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

Transcription

1 Incentives and Nutrition for Rotten Kids: Intrahousehold Food Allocation in the Philippines Pierre Dubois and Ethan Ligon presented by Rachel Heath November 3, 2006

2 Introduction Outline Introduction Modification 1 Nutritional Investment Modification 2 Moral Hazard Conclusion

3 Introduction Motivation Want to do a direct test of household efficiency Allocational efficiency implies that 1. Marginal rate of substitution between any two commodities will be equated across household members 2. Full insurance within household Title recalls Becker s Rotten Child Theorem given the right incentives, a selfish child can be induced into behaving in the best interest of the household by an altruistic head

4 Introduction A Unique Dataset allows them to do this Collected by the International Food Policy Research Institute and the Research Institute for Mindanao Culture in Bukidnon, Phillipines Bukidnon is a poor rural, agricultural region The sample taken from the population of household farming less than 15 hectares and with at least one child under the age of 5 The nutritional component interviewed respondents to elicit a 24-hour recall of food intake (by quantity consumed)

5 Introduction Summary Statistics Consumption

6 Introduction Summary Statistics Consumption (cont.) Things to note about this table: The average person in the sample appears to be malnourished, based on WHO energy guidelines Inverted U-shape pattern as age increases (expected) Differential patterns in inferior vs. superior goods

7 Outline Introduction Modification 1 Nutritional Investment Modification 2 Moral Hazard Conclusion

8 Outline Introduction Modification 1 Nutritional Investment Modification 2 Moral Hazard Conclusion

9 Each Member s Utility Household members: i = 1 (head), 2,... N Time periods: t = 1, 2,.... T (T may be finite or infinite) each member gets utility U(c it, b it ) + Z i (a it, b it ) where c it is a vector of consumption goods of individual i at time t The utility function is increasing, concave, and continuously differentiable in each consumption item. b it is a vector of individual specific characteristics (age, gender, etc.) at time t a it is a vector of actions undertaken by an individual i at time t each action may increase or decrease the individual s utility

10 Altruism weights within the Household The altruistic household head associates an altruism weight α it with each member at a certain time The weights vary over time based on the equation: log α it+1 = log α it + ɛ it+1 where E t (α it+1 ) = α it Efficiency tells us nothing about the level of shares of consumption, but does tells us something about the change of the shares over time

11 Household Head s Problem The altruistic household head solves the following dynamic programming problem: β where H(α, b, p, x) = H(ˆα, ˆp, ˆp max {(c i,a i ) n i=1 } n α i (U(c i, b i ) + Z i (a i, b i )) + i=1 n y i )dg(ˆα, ˆp, y 1,..., y n, ˆb α, p, a 1,..., a n, b) i=1 s. t. p n i=1 c i x hats denote future realizations of variables the distribution function G denotes the joint distribution of next period s prices and output (for each member) given this period s activities and prices

12 Implications of the model FOC s imply that: U k (c 1t, b 1t ) U k (c it, b it ) = α it i, k And ratios of MRS between the head and any individual member will vary over time only in unpredictable ways: U k (c 1t+1,b 1t+1 ) U k (c 1t,b 1t ) U k (c it+1,b it+1 ) U k (c it,b it ) = α it+1 α it = e ɛ it+1

13 Indirect Utility Version of Problem A solution to the head s problem is a set of functions which determine the spending assigned to each household member i and the corresponding demand functions c( ): x i = ẽ i (α, x, p, b), i = 1,..., n c i = c(x i, p, b i ), i = 1,..., n Use these demands to define indirect period-specific utilities from consumption: v(x i, p, b i ) = U(c(x i, p, b i ), b i ), i = 1,..., n And let x i map utility of consumption into expenditures, so that: x i = e(v(x i, p, b i ), p, b i ) = e(w, p, b i ), i = 1,..., n

14 Indirect Utility Version of Problem, cont. Plug into the head s problem to get H(α, b, p, x) = β H(ˆα, ˆp, ˆp max {(a 1,c i,a i ) n i=2 } v(x n x i, p, b 1 ) + Z 1 (a 1, b 1 ) + i=2 n α i (v(x i, p, b i ) + Z i (a i, b i )) + i=1 n y i )dg(ˆα, ˆp, y 1,..., y n, ˆb α, p, a 1,..., a n, b) i=1

15 Implications of indirect utility maximization FOC s imply that α it = v (x 1t, p t, b 1t ) v (x it, p t, b it ) i, t And we can a similar restriction on MRS as in the earlier case v (x 1t+1,p t,b 1t+1 ) v (x it+1, p t, b it+1 ) v (x 1t, p t, b 1t ) v = α it+1 (x it, p t, b it ) α it = e ɛ it+1

16 Aggregation Want to make a restriction on utility that allows them to consider S groups of consumption goods officially, there exist household-specific, possibly time-varying price indices π S hs (p) and functions V s such that υ S (p, x 1,..., x s, b) = υ(p, x, b) and x s v s = πhs S (p) x s V s This implies that the ratio of marginal utilities of expenditures of any two members of a household doesn t depend on the unknown price index

17 Functional Form for Utility They want to use a flexible form for utility U(c it, b it ) = K exp(υ γ k + ζ it δ k + ξ it )A k i Bk t k=1 (c k it )1 θ k υ i 1 θ k υ i where the vector of personal characteristics b it is partitioned into υ i = observable time-invariant characteristics of person i (e. g. sex) ζ it = observable time-varying characteristics of person i (e. g. age, health) ξ it = unobservable time-varying characteristics of person i

18 Functional Form for Utility continued = idiosyncratic (relative) utility a person gets from different consumption goods (e. g. sweet tooth) {A k i }K k=1 } = time-varying differences in preferences over different commodities (e. g. people like fruit in the summer) {B k t θ k υ i = relative risk aversion that person i has over variation in the consumption of good k risk attitudes can vary according to sex, ethnicity, and other time-invariant characteristics

19 An Estimable Equation (almost) Given this utility function, under the unitary model, the ratio of the intertemporal MRS of consumption between the HH head and person i is equal to the proportional change in the altruism parameter for person i exp[( ζ 1t+1 ζ it+1 )δ + ( ξ 1t+1 ξ it+1 )]( x k 1t+1 x k 1t ) θ k υ 1 ( x it k xit+1 k ) θ k υ i = e ɛ it+1 Note that these preferences are not Gorman-aggregable, i. e., that an efficient allocation will not necessarily give household members fixed shares Instead shares vary with household expenditures and with changes in the time-varying characteristics of household members

20 Estimation Take logs and rearrange the previous equation: log(xit k ) = log(x 1t) k θ k υ 1 θ k υ + ( ζ it ζ 1t ) δ i θ k υ i + ɛ it + ξ 1t ξ it θ k υ i s. t. unobserved time-varying characteristics ξ it are mean-independent of the unobserved characteristics (υ i, ζ it ) if the unitary household model is correct, the disturbances in this equation will be unrelated to individual-specific outcomes

21 Estimation procedure We can use three different dependent variables (expenditure, calories, protein) because of the close relationship between the direct and indirect utility ratios implied by the unitary household model seemingly unrelated regression framework Use three-stage least squares to deal with the fact the residuals from the equations are correlated use changes in log HH-level food expenditure to instrument for changes in the log of HH-head consumption Third stage constructs a covariance matrix of residuals across equations and then uses it to improve efficiency of the point estimates in each equation Construct predicted earnings by regressing predictable weather trends, education, age, sex on wages (so that the residual can be treated as unexplained income). Over-ID test this shouldn t affect expenditure or nutrient intake

22 Regression Results

23 Notes on these results If all household members had homogenous risk attitudes, these coefficients would be 1 Differential patterns with aging (males vs. females) Days sick, nursing don t affect consumption shares, pregnancy does (negatively) though not significantly Unexpected income does affect consumption shares reject unitary household model

24 Modification 1 Nutritional Investment Outline Introduction Modification 1 Nutritional Investment Modification 2 Moral Hazard Conclusion

25 Modification 1 Nutritional Investment Household Head s Problem is now β H(α, b, p, x) = H(ˆα, ˆp, ˆp n i=1 max {(c i,a i ) n i=1 } n α i (U(c i, b i ) + Z i (a i, b i )) + i=1 y i, ˆ b1,... ˆ bn)dg(ˆα, ˆp, y 1,..., y n α, p, a 1,..., a n ) where s. t. p n i=1 c i x s. t. b i = M(b i, c i ) ( first order Markov law of motion) hats denote future realizations of variables the distribution function G denotes the joint distribution of next period s prices and output (for each member) given this period s activities and prices

26 Modification 1 Nutritional Investment Regression Results

27 Modification 2 Moral Hazard Outline Introduction Modification 1 Nutritional Investment Modification 2 Moral Hazard Conclusion

28 Modification 2 Moral Hazard Moral Hazard Intuition By the Revelation Principle, we know that we can write the head s new problem as the original problem subject to a set of incentive compatibility constraints Look for evidence that these constraints bind members with positive shocks to off-farm earnings receive rewards (in the form of higher quality calories)

29 Modification 2 Moral Hazard Regression Results

30 Conclusion Outline Introduction Modification 1 Nutritional Investment Modification 2 Moral Hazard Conclusion

31 Conclusion Conclusions Conditional on their specification of utility function, reject household efficiency unexpected income affects changes in consumption shares Find some support that nutrition used as 1. An investment in a member s future productivity 2. An incentive to work, when labor unobserved