intrahousehold investment decisions and child mortality ......explaining the first child preference...

Intrahousehold Investment Decisions and Child Mortality:

Explaining the First Child Preference in India ∗

Katy Bergstrom† William Dodds ‡

February 22, 2016

Abstract

Jayachandran and Pande (2015) discovered the existence of a strong first child bias inIndia. They suggest Hindu culture is responsible for this birth-order-gradient. We arguethis phenomenon could arise as a rational investment decision from the parents’ perspective.We develop a simple model to show that if parents are faced with significant child mortalityrisk and plan to rely on their children for support in old age, parents will invest more intheir first child relative to their second. Using data on the heights of Indian children fromdemographic health surveys, we find empirical support for our model.

Keywords: birth-order-gradient; social insurance; child mortality; India

∗We are extremely grateful to our advisor, Pascaline Dupas, for her guidance and support. We would also liketo thank the participants at various seminars at Stanford University for their useful comments.†Department of Economics, Stanford University. Email: [email protected].‡Department of Economics, Stanford University. Email: [email protected].

1 Introduction

Throughout developing, and developed, economies there is evidence that parents do not investequally in children’s human capital and health. The most documented example of this bias isthe preference for sons over daughters, which is particularly evident in the world’s two mostpopulous nations: China and India. One of the most common explanations for the existenceof this son bias is the lack of social insurance in developing countries, and the fact that sonsare more likely to earn higher wages and support their parents (Rosenzweig and Schutz, 1982;Ebenstein and Leung, 2010; and many more). However, there also exists another bias whichhas received far less attention: the bias for firstborns in India.

The first child bias in India was initially noted by Jayachandran and Pande (2015), wherethey compared the average height of Indian children to that of African children, disaggregatedby birth order. They find that, on average, children in India are shorter than children in Africadespite the fact that India outperforms Africa on most other health and socioeconomic indicatorssuch as infant mortality, maternal mortality, and life expectancy. However, the authors thenshow that despite this overall height disadvantage, Indian firstborns are actually taller thanAfrican firstborns and that the Indian height disadvantage only appears with the second childand increases with birth order. Specifically, by comparing the height-for-age z scores of Indianchildren to African children by birth order, they find that, on average, the first child in Indiais taller than the first child in Africa, yet all subsequent children are significantly shorter.1

Jayachandran and Pande further investigate this phenomenon by gender. They find that whilethe birth-order-gradient remains for both boys and girls separately, the height advantage forIndian firstborns relative to African firstborns only exists among boys. The authors suggest aneldest son preference is responsible for explaining these patterns and for why Indian childrenare on average shorter than African children.2

It has been shown that taller children grow up to earn more and lead healthier lives, onaverage. These long-run advantages of child height have been closely linked to childhood nu-trition, which has a strong influence on cognitive development and later-life diseases (Glewweand Miguel, 2007). Given that India is the world’s second most populous country with the fifthhighest stunting rate in the world (UNICEF, 2013), it is important to understand the underlyingmechanisms driving this first-child bias in order to help address stunting of later born children.As mentioned, Jayachandran and Pande (2015) suggest the observed birth-order gradient is theresult of a preference for eldest sons - encompassing both a desire to have at least one son andfor the eldest son to be healthy - leading to a negative birth-order-gradient among siblings (withthis birth order gradient varying by siblings’ gender). They relate this eldest son preferenceback to two aspects of Hindu religion: “Hinduism prescribes a patrilocal and patrilineal kinshipsystem: aging parents live with their son, typically the eldest, and bequeath property to him(Dyson and Moore, 1983; Gupta, 1987). Second, Hindu religious texts emphasize postdeathrituals which can only be conducted by a male heir. These include lighting the funeral pyre,taking the ashes to the Ganges River, and organizing death anniversary ceremonies (Arnold etal., 1998)”. Supporting this idea, the authors observe a more pronounced birth order gradientin height among Indian Hindus compared to Indian Muslims.

1This birth-order-gradient persists when comparing height between siblings, suggesting that birth order is notjust proxying for family background differences between smaller and larger families.

2A number of other studies have documented the existence of birth order effects. For example, using rich dataon child nutrition for 240 Indian families, Behrman (1988) finds that parents have a preference for earlier bornchildren. In an entirely different context, Black et. al. (2005) use Norweigan data to show that children of lowerbirth order have better educational outcomes.

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This paper proposes an alternative rationale for the existence of a birth order height gradientamong Indian children. In particular, we argue that this phenomenon could arise, in part, asa rational investment decision from the parents’ perspective. We hypothesize that if parentsare faced with significant child mortality risk and plan to rely on their children for support inold age, differential investment in children of different birth orders may be perfectly rational.Note, we do not seek to dispute the existence of an eldest son preference (in fact, if parentsbelieve sons will provide more support for them in their old age relative to daughters, then ourmodel can generate an eldest son bias), but rather provide an alternative explanation for boththe origination and continuation of this preference.

Notably, there are two assumptions imbedded in our hypothesis: 1) Parents face significantchild mortality risk and 2) Parents rely on their children for support in old age. As far asmortality rates, the overall under-five mortality rate in India was approximately 7% in 2006 (10times higher than the United States) - thus suggesting parents face significant child mortalityrisk (United Nations, 2011). Moreover, there is evidence to suggest that Indian parents expecttheir children to care for them in old age: “Caring for parents is the children’s duty; it is dharma[moral-religious order, the right way of living]. As parents raised their children, children willalso care for their parents during their sick years, when they get old.” (Lamb, 2009).

Thus, the primary goal of the paper is to develop and empirically test a model of childinvestment decisions with child mortality risk so as to explain this first-child bias. We constructa model of child investment that incorporates two stages of child mortality (infant and early-childhood) as well as a social security motive for parents to invest in their children. Using thissimple model, we show that parents may optimally invest more in their first child relative totheir second. This arises because parents have additional information about the first child’sprobability of survival when the second child is born: if the first child has already survivedthe infancy stage, parents are now more certain they will have at least one child survive tosupport them in their old age, and, hence, do not invest as heavily in the second child. Analternative way to think about this idea is that, conditional on the first child surviving infancy,the expected marginal value of investment in the second child is lower relative to the first, asparents are more certain about the first child’s survival. In addition, if we incorporate genderinto our model, with the assumption that parents believe boys will contribute more to them inlater life than girls, our model generates an eldest son bias.

Therefore, we hypothesize that the first child bias is, in part, the result of parents rationallyresponding to social security concerns. However, as noted by Jayachandran and Pande (2015),there exist numerous other explanations that could generate a first child bias (for example,cultural and religious practices). Hence, merely showing the existence of a first child bias inIndia is an inadequate test of our model. The crux of our paper is to test two additionalpredictions of our rational investment model - predictions which are more difficult to reconcilewith the standard alternative explanations for the first child bias.

Specifically, our model predicts, under certain assumptions, that investment differences be-tween first and second children increase as early-childhood (post-infancy) survival probabilityincreases and decreases as infant survival probability increases. Intuitively, as early-childhoodsurvival probability increases, investment in child 2 becomes less necessary as parents becomemore confident that child 1 will survive to adulthood (thus increasing investment differences). Incontrast, as infant survival probability increases, less information about child 1 relative to child2 is revealed by the time child 2 is born, hence parents increase the amount they invest in child2 relative to child 1 (decreasing investment differences). Our paper’s main contribution will beto test these two predictions as a validity check of our proposed social security mechanism.

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Empirically, we begin by reconfirming the result that first children are on average taller thansecond children (within a given family).3 To do so, we construct a measure of child height thatis invariant to age and gender, so that we can fairly compare heights across siblings. We refer tothis height measure as the Height-for-Age Rank score, or HAR for short. We show that usingour HAR score solves a little known but important problem: the fact that the Height-for-ageZ-score, the commonly used measure for stunting, is decreasing in age over the first 18 monthsof life and therefore makes comparisons between young siblings difficult (Cummins, 2013). Thecreation and use of this measure is a novel contribution of this paper.

Next, we test for the presence of a relationship between child mortality rates and intra-familyinvestment differences in India. To the best of our knowledge, our paper is the first to test alink between child mortality risk and intra-family investment differentials between children. Wefind that, everything else held constant, as infant survival probabilities increase, intra-familyinvestment differences decrease; further, as early-childhood survival probabilities increase, intra-family investment differences increase as well. Specifically, we find that if the infant survivalprobability increases by 1 percentage point, the height rank difference between first and secondborn siblings decreases by 25%, and if the early-childhood (post-infancy) survival probabilitydecreases by 1 percentage point, the height rank difference between first and second born siblingsdecreases by 65%. These results are, of course, local given our limited variation in survivalprobabilities. Thus, we conclude that both the presence of a first child bias, and the negative(positive) relationship between infant (early-childhood) survival probabilities and intra-familyinvestment differences provides strong evidence towards our hypothesis that the first child biasin India are, in part, explained by parents responding to a social security motive.

Finally, Jayachandran and Pande investigate the existence of a first child bias in Sub-SaharanAfrica. They find a much weaker first child bias in Africa, and suggest this weaker bias is theresult of a far weaker eldest son preference. In theory, our model should apply not only in India,but also in other developing countries in which parents rely on their children for support in oldage. Hence, we could further test our model by using cross-continent variation in infant andearly childhood mortality rates to explain the difference in strength of biases. However, due tolack of common support between the two continents’ mortality rates, as well as a plethora ofother differences between the two settings, such cross-continent analysis is difficult. In the finalsection of the paper, we instead investigate the predictions of our model within sub-SaharanAfrica. Using the same approach as for our within India analysis, we find that while thereexists a much smaller first child bias in Africa, there does not exist a relationship betweenchild investment differentials and infant and child mortality rates. This leads us to investigatewhich aspects of our model are not applicable for our African sample. We are able to show,once restricting our sample to African countries that are more in line with our model, that thefirst child bias becomes much larger (although still smaller than that in India), and that thedesired relationship between investment differentials and moratilty rates holds (although notsignficantly). We take this as preliminary evidence that our model holds in parts of Africa thatare reasonably similar to India.

The rest of the paper proceeds as follows: Section 2 presents our model of intrahouseholdinvestment decisions, Section 3 presents the data we use to test our model and the creation ofthe Height-for-Age Rank (HAR) score, Section 4 presents the results from testing our model’spredictions in India, Section 5 tests our model for Africa, and Section 6 concludes.

3Following Jayachandran and Pande (2015), and several other studies, we interpret height differences asdifferences in nutritional investments.

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2 Model of Intrahousehold Investment Decisions when facedwith Child Mortality Risk

In this section, we present a simple model of parental investment in which parents are facedwith child mortality risk and a social security motive to invest in their children. For simplicitywe choose not to model fertility decisions but instead assume parents have two children andthis is known and exogenous (in other words, we assume parents optimally choose to have twochildren). This seems like a reasonable assumption given the average fertility rate in India isaround 2.5.4 We introduce two stages of mortality risk: in infancy and in early-childhood.The probability a child survives infancy is denoted si, and the probability the child survivesearly-childhood is denoted sc. If the child survives early-childhood we assume it will make it toadulthood with probability 1. For simplicity we allow parents to only invest in their childrenduring infancy (i.e. investment in later periods is exogenous to infancy level investments).

Naturally, parents invest in their children in large part because they get severe disutilityfrom their children dying. We assume that the survival function (at least to parents) lookssomething like Figure 1. This is consistent with investments in basic health and basic foodlevels dramatically increasing the likelihood of survival. Any investments past this level willlikely have a relatively negligible effect on surival. Given a high disutility from a child dying,parents will always invest this minimal amount (i in Figure 1). Thus, we assume parents willalways invest the minimum i for all children and view any investment after this as exogenous tosurvival. In other words, any investment above i can be viewed as a “luxury” type investment.We assume this “luxury” investment, at least from the parents’ point of view, will only affectthe future earnings ability of the child.5 We examine the validility of this assumption in Section4.

Figure 1: Investment function

Finally, we assume surviving children support their parents in their old age, and the amountthey transfer is an increasing function of their level of investment, w′c(I) > 0. We assume

4Source: World Bank Development Indicators.5Note that this “luxury investment” in reality could affect the survival probabilities of the children, however,

provided parents do not view it as such, our modeling strategy will not be affected.

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parents earn a constant per period income of w for the first K periods of their life. Given ourprior assumption, parents will always spend a minimum of i on each child, thus parents havew = w − i available for consumption and “luxury” investments each period in which they havean infant (if there is no infant around they consume w, i.e. parents cannot save). In periodK + 1 parents do not earn any income, and either receive wc(I) from each surviving child or ifthey have no surviving children, receive wold where wold < wc(0). Without loss of generality,parents only live for K + 1 periods, i.e., parents live for only one period after “retirement”.

The problem from period 1 can be written as:

maxI1,IA2 ,ID2

u(w − I1) + δsiu(w − IA2 ) + δ(1− si)u(w − ID2 ) + δ2u(w) + ....

+δK+1

(s2i s

2cu(wc(I1) + wc(I

A2 ))

+ sisc(1− sisc)u (wc(I1))

+s2i sc(1− sc)u(wc(I

A2 ))

+ (1− si)siscu(wc(I

D2 ))

+(1− sisc)2u (wold)

)(1)

where I1 is the amount they invest in the first child during infancy; IA2 is the amount theyinvest in the second child during infancy conditional on the first child surviving infancy; andID2 is the amount they invest in the second child conditional on the first not surviving infancy.(Note all these investments are those above and beyond i).

2.1 Propositions (see Appendix A.5 for proofs)

Proposition 1 : I∗1 > IA∗2 for δ close to 1 and w′′(I) ≤ 0.

In words, if parents respond to a social security motive by investing in their children, optimalinvestment in the first child is higher than optimal investment in the second child. This resultreflects the idea that if the first child has already survived the infancy stage, parents are nowmore certain they will have at least one child survive to support them, and, hence, do not investas heavily in the second child. The assumption on δ is substantive; for sufficiently small δ,parents care mostly about consumption today and very little about retirement. As a result,for very small δ, parents will invest more in their second child due to their high preferencefor consumption today. The assumption that w′′(I) ≤ 0 leads to a negative definite Hessian,ensuring that an interior maximum exists.

Proposition 2 : I∗1 − IA∗2 is increasing in sc and decreasing in si if we have the followingsufficient (yet far from necessary) conditions: w′′(I) = 0, u′′′(w) = 0, and if δ, si, sc are allrelatively close to 1.

In words, this proposition states that the optimal investment difference between first andsecond children increases in early-childhood survival probability (decreases in early-childhoodmortality) and decreases in infant survival probability (increases in infant mortality). As early-childhood survival probability increases, investment in child 2 becomes less necessary as parentsbecome more confident that child 1 will survive to adulthood (thus increasing investment dif-ferences). In contrast, as infant survival probability increases, less information about child 1relative to child 2 is revealed by the time child 2 is born, hence parents increase the amount

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they invest in child 2 relative to child 1 (decreasing investment differences). The assumptionsthat δ close to 1 and w′′(I) ≤ 0 are still necessary as in Proposition 1. The other assumptions(that w′′(I) = 0, u′′′(w) = 0, and si, sc are close to 1) are for tractability purposes.

Intuitively, considering the limiting cases in which si = 1 or sc = 1 is useful. If si = 1,parents have no additional information in period 2 about child 1’s survival relative to child 2,and, thus, they invest equally in both (ignoring discounting). On the other hand, if sc = 1,parents are sure that child 1 will survive in period 2, hence they invest significantly less in child2.

Proposition 2 stipulates a particular relationship between optimal investment differencesand mortality rates provided parents’ investment decisions are influenced by a social securitymotive. Thus, testing Proposition 2 will constitute our key test as to whether the first childbias in India is a result of rational investment decisions made by parents in response to a socialsecurity motive.6

2.2 Illustration

Here we present a simple numerical illustration of our model for the following functions andparameters: wc(I) = 3I, u(w) = log(w), δ = 0.99, K = 10 and we normalize w = 1.

6As mentioned earlier, merely showing there exists a first child bias in India is an inadequate test of our model(due to the existence of many other possible mechanisms generating a first child bias). Thus, Proposition 2 servesas an additional test for the validity of our model.

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2.2.1 Investment levels when varying the probability of suriving infancy, si

Figure 2:Optimal Investment levels I∗1 , I

A∗2 when varying infant survival probability si, where I∗1 is the

optimal investment in child one, and IA∗2 is the optimal investment in child 2, conditional onchild one suriving infancy. Early-childhood survival probability: sc = 0.98; utility:

u(w) = log(w); and “social security” payment from each child conditional as a function ofinfancy investment I: wc(I) = 3I.

Figure 3: Difference in Investments I∗1 − IA∗2 when varying si. sc = 0.98, u(w) = log(w),wc(I) = 3I. See footnote of Figure 2 for variable descriptions.

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2.2.2 Investment levels when varying the probability of suriving childhood, sc

Figure 4: Investment levels I∗1 , IA∗2 when varying sc. si = 0.95, u(w) = log(w), wc(I) = 3I. See

footnote of Figure 2 for variable descriptions.

Figure 5: Difference in Investmnets I∗1 − IA∗2 when varying sc. si = 0.95, u(w) = log(w),wc(I) = 3I. See footnote of Figure 2 for variable descriptions.

2.3 Gender Differences

Jayachandran and Pande (2015) show that the height advantage Indian first-borns have overSub-Saharan African first-borns only exists for boys, and further, that a son born at birth order2 is taller than his African counterpart if and only if he is the first-born son (i.e. his older siblingis a girl). In order to reconcile these results with the above model, we need to incorporate gender

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differences into our model. Specifically, we introduce the belief that sons contribute more totheir parents in old age than daughters.

The simplest way to incorporate this belief is to allow the function wc(I) to vary by gender.In other words, we have wc,girl(I) and wc,boy(I) where wc,girl < wc,boy. From the perspective ofthe first period, parents must now maximize expected utility, where the expectation is takenover the gender of their second child. It’s easy to see that, relative to the the above model,parents will invest more in their first child if its a boy and less in their first child if its a girl.Loosely speaking, this is because if the first child is a boy (girl), its contribution to its parents,for a given level of investment, is higher (lower) in expectation than the second child. Thisis consistent with the finding that the height advantage Indian first-borns have over Africanfirst-borns only exists if the first-born is a boy.

In addition, our model will predict that investment in the second child will be higher if thesecond child is a boy compared to if it’s a girl (for any level of child 1 investment). Finally, if thefirst child is a boy, for any given level of investment in child 1, investment in child 2 (regardlessof gender) will be lower in this gender specific model (i.e. the birth-order gradient will be

steeper). This is because investments in child 1 and child 2 are substitutes (asdIA∗2 (I1)

dI1< 0).

Symetrically, if the first child is a girl, for any given level of investment in child 1, investmentin child 2 (regardless of gender) will be higher in this gender specific model (i.e. the birth-ordergradient will be flatter). Thus, our model predicts that second-born sons that are the eldest sonin a family do better than second-born sons who are the second eldest son in a family, consistentwith the finding of Jayachandran and Pande (2015).

This last prediction implies that the birth order gradient will be steepest for a male first childand a female second child. This is in direct contradiction with the conjecture in Jayachandranand Pande (2015), where they suggest that the birth order gradient is steepest among two femalesiblings. Their reasoning is as follows: the birth of a girl into a family with only daughters isassociated with parents having a desire to have more children (due to the desire to have a son).Each daughter’s additional birth will cause an upward revision of fertility plans and reducedexpenditure on the most recently born child. Since our model abstracts from fertility decisions,such a mechanism cannot be produced.7 However, due to lack of statistical power, Jayachandranand Pande (2015) are unable to provide evidence as to whether the birth order gradient amonggirls is steeper than for boys. For the same reason, we too are unable to test the predictions ofour model with the inclusion of gender differences.

3 Data

Following Jayachandran and Pande (2015), we use the 2005-2006 National Family Health Survey(NFHS-3), which employs the same sampling methodology as the internationally-used Demo-graphic and Health Surveys (DHS), as our datasource for Indian children. This is the mostrecent Indian survey that collects child height data and is representative of India’s twentylargest states. These surveys sample and interview mothers who are 15 to 49 years old, collect-ing extensive demographic information on both the mother and children aged five and under,and, crucially for us, measures the height for these children.

7This does not mean that we do not believe the mechanisn exists! Rather, modeling fertility along withdifferential child investments yields an untractable model.

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Tables A1 and A2 present summary statsitics for the entire sample, and for the sample ofmothers who have at least two children, where the first two children are alive and under theage of five, and for which we have height data on the first two children. We concentrate on thelatter sample as this is the relevant sample for our analysis.8

3.1 Comparative Child Height Measures: the HAZ score and the HAR score

Net nutrional intake in childhood is reflected in child height and subsequently adult height. Asa result child height has become a widespread measure of child malnutrition (mainly due to therelative ease of measuring child height). A common measure used is the child’s height-for-agez-score (HAZ) based on the World Health Organziation (WHO) growth standard for childrenaged 0 to 5 years. This is a universally applicable standard, describing how children shouldgrow if they receive proper nutrition and health care. The WHO constructs the distribution ofheight using a sample of children from six affluent populations across five continents (childrenfrom Brazil, Ghana, India, Norway, Oman, and the United States with no known health or en-viromental constraints to growth and who were given recommended nutrion and health inputs).A z-score of 0 represents the median of the gender- and age-specific reference population, anda z-score of -1 indicates that the child is 1 standard deviation below that reference-populationmedian. Following the formula given by the WHO, we construct a HAZ for each child we thathave height information on (see Appendix A.1 for more details on how we construct the HAZscore).

Jayachandran and Pande follow the literature and use HAZ score for their analysis. However,a concern with using HAZ is that, as shown in Cummins (2013), the HAZ score is not constantover the first 18 months of life. 9 This is the case in our Indian data (see Figure 6), and apotential explanation for this pattern is that stunting is a gradual process which is compoundedby older children spending more time in a state of malnourishment. Given that we wish tomodel investment differences across children within a family, we need to construct a relativeheight measure that does not vary with age.

One potential way to address the problem of the HAZ-age relationship is to control flexiblyfor the age of child, for example, by including age (in months) fixed effects (or age-gender fixedeffects if there is substantial difference in HAZ scores across genders for a given age group).1011 We argue, in our setting, that this approach is sub-optimal (and potentially flawed) forthree reasons. To illustrate why, first consider the setting in which we wish to identify theheight birth-order gradient by regressing the HAZ score on birth-order dummies. Given thatbirth order could be proxying for high-fertility families, we include mother fixed effects and,therefore, only use within-family variation for identification. In an attempt to correct for theage-declining relationship in the HAZ score we also include age (in months) fixed effects. Hence,the regression we are interested in is as follows, where k,m indicate child k from mother m, αm

indicate mother fixed effects, and αage indicate age fixed effects.

8We only observe height data on children aged five and under and who are currently alive. Since our modellooks at the first two children within a family, this is the relevant subsample for our analysis.

9The HAZ is often described as age-adjusted height. Howeve, age may be the single best predictor of the HAZavailable for children in less developed countries, Cummins (2013).

10Note there does not appear to be much variation in HAZ scores across gender for each age-group.11This is line with Cummins (2013) first recommendation about how to address the HAZ-age relationship,

namely controlling flexibly for age.

10

HAZk,m = βBirth Order dummiesk,m + αm + αage + εk,m (2)

Our three reasons for why this approach is sub-optimal are as follows: first including age-of-child fixed effects will limit our identifying variation, thus reducing the power of identifying thebirth-order gradient (represented by the vector of coefficients β). Second, and more importantly,our estimate of the birth-order gradient will be biased if our sample is not representative acrossall age groups. This will be the case when using the DHS surveys, as we only observe informationon children under the age of five. Thus, age effects for younger children will be primarilyestimated on higher birth order children, while age effects for older children will be primarilyestimated on lower birth order children.12 If there exists a first-child-bias, this will resultin younger children being compared to a sample of relatively shorter children (as they are, onaverage, higher birth order children), and older children being compared to a sample of relativelytaller children (as they are, on average, lower birth order children), thus decreasing the estimateof the birth-order gradient (i.e. biasing β towards zero).13 Third, if one hypothesizes that agedifference of siblings is an important determinant of child height, they cannot separately estimatethe effect of age-difference from the effect of HAZ declining with age.

Given all this, to compare heights of children of different ages and genders in our popula-tions of interest, we generate a height-rank measure based on the age and gender of a child.Specifically, we rank each child’s height within the child’s age and gender group within a rep-resentative sample (for our analysis the representative sample will be the population of India).We refer to this measure as the height-for-age-rank score, or HAR for short. By constructionthis measure will not vary with age or gender. This procedure is consistent with the second,of two, recommendations in Cummins (2013); to use within age-cohort variation in height. Weconstruct the HAR variable using the entire sample of Indian children and use this as our age-and gender-invariant height measure. In the following section we show that the (in principlebiased) HAZ-based first-child bias result of Jayachandran and Pande (2015) turns out to holdusing our HAR methodology.

12This results from the fact that we are using within-family variation (i.e. including mother fixed effects) ona censored sample. As a result, older children are more likely to be of lower birth order, while younger childrenare more likely to be of higher birth order.

13This is what Coffey et al. (2015) do in their analysis (see appendix B of their paper) claiming the first-childbias result in Jayachandran and Pande (2015) is biased. In fact, both approaches are in principle biased.

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Figure 6: Mean HAZ scores by age and gender: India

3.2 Mortality Rates

Our empirical analysis will require regional data on child mortality rates (or equivalently survivalprobabilities) across India. We use four different estimates of mortality rates: first, we use 2010state-urban level mortality rates, the finest level of disaggregation available to us, obtained fromthe 2011 Indian Census. These mortality rates will vary within a state by whether the regionin the state is rural or ubran (i.e. for each state we will have two mortality rate measures).Second we use the 2010 state-urban level mortality rates calculated only for boys. We use to thismeasure to address the concern that some regions may have higher levels of female infanticide,thus, “artificially” raising overall child mortality rates.14 Third we use 2010 state level mortalityrates from the 2011 Indian Census; and fourth we use the projected mortality rates over 2001-2005 from the 2001 Indian Census. Notably, the revelant mortality rate is whichever parentsperceive to be the mortality risk their child will face. Given the average population of an Indianstate is around 50 million, we believe the most disaggregated level of child mortality rates is best,that is the state-urban level. However, for robustness purposes, we will present our analysisusing all four sources of mortality rates. In the notation of our model from Section 2, we definesi as the probability of surviving until age one, and sc as the probability of surviving from ageone to age five, conditional on surviving until age one. In particular, si is defined as one minusthe mortality rate until age one and sc is defined as one minus the mortality rate from age oneto age five.15

14Coffey et al (2015) note that the social status of women is higher in the southern states of India relative tothe northern states. Thus, we may expect higher rates of female inftanticide in the northern states.

15See Figures A8, A9 A10, and A11 for how these three different sources of survival probabilities vary by region.

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4 Testing our Model in India

4.1 Testing the model assumptions

In this section we test the validility of our model for India. First we investigate our assump-tion that parents will always invest as much as possible to keep their children alive, and anydifference after that is a “luxury” style investment. A stronger version of this assumption isthat parent’s differential investment between their children does not affect resulting survivalprobabilities.16 Restricting our sample to just first- and second-borns, we show that, despiteevidence suggesting parents invest more in first-borns relative to second-borns, first-borns havea slightly lower probability of survival relative to second-borns. Specifically we regress the frac-tion of recommended vaccinations received on an indicator for whether the child is the secondchild, controlling for household covariates and age of month dummies. We find that, on average,second-borns receive 2.5 percentage points fewer vaccinations. Next we regress an indicator forwhether the child is deceased on the second child indicator, controlling for household covariates,and find that first children are around 2% more likely to die before age 5 than are second chil-dren. Given that first children get more vaccinations and appear to be more well nourished (seenext sub-section), we believe this evidence supports our hypothesis that while parents investdifferentially in their children, they aren’t actively changing survival probabilities by birth-orderthrough investment.

Table 1: Testing Model Assumptions

(1) (2)Percent of Vaccinations Deceased

2nd child -0.0246*** -0.0181***(0.004) (0.005)

mean dependent 0.727 0.0748N 27798 23800r2 0.349 0.0213

Note: Standard errors are clustered by mother and are presented in brackets. * p < 0.10, ** p < 0.05, ***p < 0.01. The dependent variable in the first column is the percentage of vaccines the child received (out of9), while the dependent variable in the second column is an indicator for whether the child is deceased. Weinclude the following household covariates: DHS wealth index, mother’s years of education, mother’s currentage, and religion dummies. In column 1, we also include age of child dummies (in months). We restrict oursample to children of birth order 1 and 2 only. Further, in column 2, we only include children over 13 monthsold due to censoring of child mortality for children under 1 year old. Regressions are weighted by the givensample weights.

4.2 Testing Proposition 1: I∗1 > IA∗2

We now move on to testing Proposition 1 of our model. Proposition 1 suggests that parentswill invest more in their first child than in their second child under the mild restriction thatthe discount rate, δ, isn’t too far from 1. Jayachandran and Pande (2015) have already shownthere exists a strong, negative height-birth-order gradient, indicating that parents do in factinvest more in their first-born relative to their second. We reconfirm this finding by runningthe following regression for children of birth-order 1 and 2 only:

16Note, our model only requires that parents do not perceive these “luxury” investments to affect survivalprobabilities.

13

HAZk,m = α1 + α22ndChildk,m + εk,m (3)

HARk,m = α1 + α22ndChildk,m + εk,m (4)

where k,m indicates child k from mother m, 2ndChild is a dummy indicating whether thechild is the second child, HAZ is our height-for-age-z score, HAR is our constructed height-for-age-rank score constructed from our entire sample of Indian children. In each regression we alsoinclude mother fixed effects and age-of-child fixed effects (in months). Note, in regression 3, theage fixed effects will control for the declining relationship between age and HAZ scores as wellas for any effect that age difference between siblings has on height. Since the HAR measure doesnot vary by age, the age fixed effects will only control for the effect that age difference betweensiblings has on the height. The results are presented in Table 2. Consistent with the findingsof Jayachandran and Pande, we find that second-born children are significantly shorter thanfirstborns within a family, using both our height-for-age scores. However, as mentioned in theprevious section, the estimates with the HAZ score need to be interpreted with caution. Usingthe HAR score, our results suggest that, on average, second children are ranked 16 percentagepoints below their older sibling.

Table 2: Birth Order Gradient: India

(1) (2)HAZ HAR

2nd child -0.951*** -0.160***(0.175) (0.030)

mean dependent -1.650 0.504N 25291 26004r2 0.914 0.905

Note: Standard errors presented in brackets. * p < 0.10, ** p < 0.05, *** p < 0.01. The first column uses theHAZ score as the dependent variable while the second column uses the HAR score. Mother fixed effects andage fixed effects (in months) are included in all regressions. The sample is restricted to birth order 1 and 2children. The regressions are weighted by the given sample weights.

4.3 Testing Proposition 2: I∗1 − IA∗2 is increasing (decreasing) in sc (si)

Testing Proposition 2 constitutes the main empirical portion of this paper. Proposition 2proposes a relationship between child investment within a family and child survival probabilities:namely, under a set of parameter restrictions, investment differences between the first twochildren are decreasing with respect to infant survivial rates and increasing with respect toearly-childhood survival rates.

However, in order to specify this relationship, one needs to make functional form assump-tions on the Bernoulli utility functions and the returns to child investment function, wc(I).Even with specified functional forms, there is no gaurantee that an explicit closed-form rela-tionship between child investment and child mortality rates can be derived. In addition, ourmodel abstracts away from other important factors that may affect whether parents will investdifferentially across their children. For example, one may expect people of Hindu faith to favorfirstborn over later-borns, and/or people with a higher level of education may have a greaterpreferene for equality across their children.

Due to these difficulties, we decide to take a naive reduced form approach in order to test

14

the presence of a relationship between child investment (measured by child height) and childsurvival rates. We by no means think this is a conclusive test of our model, but rather a simpleway to lend support to the link between child investment and child survival rates.

Thus, we propose the following flexible, linear relationship between child height-rank, motherand area fixed effects, child investment, and season of birth:

HARk,m,s = αm + αs + βinvestmentk,m,s + season birthk + εk (5)

where k,m, s indicate child k with mother m in area s. Note, as mentioned earlier, our HARmeasure is conditional on a child’s age and gender, hence, neither age nor gender enter equation5 directly, and investmentk,m,s is the level of investment conditional on age and gender. Wefurther assume investmentk,m,s is a linear function of the following form:

investmentk,m,s =

(λ0 + λ1(si)s + λ2(sc)s + λ3wealthm + λ4mom educationm+

λ5age mom at birthm + λ6religionm + λ7desired no kidsm + λ8sibling characteristicsk + γk

)×(

1 +∑n=2

1(birth order = n)

)(6)

Note equation 6 simply allows for the effects of the covariates to vary by birth order.

In accordance with our theoretical model, we focus solely on the HAR difference betweenfirst and second children. This is also because we only observe data on children aged five andunder. Hence, it is not common to observe a family with all of it’s first three or more childrenunder the age of five.

To remove mother and area fixed effects, we difference equation 5 across the first two siblings.Thus, the dependent variable is now the difference in HAR scores between the first two siblings,HAR diffm,s. Finally, for simplicity, we use age and gender of siblings as sibling characteristics.This gives us our primary estimating equation:

HAR diffm,s = ψ0 + ψ1(si)s + ψ2(sc)s + ΓXm + um,s (7)

where Γ is a vector of coefficients and X is a matrix including the following variables: wealth;mother’s education; age of the mother at first birth; religion of mother; desired number ofchildren; age difference between the first two children; season of birth of the first and secondchild; age of the second child; and four dummies for all possible gender combinations of the firsttwo children.

We control for several household characteristics, enumerated above. We estimate equation 7separately for all four sources of mortality rates (2010 state-urban mortality rates, 2010 state-urban boy mortality rates, 2011 state mortality rates , and projectted 2001-2005 mortalityrates). We then run additional regressions where we include interactions of childhood survivalrates with an urban dummy to allow the relationship between survival rates and child investment

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differences to vary by whether a family lives in a rural or urban setting. There are two reasonsthat we might expect rural families to be more responsive to social security motives (and hencebe more responsive to changes in survival probabilities). First, rural elderly are more likely tohave health problems and suffer from disabilities than their urban counterparts (Jeyalakshmi etal., 2011); hence, they may derive greater utility from increased assistance in old age. Second,elderly people in rural areas are much more likely to lack property and assets than elderly peoplein urban areas, resulting in increased dependence on their children (Pal, 2006).

Lastly, we only include families where the second child is older than 12 months; this isbecause stunting is a gradual process and we do not expect to see clear evidence of stuntinguntil children have reached a certain age. This is evident in our previous Figure 6 where wesee that average HAZ scores decrease with age for the first 18 months and then become stable.In addition we illustrate in Figure 7 that second child stunting relative to the first child onlybecomes evident after the second child is at least 12 months.17 Given that the NFHS3 onlycollects data for children less than five years of age, we face a trade-off between increasing theage of the second child and reducing our sample size. We believe 12 months is a reasonablecut-off choice.18

Figure 7: Mean HAR by birth order split by age of second child: India

Our results using the four different sources of mortality rates are presented in Tables 3, 4, 5, and 6. From the first two columns of Tables 3, 4, 5, and 6, we find that, as predicted byour model, all coefficients on the early childhood survival probability (sc) are positive whileall coefficients on the infant survival probability (si) are negative, regardless of the source ofmortality rates we use.19 Interpreting the results from Column 2 Table 3, we find that asearly-childhood survival probability, sc, increases by 1 percentage point, the difference in child

17Note that our sample now includes only families that have at least two children, where both the first andsecond child are alive and under the age of five.

18For robustness, we also run our regression (using state-urban level mortality rates) with a cut-off of 18 months- i.e. we only include families where the second child is 18 months or older. These results are presented in TableA3. While our point-estimates have the expected sign, they are not always significant, likely due to the reductionin sample size.

19While the coefficients are not always significant, we find these results promising given the small samplesize and limited variation in mortality rates. All coefficients on infant and early-child survival probabilities aresignificant in our preferred specification (Table 3).

16

height percentile increases by 4.2 percentage points. Relating this coefficient to the mean of thedependent variable, as the early-childhood survival probability increases by 1 percentage point,the average height rank difference between first and second born siblings increases by 65%.Similarly, if the infant survival probability, si increases by 1 percentage point, the difference inchild height percentile decreases by 1.7 percentage points. Equivalently, as the infant survivalprobability increases by 1 percentage point, the average height rank difference between firstand second born siblings decreases by 25%. However, given the support of the infant andearly-child survival probabilities is approximately (0.9, 1) and (0.96, 1), respectively, we need toacknowledge that these estimates are local, and should not be expected to hold over a largerange of survival probabilities.20

Finally, we look at heterogeneity along the urban/rural dimension. In the last two columnsof Tables 3, 5 and 6 we interact both survival probabilities with an urban dummy. We find thatthe effect of survival probabilities on height differences is as predicted in rural areas, however,we find no significant relationship in urban areas. These results support our hypothesis thatthere exists a greater social security motive to invest in children in rural areas relative to urbandue to the greater dependence on children in rural areas due to higher incidences of healthproblems and lack of property/assets in rural areas relative to urban areas.

Overall we find evidence to support both Propositions 1 and 2 in India. As we have no othertheory that would predict both of these results, we believe this provides strong evidence towardsthe idea that the first child bias in India is, in part, a result of rational investment decisionsmade by parents in response to a social security motive.

20Note, the predictions of our model are also only valid for values of si and sc reasonably close to 1.

17

Table 3: HAR difference on Survival Probabilities (2010 state-urban survival probs)

(1) (2) (3) (4)2 Only 2 Plus 2 Only 2 Plus

Infant Survival Prob. -1.671* -2.083** -1.566 -2.174**(0.948) (0.859) (1.132) (1.027)

Early Child Survival Prob. 4.241** 4.460** 4.480** 4.856**(1.962) (1.791) (2.244) (2.032)

Infant Surv. Prob. X urban 3.076 3.175(2.524) (2.418)

Early Child Surv. Prob. X urban -3.064 -3.789(4.673) (4.468)

Urban Effect Pvalue 0.396 0.628mean dependent 0.0648 0.0701 0.0648 0.0701N 1706 2007 1706 2007r2 0.0387 0.0422 0.0414 0.0437

Note: Standard errors presented in brackets. * p < 0.10, ** p < 0.05, *** p < 0.01. The dependent variableis the difference in HAR score between the first and second child within a family. Survival probabilities arethe 2010 state-urban level probabilities. Columns with the heading 2 Plus indicate that the regression is es-timated for families with 2 or more children, while columns with the heading 2 Only indicate families withonly 2 children thus far. We only include families for which the first two children are alive, under 5 years old,and the second child is over a year old. The regressor “Infant Survival Prob.” is the state-urban level prob-ability that a child survives the first 12 months, while“Early Child Survival Prob.” is the state-urban levelprobability that a child survives until the age of 5 conditional on surviving the first 12 months. Columns 3and 4 interact state-wise probabilities with the urban dummy. We include the following household covari-ates: DHS wealth index, mother’s years of education, mother’s age at 1st birth, religion dummies, quarterchild was born, age of the second child, age difference between the first two children, dummies for differentgender combinations of first two children, and the number of desired children. The regressions are weightedby the given sample weights.

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Table 4: HAR difference on Survival Probabilities (2010 state-urban male survival probs)


Infant Survival Prob. -1.447 -1.653** -1.085 -1.552(0.903) (0.805) (1.073) (0.960)

Early Child Survival Prob. 4.022** 3.587** 3.643 3.587*(1.988) (1.797) (2.280) (2.043)




Note: Standard errors presented in brackets. * p < 0.10, ** p < 0.05, *** p < 0.01. The dependent variableis the difference in HAR score between the first and second child within a family. Survival probabilities arethe 2010 state-urban level probabilities for boys only. Columns with the heading 2 Plus indicate that theregression is estimated for families with 2 or more children, while columns with the heading 2 Only indicatefamilies with only 2 children thus far. We only include families for which the first two children are alive,under 5 years old, and the second child is 12 months or older. The regressor “Infant Survival Prob.” is thestate-urban level probability that a male child survives the first 12 months, while“Early Child Survival Prob.”is the state-urban level probability that a male child survives until the age of 5 conditional on surviving thefirst 12 months. Columns 3 and 4 interact state-wise probabilities with the urban dummy. We include thefollowing household covariates: DHS wealth index, mother’s years of education, mother’s age at 1st birth,religion dummies, quarter child was born, age of the second child, age difference between the first two chil-dren, dummies for different gender combinations of first two children, and the number of desired children.The regressions are weighted by the given sample weights.

19

Table 5: HAR difference on Survival Probabilities (2010 state survival probs)


Infant Survival Prob. -0.319 -1.028 -2.247* -2.898**(1.110) (1.033) (1.361) (1.234)

Early Child Survival Prob. 2.001 2.730 5.878** 6.324***(2.209) (2.043) (2.694) (2.437)

Infant Surv. Prob. X urban 5.178** 5.370***(2.175) (2.067)

Early Child Surv. Prob. X urban -10.46** -10.19**(4.341) (4.105)


Note: Standard errors presented in brackets. * p < 0.10, ** p < 0.05, *** p < 0.01. The dependent variableis the difference in HAR score between the first and second child within a family. Survival probabilities arethe 2010 state level probabilities. Columns with the heading 2 Plus indicate that the regression is estimatedfor families with 2 or more children, while columns with the heading 2 Only indicate families with only 2children thus far. We only include families for which the first two children are alive, under 5 years old, andthe second child is over a year old. The regressor “Infant Survival Prob.” is the state level probability thata child survives the first 12 months, while“Early Child Survival Prob.” is the state level probability that achild survives until the age of 5 conditional on surviving the first 12 months. Columns 3 and 4 interact state-wise probabilities with the urban dummy. We include the following household covariates: DHS wealth index,mother’s years of education, mother’s age at 1st birth, religion dummies, quarter child was born, age of thesecond child, age difference between the first two children, dummies for different gender combinations of firsttwo children, and the number of desired children. The regressions are weighted by the given sample weights.

Table 6: HAR difference on Survival Probabilities (2001-2005 state survival probs)


Infant Survival Prob. -0.765 -1.311 -1.508 -1.970**(0.866) (0.813) (1.061) (0.967)

Early Child Survival Prob. 1.712 2.088* 2.631* 2.882**(1.281) (1.181) (1.566) (1.403)




Note: See footnote of Table 5. Survival probabilities are the projected 2001-2005 state level probabilities.

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5 What About Africa?

The model presented in Section 2 should, in theory, apply not only in India, but also in otherdeveloping countries in which parents rely on their children for support in old age. As such,we turn to investigating the extent to which Propositions 1 and 2 hold in Sub-Saharan Africa(see Appendix A.4 for a list of African countries used). Our data for this section come fromthe African DHS surveys as well as country level mortality rates from the United Nations. Webegin with Proposition 1, examining whether parents invest more in their first child than intheir second child. To mirror our analysis in India, we construct a height rank measure basedon age and gender. Specifically, we rank each child’s height within the child’s age (months) andgender group, for all of our sample of Africa (i.e. a boy of 18 months from Tanzania is rankedin the same group as a boy of 18 months from Kenya). Just as in our analysis for India, weregress our height rank measure on a dummy for second born as well as mother and age fixedeffects:

HARk,m = α1 + α22ndChildk,m + εk,m

These results are presented in Table 7. Just as in India, second children are significantlyshorter than first children. However, comparing the magnitudes from Table 2 and Table 7, wesee that the second child bias is significantly more pronounced in India than in Sub-SaharanAfrica. Nonetheless, the existence of a first child bias provides evidence that Proposition 1 holdsin Africa. Furthermore, as almost no Africans are Hindus, this shows that at least some of thefirst child bias is not due to Hindu culture.

Table 7: Birth Order Gradient: Africa

(1) (2)HAZ HAR

2nd child -0.262** -0.0559***(0.110) (0.016)

mean dependent -1.650 0.504N 49141 51334r2 0.892 0.883

Note: Standard errors presented in brackets. * p < 0.10, ** p < 0.05, *** p < 0.01. The first column uses theHAZ score as the dependent variable while the second column uses the HAR score. Mother fixed effects andage fixed effects (in months) are included in all regressions. The sample is restricted to birth order 1 and 2children. The regressions are weighted by the given sample weights.

Next, we turn to investigating whether Proposition 2 holds in Africa. We estimate Equation7 in Africa:

HAR diffm,s = ψ0 + ψ1(si)s + ψ2(sc)s + ΓXm + um,s

Notably, we use country level survival probabilites in Africa whereas we used state levelsurvival probabilities in India. This is actually a convenient comparison as the size distributionof African countries in our sample is similar to the size distribution of Indian states. Theresults from estimating Equation 7 are presented in Table 8. As can be seen from the table, allof the coefficients are small and highly statistically insignificant. Thus, it appears that parentsin Africa are not responding to differences in surivival probabilities by differentially allocatingresources to their children.

21

Table 8: Height Rank Differences on Child Mortality across Africa


Infant Survival Prob. 0.106 0.248 -0.339 -0.159(0.599) (0.545) (0.687) (0.627)

Early Childhood Survival Prob. -0.391 -0.420 -0.228 -0.266(0.469) (0.435) (0.521) (0.483)




Note: Standard errors presented in brackets. * p < 0.10, ** p < 0.05, *** p < 0.01.The dependent variableis the difference in HAR score between the first and second child within a family. Survival probabilities arecountry level survival probabilites for 2000-2005 from the UN. We only include families for which the first twochildren are alive, under 5 years old, and the second child is over a year old. The regressor “Infant SurvivalProb.” is the country level probability that a child survives the first 12 months, while“Early Child SurvivalProb.” is the country level probability that a child survives until the age of 5 conditional on surviving thefirst 12 months. Columns 3 and 4 interact these country probabilities with the urban dummy. We includethe following household covariates: DHS wealth index interacted with log GDP from each country, mother’syears of education, mother’s age at 1st birth, religion dummies, quarter child was born, age of the first child,age difference between the first two children, dummies for different gender combinations of first two children,and the number of desired children. The regressions are weighted by the given sample weights.

Given this, we attempt to investigate why Proposition 2 does not seem to hold in Africa. Wehave three non-competing explanations that hinge on fundamental differences between India andSub-Saharan Africa: differences in discount rates, differences in fertility rates, and differencesin infant and child survival probabilities.

First, African parents’ discount rates may be significantly higher than Indian families dis-count rates. This seems reasonable given the drastically higher mortality rates in Africa (seeTable 9). In the context of our model from Section 2, a reasonably high discount rate wasrequired to generate both of our theoretical preditions. To support this concern, we investi-gate the birth-order-gradient for low adult mortality African countries and high adult mortalityAfrican countries (low as in mortality rates are below the median for our sample, and high asin mortality rates are above the median for our sample). Results are presented in Table 10.As we can see, the birth-order-gradient more than doubles when we restrict our sample to lowadult mortality countries.

22

Table 9: Adult Mortality Rates (Probablity of Dying Between 15 and 60 Years (WHO, 2000))

Country 15-59 Mortality Rate

Cameroon .386Chad .462Congo .426DRC .388Ethiopia .386Ghana .297Guinea .344India .239Kenya .438Lesotho .574Libera .355Madagascar .284Malawi .595Mali .361Namibia .414Niger .284Nigeria .400Rwanda .472Sao Tome and Principe .221Senegal .252Sierra Leone .536Swaziland .526Uganda .577United Republic of Tanzania .440Zambia .670Zimbabwe .751

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Table 10: Birth Order Gradient, Africa: Split by Adult Mortality

(1) (2)Low Mortality High Mortality

2nd child -0.108*** -0.0440*(0.032) (0.026)


Note: Standard errors presented in brackets. * p < 0.10, ** p < 0.05, *** p < 0.01. The dependent variable inboth columns is the HAR score. Mother fixed effects and age fixed effects (in months) are included in bothregressions. The sample is restricted to birth order 1 and 2 children. The regressions are weighted by thegiven sample weights. Column (1) restricts to Sub-Saharan African countries in our sample that have belowmedian adult mortality rates, while column (2) restricts to countries with above median adult mortality rates.

Second, fertility rates are much higher in Africa than in India.21 Both Proposition 1 andProposition 2 were derived in a model that abstracted away from fertility decisions and setthe exogenously given number of children to two. While abstracting from fertility decisionsis required to yield a tractable model, the exogenous number of children could, in principle,be any number. Therefore, to construct a more appropriate model for Africa we should setthe exogenous fertility rate at 5 rather than 2. However, while solving such a model is com-putationally feasible, it produces no analytically tractable predictions. Nonetheless, it seemsentirely reasonable that differences in fertility decisions in Africa (relative to India) may yieldan entirely different environment in which parents respond very little to differences in infantand early childhood mortality.

Finally, our model predicts that investment differences will be decreasing in si and increasingin sc, as long as si and sc are sufficiently close to 1. While this restriction seems reasonablein India, a number of African countries have child and infant survival probabilities lower than90%. Given that we see such low survival probabilites in Africa, we may not expect Proposition2 to hold.

To address these concerns, we attempt to restrict our sample in several ways. First, toproxy for varying parental discount rates, we add in additional controls for the adult survivalprobabilitiy by country. Second, we only include families who desire 4 children or less (thiscorresponds to roughly 50% of our sample). Finally, we restrict our sample further to onlycountries with both infant and child survival probabilities greater than 0.9. This leaves us withonly 1,100 observations.

While these restrictions severely limit the sample size as well as identifying variation in siand sc, we now get reasonably similar coefficients on si and sc as in India (however, they arenot statistically significant). These regressions are presented in Table 11. 22 Despite the limitedsample size and variation, we interpret this result as suggestive evidence that 1) differences indiscount rates, differences in fertility rates, and differences in infant and child survival proba-bilities are affecting parents’ responses to survival probabilities and 2) that Proposition 2 mayhold to some extent in Africa when applied only to smaller families in areas where mortalityrates are not overly high.

21The total fertility rate in Sub-Saharan Africa is 5.1 versus 2.5 in India (World Bank Development Indicators).22Regressions with just 1 or 2 of the changes to the estimating sample are included in Appendix Table A4.

24

Table 11: HAR difference on Survival Probabilities

(1) (2)Non-Restricted Sample Restricted Sample

Infant Survival Prob. 0.248 -1.453(0.545) (2.119)

Early Childhood Survival Prob. -0.420 1.659(0.435) (1.952)


Note: Standard errors presented in brackets. * p < 0.10, ** p < 0.05, *** p < 0.01. The dependent variableis the difference in HAR score between the first and second child within a family. Survival probabilities arecountry level survival probabilites for 2000-2005 from the UN. We only include families for which the first twochildren are alive, under 5 years old, and the second child is over a year old. The regressor “Infant SurvivalProb.” is the country level probability that a child survives the first 12 months, while“Early Child SurvivalProb.” is the country level probability that a child survives until the age of 5 conditional on surviving thefirst 12 months. The restricted sample only includes countries in which both the infant and early childhoodsurvival probabilites are above 0.9 and families in which the desired number of children is less than 4. Weinclude the following household covariates in both regressions: mother’s years of education, mother’s age at1st birth, interaction terms between the DHS wealth index and log GDP, religion dummies, quarter childwas born, age of the second child, age difference between the first two children, dummies for different gendercombinations of first two children, and the number of desired children. The restricted sample also includes aquadratic in adult survival probability. The regressions are weighted by the given sample weights.

6 Conclusion

Recent work by Jayachandran and Pande (2015) discovered the existence of a strong height-birth-order gradient in India, suggesting the presence of a first child bias. They suggest thatsuch a bias is the result of an eldest son preference driven by cultural norms. Our paper,however, investigates whether a first child bias can result from rational investment decisionsmade by parents, and whether it appears that the first child bias in India is, in part, a result ofparents optimally investing differently across their children.

We first develop a model wherein parents are faced with child mortality risk and have a socialsecurity motive to invest in their children. Our model predicts that, given the existence of asocial security motive, parents will invest more in their first child relative to their second. Inaddition, if we incorporate childrens’ genders, our model can generate an eldest son bias. Finally,our model predicts the existence of a negative relationship between investment differentialsbetween the first two children and the infant survival rate, as well as a positive relationshipbetween investment differentials and the early-childhood survival rate.

Empirically, we focus on testing our model’s prediction on the relationship between childhoodsurvival rates and investment differentials between the first two children within a family. We finda negative (positve) relationship between infant (early-childhood) survival rates and investmentdifferentials, as predicted. Combined with the existence of a first child bias in India, we believethese two results provide substantial evidence in favor of our model. Thus, we conclude thatthe first child bias is likely driven (in part) by parents’ reponses to social security motives inIndia. In addition, further analysis reveals that our model appears more relevant for rural areascompared to urban. We hypothesize that this is because social security motives for investingin children are stronger in rural areas due to increased dependence on children resulting from

25

worse health outcomes and lack of property/assets relative to urban areas.

Given that India is the second most populous country in the world with the fifth highest childstunting rate, it is important to understand the driving mechanisms behind the first child bias.This paper provides evidence suggesting that parents are strategically investing differentiallyacross their children in response to a social security motive. Thus, if one wishes to addressequality across children of different birth orders and genders within a family in Inida, our modelwould suggest reducing the dependence of parents on their children in old age, reducing theinfant mortality rate, and/or increasing the return to education for girls.

Finally, we investigate the predictions of our model in Sub-Saharan Africa. In theory, ourmodel should apply not only in India, but also in other developing countries in which parentsrely on their children for support in old age. We find that, once restricting our sample to Africancountries that align more closely with the assumptions of our model, there does indeed exista significant first child bias. Further, we find the expected relationship between investmentdifferences and mortality rates, although this relationship is not significant. We take this aspreliminary evidence that our model holds, to some extent, in parts of Africa. Investigating thedegree to which our model holds in other parts of the developing world, or will hold as morecountries see their child mortality rate fall before formal old age pension systems are put inplace, is a potential area for future research.

26

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http://faculty.wcas.northwestern.edu/~sjv340/height.pdf

http://mospi.nic.in/mospi_new/upload/elderly_in_india.pdf

http://mospi.nic.in/mospi_new/upload/elderly_in_india.pdf

Abroad.

Pal, S. (2006): “Elderly Health, Wealth and Coresidence with Adult Chil-dren in Rural India,” Brunel University, Economics and Finance DiscussionPapers, http://www.researchgate.net/publication/4799231_Elderly_Health_

Wealth_and_Coresidence_with_Adult_Children_in_Rural_India

Rosenzweig, M.R., and T.P. Schultz (1982): “Market Opportunities, GeneticEndowments, and Intrafamily Resource Distribution,” The American Economic Review,72(4), 803-815.

UNICEF (2013): Improving Child Nutrition: The Achievable Imperative for GlobalProgress. UNICEF, New York.

United Nations, Department of Economic and Social Affaris, PopulationDivision (2011): World Population Prospects: The 2010 Revision, Volume I: Compre-hensive Tables. ST/ESA/SER.A/313.

WHO Multicentre growth reference study group (2006a): “Assessment ofDifferences in Linear Growth Among Populations in the WHO Multicentre Growth Ref-erence Study,” Acta Paediatrica, 450.

WHO Multicentre growth reference study group (2006b): WHO Child GrowthStandards: Methods and Development. World Health Organization, Geneva, (available athttp://www.who.int/childgrowth/standards/technical_report/en/index.html).

28

http://www.researchgate.net/publication/4799231_Elderly_Health_Wealth_and_Coresidence_with_Adult_Children_in_Rural_India

http://www.researchgate.net/publication/4799231_Elderly_Health_Wealth_and_Coresidence_with_Adult_Children_in_Rural_India

http://www.who.int/childgrowth/standards/technical_report/en/index.html

A Appendix

A.1 Creating Height-for-age z scores (HAZ scores)

To highlight potential issues with the height-for-age z score, we create this variable using theWorld Health Organization (WHO) method (WHO Multicentre Growth Reference Study Group,2006B). The WHO provides the distribution of height separately for boys and girls, by age inmonths from a reference population of children from Brazil, Ghana, India, Norway, Oman,and the United States. Because child height has a skewed distribution, the WHO recommendsapplicatoin of the LMS method using a Box-Cox normal distribution. The formula used is asfollows:

z-score =(observed value/M)L − 1

L× S(8)

The WHO provides the values of M,L, and S for each reference population by gender andage. M is the reference median value for estimating the population mean, L is the power usedto transform the data to remove skewness, and S is the coefficient of variation. We constructthe z-score using the height and age information in the data rather than using the truncatedz-score variables included in the DHS data sets. We replace the HAZ score to missing if theabsolute value exceeds 6.

A.2 Appendix Tables: India

Table A1: Summary Statistics: Entire Sample

Child-level Mean Std. Dev.

Age child (months) 29.6 17.2Birth Order 2.62 1.82Child is a boy 0.52 0.50Child is deceased 0.053 0.22HAZ score -1.66 1.75HAR score 0.50 0.29

Mother-level Mean Std. Dev.

Age of mom at first birth 20.2 3.89Mom’s education (years) 5.42 5.20Number of children ever born 2.72 1.84Desired number of children 2.47 1.00Urban 0.39 0.49Wealth Index 3.18 1.40

29

Table A2: Summary Statistics: Families with at least two children, where the first two childrenare under five years old

Description Mean Std. Dev.

Age of mom at first birth 20.6 3.67Mom’s education (years) 6.22 4.91HAR difference btw 1st and 2nd born 0.041 0.31Age child 1 42.9 10.8Age child 2 16.6 11.0Boy, boy 0.25 0.43Boy, girl 0.25 0.43Girl, boy 0.28 0.45Girl, girl 0.22 0.41Age difference btw 1st and 2nd born 26.3 9.60Age difference (first born girl) 26.2 9.68Age difference (first born boy) 26.4 9.53Two kids only 0.91 0.29Number of children ever born 2.10 0.32Desired number of children 2.34 0.77Urban 0.39 0.49Wealth Index 3.33 1.33

Note: The subsample here is restricted to families with at least two children, where the firsttwo children are alive and under the age of five, and have height data recorded for them.

Table A3: HAR difference on Survival Probabilities (2010 state-urban survival probs) (age-cut-off: 18months)


Infant Survival Prob. -1.663 -2.193** -1.267 -2.120*(1.135) (1.003) (1.358) (1.199)

Early Child Survival Prob. 3.096 3.568* 2.939 3.743(2.312) (2.055) (2.692) (2.367)




Note: Standard errors presented in brackets. * p < 0.10, ** p < 0.05, *** p < 0.01. The dependent variableis the difference in HAR score between the first and second child within a family. Columns with the heading2 Plus indicate that the regression is estimated for families with 2 or more children, while columns with theheading 2 Only indicate families with only 2 children thus far. We only include families for which the firsttwo children are alive, under 5 years old, and the second child is 18 months or older. The regressor “InfantSurvival Prob.” is the state-urban level probability that a child survives the first 12 months, while “EarlyChild Survival Prob” is the state-urban level probability that a child survives until the age of 5 conditionalon surviving the first 12 months. Columns 3 and 4 interact state-wise probabilities with the urban dummy.We include the following household covariates: DHS wealth index, mother’s years of education, mother’s ageat 1st birth, religion dummies, quarter child was born, age of the second child, age difference between thefirst two children, dummies for different gender combinations of first two children, and the number of desiredchildren. The regressions are weighted by the given sample weights.

30

A.3 Appendix Figures: India

Figure A8: Survival probabilities for each Indian state 2010 split by urban rural. Source: 2011Census.

Figure A9: Boy survival probabilities for each Indian state 2010 split by urban rural. Source:2011 Census.

31

Figure A10: Survival probabilities for each Indian state 2010. Source: 2011 Census.

Figure A11: Projected survival probabilities for each Indian state 2001-2005. Source: 2001Census.

A.4 Appendix: Africa

Following Jayachandran and Pande (2015), we use DHS surveys from several Sub-SaharanAfrican countries. These include Congo (2007,V), Republic of Congo (2005, V), Cameroon(2004,IV), Chad (2004, IV), Ethiopia (2005, V), Ghana (2008, V), Guinea (2005, V), Kenya(2008-2009, V), Liberia (2007, V), Lesotho (2004, IV), Lesotho (2009, VI), Madagascar (2003-2004, IV), Mali (2006, V), Malawi (2004, IV), Niger (2006, V), Nigeria (2008, V), Namibia(2006-2007, V), Rwanda (2005, V), Sierra-Leone (2008, V), Senegal (2005, IV), Sao Tome

32

(2008, V), Swaziland (2006-2007, V), Tanzania (2004-2005, V), Tanzania (2010, VI), Uganda(2006, V), Zambia (2007, V), Zimbabwe (2005-2006, V). In parallel with the NFHS conductedin India, these surveys interview mothers between the ages of 15-49 and collect data on boththe mother and chilren under age five.

A.4.1 Tables: Africa

Table A4: HAR difference on Survival Probabilities: Africa

(1) (2) (3) (4) (5) (6) (7)

Infant Survival Prob. -0.324 -0.0712 1.375 0.619 -1.131 -0.547 -1.725(0.746) (0.998) (1.156) (1.495) (1.291) (1.696) (2.106)

Early Childhood Survival Prob. -0.176 -0.209 -0.948 -0.650 0.387 1.514 1.928(0.537) (0.890) (1.234) (1.327) (1.050) (1.819) (1.921)

Adult Mortality Rate Controls Yes No No Yes Yes No Yes

Desires Less Than 5 No Yes No No Yes Yes Yes

Inf. and Child Mortality Greater than 0.9 No No Yes Yes No Yes Yes

mean dependent 0.0420 0.0363 0.0368 0.0368 0.0363 0.0355 0.0355N 3769 1667 1972 1972 1667 1100 1100r2 0.0293 0.0474 0.0337 0.0345 0.0487 0.0424 0.0437

Note: Standard errors presented in brackets. * p < 0.10, ** p < 0.05, *** p < 0.01. The dependent variable isthe difference in HAR score between the first and second child within a family. The regressor “Infant SurvivalProb.” is the country level probability that a child survives the first 12 months, while“Early Child SurvivalProb.” is the country level probability that a child survives until the age of 5 conditional on surviving thefirst 12 months. Survival probabilities are country level survival probabilites for 2000-2005 from the UN. Weonly include families for which the first two children are alive, under 5 years old, and the second child is overa year old. We include the following household covariates in both regressions: mother’s years of education,mother’s age at 1st birth, interaction terms between the DHS wealth index and log GDP, religion dummies,quarter child was born, age of the second child, age difference between the first two children, dummies fordifferent gender combinations of first two children, and the number of desired children. The regressions areweighted by the given sample weights.

33

A.4.2 Figures: Africa

Figure A12: Survival probabilities for each African country 2000-2005. Source: United NationsDivision of Population

A.5 Appendix: Proofs

A.5.1 Propositon 1: I∗1 > IA∗2 for δ close to 1 and w′′ ≤ 0

The first order conditions with resepct to I1 and IA2 are given by equations 9 and 10, respectively:

u′(w − I1) = δK+1(

(sisc)2u′(wc(I1) + wc(I

A2 )) + u′(wc(I1))sisc(1− sisc)

)w′c(I1) (9)

u′(w − IA2 ) = δK(sis

2cu′(wc(I1) + wc(I

A2 )) + u′(wc(I

A2 ))sisc(1− sc)

)w′c(I

A2 ) (10)

By concavity of u(.) and wc(.) in equation 9 the LHS is increasing in I1 and the RHS isdecreasing in I1. Similarly, in equation 10 the LHS is increasing in IA2 and the RHS is decreasingin IA2

We show that I∗1 > IA∗2 in two steps:

1. We first show the existence of a fixed point of equation 10 such that IA2 (I1) = I1. Thisfollows from the Brouwer Fixed-Point Theorem: as we have IA2 > 0, IA2 < w (as we assumeu′(0) = +∞), and the continuity of IA2 (I1) (we assume w(.) and u(.) are continuous).

2. Let’s denote the fixed point of equation 10 as IA2 (I1) = I1 = I2,FP . Plug I2 = I2,FP intoequation 9 and solve for I1 = I1(I2,FP ). We show it is the case (below) that I1(I2,FP ) >

34

I2,FP . Next we show it is the case (below) thatdIA2 (I1)

dI1< 0. As a result I2(I1(I2,FP )) <

I2,FP . By induction, this produces sequences of {In1 }, {In2 } such that I(k+1)1 > I

(k)1 and

I(k+1)2 < I

(k)2 where I

(0)1 = I

(0)2 = I2,FP . As both sequences are bounded in [0, w] and

monotonic, they must converge. These two points, by construction, solve the originalFOC’s. As the original problem is concave, the solution is unique. Hence, the limit pointsof these two sequences are, in fact, I∗1 and IA∗2 .

Showing that I1(I2,FP ) > I2,FP : rearranging the above first order conditions we have:

u′(w − I1) = δK+1

((sisc)

2(u′(wc(I1) + wc(I

A2 ))− u′(wc(I1))

)+ u′(wc(I1))sisc

)w′c(I1)

(11)

u′(w − IA2 ) = δK(sis

2c

(u′(wc(I1) + wc(I

A2 ))− u′(wc(I

A2 )))

+ u′(wc(IA2 ))sisc

)w′c(I2)

(12)

Equation 12 is solved at I1 = I2 = I2,FP . Plugging in I2 = I2,FP into equation 11 resultsin the RHS being greater than the LHS as long as δ is close to 1. Hence, by concavity,I1(I2,FP ) > I2,FP .

Showing thatdIA2 (I1)

dI1< 0: this is a straightforward application of the Implicit Function

Theorem on Equation 12.

Steps 1 and 2 of the above proof are illustrated in Figures A13-A15 below:

Figure A13: Step 1: Solving for the Fixed Point of Equation 10

35

Figure A14: Step 2: Plug I2,FP into Equation 9

Figure A15: Step 2: Plug I1(I2,FP ) into Equation 10

A.5.2 Proposition 2: I∗1 − IA∗2 is increasing in sc and decreasing in si

Throughout, denote w′c(I1) = w′c(IA2 ) = k > 0

First, we use the implicit function theorem to write out dI1dsi

anddIA2dsi

:

dI1dsi

=δK+1

((2sis

2c)(u

′ (wc(I1) + wc(IA2 ))

+ (sc − 2s2csi)u′(wc(I1))

)k

−(u′′(w − I1) + δK+1

((sisc)2u′′(wc(I1) + wc(IA2 )) + u′′(wc(I1))sisc(1− sisc)

)k2)

+u′′(wc(I1) + wc(I

A2 ))δK+1(sisc)

2k2

−(u′′(w − I1) + δK+1


)k2) dIA2dsi

(13)

36

dIA2dsi

=δK(s2c(u

′ (wc(IA2 ) + wc(I

A2 ))

+ (sc − s2c)u′(wc(IA2 )))k

−(u′′(w − IA2 ) + δK

(sis2cu

′′(wc(I1) + wc(IA2 )) + u′′(wc(IA2 ))sisc(1− sc))k2)

+u′′(wc(I1) + wc(I

A2 ))δKsis

2ck

2

−(u′′(w − IA2 ) + δK

(sis2cu

′′(wc(I1) + wc(IA2 )) + u′′(wc(IA2 ))sisc(1− sc))k2) dI1dsi

(14)

Next, we assume that u′′′(.) = 0 and take approximations around δ = si = sc = 1.

The approximations are now:

dI1dsi

=

(2u′(wc(I1) + wc(I

A2 ))− u′(wc(I1))

)k

−(u′′(w − I1) + u′′(wc(I1) + wc(IA2 ))k2

)+

u′′(wc(I1) + wc(IA2 ))k2

−(u′′(w − I1) + u′′(wc(I1) + wc(IA2 ))k2

) dIA2dsi

(15)

dIA2dsi

=u′(wc(I1) + wc(I

A2 ))k

−(u′′(w − IA2 ) +

(u′′(wc(I1) + wc(IA2 ))

)k2)

+u′′(wc(I1) + wc(I

A2 ))k2

−(u′′(w − IA2 ) + u′′(wc(I1) + wc(IA2 ))k2

) dI1dsi

(16)

Now u′′′(.) = 0 gives us that:

−(u′′(w − IA2 ) + u′′(wc(I1) + wc(I

A2 ))k2

)= −

(u′′(w − I1) + u′′(wc(I1) + wc(I

A2 ))k2

)(17)

37

Putting this all together, we have that(1 +

u′′(wc(I1) + wc(IA2 ))k2

−(u′′(w − I1) + u′′(wc(I1) + wc(IA2 ))k2

))d(I∗1 − IA∗2 )

dsi=

(1 +

u′′(wc(I1) + wc(IA2 ))k2

−(u′′(w − I1) + u′′(wc(I1) + wc(IA2 ))k2

))dI∗1dsi−

(1 +

u′′(wc(I1) + wc(IA2 ))k2

−(u′′(w − IA2 ) + u′′(wc(I1) + wc(IA2 ))k2

))dIA∗2

dsi

=

(2u′(wc(I1) + wc(I

A2 ))− u′(wc(I1))

)k

−(u′′(w − I1) + u′′(wc(I1) + wc(IA2 ))k2

) − u′(wc(I1) + wc(I

A2 ))k

−(u′′(w − IA2 ) +

(u′′(wc(I1) + wc(IA2 ))

)k2)

=

(u′(wc(I1) + wc(I

A2 ))− u′(wc(I1))

)k

−(u′′(w − I1) + u′′(wc(I1) + wc(IA2 ))k2

) < 0

(18)Where the last inequality follows from concavity of u(.) and that wc(I1) + wc(I

A2 ) > wc(I1).

Hence, we have thatd(I∗1−IA∗2 )

dsi< 0.

A similar proof shows thatd(I∗1−IA∗2 )

dsc> 0:

First, we use the implicit function theorem to write out dI1dsc

anddIA2dsc

:

dI1dsc

=δK+1

((2scs

2i )(u

′ (wc(I1) + wc(IA2 ))

+ (si − 2s2i sc)u′(wc(I1))

)k

−(u′′(w − I1) + δK+1


)k2)

+u′′(wc(I1) + wc(I

A2 ))δK+1(sisc)

2k2

−(u′′(w − I1) + δK+1


)k2) dIA2dsc

(19)

dIA2dsc

=δK(

2scsi(u′ (wc(I

A2 ) + wc(I

A2 ))

+ (si − 2scsi)u′(wc(I

A2 )))k

−(u′′(w − IA2 ) + δK

(sis2cu

′′(wc(I1) + wc(IA2 )) + u′′(wc(IA2 ))sisc(1− sc))k2)

+u′′(wc(I1) + wc(I

A2 ))δKsis

2ck

2

−(u′′(w − IA2 ) + δK

(sis2cu

′′(wc(I1) + wc(IA2 )) + u′′(wc(IA2 ))sisc(1− sc))k2) dI1dsc

(20)

Next, we assume that u′′′(.) = 0 and take approximations around δ = si = sc = 1.

38

The approximations are now:

dI1dsc

=

(2u′(wc(I1) + wc(I

A2 ))− u′(wc(I1))

)k

−(u′′(w − I1) + u′′(wc(I1) + wc(IA2 ))k2

)+

u′′(wc(I1) + wc(IA2 ))k2

−(u′′(w − I1) + u′′(wc(I1) + wc(IA2 ))k2

) dIA2dsc

(21)

dI2dsc

=

(2u′(wc(I1) + wc(I

A2 ))− u′(wc(I

A2 )))k

−(u′′(w − I1) + u′′(wc(I1) + wc(IA2 ))k2

)+

u′′(wc(I1) + wc(IA2 ))k2

−(u′′(w − I1) + u′′(wc(I1) + wc(IA2 ))k2

) dI1dsc

(22)

As before, u′′′(.) = 0 gives us that:

−(u′′(w − IA2 ) + u′′(wc(I1) + wc(I

A2 ))k2

)= −

(u′′(w − I1) + u′′(wc(I1) + wc(I

A2 ))k2

)(23)

Putting this all together, we have that(1 +

u′′(wc(I1) + wc(IA2 ))k2

−(u′′(w − I1) + u′′(wc(I1) + wc(IA2 ))k2

))d(I∗1 − IA∗2 )

dsc=

(1 +

u′′(wc(I1) + wc(IA2 ))k2

−(u′′(w − I1) + u′′(wc(I1) + wc(IA2 ))k2

))dI∗1dsc−

(1 +

u′′(wc(I1) + wc(IA2 ))k2

−(u′′(w − IA2 ) + u′′(wc(I1) + wc(IA2 ))k2

))dIA∗2

dsc

=

(2u′(wc(I1) + wc(I

A2 ))− u′(wc(I1))

)k

−(u′′(w − I1) + u′′(wc(I1) + wc(IA2 ))k2

) −(

2u′(wc(I1) + wc(I

A2 ))− u′(wc(I

A2 )))k

−(u′′(w − IA2 ) +

(u′′(wc(I1) + wc(IA2 ))

)k2)

=

(u′(wc(I

A2 ))− u′(wc(I1))

)k

−(u′′(w − I1) + u′′(wc(I1) + wc(IA2 ))k2

) > 0

(24)Where the last inequality follows from concavity of u(.), that w(.) is increasing, and thatI∗1 > IA∗2 .

Hence, we have thatd(I∗1−IA∗2 )

dsc> 0.

39

intrahousehold investment decisions and child mortality ......explaining the first child preference...

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