incentives and nutrition for rotten kids: intrahousehold...

Incentives and Nutrition for Rotten Kids: Intrahousehold Food Allocation in the Philippines

Incentives and Nutrition for Rotten Kids:Intrahousehold Food Allocation in the

Philippines

Pierre Dubois and Ethan Ligon

presented by Rachel HeathNovember 3, 2006


Introduction

Outline

Introduction

Three models of Nutritional AllocationBase ModelModification 1 – Nutritional InvestmentModification 2 – Moral Hazard

Conclusion


Introduction

Motivation

I Want to do a direct test of household efficiencyI Allocational efficiency implies that

1. Marginal rate of substitution between any two commoditieswill be equated across household members

2. Full insurance within household

I Title recalls Becker’s Rotten Child Theorem → given theright incentives, a selfish child can be induced intobehaving in the best interest of the household by analtruistic head


Introduction

A Unique Dataset allows them to do this

I Collected by the International Food Policy ResearchInstitute and the Research Institute for Mindanao Culture inBukidnon, Phillipines

I Bukidnon is a poor rural, agricultural regionI The sample taken from the population of household

farming less than 15 hectares and with at least one childunder the age of 5

I The nutritional component interviewed respondents to elicita 24-hour recall of food intake (by quantity consumed)


Introduction

Summary Statistics – Consumption


Introduction

Summary Statistics – Consumption (cont.)

Things to note about this table:

I The average person in the sample appears to bemalnourished, based on WHO energy guidelines

I Inverted U-shape pattern as age increases (expected)I Differential patterns in inferior vs. superior goods


Three models of Nutritional Allocation

Outline

Introduction


Conclusion



Base Model

Outline

Introduction


Conclusion



Base Model

Each Member’s UtilityHousehold members: i = 1 (head), 2, . . . NTime periods: t = 1, 2, . . . . T(T may be finite or infinite)

each member gets utility U(cit , bit ) + Zi (ait , bit ) whereI cit is a vector of consumption goods of individual i at time t

The utility function is increasing, concave, andcontinuously differentiable in each consumption item.

I bit is a vector of individual specific characteristics (age,gender, etc.) at time t

I ait is a vector of actions undertaken by an individual i attime t → each action may increase or decrease theindividual’s utility



Base Model

Altruism weights within the Household

I The altruistic household head associates an altruismweight αit with each member at a certain timeThe weights vary over time based on the equation:

log αit+1 = log αit + εit+1

where Et(αit+1) = αit

I Efficiency tells us nothing about the level of shares ofconsumption, but does tells us something about thechange of the shares over time



Base Model

Household Head’s ProblemThe altruistic household head solves the following dynamicprogramming problem:

H(α, b, p, x) = max{(ci ,ai )

ni=1}

n∑i=1

αi(U(ci , bi) + Zi(ai , bi)) +

β

∫H(α, p, p′

n∑i=1

yi)dG(α, p, y1, ..., yn, b|α, p, a1, ..., an, b)

s. t. p′∑n

i=1 ci ≤ x

whereI ”hats” denote future realizations of variablesI the distribution function G denotes the joint distribution of next

period’s prices and output (for each member) given this period’sactivities and prices



Base Model

Implications of the model

I FOC’s imply that:

Uk (c1t , b1t)

Uk (cit , bit)= αit∀i , k

I And ratios of MRS between the head and any individualmember will vary over time only in unpredictable ways:

Uk (c1t+1,b1t+1)Uk (c1t ,b1t )

Uk (cit+1,bit+1)Uk (cit ,bit )

=αit+1

αit= eεit+1



Base Model

Indirect Utility Version of ProblemA solution to the head’s problem is a set of functions whichdetermine the spending assigned to each household member iand the corresponding demand functions c( ):

xi = ei(α, x , p, b), i = 1, . . ., nci = c(xi , p, bi), i = 1, . . ., n

Use these demands to define indirect period-specific utilitiesfrom consumption:

v(xi , p, bi) = U(c(xi , p, bi), bi), i = 1, . . ., n

And let xi map utility of consumption into expenditures, so that:

xi = e(v(xi , p, bi), p, bi) = e(w , p, bi), i = 1, . . ., n



Base Model

Indirect Utility Version of Problem, cont.

Plug into the head’s problem to get

H(α, b, p, x) = max{(a1,ci ,ai )

ni=2}

v(x −n∑

i=2

xi , p, b1) + Z1(a1, b1) +

n∑i=1

αi(v(xi , p, bi) + Zi(ai , bi)) +

β

∫H(α, p, p′

n∑i=1

yi)dG(α, p, y1, ..., yn, b|α, p, a1, ..., an, b)



Base Model

Implications of indirect utility maximization

I FOC’s imply that

αit =v ′(x1t , pt , b1t)

v ′(xit , pt , bit)∀i , t

I And we can a similar restriction on MRS as in the earliercase

v ′(x1t+1,pt ,b1t+1)

v ′(x1t , pt , b1t)

v ′(xit+1, pt , bit+1)

v ′(xit , pt , bit)=

αit+1

αit= eεit+1



Base Model

Aggregation

I Want to make a restriction on utility that allows them toconsider S groups of consumption goods→ officially, there exist household-specific, possiblytime-varying ”price indices” πS

hs(p) and functions V s suchthat υS(p, x1, ..., xs, b) = υ(p, x , b) and

∂

∂xs vs = πShs(p)

∂

∂xs V s

I This implies that the ratio of marginal utilities ofexpenditures of any two members of a household doesn’tdepend on the unknown price index



Base Model

Functional Form for Utility

They want to use a flexible form for utility

U(cit , bit) =K∑

k=1

exp(υ′γk + ζ ′itδk + ξit)Aki Bk

t(ck

it )1−θ′

k υi

1− θ′kυi

where the vector of personal characteristics bit is partitionedinto

I υi = observable time-invariant characteristics of person i(e. g. sex)

I ζit = observable time-varying characteristics of person i (e.g. age, health)

I ξit = unobservable time-varying characteristics of person i



Base Model

Functional Form for Utility continued

I {Aki }

Kk=1 = idiosyncratic (relative) utility a person gets from

different consumption goods (e. g. sweet tooth)I {Bk

t } = time-varying differences in preferences overdifferent commodities (e. g. people like fruit in the summer)

I θ′kυi = relative risk aversion that person i has over variationin the consumption of good k→ risk attitudes can vary according to sex, ethnicity, andother time-invariant characteristics



Base Model

An Estimable Equation (almost)Given this utility function, under the unitary model, the ratio of theintertemporal MRS of consumption between the HH head and personi is equal to the proportional change in the altruism parameter forperson i

exp[(∆ζ1t+1 −∆ζit+1)δ + (∆ξ1t+1 −∆ξit+1)](xk

1t+1

xk1t

)−θ′k υ1(

xkit

xkit+1

)−θ′k υi

= eεit+1

I Note that these preferences are not ”Gorman-aggregable”, i. e.,that an efficient allocation will not necessarily give householdmembers fixed shares

I Instead shares vary with household expenditures and withchanges in the time-varying characteristics of householdmembers



Base Model

Estimation

Take logs and rearrange the previous equation:

∆log(xkit ) = ∆log(xk

1t)θ′kυ1

θ′kυi+ (∆ζit −∆ζ1t)

′ δ

θ′kυi+

εit + ∆ξ1t −∆ξit

θ′kυi

I s. t. unobserved time-varying characteristics ξit aremean-independent of the unobserved characteristics (υi , ζit)

I if the unitary household model is correct, the disturbances in thisequation will be unrelated to individual-specific outcomes



Base Model

Estimation procedureI We can use three different dependent variables (expenditure,

calories, protein) because of the close relationship between thedirect and indirect utility ratios implied by the unitary householdmodel – seemingly unrelated regression framework

I Use three-stage least squares to deal with the fact the residualsfrom the equations are correlated → use changes in logHH-level food expenditure to instrument for changes in the log ofHH-head consumption

I Third stage constructs a covariance matrix of residuals acrossequations and then uses it to improve efficiency of the pointestimates in each equation

I Construct predicted earnings by regressing predictable weathertrends, education, age, sex on wages (so that the residual canbe treated as unexplained income).Over-ID test → this shouldn’t affect expenditure or nutrient intake



Base Model

Regression Results



Base Model

Notes on these results

I If all household members had homogenous risk attitudes,these coefficients would be 1

I Differential patterns with aging (males vs. females)I Days sick, nursing don’t affect consumption shares,

pregnancy does (negatively) – though not significantlyI Unexpected income does affect consumption shares →

reject unitary household model



Modification 1 – Nutritional Investment

Outline

Introduction


Conclusion




Household Head’s Problem is now

H(α, b, p, x) = max{(ci ,ai )

ni=1}

n∑i=1

αi(U(ci , bi) + Zi(ai , bi)) +

β

∫H(α, p, p′

n∑i=1

yi , b1, ...bn)dG(α, p, y1, ..., yn|α, p, a1, ..., an)

s. t. p′∑n

i=1 ci ≤ xs. t. bi = M(bi , ci) (⇔ first order Markov law of motion)

where

I ”hats” denote future realizations of variables

I the distribution function G denotes the joint distribution of nextperiod’s prices and output (for each member) given this period’sactivities and prices




Regression Results



Modification 2 – Moral Hazard

Outline

Introduction


Conclusion




Moral Hazard Intuition

I By the Revelation Principle, we know that we can write thehead’s new problem as the original problem subject to aset of incentive compatibility constraints

I Look for evidence that these constraints bind – memberswith positive shocks to off-farm earnings receive rewards(in the form of higher quality calories)




Regression Results


Conclusion

Outline

Introduction


Conclusion


Conclusion

Conclusions

I Conditional on their specification of utility function, rejecthousehold efficiency → unexpected income affectschanges in consumption shares

I Find some support that nutrition used as

1. An investment in a member’s future productivity2. An incentive to work, when labor unobserved

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