Dynamic modeling of child malnutrition and morbidity:Evidence from Nairobi’s slums

Faye, O.a, N. Islamb, H. Essendic, and J.C. Fotsod

a: CRES, Dakar - Senegal

b: CEPS/INSTEAD, Luxembourg

c: University of Southampton, UK

d: APHRC, Nairobi - Kenya

(Preliminary and uncompleted draft; do not quote, do not circulate without permission)

This version: July 2012

Abstract: This paper contributes to the analysis of the relation between child malnutrition andmorbidity by providing a comprehensive assessment of the mutual impacts of the twophenomena. We investigate the synergistic relationship between malnutrition and morbidityamong infants in Nairobi's poor urban settlements. We use data from 3,459 children enrolledin an ongoing Maternal and Child Health Longitudinal study of the Africa Population andHealth Research Center (APHRC) in Korogocho and Viwandani slums of Nairobi. Weconsider a joint dynamic framework for our analysis. The dynamic framework allowsaccounting for persistence in a given nutritional or morbidity status. Beside the self dynamicspatterns in malnutrition and morbidity, our analytical framework also account for dynamiccross-effects between the two phenomena. We address the econometric challenges associatedto our analytical framework using a bivariate random effects dynamic probit model, abivariate extension of Wooldridge (2005) approach. This paper contributes to the literature intwo ways. First, we propose an analytical framework that examines both dynamics ofmalnutrition and morbidity and analyze the contamination process between them, whichpermits to investigate the interactions existing across the two problems. Second, wecontribute to shed light on a very important empirical question: does malnutrition interactidentically with all common forms of morbidity, or is its effects stronger for some types ofmorbidity than others? Answer to this question may have important policy implications.

1. IntroductionMalnutrition (suboptimal nutrition or micronutrient deficiencies) and childhood morbidity are issues

of great public health importance throughout developing countries due to their contribution to childmortality and disability-adjusted life years (DALYs). Various studies demonstrated that these twophenomena are generally synergistic (WHO, 1968; Pelletier et al., 1993; Pelletier, 1994; Scrimshaw,2003). Malnutrition makes a child more susceptible to infection (or increases severity of infection), andinfection contributes to malnutrition, which causes a vicious circle. In fact, malnutrition causes impairedimmunity and makes the body susceptible to disease and death, while infection poses a challenge tonutrient absorption by the body and loss of appetite which also reduces nutritional benefits to the body.

It noteworthy, however, that malnutrition does not kill on its own. Rather, it is a risk factor for deathand loss of healthy life years. It interacts with disease and exacerbates the role of the latter in causingdeaths and DALYs. Pelletier et al. (1993) demonstrated that one cannot partition deaths into those due tomalnutrition and those due to other causes. Using a mathematical model, they showed that malnutritionhas a potentiating (multiplicative) effect on mortality within populations rather than an additive effect.Malnutrition increases exponentially the fatality rate per exposure to disease within any given population.This means that population with high levels of baseline mortality experience a larger increase in mortalityfor given prevalence of malnutrition than do population with low baseline of mortality (Pelletier, 2004).

The identification of malnutrition as the leading cause of child deaths and loss of healthy life years indeveloping countries is quite widespread in the literature. Numerous studies centered on quantifying theimpact of malnutrition on deaths and DALYs in children less than 5 years. A seminal appraisal in the1970s established that malnutrition was the primary contributing cause of death for roughly half of alldeaths in children under 5 years old in several Latin American countries (Puffer and Serrano, 1973).Subsequent studies using different data across various populations confirmed this finding associatingmalnutrition with higher level of child mortality (for instance Chen et al., 1980; Pelletier et al., 1993;Pelletier, 1994; WHO, 2009). These studies also demonstrated that such a link is ubiquitous. All grades ofmalnutrition are associated to higher mortality. In most studies, 46-80 percent of all nutrition-relateddeaths are in the mild-to-moderate category.

Less quantified is the inverse relationship, from infection to malnutrition. Indeed, variousexperimental and clinical studies established that all infections have an adverse effect on nutritional status(Scrimshaw, 2003). This means that infection could trigger or worsen malnutrition. The underlyingmechanisms include decreased food intake because of anorexia, decreased nutrient absorption, increasedmetabolic requirements and direct nutrient losses (Muller and Krawinkel, 2005). However, what is thecontribution of infection to a child’s susceptibility to and severity of malnutrition? This issue is seldomassessed. It is the missing piece in the literature on the synergistic relationship between child malnutritionand morbidity. Most existing studies tend to overlook the estimation of the fraction of child malnutritionattributable to infection, notwithstanding that this evidence is of central importance for designingeffective policies to promote child survival. This situation may have resulted from a lack of complexstatistics or econometric models, restricting researchers to descriptive analysis.

This paper contributes to the analysis of the relation between child malnutrition and morbidity byproviding a comprehensive assessment of the mutual impacts of the two phenomena. The inter-relationbetween child malnutrition and infection that we intend to study is without doubt dynamic in nature.

Therefore, we consider a joint dynamic framework to analyze both issues in children under five inNairobi’s slums.

The dynamic framework allows accounting for persistence in a given nutritional or morbidity status.For instance, a child who is underweight at time t may incline to be in the same nutritional status at timet+1. Likewise, being ill in time t may depend on prior experiences of being ill. The persistence in a givennutritional or morbidity status is comparable to many other economic situations (unemployment, poverty,low-pay, health status) where an individual who has experienced an event in the past is more likely toexperience that event in the future than an individual who has not experienced that event. Two possiblesources of this persistence are unobservable heterogeneity and true state dependence (Heckman, 1981).Heterogeneity arises because of differences in unobservable individual characteristics that make the latterprone to experience the same events repeatedly. Good examples that could reflect unobservedheterogeneity are child-specific genetic, biological or health endowments that are unknown byresearchers. These traits make those concerned children susceptible to some conditions that increase theirchance of being malnourished or ill. Thus, they should be taken as important determinants of children’snutritional or health profile. Failure to account for them could lead to serious bias. That is, one mightfalsely attribute persistence to causal effects of past to future morbidity or malnutrition statuses (spuriousstate dependence effect). On the contrary, true state dependence emerges when the fact of experiencing anevent in a specific period might in itself increase the probability of living the same event repeatedly in thesubsequent periods. That is, past events cause future events.

Distinguishing a true state dependency from a spurious one due to unobserved heterogeneity hassubstantial policy implication. If the persistence in malnutrition or illness is mainly driven by unobservedheterogeneity, short-run policies will not make sense since they will have little impacts on children’slong-term malnutrition or morbidity status. In contrast, in the presence of true state dependency, policiesaddressing current malnutrition and infection situations will have much more profound impacts, as notonly current situation but also future ones are prevented. When true state dependency prevails, short-runactions yield long-lasting effects.

Beside the self dynamics patterns in malnutrition and morbidity, our analytical framework alsoaccount for dynamic cross-effects between the two phenomena. We will examine the presence over timeof mutually worsening interactions between the two issues. Positive interactions suggest a multiplicativeinterrelationship between malnutrition and morbidity, which reflects a synergistic link.

We address the econometric challenges associated to our analytical framework using a bivariaterandom effects dynamic probit model, a bivariate extension of Wooldridge (2005) approach.

This paper contributes to the literature in two ways. First, we propose an analytical framework thatexamines both dynamics of malnutrition and morbidity and analyze the contamination process betweenthem, which permits to investigate the interactions existing across the two problems. Second, wecontribute to shed light on a very important empirical question: does malnutrition interact identically withall common forms of morbidity, or is its effects stronger for some types of morbidity than others? Answerto this question may have important policy implications.

The paper is organized as follows. The context of the study is presented in section 2. Theeconometric model is described in section 3. The data we use is described in section 4 where somedescriptive statistics are discussed. We then present and comment the estimation results in section 5. Thelast section concludes

2. ContextMalnutrition remains a huge public health problem throughout the developing countries, particularly

in sub-Saharan Africa. According to the World Health Organization – WHO, about 174 million childrenunder five years old in the developing countries are malnourished, over 800 million people still cannotmeet basic needs for energy and protein, over 2 000 million people experience micronutrient (vitaminsand minerals) deficiencies (WHO). Globally, suboptimal nutrition and micronutrient deficiencies(vitamins, iron, iodine, and zinc) are the most important risk factors contributing to the burden of diseasein these countries.

In 2004, the WHO (2009) counted 10.4 million children less than 5 years of age who died, mostly insub-Saharan Africa (45 percent) and in the South-East Asia (30 percent). Child underweight, togetherwith micronutrient deficiencies and suboptimal breastfeeding accounted for an estimated 3.9 milliondeaths (35 percent of total deaths) and 144 million DALYs (33 percent of loss of healthy life years) inchildren less than 5 years old. Of these deaths, a total of 2.2 million were attributable to underweight, withalmost half (1.0 million) occurring in sub-Saharan Africa, and more than 800 000 in South-East Asia.Child underweight alone is the largest cause of deaths and loss of healthy life years in children less than 5years in developing countries, causing 21 percent of deaths and DALYs (disability-adjusted life years),followed by suboptimal breastfeeding. The situation is even worse in urban poor informal settlementscharacterized by little access to health and social services, safe water, sanitation, and garbage disposal.WHO (2009) reports that, of all infectious and parasitic deaths in 2004 (including those caused by acutelower respiratory), 26 percent can be attributed to unsafe water, hygiene and sanitation; and 15 percent tosmoke from indoor use of solid fuels. In addition, the joint effect of these two risk factors withmalnutrition accounts for 46 percent of the deaths.

Notwithstanding that, malnutrition seems to be a neglected issue. The scale of the problem has notchanged much in most developing regions since 1990. Moreover, malnutrition is not still givenappropriate attention in most strategies aimed at promoting child survival. This could be explained by oneor both of the following reasons: i) a lack of evidence on the relative magnitude of link betweenmalnutrition and risk of mortality; and ii) a general perception that nutrition intervention programs are toocomplicated or costly compared with alternative diseases control programs.

Furthermore, according to Mosley and Chen’s framework for child survival, children may oscillatebetween ‘healthy’ and ‘sick’ states before succumbing to death in extreme situations[8]. Hence, a focuson child morbidity is an important contribution to child survival strategies as it offers an opportunity toinvestigate the circumstances preceding the death of a child in developing countries.

In Kenya, one in every nine children dies before the age of five mainly of acute respiratory tractinfections, diarrhea, fever, malnutrition and malaria [9]. The infant mortality rate (IMR) and the under-five mortality rate (U5MR) as reported in the Kenya Demographic and Health Survey (KDHS) of 2003were estimated at 77 and 115 deaths per 1,000 live births, respectively [10]. This is of great concern sincethe figures indicate an upturn in child mortality from 1990s, where IMR and U5MR were 74 and 112deaths per 1,000 live births respectively in 1998 up from an IMR and U5MR of 62 and 96 deaths per1,000 live births respectively in 1993 [11, 12]. Further, the Kenya Service Provision Assessment (KSPA)report indicates that 70 percent of the illnesses that cause death among the under five children in Kenyaare exacerbated by malnutrition whose indicators include stunting, wasting and underweight[9].

Moreover, studies showed that 30 percent of under-five children in the country are chronicallymalnourished (stunted) and 6 percent acutely malnourished (wasted), while 20 percent are underweight[10].

In addition, Kenya’s poverty alleviation efforts are not bearing much fruit for a significant fraction ofits population. The proportion of Kenyans living below the poverty line is hardly changing, while thelevel of inequality in consumption between the poor and the rich is growing (World Bank, 2008). This islikely to be hampered further in the future given the global economic downturn and the fact that we arewitnessing an upsurge in poverty among populations that have traditionally done relatively well, such asurban residents. Indeed, while rural poverty remains critical because most poor people live in rural areas,urban poverty is becoming a growing development concern. A combination of rapid urbanization,growing unemployment, poor planning, and bad governance have resulted in mushrooming of slumsettlements in major cities in Kenya. And most of these slum settlements are characterized by high levelson unemployment and under-employment, unstable livelihoods, lack of basic amenities (including safewater, sanitation, and garbage disposal), and social services.

Data from two Nairobi slums (Korogocho and Viwandani) show that very few slum residents are instable and salaried employment, and that the majority earn their living through casual employment andinformal businesses. Using data collected in 2003 and 2004, Zulu et al. (2006) showed that for malesaged 15 and above, only 9 percent of recent migrants and 13 percent of long term residents were insalaried employment while less than 57 percent were either in casual employment or informal business,and about 25 percent were economically inactive. The economic situation for females is much moreprecarious, with only around 2 percent being in salaried employment, and 67 percent of the recentmigrants and 56 percent of the long term residents being economically inactive. Moreover, Faye et al.(2001) found that food insecurity is widespread amongst dwellers in Korogocho and Viwandani. Abouthalf of the households are categorized as ‘food insecure with both adult and child hunger’ and only onehousehold out of five is food secure.

3. MethodologyUsually, state dependence and interactions between two supposedly related phenomena are

investigated using dynamic bivariate probit models where random effects of the two endogenousvariables (here, malnutrition and morbidity) are allowed to be correlated (Alessie et al., 2005; Clark andEtile, 2006; Stewart, 2007). These models often assume the existence of feedback effects between the twophenomena. However, they do not consider contemporaneous (direct) effects between the twoendogenous variables. In contrast, Biewen (2008) explicitly allows simultaneous (not truly) relationshipbetween the dependent variables and feedback effects. In what follows, we adopt Biewen’s approachusing a recursive bivariate probit model where current morbidity status enters into the malnutritionequation1.

Let and be the ith child’s malnutrition and morbidity states at time t, respectively.

(i= 1, …, N).

1 Greene (2000) shows that the simultaneity of such a model can be ignored since we are maximizing the log-likelihood function.

′ ( = 1,… , ) . We assume that a stochastic process governs the joint dynamics of ith child’s ′malnutrition and morbidity states as follows:∗ = + + + + + (1)∗ = + + + + (2)= 1 ∗ > 0 ; = , ℎ; = 2,… , (3)

Where: the dependent variables are the dummy indicators y (equals one if the child i ismalnourished at time t , and zero otherwise) and y (equals one if the child i is ill at time t, and zerootherwise); x is a vector of independent variables, assumed strictly exogenous; and β = (β , β ) is thecorresponding vector of parameters to be estimated. The errors terms ε and ε are independent overtime (idiosyncratic), and are assumed following a bivariate normal distribution with zero means, unitvariances, and cross-equation covariance ρ. The individual-specific terms μ and μ stand for allunobserved determinants of malnutrition and morbidity that are time-invariant for a given child(unobserved heterogeneity). The vector x summarizes the exogenous information; x is assumed strictlyexogenous.

In equations (1) and (2), coefficients of own lagged dependent variables, γ and γ , capture thetrue dependency effects. Coefficients γ , γ , and γ capture the spillover effects between the twophenomena: γ and γ correspond to the cross-effect (contemporaneous and feed-back effect,respectively) of morbidity on malnutrition while γ is the feed-back effect of malnutrition on morbidity.

The lagged dependent variables y and y are endogenous as they may be correlated with thefactors captured by μ and μ respectively. Therefore, y and y must be modeled in order toobtain consistent parameters estimation. However, one difficulty arises when modeling y andy since lagged exogenous variables are not collected in the data to allow estimating the firstobservation of these two dependent variables (initial condition problem). Nevertheless, one can posit thatthe data generation process is such that y and y are affected by the same process and so areendogenous. Various approaches exist to capture the process generating the first period observations ofthe dependent variables (Heckman, 1981; Wooldridge, 2005).

In what follows, we adopt the approach proposed by Devicienti and Poggi (2007) who extend to thebivariate case the method proposed by Wooldridge (2005) for univariate random effect probit. Devicientiand Poggi specify the individual-specific terms μ and μ and given the initial conditions (yand y ) and x the time series average of explanatory variables x , as follows:μ = a + a y + a y + x a + π (4)μ = a + a y + a y + x a + π (5)

Where: where a , a , a , and a (j = m, h) are parameters to be estimated, and (π , π ) are

normally distributed with covariance matrix Σ and

2

2

h

hmhm

hmhm

m

After insertion of (4) and (5) in (1) and (2) respectively, the model becomes:

y∗ = γ y + γ y + γ y + a + a y + a y + x a + x β + π + ε (6)y∗ = γ y + γ y + a + a y + a y + x a + π + x β + ε (7)Under our assumptions, the likelihood function is

(INSERT LIKELIHOOD FUNCTION)

4. Data and descriptive statisticsWe use data from 3,459 children enrolled in an ongoing Maternal and Child Health Longitudinal

study being conducted by the Africa Population and Health Research Center (APHRC) in Korogocho andViwandani slums of Nairobi. The project, started in 2006, has the overall aim of examining the impact ofmigration, poverty and household composition on morbidity and mortality among under-five childrenliving in informal settlements in Nairobi. The two slum areas, Korogocho and Viwandani in Nairobi City,are characterized by high unemployment, poverty, unsafe water, poor hygiene and poor environmentalsanitation.

Data in this study are collected through household interviews and measuring of babies’ heights andweights with follow-ups about every four months. The unit of analysis is children who were born in thetwo slums from September 2006 and all new births in the surveillance area are systematically included inthe study. Child nutritional status is measured using the 1978 WHO/NCHS malnutrition references.Stunting is measured using height-for-age z-scores (HAZ) while underweight is measured using weight-for-age z-scores (WAZ).

Child morbidity and malnutrition have been found to have similar determinants which include poormaternal health during pregnancy, poorly-resourced health systems, food insecurity, inadequate andinappropriate feeding practices, lack of hygiene, and poor access to safe water. At a distal level, thesedeterminants may be influenced by a range of factors such as female literacy, early marriage andchildbearing, food taboos, and proximity to essential health and social services [9, 10, 18] and yet littleresearch has been done indicating the effects of these issues on child malnutrition and morbidity. Otherspecific individual child characteristics that are likely to have an impact on a child’s nutritional status andmorbidity include age, sex, the size at birth, breastfeeding status, and previous illness episodesexperienced by the child[20]. Macro and community level factors such as national policies on health andnutrition, and the physical environment, may also have a bearing on child health and survival [8, 20, 22].

5. Estimation resultsWe estimated the model for a series of combinations of malnutrition and morbidity (underweight-

diarrhea, underweight-fever, underweight-cough, stunted-diarrhea, stunted-fever, and stunted-cough). Theresults are presented in four subsections. First, we present the structure of the covariance matrix for eachspecification and interpret the estimates of the unobserved heterogeneity and the idiosyncratic terms. Inthe second subsection, we discuss both the self- and cross-dynamic effects of malnutrition and morbidityacross the different combinations. In the next section, we analyze the impacts of other observedcharacteristics on malnutrition and morbidity. Finally, we quantify the magnitude of the most interestingregressor effects using the average partial effect of Wooldridge (2005).

5.1 Variance-covariance matrixEstimates of variance-covariance matrices are given in Table 1. Panel (a) of the table gives the estimatesof the correlation between the idiosyncratic terms. Note that the variances of the error terms arenormalized to unity. Results indicate that the correlation between the errors terms is statisticallysignificantly different from zero in all specifications. This means that a shock that affects malnutrition hasimpact on morbidity at the same time. Likewise, a shock on morbidity will affect malnutrition at the sametime. However, the sign and the magnitude of this correlation change across models. The correlation ispositive and high in the specification underweight-diarrhea (0.204), while it is negative and a bit low inthe specification stunted-diarrhea (-0.070).

Panel (b) of the table shows the parameters for unobserved heterogeneity. Results suggest that unobservedcharacteristics contribute substantively and significantly to the unsystematic variation in our models. Thevariance of the unobserved heterogeneity in our different specifications is always significantly differentfrom zero. However, there is more heterogeneity in the malnutrition equations (underweight and stunted)than in the morbidity ones. For instance, in the specifications including diarrhea, unobservedcharacteristics are responsible for about 56 percent of the unsystematic variation in underweight, and for53 in stunted. Meanwhile, for diarrhea, unobserved characteristics are indeed significant but themagnitude of their effects is largely lower (11 percent). The larger coefficient estimate of the randomterms in the malnutrition equations (underweight and stunted) could be indicative of the existence ofsome unobserved genetic, biological or health problems so that certain children tend to experiencemalnutrition. In contrast, these hidden traits seem to have a fairly limited impact on the probability forthese children to experience diarrhea.

Table 1. Variance-covariance matricesDynamics bivariate models

Underweight StuntedDiarrhea Fever Cough Diarrhea Fever Cough

a. Structure of idiosyncratic terms

Correlation0.204***

(0.020)-0.070***

(0.009)

b. Structure of unobserved heterogeneity

Malnutrition1.257***

(0.027)1.111***

(0.012)

Morbidity0.123***

(0.013)0.119***

(0.008)

Correlation0.059***

(0.009)-0.010***

(0.012)

Conversely, the correlation between the random effects ( ) is statistically significant in both

specifications. This shows that cross lagged effects in the dynamic equations are endogenous and that thesingle equation estimates (i.e., by estimating two separate equations) are inconsistent and biased. It isnoteworthy, however, that the magnitude of the correlation between the unobserved heterogeneity termsis very low in both specifications (0.059) in the specification underweight-diarrhea and (-0.010) in

stunted-diarrhea. The positive correlation suggests that the unobserved characteristics that make childrenprone to be underweight also increase the probability for these children to experience diarrhea. Incontrast, the negative correlation means that the unobserved characteristics, which make a child morelikely to be stunted, tend to reduce his probability to experience diarrhea.

5.2 Self- and cross-dynamic effects of malnutrition and morbidity

5.2.1 True state dependence and initial conditions

Our empirical specification allows analyzing both true state dependence and initial condition effects inmalnutrition and morbidity dynamics. The true state dependence effect is evaluated using the estimates ofthe own lagged dependent variables. The effects of the initial conditions are captures using the treatmentmethod proposed by Wooldridge (2005). Table 2 gives the estimates of both true state dependence andinitial conditions across our different specifications. Results indicate that diarrhea shows sizeable andstatistically significant true state dependence effects in both specifications (underweight-diarrhea andstunted-diarrhea). This means that there is a ‘vicious circle’ of diarrhea. This suggests that past diarrheaexperience implies a higher risk of experiencing diarrhea in the future. This genuine persistence observedin diarrhea could be related to parents’ lack of learning and/or to environmental problems. In fact, ifparents did not learn from a previous experience of diarrhea of their child, they are will not be aware ofthe factors that may trigger the disease. Therefore, they barely would be able to prevent it in the future.Another potential source of diarrhea true state dependence effect is the environmental perils prevailing inour study settings. The two slum areas, Korogocho and Viwandani are characterized by unsafe water,poor hygiene and sanitation system, lack of sewage and drainage, and the absence of garbage disposal.

The implication the presence of a true state dependence effect is that a short-run policy geared at breakingthe diarrhea ‘vicious circle’ will be the most effective. In other words, a short-term rescuing interventionaimed at fixing the disease at present will be enough for preventing future occurrences of diarrhea amongthe children.

We also observe from estimates in table 2 that the effect of the initial conditions for diarrhea is positiveand statistically significant for both specifications. Children who experienced diarrhea at the beginning ofthe process have then higher probabilities of experience it again the subsequent periods. This effectreflects the impact of initial diarrhea experience on the conditional mean of the random effect specific tothe diarrhea equation. The initial conditions effect reveals the distribution of the random effect specific tothe diarrhea equation.

It is worth noting that in diarrhea specific equations, initial condition effects are significant alongside thepresence of true state dependence effect. Evidence also shows that the magnitude of initial conditionestimate is almost identical or a bit higher than the magnitude of the coefficients of lag diarrhea. Thissuggests that, for fixing the disease, an early intervention is crucial. An early intervention offers themaximum of benefits, because it has greater chance to have long-lasting effects than a late rescuingintervention. The consequent recommendation for policy is a preventive action for avoiding childrenfalling into the disease, so that persistence does not add its effects keeping them ill. In this context, apreventive policy is worthiest than a rescuing intervention policy.

In malnutrition specific equations (underweight, stunted), we observe that being stunted is not trulypersistent over time. There is no statistically significant influence of lag stunted on current stunted.However, there is a significantly positive (but small) effect of past underweight status on current one. In

fact, in the malnutrition dynamics, there is almost no true state dependence effect. In contrast, theestimates show a sizable positive and significant effect of the initial conditions in both specifications. Thismeans that, once the initial conditions are taken into account, the probability of being underweight orstunted is essentially driven by the structural variables. Therefore, in terms of policy recommendation, themost effective plan for fixing the issue is the provision of long-term strategies working on the structuralvariables.

Table 2. Self-dynamic effects: True state dependence and initial conditionsDependent variable: Morbidity at time t

Diarrhea Fever CoughUnderweight stunted Underweight stunted Underweight stunted

Morbidity at:

Initial time0.195***

(0.022)0.204***

(0.030)

Time t-10.197***

(0.010)0.198***

(0.020)

Dependent variable: Malnutrition at time tUnderweight Stunted

Diarrhea Fever Cough Diarrhea Fever CoughMalnutrition at:

Initial time1.204***

(0.064)1.542***

(0.080)

Time t-10.063***

(0.016)0.005

(0.013)

5.2.2 Cross-dynamic effects: interactions between malnutrition and morbidity

The estimates of the cross-effect parameters are given in table 3. The first panel of the table gives theestimates for both direct effect (short-run) and dynamic (long-run) effects of malnutrition on morbidityprobabilities. We first observe that the cross-effects of lagged parameters of the malnutrition variables(underweight and stunted) on diarrhea are both negative and significant. This means that those childrenwho have been presenting signs of being malnourished in the previous period are less likely to catchdiarrhea at the present. This result seems indeed counter-intuitive. However, one explanation could befound in a potential positive spill-over effect of treatments against malnutrition. Actions taken to addresschild malnutrition in a given period could go beyond their primary objective, and improve the resilienceof the child against diarrhea in the subsequent periods.

On the other hand, the direct effect of malnutrition on diarrhea seems less homogeneous. The directeffect of being stunted is negative, but weakly significant. In contrast, we observe a positive directmultiplier effect of underweight on the probability of having diarrhea. The estimated coefficient ofcurrent underweight status is positive and statistically significant. This means that in the short-run, beingunderweight has a detrimental effect on children’s exposure to diarrhea, through e.g. worsening their anti-bodies. This result is very much aligned with findings in other studies, which explain the synergistic linkbetween malnutrition and child morbidity (WHO, 1968; Pelletier et al., 1993; Pelletier, 1994; Scrimshaw,2003).

We also notice that diarrhea has strong and sizeable dynamic effects on both malnutrition forms. Resultsin the second panel of table 3 show positive, statistically significant and relatively large estimatedcoefficient associated with lagged diarrhea in both malnutrition equations (underweight and stunted). Thismeans that current child malnutrition status is not independent of previous-period diarrhea experience.The probability of being malnourished is exacerbated by previous experience of diarrhea. This finding isalso consistent with the arguments that explain the multiplicative interrelationship between malnutritionand morbidity.

Table 3. Cross-dynamic effects: Interactions effects between malnutrition and diarrheaDependent variable: Morbidity at time t

Diarrhea Fever CoughMalnutrition variables

UnderweightTimet-1

-0.130***

(0.012)

Time t0.111***

(0.015)

StuntedTimet-1

-0.037**

(0.018)

Time t-0.024*

(0.017)

Dependent variable: Malnutrition at time tUnderweight Stunted

Morbidity variables at time t-1

Diarrhea0.803***

(0.042)0.879***

(0.053)FeverCough

5.3 Estimates of other structural parameters

The effects of the other structural characteristics are mostly in line with prior expectations.

5.4 Average partial effectsTo assess the magnitude of state dependence, direct, and feedback effects, the difference of counter-

factual probabilities caused by the regressors are more interesting than structural parameters per se. Incross-sectional Probit analysis, the marginal effects are routinely adopted where the probability isevaluated at the fixed levels of regressors. In panel Probit models, however, unobserved heterogeneitiesremain in the probability statement and they are continuous and do not have natural measurement unit.Therefore, it is desirable to avoid interpolating a fixed value (theoretical mean zero).

We use the average partial effect (APE) of Wooldridge (2005) for quantifying regressors’ effectswhere the effect is averaged over the distribution of the unobserved heterogeneity. We focus on the APE.

6. Conclusion

Underweight Diarrhea

Variables name Coefficients SE Coefficients SE

Constant -2.035*** 0.107 -0.936*** 0.031

Child age 2.238*** 0.057 0.128*** 0.026

(Child age)^2 -0.439*** 0.017 -0.114*** 0.005

Average child age -0.217*** 0.033 0.010** 0.006

Mother age -1.435*** 0.066 -0.319*** 0.019

Average mother age 1.188*** 0.090 0.213*** 0.010

Cohorte1 -0.033 0.030 0.199*** 0.035

Cohorte2 -0.029 0.030 0.181*** 0.025

Cohorte3 0.032* 0.017 0.249*** 0.019

Cohorte4 -0.128*** 0.008 0.227*** 0.014

Child gender 0.344*** 0.015 0.088*** 0.006

wedu1 0.120*** 0.017 -0.142*** 0.008

wedu2 -0.046*** 0.013 -0.194*** 0.015

District dummy1 -0.075*** 0.025 0.205*** 0.032

District dummy2 -0.137*** 0.031 0.442*** 0.062

District dummy3 -0.139*** 0.026 -0.077*** 0.020

District dummy5 -0.085*** 0.011 0.500*** 0.038

District dummy6 -0.223*** 0.034 0.190*** 0.034

District dummy7 -0.197*** 0.017 0.211*** 0.029

District dummy8 -0.698*** 0.097 0.421*** 0.054

District dummy9 -0.362*** 0.040 0.471*** 0.041

District dummy10 -0.472*** 0.060 0.503*** 0.044

District dummy11 -0.499*** 0.069 0.465*** 0.047

District dummy12 -0.931*** 0.205 0.283*** 0.099

District dummy13 -0.636*** 0.059 0.308*** 0.030

District dummy14 -0.454*** 0.039 0.421*** 0.034

Twin 0.400*** 0.041 0.129*** 0.030

Parity2 0.281*** 0.046 0.092*** 0.011

Parity3 0.319*** 0.042 0.053*** 0.010

Parity4 0.507*** 0.071 0.178*** 0.019

Birth weight < 2.500 kg 0.422*** 0.083 0.061*** 0.025

Underweight(t) 0.111*** 0.015

Underweight(t-1) 0.063*** 0.016 -0.130*** 0.012

Diarrhea(t-1) 0.803*** 0.042 0.197*** 0.010

Initial underweight(t=0) 1.204*** 0.064

Initial diarrhea(t=0) 0.195*** 0.022

Underweight sigma1 0.053*** 0.006

Diarrhea sigma2 -1.061*** 0.033

Rho unobs. Hetero -0.100*** 0.012

Rho biva -0.070*** 0.009

Stunted Diarrhea

Stunted Diarrhea

Variables nameCoefficients SE Coefficients SE

Constant -2.191*** 0.096 -0.911*** 0.043

Child age 0.711*** 0.045 0.130*** 0.028

(Child age)^2 -0.152*** 0.011 -0.117*** 0.010

Average child age -0.262*** 0.024 0.006 0.009

Mother age -1.891*** 0.117 -0.333*** 0.030

Average mother age 1.627*** 0.126 0.227*** 0.028

Cohorte1 0.043 0.045 0.203*** 0.041

Cohorte2 0.154*** 0.049 0.185*** 0.038

Cohorte3 0.150*** 0.027 0.250*** 0.033

Cohorte4 0.020** 0.016 0.225*** 0.018

Child gender 0.314*** 0.026 0.088*** 0.013

wedu1 0.022 0.029 -0.147*** 0.020

wedu2 -0.135*** 0.038 -0.197*** 0.026

District dummy1 0.323*** 0.059 0.200*** 0.054

District dummy2 -0.123*** 0.047 0.446*** 0.070

District dummy3 -0.328*** 0.061 -0.087*** 0.024

District dummy5 0.321*** 0.050 0.497*** 0.053

District dummy6 0.112*** 0.043 0.191*** 0.064

District dummy7 -0.005 0.025 0.208*** 0.034

District dummy8 -0.086** 0.037 0.414*** 0.048

District dummy9 0.108*** 0.023 0.462*** 0.046

District dummy10 0.017 0.034 0.507*** 0.058

District dummy11 0.229*** 0.050 0.465*** 0.051

District dummy12 -0.057 0.064 0.272*** 0.090

District dummy13 -0.065*** 0.018 0.306*** 0.043

District dummy14 -0.076* 0.041 0.419*** 0.058

Twin 0.401*** 0.068 0.123*** 0.047

Parity2 0.222*** 0.030 0.095*** 0.020

Parity3 0.382*** 0.042 0.058*** 0.023

Parity4 0.590*** 0.063 0.186*** 0.024

Birth weight < 2.500 kg 0.494*** 0.053 0.073*** 0.030

Stunted(t) -0.024* 0.017

Diarrhea(t-1) 0.879*** 0.053 0.198*** 0.020

Initial diarrhea(t=0) 0.204*** 0.030

Stunted(t-1) 0.005 0.013 -0.037** 0.018

Initial stunted(t=0) 1.542*** 0.080

Stunted sigma1 0.114*** 0.011

Diarrhea sigma2 -1.048*** 0.052

Rho unobs hetero 0.059*** 0.009

Rho biva 0.207*** 0.021

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