0.468 0.674 0.192 0.168 0.136 0.190 0.093 -0.066(0.056) (0.278) (0.144) (0.144) (0.203) (0.241) (0.187) (0.180) (0.096) (0.100) (0.106) (0.141)

F tests (p value): 0.028 0.950 0.880 0.942 0.173 0.899 0.668 1.139 0.110 0.257 1.448Overidentification (0.973) (0.387) (0.416) (0.391) (0.841) (0.408) (0.514) (0.321) (0.896) (0.774) (0.237)Restriction test

Note: The table present the OLS coefficient of difference the number of household members on difference in predicted log income (obtained from the equation presented in table A1). Standard errors are shown in parenthesis. The regression include year dummies, region dummies, and their interactions.The overidentification test is a non-linear wald test for the hypothesis that the coefficients in each regression are proportionalto their coefficient in column (1)

Dependent variable: Change in the numbers of household members in each categoryOlder adults >60Infants 0-4 Children 5-14 Teenagers 15-19 Prime age 20-60

3.3.2 Time Separability of Preferences

potential problem: durables, habit formation.Breaks recursivity.

Table 4, panel B shows no problem.There are strong dynamics: e.g., laggedcash crops have continuing effects on overallconsumption expenditure (that’s why weconditioned on expenditure in the first place).But no differential effect on commoditydemand.

26

Table 4: Restricted overidentification tests

Total expenditure

Food consumption

Adult goods Clothing Prestige


Purchased foods


(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12)

PANEL AOLS coefficients:Predicted change in male non-yam 0.126 0.062 0.870 -0.164 0.683 -0.101 0.113 0.002 0.345 0.004 -0.029 0.098income (0.049) (0.054) (0.425) (0.334) (0.209) (0.128) (0.072) (0.126) (0.210) (0.139) (0.078) (0.119)Predicted change in yam 0.207 0.227 -0.473 0.296 -0.272 0.320 0.345 0.135 0.023 0.122 0.087 0.444income (0.037) (0.041) (0.320) (0.252) (0.158) (0.108) (0.054) (0.096) (0.159) (0.105) (0.059) (0.090)Predicted change in female 0.309 0.235 1.537 0.535 0.993 -0.098 0.193 0.492 0.995 0.474 0.412 0.313income (0.056) (0.061) (0.490) (0.382) (0.239) (0.159) (0.082) (0.144) (0.239) (0.159) (0.089) (0.136)

F tests (p value) : 0.934 5.064 0.514 7.595 2.260 5.870 1.824 3.277 1.397 4.777 1.912Overidentification (0.393) (0.007) (0.598) (0.001) (0.106) (0.003) (0.162) (0.038) (0.248) (0.009) (0.148)Restriction test

PANEL B: LAGGED RAINFALLOLS coefficients: Predicted change in lagged male 0.073 0.039 0.350 0.044 0.047 0.091 0.038 0.150 0.039 0.115 0.155 -0.007non-yam income (0.020) (0.022) (0.169) (0.133) (0.082) (0.056) (0.029) (0.050) (0.083) (0.055) (0.031) (0.047)Predicted change in lagged yam -0.003 0.004 0.008 -0.125 -0.076 -0.031 -0.021 0.015 0.011 0.027 0.024 -0.018income (0.009) (0.009) (0.073) (0.059) (0.036) (0.029) (0.013) (0.022) (0.036) (0.024) (0.013) (0.021)Predicted change in lagged female -0.001 0.018 -0.024 -0.251 -0.289 0.093 0.044 0.023 -0.054 -0.010 0.062 -0.035income (0.026) (0.028) (0.220) (0.173) (0.107) (0.079) (0.038) (0.064) (0.107) (0.071) (0.040) (0.061)

F tests (p value) : 0.105 0.128 0.254 0.043 0.016 0.049 0.052 0.024 0.058 0.054 0.057Overidentification (0.900) (0.880) (0.776) (0.958) (0.984) (0.952) (0.949) (0.976) (0.943) (0.948) (0.945)Restriction testNote: The table presents the OLS coefficient of the difference in log consumption of each item on the difference in predicted log income (obtained from the equation presented in table A1). Standard errors are shown in parentheses. The regressions include year dummies, region dummies, and their interactions.The overidentification test is a non-linear wald test for the hypothesis that the coefficients in each regression are proportionalto their coefficients in column (1)

Dependent variable: Change in log (item consumption)

4 Information Asymme-tries?Note, we are finding hh members don’t insureeach other against public shocks. Doesn’tlook good for information story, but we knowthat there is lots of imperfect info. Can thisexplain finding?

Add info asymmetry: fi(r) + εi. fi(r) isdefined so that Ei(εi|r) = 0. The distributionof εi is defined by the density hi(εi|r).

maxci,t

Euf(cf) + λEum(cm)

subject to the household resource constraintcf + cm ≤ ff(r) + εf + fm(r) + εm (3)

In addition to the standard non-negativityconstrains, there are now two new incentivecompatibility constraints:

cf ∈ argmaxcf

Euf(cf)

s.t.cf ≤ t + εf

27

cm ∈ argmaxcm

Eum(cm)

s.t.cm ≤ fm(r) + εm + ff(r)− t

substituting, we find constrained PE solvesmaxt(r)

Euf(εf+t(r))+λEum(fm(r)+ff(r)+εm−t(r)).SoZ

∂uf(εf + t(r))

∂chf(εf ; r)dεf =

λ

Z∂um(fm(r) + fr(r) + εm − t(r))

∂chm(εm; r)dεm

for any rainfall realization r. Observed com-position of consumption does not depend onrainfall realizations conditional on observedtotal expenditure, unless the distribution ofunobserved income depends on rainfall. Forexample, if two distinct realizations of rainfallare associated with the same observed expen-diture, but the second involves higher varianceof εf than the first (but the same variance ofεm), then the net transfer from the husband tothe wife will be higher in the second.

28

5 Conclusion• Shocks to production of “appreciated good”(yams) translate to education, staples,overall food and away from individualgoods

• Fluctuations in male cash or female incomeassociated with more changes in individualconsumption: adult goods and prestigegoods.

• Shocks to female income associated withchanges in expenditures on all kinds offood, except staples (chop money).

• The important lesson is not (for example)that income from cash crops controlled bymen is directed towards prestige goods.Rather it is that economists may have muchto learn from the detailed observationsavailable from neighboring disciplines.This is particularly so in a case such asthat of intrahousehold resource allocationin West Africa, where the broad contours

29

of the descriptions are at once very similaracross many studies in a large number oflocal settings and strongly inconsistentwith the routine models available to appliedeconomists.

• How to interpret? Think about lim-ited commitment (like Coate/Ravallion,Kocherlakota, Ligon et al). This providesa simple explanation of the imperfect in-surance of individual shocks. Little moredificult to explain yam results. Hypothesizethat separate accounts is an endogenousresponse to limited commitment.

30

Documents

Intrahousehold Resource AllocationinCôte d’Ivoire: Social ...cru2/econ731_files/ivoireslides.pdf · ucts’ (e.g., yam) are under the control of the household head for feeding