Does Ethiopia’s Productive Safety Net Program improve child nutrition?

Abstract

We studied the link between household membership in Ethiopia’s Productive Safety Net Program (PSNP) and short-run nutrition outcomes among children aged 5 years and younger. We used 2006 and 2010 survey data from Northern Ethiopia to estimate parameters of an exogenous switching regression. This allowed us to measure the differential impacts of household characteristics on the weight-for-height Z-scores of children in member and non-member households. The magnitude and significance of household covariates differed in samples of children from PSNP and non-PSNP households and the supply of female labour seemed to matter for promoting child health in member households. Controlling for a set of observable features of children and households we found that children in member households had weight-for-height Z-scores that were 0.55 points higher than those of children in non-member households. We conclude that the PSNP is providing positive short-term nutritional benefits for children, especially in those households that are able to leverage underemployed female labor.

Appendix 1

Theoretical Model

This section presents the theoretical model, which underpins the logic outlined in the theoretical framework. We begin by developing a multi-period dynamic model of household production and consumption in which household health evolves as a stock. As a simple starting point, we assume a unitary household in which household members make decisions, including those that affect child nutrition, jointly.¹⁴ The representative household maximizes a discounted stream of utility, defined over consumption, subject to the technology of production and the evolution in stocks of human and physical capital. The problem can be written as:

$$ \mathrm{Max}{\displaystyle {\sum}_{t=0}^T{\beta}^t}U\left({C}_s\right) $$

(3)

$$ \mathrm{Subject}\ to\ {\mathrm{C}}_{\mathrm{t}}={\mathrm{I}}_{\mathrm{t}} - {\mathrm{S}}_{\mathrm{t}} $$

(4)

$$ {\overset{-}{L}}_b={L}_{tb}^G+{L}_{tb}^o+{L}_{tb}^F+{L}_{tb}^H $$

(5)

$$ {\overset{-}{L}}_d={L}_{td}^G+{L}_{td}^F+{L}_{td}^H $$

(6)

$$ {Q}_t=q\left({L}_{tb}^G,{L}_{td}^G,{A}_t,\eta \right) $$

(7)

$$ {I}_t={P}_t{Q}_t+{w}_t^o{L}_{tb}^F+{w}_t^F{L}_{tb}^F+{w}_t^F{L}_{td}^F $$

(8)

$$ {\mathrm{A}}_{\mathrm{t}}=\left(1+\mathrm{r}\right)\ {\mathrm{A}}_{\mathrm{t}-1} + {\mathrm{S}}_{\mathrm{t}} $$

(9)

$$ {H}_t=h\left({L}_{tb}^H,{L}_{td}^H,{C}_t\right)+{H}_{t-1} $$

(10)

where C _t is a vector containing consumption of food, manufactured goods and health; I_t is the income of the household; and S _t. represents savings. Equations (5) and (6) represent labor constraints for each gender category where subscripts b and d refer to male and female labor, respectively. $\overline{L}$ is the total labor endowment; ${L}_t^G$, ${L}_t^o,{L}_t^F\ \mathrm{and}\ {L}_t^H$ represent labor allocated to agricultural production, off-farm work, food-for-work (FFW) and health, respectively. Gender disaggregation of the labor force endowment is important because household health outcomes may vary depending on whether new activities require the (re)allocation of male or female labor. As off-farm employment is generally unavailable or greatly limited for women in Tigray, we assume in equation (6) that female labor cannot be allocated to off-farm employment. Q _t is an agricultural production function which is increasing in labor and stock of land and non-land productive assets (A _t ) and decreasing in negative shocks that affect production (η); P _t refers to the price of a composite agricultural product; ${w}_t^o$ and ${w}_t^F$ are wages from off-farm employment and food-for-work, respectively.

The dynamic system is governed by two equations of motion, one for physical capital (equation (8)) and one for human capital (equation (10)). A _t appreciates at the rate r and can be augmented through savings. Of course, the stock of land may depreciate from degradation and the stock of animals may depreciate from disease. The household’s stock of human capital is represented as an aggregate index of health, H _t , which evolves subject to previous health status (H _t-1 ) and improvements in health generated through the health production function [h (•)]. We assume the health production function is concave in its arguments and depends on the labor allocated to health (child care) and the current level of consumption (C _t ). In subsequent modeling, we consider child health to be part of H _t .

2Substitution of equation (7) into equation (8); equation (8) into equation (4) and equation (4) into the objective function yields the following fixed-horizon optimization problem:

$$ Max{\displaystyle {\sum}_{t=0}^T{\beta}^t}U\left[{P}_t\left(q\left({L}_{tb}^G,{L}_{td}^G,{A}_t,\eta \right)\right)+{w}_t^o{L}_{tb}^o+{w}_t^F{L}_{tb}^F+{w}_t^F{L}_{td}^F-{S}_t\right] $$

(11)

$$ Subject\ to:{\overset{-}{L}}_b={L}_{tb}^G+{L}_{tb}^o+{L}_{tb}^F+{L}_{tb}^H $$

(12)

$$ {L}_d={L}_{td}^G+{L}_{td}^F+{L}_{td}^H $$

(13)

$$ {\mathrm{A}}_{\mathrm{t}} - {\mathrm{A}}_{\mathrm{t}-1} = \mathrm{r}\ {\mathrm{A}}_{\mathrm{t}-1} + {\mathrm{S}}_{\mathrm{t}} $$

(14)

$$ {H}_t-{H}_{t-1}=h\left({L}_{tb}^H,{L}_{td}^H,{C}_t\right) $$

(15)

The choice variables in the problem are${L}_{tb}^G$,${L}_{td}^G$, ${L}_{tb}^o,{L}_{tb}^F,{L}_{td}^F,{L}_{tb}^H\ \mathrm{and}$ ${L}_{td}^H$ while the state variables are A _t and H _t . We assume that initial conditions for the state variables are given as A (0) = A ₀ and H (0) = H ₀ where A ₀ =$\overline{A}$>0 and H ₀ =$\overline{H}$>0. With a fixed terminal time T, transversality conditions for the state variables (with initial values $\overline{A}$ and $\overline{H}$) imply that the values of physical and human capital may vary at the terminal time depending on the shadow values of increments to these stocks compared with the cost of further improvements.

Accounting for the constraints on the choice variables, the dynamic Lagrangian associated with the problem is:

$$ \begin{array}{l}\mathcal{L}={\upbeta}^{\mathrm{t}}\ \mathrm{U}\left[{\mathrm{P}}_{\mathrm{t}}\left(\mathrm{q}\left(\ {\mathrm{L}}_{\mathrm{t}\mathrm{a}}^{\mathrm{G}},\ {\mathrm{L}}_{\mathrm{t}\mathrm{b}}^{\mathrm{G}},{\mathrm{A}}_{\mathrm{t}},\upeta \right)\right)+{\mathrm{w}}_{\mathrm{t}}^{\mathrm{o}}{\mathrm{L}}_{\mathrm{t}\mathrm{b}}^{\mathrm{o}}+{\mathrm{w}}_{\mathrm{t}}^{\mathrm{F}}\ {\mathrm{L}}_{\mathrm{t}\mathrm{b}}^{\mathrm{F}}+{\mathrm{w}}_{\mathrm{t}}^{\mathrm{F}}\ {\mathrm{L}}_{\mathrm{t}\mathrm{d}}^{\mathrm{F}}-{\mathrm{S}}_{\mathrm{t}}\right]+{\uptheta}_{\mathrm{t}}\left(\mathrm{r}\ {\mathrm{A}}_{t-1}+{\mathrm{S}}_{\mathrm{t}}\right)\kern1em \\ {}\kern1em +{\updelta}_{\mathrm{t}}\left[\mathrm{h}\ \left(\overline{\mathrm{L}}\mathrm{b}-{\mathrm{L}}_{\mathrm{t}\mathrm{b}}^{\mathrm{G}}-{\mathrm{L}}_{\mathrm{t}\mathrm{b}}^{\mathrm{o}}-{\mathrm{L}}_{\mathrm{t}\mathrm{b}}^{\mathrm{F}},\overline{\mathrm{L}}\mathrm{d}-{\mathrm{L}}_{\mathrm{t}\mathrm{d}}^{\mathrm{G}}-{\mathrm{L}}_{\mathrm{t}\mathrm{d}}^{\mathrm{F}},{\mathrm{C}}_{\mathrm{t}}\right)\ \right]\kern1em \\ {}\kern1em +{\uplambda}_{\mathrm{t}}\left(\overline{\mathrm{L}}\mathrm{b}-{\mathrm{L}}_{\mathrm{t}\mathrm{b}}^{\mathrm{G}}-{\mathrm{L}}_{\mathrm{t}\mathrm{b}}^{\mathrm{o}}-{\mathrm{L}}_{\mathrm{t}\mathrm{b}}^{\mathrm{F}}-{\mathrm{L}}_{\mathrm{t}\mathrm{b}}^{\mathrm{H}}\right)+\upgamma \mathrm{t}\ \left(\overline{\mathrm{L}}\mathrm{d}-{\mathrm{L}}_{\mathrm{t}\mathrm{d}}^{\mathrm{G}}-{\mathrm{L}}_{\mathrm{t}\mathrm{d}}^{\mathrm{F}}-{\mathrm{L}}_{\mathrm{t}\mathrm{d}}^{\mathrm{H}}\right)\kern1em \end{array} $$

(16)

The first-order necessary conditions (FOC) with respect to labor allocated to health and FFW for male labor are given by equation (17) and equation (18).

$$ \begin{array}{l}\frac{\partial \mathrm{\mathcal{L}}}{\partial {\mathrm{L}}_{tb}^{\mathrm{F}}} = {\upbeta}^{\mathrm{t}}\frac{\partial \mathrm{U}}{\partial {\mathrm{C}}_{\mathrm{t}}}\frac{\partial {\mathrm{C}}_{\mathrm{t}}}{\partial {\mathrm{L}}_{tb}^{\mathrm{F}}} + {\updelta}_{\mathrm{t}}\frac{\partial \mathrm{h}}{\partial {\mathrm{L}}_{tb}^{\mathrm{F}}} - {\uplambda}_{\mathrm{t}}=0\to {\upbeta}^{\mathrm{t}}\frac{\partial \mathrm{U}}{\partial {\mathrm{C}}_{\mathrm{t}}}{\mathrm{w}}_{\mathrm{t}}^{\mathrm{F}} + {\updelta}_{\mathrm{t}}\frac{\partial \mathrm{h}}{\partial {\mathrm{L}}_{tb}^{\mathrm{F}}} - {\uplambda}_{\mathrm{t}}=0\hfill \\ {}\kern16em \to {\uplambda}_{\mathrm{t}} = {\upbeta}^{\mathrm{t}}\frac{\partial \mathrm{U}}{\partial {\mathrm{C}}_{\mathrm{t}}}{\mathrm{w}}_{\mathrm{t}}^{\mathrm{F}} + {\updelta}_{\mathrm{t}}\frac{\partial \mathrm{h}}{\partial {\mathrm{L}}_{tb}^{\mathrm{F}}}\hfill \end{array} $$

(17)

$$ \frac{\partial \mathrm{\mathcal{L}}}{\partial {\mathrm{L}}_{tb}^{\mathrm{H}}}={\updelta}_{\mathrm{t}}\frac{\partial \mathrm{h}}{\partial {\mathrm{L}}_{tb}^{\mathrm{H}}}-\kern0.5em {\uplambda}_{\mathrm{t}}=0\to {\uplambda}_{\mathrm{t}}={\updelta}_{\mathrm{t}}\frac{\partial \mathrm{h}}{\partial {\mathrm{L}}_{tb}^{\mathrm{H}}} $$

(18)

Analogously, the FOC with respect to the choice variables of interest (labor allocated to health and FFW) for female labor are presented in equation (19) and equation (20).

$$ \gamma t={\beta}^t\frac{\partial U}{\partial {C}_t}{w}_t^F+{\delta}_t\frac{\partial h}{\partial {L}_{td}^F} $$

(19)

$$ \gamma t={\delta}_t\frac{\partial h}{\partial {L}_{td}^H} $$

(20)

Solving equations (17) and (18) for male labor and equations (19) and (20) for female labor results in a pair of equations that illustrate the potential connections between a program like Ethiopia’s PSNP and nutrition outcomes. Equations (21) and (22) show these links.

$$ {\upbeta}^{\mathrm{t}}\frac{\partial \mathrm{U}}{\partial {\mathrm{C}}_{\mathrm{t}}}{\mathrm{w}}_{\mathrm{t}}^{\mathrm{F}} + {\updelta}_{\mathrm{t}}\frac{\partial \mathrm{h}}{\partial {\mathrm{L}}_{tb}^{\mathrm{F}}} = {\updelta}_{\mathrm{t}}\frac{\partial \mathrm{h}}{\partial {\mathrm{L}}_{tb}^{\mathrm{H}}}\kern0.5em \to \kern0.5em {\updelta}_{\mathrm{t}}\frac{\partial \mathrm{h}}{\partial {\mathrm{L}}_{tb}^{\mathrm{F}}} = {\updelta}_{\mathrm{t}}\frac{\partial \mathrm{h}}{\partial {\mathrm{L}}_{tb}^{\mathrm{H}}} - {\upbeta}^{\mathrm{t}}\frac{\partial \mathrm{U}}{\partial {\mathrm{C}}_{\mathrm{t}}}{\mathrm{w}}_{\mathrm{t}}^{\mathrm{F}} $$

(21)

$$ \begin{array}{lll}{\upbeta}^{\mathrm{t}}\frac{\partial \mathrm{U}}{\partial {\mathrm{C}}_{\mathrm{t}}}{\mathrm{w}}_{\mathrm{t}}^{\mathrm{F}} + {\updelta}_{\mathrm{t}}\frac{\partial \mathrm{h}}{\partial {\mathrm{L}}_{td}^{\mathrm{F}}} = {\updelta}_{\mathrm{t}}\frac{\partial \mathrm{h}}{\partial {\mathrm{L}}_{td}^{\mathrm{H}}}\hfill & \to \hfill & {\updelta}_{\mathrm{t}}\frac{\partial \mathrm{h}}{\partial {\mathrm{L}}_{td}^{\mathrm{F}}} = {\updelta}_{\mathrm{t}}\frac{\partial \mathrm{h}}{\partial {\mathrm{L}}_{td}^{\mathrm{H}}} - {\upbeta}^{\mathrm{t}}\frac{\partial \mathrm{U}}{\partial {\mathrm{C}}_{\mathrm{t}}}{\mathrm{w}}_{\mathrm{t}}^{\mathrm{F}}\hfill \end{array} $$

(22)