Height and calories in early childhood

Economics and Human Biology 20 (2016) 55–69

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Height and calories in early childhood Andrew S. Griffen * Economics Research Building, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan

A R T I C L E I N F O

A B S T R A C T

Article history: Received 26 November 2014 Received in revised form 23 October 2015 Accepted 26 October 2015 Available online 9 November 2015

This paper estimates a height production function using data from a randomized nutrition intervention conducted in rural Guatemala from 1969 to 1977. Using the experimental intervention as an instrument, the IV estimates of the effect of calories on height are an order of magnitude larger than the OLS estimates. Information from a unique measurement error process in the calorie data, counterfactuals results from the estimated model and external evidence from migration studies suggest that IV is not identifying a policy relevant average marginal impact of calories on height. The preferred, attenuation bias corrected OLS estimates from the height production function suggest that, averaging over ages, a 100 calorie increase in average daily calorie intake over the course of a year would increase height by 0.06 cm. Counterfactuals from the model imply that calories gaps in early childhood can explain at most 16% of the height gap between Guatemalan children and the US born children of Guatemalan immigrants. ß 2015 Elsevier B.V. All rights reserved.

Keywords: Height Production function Calorie gaps Guatemala INCAP experiment

1. Introduction The formation of human height has been the subject of interest by economists in recent years because of its importance as a predictor of wages (Persico et al., 2004; Case and Paxson, 2008), health (Deaton, 2007), productivity (Schultz, 2003), cognitive skills (Case and Paxson, 2008), longevity (Fogel and Costa, 1997) and life satisfaction (Deaton and Arora, 2009). The causal mechanisms behind these associations are complex but the economics profession has adopted the ‘‘nutritionist view’’ on human height as an easily measured indicator of general health status (Steckel, 1995). Understanding the formation of height can be an important guide for programs that attempt to improve health, especially in developing countries. Although sibling and twin research suggests that environmental factors explain only 20% of the variation in human height (Silventoinen, 2003), the role of the potentially

* Tel.: +81 0358415655. E-mail address: [email protected] http://dx.doi.org/10.1016/j.ehb.2015.10.004 1570-677X/ß 2015 Elsevier B.V. All rights reserved.

policy specific environmental factors is disputed.1 Some research finds strong correlations between per capita GDP during childhood (as a proxy for nutrition) and subsequent average adult population heights (Steckel, 1995) while others argue that cross population differences in averages heights are driven more by selective survival of taller children (Bozzoli et al., 2009; Gørgens et al., 2012) than by nutritional differences in early childhood (Deaton, 2007). Silventoinen (2003) states that one difficultly with much auxology (human growth) research is that it tends to use aggregate or cross-sectional data, which makes causal conclusions difficult.2

1 Silventoinen (2003) also speculates that the effects of the environment explain more of the variation in height in developing countries. 2 An exception is work in public health studying inputs into stunting and child mortality that uses meta analyses of cross country RCTs as inputs into a simulation model to predict child mortality in developing countries (Bhutta et al., 2008, 2013). Although less attention is paid to the behavioral interpretation of parameters and the focus of that work is more on child mortality, the conclusions from my preferred OLS model are, broadly speaking, of a similar magnitude to their findings and the IV models presented in my paper are inconsistent with their work.

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The formation of human height involves a complex interplay between polygenetic markers for height, the use of energy inputs by cells to divide, and how disease and deprivation causes feedback from the endocrine system to actually pause or suspend cellular division and growth (Tanner, 1990). Essentially theory points to genetics, nutrition and disease as all playing roles in the formation of height (Silventoinen, 2003) and a succinct characterization given by Deaton (2007), who states that ‘‘[h]eight is determined by genetic potential and by net nutrition,’’ is a useful starting point for empirical work. A variety of observational, quasi-experimental and experimental evidence are all consistent with this biological theory of height formation and further suggest the importance of early environmental factors. Studies have examined the co-movement of secular trends in height and living standards (Fogel and Costa, 1997) and used heights to measure variation in standards of living by socioeconomic class (Komlos, 1994). Quasi-experimental evidence has found impacts on average population heights from famines (Meng and Qian, 2009), neonatal mortality (Bozzoli et al., 2009), and income shocks (Banerjee et al., 2010), and nutrition experiments, such as the Institute of Nutrition of Central America and Panama (INCAP) Longitudinal Study 1969–1977, which is the focus of the current paper, provide strong evidence that nutrient intake during early childhood has both short and long term impacts on many anthropometric measures and other kinds of human capital (Martorell, 1995b; Hoddinott et al., 2008; Behrman et al., 2009). Heckman (2007) argues that while health economics has focused on documenting sensitive periods of development, more work should take a life-cycle perspective in understanding the timing of investments and the possibility of remediation following the production function literature on cognitive and noncognitive skills.3 For height, some studies strongly imply the possibility of such remediation; a study of the Dutch Hunger Winter 1944–45 (Stein et al., 1975) did not find impacts on adult height from famine exposure. A production function is the appropriate tool to answer many questions about such hypothetical inputs interventions (Rosenzweig and Schultz, 1983).4 Furthermore, the parallels between the production process for skills and for height are actually quite strong and a common framework (Todd and Wolpin, 2003, 2007; Cunha and Heckman, 2007) can be brought to bear on both processes. A drawback relative to quasi-experimental methods for investigating height formation is the often strong modeling assumptions and the extensive panel data requirements on height, nutrition and disease.

The related literature on height is truly towering and spans the biomedical, public health and social sciences with sometimes seemingly little interaction between the fields. In economics, Behrman and Deolalikar (1988) and Strauss and Thomas (1998) both review a large literature on nutrition and health. Early height research in economics focused on whether there were causal links between maternal education and child height (Wolfe and Behrman, 1987; Behrman and Wolfe, 1987) and unpacking those mechanisms (Thomas et al., 1991). Martorell and Habicht (1986) provide a review of growth in childhood specifically in developing countries from an auxology perspective and Bhutta et al. (2008, 2013) provide an extensive metaanalyses from RCT public health interventions in developing countries. Even the literature on the INCAP experiment itself is quite extensive with much early work on the experimental impacts and subsequent analyses examining longer term impacts for each of the follow-up data collections during adolescence and adulthood (Martorell, 1995b). This paper contributes to this literature by estimating a height production function using data from the INCAP Longitudinal Study, a randomized nutrition experiment conducted in rural Guatemala from 1969 to 1977, that collected extensive longitudinal data on calorie intake, disease measures and height for children until the age of 7.5 The experiment consisted of a feeding center in each participating village that provided calorie supplements and in which the type of supplement was randomized across villages to create an experimental contrast in calorie intake. Using the INCAP experimental intervention and distance to the feeding center in the INCAP experiment as instrumental variables for calorie inputs, the IV estimates of the production function suggest that the effect of calories on height is an order of magnitude larger than the OLS estimates. To explore the divergence between the OLS and IV estimates, I investigate the role of measurement error in attenuating the OLS estimates and the plausibility of the model counterfactuals using both the OLS and IV estimates. Information from a unique measurement error process in the collected INCAP calorie data collection allows me to bound the effects of attenuation bias. The size of this attenuation bias cannot explain the divergence between the OLS and IV estimates. Furthermore, comparing calorie differences between the US and Guatemala during the same period as the INCAP experiment, I use the estimated production function to investigate the role of the US–Guatemala ‘‘calorie gap’’ in increasing the height of Guatemalan children. The difference between the OLS and IV estimates implies large differences in the counterfactual

3 Combining theory with experimental and non-experimental evidence has provided an extremely rich characterization of the efficient timing of investment for the production of skills (Doyle et al., 2009). 4 A different strategy would be to estimate demand functions for child health, which can account for the effects of household resources and for household responses to the public provision of inputs. See Behrman and Skoufias (2004) for an overarching framework and a review of studies examining estimates of the demand for child health in Latin America. Related to this distinction, Todd and Wolpin (2003) have an extended discussion of the uses of production function versus policy parameters.

5 In addition to height, the INCAP data have extensive measurement of other anthropometric outcomes. The basic pattern of regression results in the paper also hold for weight, head circumference, arm circumference, calf circumference, tricep skinfold, bicondylar breadth, arm length, subscapular skinfold and calf skinfold as outcome measures. The consistency across outcomes is perhaps not surprising given their correlation with height. Of the different anthropometric outcomes, I chose height as the outcome of interest given the focus on height in the economics literature as well as height information from Guatemalan migration studies.

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height gaps. Comparing these counterfactual height gap estimates from the production function to height gap estimates from migration studies of Guatemalan families to the US suggests that the IV estimates produce widely varying and sometimes very unrealistic counterfactual estimates. Failing this out-of-sample validation test, the failure of traditional over-identification tests, and the variation in the IV estimates across instruments, despite the prima facie validity of the instruments, suggest that the IV estimates are not identifying policy relevant production function parameters (Heckman, 2007; Heckman et al., 2006). The attenuation adjusted, change in height OLS estimates imply that the average difference in calories between the US and Guatemala can explain at most 16% of the average difference in height between the INCAP children and height of the US born children from a sample of Guatemalan immigrants to the US. These results are consistent with Deaton (2007) who questions the specific role of nutrition in explaining population differences in height. In the conclusion, I discuss several other policy relevant inputs of interest and the interpretation of these findings. This paper builds on earlier work estimating models of height formation using these data (Schroeder et al., 1995; Habicht et al., 1995) through incorporating instrumental variables estimation into the estimation of the effects of calories on height, addressing the role of measurement error in calories, conducting extensive specification testing and using and validating the estimated models with out of sample forecasts. An additional broader contribution is the use of instrumental variables in auxology research, which is apparently rare. The instrumental variable strategy in this paper follows several second generation papers using the INCAP data that have used the initial experimental variation as an instrumental variable to understand how early childhood nutrition effects educational outcomes (Maluccio et al., 2009), cognitive skills (Behrman et al., 2014) and wages (Calderon, 2009). Other recent related work also specifically focused on Guatemala tackles the important emerging issue of the ‘‘double burden’’ of malnutrition (Lee et al., 2010) and interesting econometric issues related to understanding distributional effects of predictors of height (Sweeney et al., 2013). The remainder of the paper proceeds as follows. Section 2 develops an empirical model and Section 3 describes the INCAP experiment and data collection. Section 4 presents the results about the INCAP measurement error process and discusses the LATE interpretation of the IV estimates. Finally, Section 5 presents the estimation results, Section 6 describes the counterfactuals and Section 7 concludes. 2. An empirical model of height formation Following theoretical notions about height formation, I model height as a function of genetic potential, disease and nutrition. In particular, I focus on diarrhea as a measure of the disease input and calories as a measure of the nutrition input. The use of both measures is motivated by theoretical and empirical evidence. Martorell and Habicht (1986) state that ‘‘[o]f all the problems of infection affecting young

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children in developing countries none is as important as diarrheal diseases.’’6 Furthermore, cells actually use caloric energy during division and will suspend or halt growth during periods of low energy intake (Tanner, 1990). Energy, measured in the form of calories, are actually an aggregated measure of protein, carbohydrates and fats all of which are potentially individually important for growth.7 However, as Pitt et al. (1990) point out, calories in developing countries often come from one or two food sources so that even if data existed with individual consumption measures of protein, carbohydrates and fats, the measures would be highly collinear and it would be difficult to identify the effects of each component separately. The same argument also applies to questions about identifying the effects of diet diversity and micronutrients. More direct evidence on micronutrients from an extensive meta analysis by Bhutta et al. (2008) suggests only small impacts on height growth from micronutrient interventions. Essentially the subsequent model and empirical results can be interpreted as the effect of calories conditional on a particular aggregation of calories, diet diversity and micronutrients. Consider the following production function for change in height:

DHi;a ¼ b0 þ b1 C i;a þ b2 Di;a þ b3 X i;a þ ei;a

(1)

where DHi,a = Hi,a  Hi,a1 is the change in height of child i between age a and a  1, Ci,a are calorie inputs between a and a  1, Di,a are disease inputs applied between period a and a  1, Xi,a consists of time-varying inputs, such as age, and time-invariant effects, such as gender, and ei,a is a shock. In terms of interpretation, Xi,a as gender would capture sexual dimorphism in growth, Xi,a as age would capture time-varying changes in the growth process and ei,a would represent either time-varying unobserved

6 In addition to number of days sick with diarrhea, the data also contain parental reported number of days their child was sick with infectious disease symptoms, had ears/eyes/nose disease symptoms, had disease skin/hair symptoms, had a lack of appetite, was apathetic or irritable, spent in bed with illness, experienced fever and was with serious illness. I tried combining the disease measures using principal-components analysis and treating the first predict component as the disease input in the production function. None of the empirical patterns in the estimated model were affected. 7 The question of whether protein deficiencies are important for height growth in developing countries has a long history and the effect of closing the ‘‘protein gap’’ was an important research and policy issue in nutrition field in the 1950s, 60s and 70s (Campbell et al., 2007). Interestingly, the original INCAP experiment helped contribute exactly to that debate (Read and Habicht, 1993) although the pattern of take-up and findings made conclusions difficult about whether energy intake (calories) or its particular form (e.g., protein) mattered for growth in the INCAP context. However, it seems the literature has not entirely reached a consensus. Tanner (1990) writes that ‘‘[p]rotein seems less important than was once thought’’ while Silventoinen (2003) states that ‘‘[i]n developing countries... [t]he lack of protein is a particularly important factor explaining the slow (height) growth rate.’’ The latter statement seems to be not supported by the INCAP data itself. However, Read and Habicht (1993) propose that protein may be limiting in certain environments but not in others, which in effect calls for a production function with complementaries in the sources of calories as inputs. Although in this case researchers would likely need cross country or cross region data to have sufficient variation in calorie composition and even then there would arise questions of omitted variables.

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environmental factors or pure stochastic variation in an individual’s growth.8 The derivation and identifying assumptions of (1) are similar to the value-added models in the education and cognitive skills literature (Griffen, 2014; De Cao, 2011) except that (1) imposes that lagged height enters with a coefficient of 1 and can be moved to the left hand side.9 Following the skills literature, lagged height is meant to eliminate time-invariant unobserved heterogeneity and to capture the entire history of inputs so that conditional on lagged height current inputs affect the change in height only. A problem often considered in economics but not previously addressed in the INCAP context is the concern that Cov(Ci,a, ei,a) 6¼ 0 in which case calories are endogenous and OLS can no longer be used to consistently estimate the main parameter of interest b1. Such a correlation could arise for many reasons. If growing children begin consuming more calories but more calories do not make children grow, then the OLS estimate b1 would overstate ˆ the causal impact b1 in Eq. (1). Parents could also allocate more food to children with lower values of ei,a, which would understate the causal impact. Measurement error in calories would likely bias b1 towards 0. Other concerns ˆ with estimating Eq. (1) include the need for a large panel data collection on inputs and height measures, enriching the model to consider many possible interactions between calories, age, sex, lagged height, and disease, parental responses to lagged shocks and potential non-linear impacts of inputs. Considering additional inputs leads to a problem with a lack of instruments that also occurs in the skills literature (Todd and Wolpin, 2003, 2007; Cunha and Heckman, 2007). Given the strengths of the data that I detail below, I will focus on trying to address the endogeneity of calorie inputs and the measurement error in calories. This involves estimating Eq. (1) with an instrumental variable procedure using the following first stage equation:

between Ci,a and ei,a that would otherwise bias estimates of Eq. (1). I provide an extensive discussion below of which variables in the data can potentially be used as such instruments. An additional potentially attractive feature of instrument variables in the current context is that they can remove the attenuating effects of measurement error. Although I primarily focus on differences in estimating Eq. (1) with OLS and with IV, I note in various places the robustness checks that I tried in particular with estimating models with more effect heterogeneity. Because the estimated parameter from a production function gives a ceteris paribus impact of an input, one can, conditional on the maintained assumptions of the model, use the estimates of Eq. (1) to perform counterfactual analyses, such as what would be the impact of changes in specific inputs on height outcomes. 3. Data

where the variable Zi is referred to as an ‘‘instrument’’ and is a child specific determinant of calorie inputs that does not directly affect growth except through its impact on calorie intake (notice that Zi does not directly enter Eq. (1). The other variables are the same as defined previously. The key identifying assumptions are that Cov(Zi, ei,a) = 0 and d1 6¼ 0 in the linear projection version of Eq. (2). Intuitively Zi can be thought of as shifting Ci,a independently of ei,a to remove any potential correlation

To estimate the different variants of the height production function, I use data from the INCAP Longitudinal Study 1969–1977, a village-wide randomized nutrition intervention and data collection in rural Guatemala. The experiment and data collection have several features that are extremely important for estimating a height production function including an extensive panel data collection and plausibly exogenous variation in calorie intake. I first describe the experiment in detail in order to understand the background of the study and to highlight the key features of the data needed for the current study. I then discuss several issues with treating the data and the characteristics of the sample used in the current study. The origination of the INCAP Longitudinal Study was important unanswered questions in the 1960s about the causes and consequences of malnutrition in developing countries (Read and Habicht, 1993).10 Although the initial research question focused on the effect of malnutrition on behavioral outcomes, the design subsequently evolved to incorporate both mental and physical development outcomes and the experimental design reflected the desire to assess causal impacts of nutritional interventions.11 Researchers selected four villages to participate in the study with two treatment villages and two ‘‘control’’ villages, which actually received a differentiated treatment. In both treatment and control villages a centralized feeding center was set up that offered supplements twice per day. All villagers could consume the supplements and more supplement was given upon request. Following a matched pair design, two treatment villages received the offer to

8 Other inputs such as medical care would seem to indirectly affect height through disease so that adding disease would control for the proximate impact. As previously discussed other potential inputs such as micronutrients, calorie composition, and work requirements (less important for young children) are either unobserved and/or constant across children in the environment considered in this paper. 9 This assumption is meant to capture that unlike cognitive skills, which may depreciate, height should not decrease. However, even imposing this assumption, predicted growth using (1) could still technically be negative for a particular set of parameter values and because the support of the shock is unbounded. However, this problem does not appear in the parameter estimates.

10 Much of the content of the subsequent two paragraphs comes from descriptions of the history and background of INCAP Longitudinal Study by Read and Habicht (1993) and Habicht and Martorell (1992). 11 Mental development was assessed in various ways depending on the age including Raven’s progressive matrices, literacy, numeracy, etc. and, as previously mentioned, the data collection included many anthropometric outcomes although many of the papers focused on height and weight related outcomes. In fact, Steckel (1995) states that the use of height as a measure of health by development economists came from the influence of a group of nutritionists, two of whom (Jean-Pierre Habicht and Reynaldo Martorell) were intimately involved in the INCAP experiment.

C i;a ¼ d0 þ d1 Z i þ d2 Di;a þ d3 X i;a þ hi;a

(2)

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consume atole, which was a high-calorie, high protein vegetable porridge, and two control villages received the offer to consume fresco, which was a slightly sweet, cool drink with fewer calories and no protein per serving. The goal of the experiment was to introduce a contrast in the diets of children and adults across the villages. The reason behind two treatments was because researchers were worried that the presence of the data collection and feeding center itself might cause impacts outside of the supplement contrast (Read and Habicht, 1993). In an effort to not interfere with home meals, the feeding centers were only open between meal times and children could only consume the supplements at the center. This design of the experiment has interesting implications for the data collection and measurement error that I explore below. The context of the villages is also important to understand the experiment and data collection. Habicht and Martorell (1992) provide an extensive description of the villages. They discuss how the villages were selected to be homogeneously very poor and describe that a typical house had dirt floors and no electricity, more than 90% of households collected water from hand-dug wells or a river, very few had latrines and almost all the villagers were small scale farmers. In addition to being relatively homogeneous, the villages were also selected to be relatively compact with 80% of the homes within 1 km of the feeding centers so that everyone would have the opportunity to participate (Habicht and Martorell, 1992). This homogeneity and compactness is important for one of the instrumental variables that I use below. Although attrition bias became a concern in the longer term follow-up studies and data collection because of increased immigration to Guatemala City and other locations (Hoddinott et al., 2008), the attrition appears to have been relatively low in the original study; Habicht and Martorell (1992) state that the annual migration rate was 2% or less and that many villagers had grown up in the area, which suggest a small potential for attrition through migration. Refusal to participate in the data collection was also less than 2% (Habicht and Martorell, 1992), reflecting the close cooperation between the villagers and the study team over the course of the study.12 The data contain two interesting sources of potentially exogenous variation in calorie intake. The first source is the experimental variation across villages itself. Although because there were only four villages clustering becomes a potential issue, Martorell (1995a) reports that at baseline that ‘‘the anthropometric characteristics of both children and adults were strikingly similar in the different villages before 1969 [when the experiment began],’’ which reflects the matched pair nature of the experimental design and should help mitigate some concerns. The second source of exogenous variation in the data is the measured distance from each child’s house to the feeding center. In contrast to the experimental variation, the distance instrument utilizes

12 I could not find any description about whether the villagers knew they were participating in an experiment or perceived that it was a kind of public health service and data collection. In various papers describing the study, there seems to be concern that the villages be isolated from each other, which perhaps suggests that the team wanted to avoid spillovers and perhaps information leakage across the sites.

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child specific, within village variation.13 Despite the relative homogeneity and compactness of the villages, a potential concern with using the distance instrument is families and children may differ in unobserved ways by their location within the villages.14 However, Eq. (1), under the maintained assumptions, cancels out time-invariant unobserved heterogeneity so that the distance instrument would need to be correlated with time varying unobserved changes in growth, which is perhaps less plausible. In addition, as I will show in the empirical results, the IV and OLS divergence is greatest when using the experimental variation only so the main argument of the paper holds a fortiori using the more plausibly exogenous instrument. Finally, the pattern of the results is not sensitive to including a variable that proxies for socioeconomic status although I elect to not include the measure of socioeconomic status as this potentially changes the interpretation of the coefficients on the calorie inputs (Rosenzweig and Schultz, 1983; Wolpin, 1997). Both the experimental and distance instruments are strong predictors of individual calorie intake and although subject to the potential caveats described above, both instruments would appear to be plausibly exogenous to unobserved determinants of child growth. The second important feature of the data is the extensive panel longitudinal data collection. Daily supplement calorie intake data was recorded at the feeding center for all children. Because supplement calories were only consumed at the feeding center, these data were collected in a controlled environment and therefore consumption of the supplement was recorded very accurately. Data on home calorie consumption was collected separately from the supplement calorie data and was collected at three, six and twelve month intervals with the frequency of data collection depending on the child’s age. In effect the two sources of calories intake, from the home and from the feeding center, were collected separately. Researchers also collected anthropometric measures, such as height and weight, on all children under the age of seven at the same three, six and twelve months intervals. Finally, data on number of days sick with diarrhea and other illnesses was also collected at three, six and twelve months intervals. Given the theoretical discussion above that height depends on net nutrient intake (calories net of disease) and genetic endowments, all the ingredients are available to estimate Eq. (1). There are three sources of variability in the frequency of data collection that need to be addressed. The first source

13 A third source of variation is that some children were treated only for parts of their life because of the beginning and ending of the experiment and data collection. For example, children born prior to 1969 only entered the sample in 1969 and children born in 1971 and after only have data collection until age 6 at the oldest. This creates some natural variation in exposure to the experiment that has been examined in previous work using longer term follow-up data. In the current work, because the data collection does not exist or ends when children enter or exit the sample at baseline and endline, I cannot make use of the timing of exposure. 14 Maluccio et al. (2009) also use the experimental variation as an instrument for supplement intake to examine the effect of nutrition intake on educational outcomes but they elect not to use the distance variation. This is, however, because schools were actually also located in the center of the villages so that there may have been a direct impact of distance on educational outcomes.

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comes from the design of the data collection for anthropometric measures and home calories intake. Children between ages 0 and 2 were purposively measured at 3-month intervals, children between 2 and 4 years old at 6 month intervals and children from 4 to 7 years old at 12 month intervals. The second source comes from the different frequency of measurement of home and supplement calories. The third source of variability arises because the actual age of the children at each data collection did not correspond exactly to the 3, 6 or 12 month intervals. For example, at the 24 months data collection, some children might be 23 months old and some children might be 25 months old. To address these forms of data frequency variability, I treat the data in the following way. First, to keep the timing consistent across data collection rounds, I use the data at a twelve month frequency. That is, I use the height and home calories measured at 1 year old, 2 years old, etc. In this way, when taking the model to the data, the interpretation of the model coefficient of interest becomes the effect on height of a one calorie increase in average daily caloric intake over the course of a year. Second, I need to address differences in the frequency of the home and supplement calorie collection. The supplement calorie inputs were actually measured on a daily basis so I just use the exact amount of average daily supplement intake recorded from the previous year. For home calories, I use the calorie intake from the 24-h recall survey at each yearly data collection round as the measure of home calories for the previous year. For the measure of total calories, I simply sum the measures to get a variable for average daily total calorie intake for the previous year. Combining the measures in this way obviously induces difference sources of measurement error given the way the home and supplement calories are measured. I address the role of measurement error in the next section and incorporate the theoretical results into the estimation. Finally, to address the variation in the age at measurement conditional on the data collection round, I linearly interpolate between data rounds so that I have an estimate of the child’s height at the exact age corresponding to 1year old, 2 years old, etc. In practice, the correlation coefficient between the interpolated height and the measured height is above 0.99 at all ages so using the interpolated height or the measured height makes no quantitative difference for the magnitude of the model estimates. Table 1 displays summary statistics from the data. The data are disaggregated by atole and fresco villages and pooled over age and time. The children in the atole villages were significantly taller by 1.82 cm and also consumed significantly more total calories (38.61 additional calories per day on average). For each kind of village, the increase in supplement calories outweighed the decrease in home calories, which is evidence of the so-called ‘‘fly-paper’’ effect where a transfer ‘‘sticks’’ to the child.15 The children in the atole villages had more days sick with diarrhea per

15 Using the INCAP data Islam and Hoddinott (2009) rigorously document this effect.

month (5.46 days vs. 6.47) and a smaller percentage of males (54% vs. 57%) although the average age of the children across the children across the villages were almost identical (49.91 months vs. 49.84 months). 4. Measurement error, IV and LATE Data on calories are typically collected from 24-h recall surveys. Families or individuals are asked to recall everything they ate in the previous 24 h. Researchers then use conversion factors to convert the types and quantities of food reported into calories, proteins, and other nutrients. 24-h food recall surveys have test–retest reliability on the order of 0.5 (Lechtig et al., 1976), where the test–retest reliability is the correlation coefficient between two repeated measures.16 If calories are measured with classical measurement error, then the OLS coefficient is attenuated according to:17

s2

E½b1;OLS  ¼ b1 2 c 2 ˆ sc þ su where s 2u is the variance of measurement error in calories and s 2c is the variance in calories. The formula for the test– retest reliability is also exactly equal to the attenuation bias, which shows an attenuation adjusted estimate can be backed out by dividing the OLS estimate by the a priori known test–retest reliability of 0.5 according to:

b bˆ1;PAdjustedOLS ¼ ˆ1;OLS :5

This analysis suggests that OLS estimates of the marginal impact of calories will be approximately half of the true coefficient. As is well-known, instrumental variables can remove attenuating effects of measurement error so one estimation strategy available in the INCAP data is to use the experimental and distance variables to purge the attenuation bias. The expected finding would be for the OLS coefficient to double in magnitude. However, one unique feature of the INCAP data is that the calorie intake data collected at the feeding center do not contain measurement error because the

16 Test–retest reliability may be affected by conversion error in converting recorded calories into actual calories consumed, recall error on the part of individuals and actual variability in consumption by individuals across days. In my model, I use average calorie intake over a period, which implicitly assumes perfect substitutability across time within a period. Clearly variation in calorie intake may be an important issue in how calories affect growth. However, given the difficulty in collecting accurate individual level calorie intake at a specific point in time, the possibility of collecting an accurate, high frequency panel of calorie intake is very remote. 17 The formula for attenuation bias is more complicated in the presence of multiple regressors but the pattern of empirical results in this paper are not sensitive to excluding the additional regressors. Another source of concern may be measurement error in diarrhea measures, which are selfreported. In addition, days sick with diarrhea may also be correlated with unobserved healthiness or tendency to grow. Unfortunately neither the experimental nor the distance instruments are strong predictors of days sick with diarrhea, which mitigates the possibility to control for endogeneity or measurement error using IV. However, the results from calories in this paper suggest some caution in estimating a biological production function with IV. In addition, the calorie results are similar when excluding days sick with diarrhea which suggests linearly independent effects.

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amount of supplement calories that each particular child consumed was measured precisely.18 This means that the degree of measurement error for each child is related to the proportion of calories consumed at the feeding center. If the child ate entirely at the feeding center then their calorie input would be measured without error whereas if the child ate entirely at home then their calorie input would be measured with the traditional amount of error. One way to model this type of measurement error is to consider that the observed total calories is a mixture of a correctly measured calorie input and an incorrectly measured calorie input with the mixing proportion determined by the amount consumed at the feeding center. Let Ch be the amount of calories consumed if the child ate only at home and let Cc be the amount of calories that would be consumed if the child ate only at the feeding center. Assume also that observed home calories in the absence of a feeding center would still be measured with classical measurement error according to: Ch,o = Ch + U. Both Ch,o and Ch are hypothetical quantities because in reality the child will eat some amount at both home and at the feeding center. Now the observed total calories CT,o is: C T;o ¼ P C h;o þ ð1PÞ C c where P is the fraction of calories consumed at home. In the data, I observe P Ch,o, (1  P) Cc and CT,o but not P, Ch,o or Cc. Under this kind of measurement error, it can be shown (Appendix B) that the OLS estimate is attenuated according to:

s2

c E½b1;OLS  ¼ b1 ˆ s 2 þ E½P2 s 2 c

u

Because the percentage of calories consumed at home P 2 [0, 1], then E½P 2 s 2u < s 2u and the attenuation bias is smaller than in the case of classical measurement error. Therefore, the estimated value of b1 from the INCAP measurement error lies between the OLS estimate and the attenuated adjusted OLS estimate. The intuition behind the result is that observing some calorie data without measurement error lowers the variance of the measurement error relative to the variance in calories, which decreases the attenuation bias. Notice that as the P becomes degenerate at 1 (calories are measured with error) then E[P2] = 1 and the standard attenuation bias result holds. Whereas if P becomes degenerate at 0 (calories are measured without error) then E[P2] = 0 and the OLS estimate correctly identifies b1 under the maintained assumptions. This analysis suggests that correction for the standard OLS attenuation bias result can serve as an upper bound on attenuation bias in the INCAP data. Because home calories are only observed with error, the true P cannot be directly constructed from the data and, therefore, the second raw moment, E[P2], needed to form the attenuation adjustment also cannot be directly formed. However, because on average the fraction of calories consumed at

18 For each child and each visit to the feeding center, the staff measured both the precise amount of atole and fresco dispensed and the amount leftover. Daily leftovers were totaled and cross-checked against the recorded total amount consumed and dispensed.

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home is between 85% and 95% of total calories, this suggests that the attenuating effects of INCAP measurement error will be closer to the 50% attenuating factor from the evidence on the reliability ratio in 24 h recall surveys.19 Another important result is this kind of mixture of a mismeasured and correctly measured variable can also be removed with an instrumental variable provided that the instrument is uncorrelated with the measurement error U (see Appendix B), which implies that under the maintained assumptions that the instruments used in this study will remove the attenuating effects of the kind of measurement error encountered in the INCAP data.20 A final issue that arises in using IV to estimate a production function is the interpretation of IV when there are random coefficients and individuals select into treatment based on the value of their random coefficient. For example, suppose that Eq. (1) is enriched so that each child has a different marginal productivity of calories, which is denoted by adding an i subscript to b1,i:

DHi;a ¼ b0 þ b1;i C i;a þ b2 Di;a þ b3 X i;a þ ei;a

(3)

This is a fairly realistic assumption and says that for certain children that increasing calories is more productive than for other children. The question that arises is what does IV estimate in such a model? A series of papers (Heckman, 2007; Heckman et al., 2006) argues that in this case of ‘‘essential heterogeneity’’ that IV can estimate a parameter that is uninterpretable for economic policy. The basic concern is that even if the instrumental variable has strong first stage explanatory power and even if the instrument is plausibly exogenous to with respect to unobserved determinants of height, which seems reasonable in the current context given the experimental and distance variation, if the children still select into treatments (calorie intake) based on the value of their child specific b1,i, then Heckman et al. (2006) demonstrate that IV in this case can be larger, smaller or even the opposite sign to the true causal effect. Although Heckman et al. (2006) develop statistical tests to test for the case of essential heterogeneity, a perhaps simpler way to assess the validity of the models is simply to test their predictive ability, which is one of the aims of the current paper. One interesting indicator of essential heterogeneity is the failure of overidentification tests, which in their model does not indicate a lack of exogeneity but rather picks up effect

19 Another way to test the prediction of this type of measurement error would be to enter the home calories and supplement calories separately into the model. The prediction would be that the coefficient on home calories is more attenuated than supplement calories. This type of analysis was done in Schroeder et al. (1995) and produces exactly the predicted effect. However, one downside of introducing multiple endogenous variables is the concomitant increase in the number of instruments needed. In addition, the arguments developed in this section allow the calorie measures to be combined, bounded and their attenuating effect removed with an instrumental variable. 20 I stress here that even if the instrument is correlated with P, which will almost certainly be the case because the instrument will change both the level of calorie intake and the relative inputs of home and supplement calorie consumption, that if the instrument is independent of the measurement error U in home calories that the IV procedure recovers the true coefficient.

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heterogeneity coming from different instrument sets identifying and weighting individuals with different effects and different margins of choice (Heckman et al., 2006).

5. Results I first present the empirical results without age specific heterogeneity and then proceed to the model with age specific effects. The baseline empirical results are given in Tables 2a and 2b, which report the first and second stage regression estimates of the change in height production function (1), treating calories as an endogenous variable and using a dummy variable for whether the child lived in an atole village and the distance from the child’s house to the feeding center within each village as instruments. I consider three different instrument sets: IV-1 uses only the atole dummy, IV-2 uses the atole dummy and distance as instruments and IV-3 uses only distance as an instrument. In Table 2a, the first stage F-stats range between 5.0 and 8.81, near to the recommended thresholds (Staiger and Stock, 1997).21 Moreover, the signs are all in the expected direction with the treatment village dummy associated with higher total calorie intake and being farther from the feeding center associated with lower total calorie intake. In Table 2b, I present both the OLS results and the second stage IV regressions of Eq. (1). Regression (1) displays estimates of the change in height production function using OLS. The coefficients have the expected signs with calories having a positive association with height and diarrhea a negative association. Regressions (2), (3), and (4) in Table 2b show estimates of Eq. (1) with the different instrument sets treating calories as an endogenous variable. The most important and salient difference between the OLS and IV estimates is that the magnitude of the coefficient on calories increases by 5 to 18-fold. The difference between the size of OLS and IV coefficients is

21 IV procedures are available in major statistical software packages and it is common for these to report statistical tests for weak instruments, endogeneity and overidentification. I provide some discussion and intuition for each test as they are presented in the text. Testing for weak instruments involves computing the F-test on first stage Eq. (2) for the variables excluded from the second stage Eq. (1). The idea is that instruments should have strong predictive power for the endogenous variable and the concern is that if the instrument are not strongly correlated with the endogenous variable then even small deviations from the identifying assumption Cov(Zi, ei,a) = 0 can have large impacts on bias. Because the standard errors are cluster-robust, these are Kleibergen–Paap F-stats. Unfortunately, there appear to be no critical values associated with these F-stats. The Cragg–Donald F-stats are above the thresholds. In addition, for the just-identified cases (IV-1 and IV-3), Angrist and Pischke (2009) state that the 2SLS estimator is approximately unbiased so that weak instruments will simply show up as large standard errors in the second stage regression, which does not occur here. For an over-identified case, Angrist and Pischke (2009) recommend to check the robustness of the estimate and standard errors using Limited Information Maximum Likelihood (LIML). In the over-identified IV-2 case in this paper, the LIML estimate of the marginal impact of calories is actually larger in magnitude than the corresponding IV estimate so if anything it would strengthen the main finding of the paper. 22 This endogeneity test reports a p-value from the null hypothesis that bˆ1;OLS ¼ bˆ1;IV . The reason the test fails in this case is that the difference between the OLS and IV coefficients are ‘‘too large’’ relative to the standard error of the difference to have occurred by chance.

statistically significant in regressions (2) and (3), reflected in failing to reject the hypothesis of equality of the OLS and IV estimators using the Durbin–Wu–Hausman (DWH) test in regressions (2) and (3).22 Regression (4) does not reject the equality of the OLS and IV estimates. Also in Table 2b, regression (3) has an overidentified instrument set and the regression fails Hansen’s J overidentification test, which suggests either a lack of exogeneity of the instruments or that the different instrument sets are picking up effect heterogeneity. 23 Given that maximum attenuation factor is 0.5, the adjusted OLS estimates would be twice the estimated effect in column (1), which suggests that the OLS attenuation adjusted estimate is below the lower end of the range of IV estimates. 24 In Table 3, I use the same estimation strategy as above except I allow for parameter heterogeneity in calories by age by interacting age dummies with the calorie inputs.25

23 When there are more instrumental variables than endogeneous variables as in IV-2, a Sargan overidentification test can used that estimates Eq. (1) using IV, then regresses the predicted residuals ei;a on ˆ the independent vector of instruments and exogenous variables from Eq. (2) to construct a test statistic. Intuitively the test is checking whether the instruments predict the outcome through the residuals in violation of the identifying assumptions of IV. In the just-identified case, the residuals are exogenous to the instrument by construction. Hansen’s J is the heteroskedastic generalization of the Sargan test. The test fails in this case because the difference in the estimated coefficients across the instrument sets are large relative to their standard errors. If the coefficient estimates change when the instrument set changes this indicates that the residuals would not be exogenous to both sets of instruments. Because it is an overidentification test it still relies on the untestable assumption that at least one of the instruments is exogenous. 24 Two other potential sources of bias are (1) a non-linear calorie input relationship and (2) reverse causality between increases in calories and change in height. To check bias (1), in results not presented here, I considered a quadratic calorie input and used both instruments in the IV estimation. The large OLS vs. IV patterns continue to hold and IV results are actually even larger than in the linear model. For bias (2), reverse causality between increases in calories and change in height would actually suggest the OLS estimates would be biased upwards because faster growing children begin to eat more but eating more does not cause faster growth. In that case an instrument that exogenously varies calories should find a smaller impact estimate than OLS. The opposite pattern is found in the empirical results. 25 Another potentially important source of effect heterogeneity would be differences in productivity by lagged height and/or lagged weight. Such a model would try to capture that children of different sizes have different basal calorie requirements and would presumably require different levels of calorie intake for maintenance versus growth. However, given the one year timing of the data collection, there is actually much more variation in height and weight across ages than within an age in the data. In addition, the height, weight and age measures are very highly correlated with correlation coefficients between 0.91 and 0.95 depending on the measures. When I tried interacting lagged height or lagged weight with calorie intake the results are very similar to the models with age specific heterogeneity. Models with combinations of interactions between calories and age, calories and lagged height and calories and lagged weight also produce very similar results. These robustness checks are complicated by the need to simulate a counterfactual height distribution, which is discussed in more detail below. Although these other forms of heterogeneity are potentially important, the structure of these data do not seem to permit such a fine grained analysis and the OLS versus IV findings continue to be robust to alternative forms of heterogeneity. There is also potential for differential growth velocity both by age and between boys and girls but I did not find any evidence that controlling for such effects changed the estimates of the marginal productivity of calories. Interactions between calories and diarrhea also proved inconclusive.

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Because of the added heterogeneity, the F-stats are much lower and below the recommended thresholds, ranging between 0.01 and 2.59. Although it seems obviously important to understand heterogeneity in effects by age, evidently considering this amount of heterogeneity stretches the statistical power of the data so the added realism of the model should be balanced against any potential statistical issues. Reflecting previous work (Schroeder et al., 1995). I replicate that the OLS results show decreasing marginal productivity of calories by age.26 The results show essentially zero marginal productivity of calories after 48 months. The IV results again display the same pattern being much larger in magnitude than the OLS results. In addition, they also display the same decreasing productivity by age. A Durbin–Wu–Hausman test rejects the equality of the OLS and IV models with age heterogeneity in most specifications and a statistical test of the equality of calorie productivity by age also rejects the null in most specifications. Although the falling productivity by age is well-known and consistent with much other work (Schroeder et al., 1995), the main finding of the large difference between the OLS and IV results continues to hold to the model with age specific heterogeneity. 6. Counterfactual The estimation results suggest a large discrepancy between the OLS and IV estimates that cannot be accounted for by measurement errors. Although economists often prefer IV to OLS as a way to deal with endogeneity, more recent scholarship questions this claim to superiority (Heckman, 2007; Heckman et al., 2006). A scientific and yet simple way to test between the validity of these estimates is to check their predictive ability and this is the goal of the current section. Therefore, to distinguish between the plausibility of the OLS versus the IV results, I next present the model predictions regarding the effect of closing ‘‘calorie gaps’’ on ‘‘height gaps’’ that exist between Guatemala and developed countries. The developed country that I focus on as a point of comparison is the US because of the existence of a migration study comparing the heights of ethnically similar children born in Guatemala versus the US. The measurement of the calorie and height gaps used in the counterfactuals raises many issues that I detail below. First, to understand the magnitude of the calorie gap between Guatemala and the US, I directly compare the calorie intake in the INCAP study with calorie information collected in the US from the National Health and Nutrition Examination Survey I (NHANES I). The NHANES I is a nationally representative survey of 32,000 people age 1–74 from 1971 to 1975. In addition to height and age information, the survey also collects information on calorie intake from a 24-h food consumption intake survey. I chose the NHANES I study because the sampling period 1971 to 1975 overlaps the INCAP study from 1969 to 1977. In

26 This is conceptually different from decreasing velocity of growth although decreasing productivity by age and their co-movement by child’s age certainly suggests a close relationship.

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addition, there were fewer problems with overeating and obesity in the 1970s. I restrict the sample to children aged 1–7 in the NHANES I data to match the ages of children in the INCAP data. Pooling the INCAP and NHANES I data, Table 4 displays a series of regressions with calories as the dependent variable. ‘‘US’’ is a variable that equals one if the observation comes from the NHANES I survey. Regression (1) shows the unadjusted calorie-gap; the average difference in calories between a child in the INCAP data and the NHANES I study. The difference is approximately 600 calories. However, the difference overstates the magnitude of the calorie gap because the US children are taller and taller children receive more calories, even in Guatemala. Adding controls for height and age lowers the calorie gap to, averaging across the estimates, approximately 430 calories. One interesting feature is that the interaction between the US indicator and age is statistically insignificant, which implies that the calorie gap is constant at 430 calories across ages. Prior to exploring the predicted impacts on height of closing the calorie gap using the model estimates, I first need a benchmark for the counterfactual height results. An interesting study by Bogin et al. (2002) provides exactly such a benchmark. Their paper compares the heights of two populations of children. The first is a group of Maya children living in Guatemala and the second is a group of American children born to Maya immigrants to the US. The authors stress that the ethnic similarity of the two groups of children allows them to attribute differences in the heights to differences in environments between Guatemala and the US. In Table 5, I reproduce the relevant comparison between the American Maya children and the Guatemalan Maya children in the Bogin et al. (2002) study. I also add average height by age from the Guatemalan INCAP children and average height by age from the NHANES I. Averaging across the Bogin et al. (2002) results, the average differences between Guatemalan Maya children and US Maya children is 9.8 cm at 7 years old, which suggests a sizable gap in average height between these two groups. Also, note that despite the large height differences between the two groups of Maya children, the US Maya children are still substantially shorter than the children in the NHANES I; the gap between an average US child and the US Maya children of Guatemalan immigrants is 6.4 cm at age 7. Before comparing the results of Bogin to the current study, several caveats are in order. First, the children in the INCAP study were ladino and not Maya, where the ladinos are a Spanish speaking population of mixed European and Maya descent, which potentially implies a different genetic makeup for height potential in the two populations. Second, both the Bogin samples and the INCAP experiment are samples of convenience and potentially non-representative. However, interestingly for both caveats is that the average heights of the Guatemalan children in the Bogin et al. (2002) paper and INCAP study in Table 5 are not quantitatively very different. Third, there is the possibility that migration to the US is related to the height of either potential migrants or the height of their children. However, Bogin et al. (2002) argue that the migration decisions were

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exogenous and driven by factors such as ‘‘civil war, economic crisis and a cholera epidemic.’’27 Setting aside the issues regarding the validity of the height gap as benchmark, I use the 9.8 cm average difference in heights to gauge the plausibility of the magnitude of the subsequent counterfactuals. Table 6 displays results from increasing the diet of the Guatemala children by 430 calories over a period of 6 years.28 Because the unit of time in the production function is one year, the interpretation on the calorie coefficient is the marginal impact on height in centimeters of a one calorie increase in average daily calories over the course of a year. Then for each possible coefficient the counterfactual is cm=year  b1 calories=day computed according to 6 years  430 calories day

where the units of the model coefficient b1 are centimeters per year per calories per day. Each row uses the corresponding estimate from Table 2b. The differences in the OLS and IV estimates translates into large differences in the counterfactuals. The OLS estimate gives a counterfactual of 0.74 cm while the IV estimates range from 3.93 cm to 13.06 cm. Finally, I add an ‘‘Adjusted OLS’’ counterfactual, which uses as the attenuation adjusted OLS estimate and gives a counterfactual increase in height of 1.49 cm. Recall that this estimate serves as an upper bound for the attenuating effects of measurement error in the INCAP data.29 Also, in Table 6, the column ‘‘% of Height Gap’’ shows the computed counterfactual as a percentage of 9.8 cm difference report in Bogin et al. (2002). Again, the differences in the OLS and IV estimates translate into large differences in magnitude between the counterfactual height impacts of the calorie intervention. While the OLS estimate suggests that only 8% of the height gap would be closed by closing the calorie gap, the IV estimates range from closing 40% to 133% of the height gap between Guatemalan children and Guatemalan children born in the US. In Table 7, I perform the same counterfactual exercise using the estimates from Table 3 with age specific heterogeneity in the marginal impact of calories and again benchmarking with the 9.8 cm difference.30 This time, instead of closing the calorie gap for all of early childhood, I

27

It is also not clear that even if those events are random with respect to parents’ height that they would not affect the height of their children through health and income shocks. It would have been interesting to compare the heights of the parents of the children in the study who decided to immigrate or not. It seems they did not collect those data. However, a previous study (Bogin, 1988) did not find evidence of ‘‘phenotypic selective migration’’ from Central America to the US, which suggests that this may not be a source of bias. 28 The INCAP data do not have ‘‘home calories’’ for children less than one-year-old because the children are primarily breastfeeding. Therefore, the production function is estimated from 1 to 7 years of age in the INCAP data so I consider a counterfactual of 6 years. Given the ever increasing recognition of the importance of early investments, antenatal investments would perhaps be the most sensitive period for investing (Doyle et al., 2009). 29 The ‘‘Adjusted OLS’’ is actually a soft upper bound because the OLS estimate is attenuated according to the INCAP measurement error and not classical measurement error. 30 Because of noise in the estimates, I impose in the counterfactuals that statistically insignificant and negative calorie coefficients have zero impact on changes in height.

consider closing the calorie gap for different durations in early childhood: between ages 1 and 2, between ages 1 and 3, etc. The results parallel the baseline model with very large differences in counterfactuals between the OLS and IV and substantial differences across IV counterfactuals. The main difference from the baseline model is that the falling impact of calories by age indicates that the height gap counterfactuals are finished by age 3. Finally, the unrealistic predictions of some counterfactuals using the IV estimates continue to hold in the age heterogeneity models. The large differences between the IV estimates and the implication of one of the IV estimates that the height gap would not only be overturned, but that the height of Guatemalans would increase by 30% more than the height gap only through calories, suggests indirectly that the IV estimates are not identifying a policy relevant average marginal impact of calories. An interesting thought exercise is to imagine having had only one of the instruments and to not have had the 9.8 cm height gap benchmark to discard estimates producing unrealistic counterfactuals. Depending on the available instrument, the conclusion reached about the impact of closing calorie gaps would be quite different. While some LATEs may be useful for policy analysis, it would not appear obvious beforehand which estimates would produce useful impact estimates. In fact, what may seem the most natural instrument to use, the experimental variation, gives the most unrealistic counterfactual. The OLS estimate counterfactual is an order of magnitude smaller. If we focus on the change in height model to address unobserved heterogeneity and the attenuation bias adjustment to address measurement error in calories, an upper bound on the impacts of closing calorie gaps in the INCAP data is given by the attenuation adjusted change in height counterfactual, which suggests that at most 16% of the height gap can be explained by closing the US–Guatemalan calorie gap during early childhood. Age specific effects give essentially the same pattern of results but that the effects would occur at earlier ages. 7. Conclusion This paper uses an extremely detailed longitudinal data set on calorie intake, disease and height to estimate a height production function on a sample of rural Guatemalan children born between 1962 and 1977. The econometric model is consistent with theoretical notions of human growth and the micro data allows me to perform several specification tests for different biases. The results suggest substantial measurement error in calories and widely varying parameter estimates likely arising from the LATE characterization of IV. Using the estimated height production functions, I compute a counterfactual effect on height of closing the ‘‘calorie gap’’ and giving Guatemalan children the average diet of a child in the United States during the 1970s. The idea of the counterfactual is to understand how important calories in early childhood are in explaining differences in average heights across populations. The attenuation adjusted OLS estimate suggests that equalizing the calorie gap would close at most 16% of the height gap. Although this estimate is

A.S. Griffen / Economics and Human Biology 20 (2016) 55–69

approximately twice the effect implied by estimates from OLS, the results still suggest that 84% of the height gap is unexplained by calorie inputs. These results are consistent with evidence by Deaton (2007) questioning the role of nutrition in explaining average differences in heights across populations. Although the results show that increased calorie consumption will clearly improve height outcomes, other potential inputs such as the composition of calories, micronutrients, diet diversity, antenatal investments (Doyle et al., 2009), the disease environment, medical inputs, intergenerational linkages in height (Behrman et al., 2009), and work requirements that affect net nutrition are also potentially important channels. These effect may operate either directly as inputs, or indirectly by affecting the productivity of other inputs, in explaining group level differences in average heights. Finally, the results suggest caution in using instrumental variables to estimate biological processes. Although with any IV study there is always the possibility for invalid instruments to be driving the results, the current setting would have to a priori be considered an almost ideal case for studying these issues; an extensive panel data collection in an impoverished environment with plausibly exogenous and experimental variation in the availability of calories. Yet, the IV estimates produce widely varying estimates of the productivity of calorie inputs that would lead to very different conclusions about the role of calorie gaps in explaining population height differences. Although certainly not definitive given the small number of villages and the potential endogeneity of distance, evidence points towards the LATE interpretation of IV as driving these findings. In particular, the wide variation in the impact estimates and consequent failure of over-identification tests despite the face validity of the instruments. Although none of original auxology studies (Schroeder et al., 1995; Habicht et al., 1995) using these data address the potential endogeneity of calories that would typically worry economists, ultimately my conclusions are consistent with their findings. However, the reason for the conclusions is quite different and instructive because the lack of endogeneity bias is certainly not obvious a priori and only through validating the models using calorie counterfactuals and the Bogin data were the issues with IV uncovered. These findings are consistent with work by (Heckman, 2007; Heckman et al., 2006) arguing against the use of IV in cases of selection on the basis of random coefficients. For biological processes, heterogeneity in the form of random coefficients may be particularly pervasive and the current results support the view that using IV methods in auxology and the conclusions drawn from them should be viewed very cautiously. Acknowledgements I would like to thank Jere Behrman, Cecilia Calderon, Flavio Cunha, Hide Ichimura, Edward Norton, Yasu Sawada, Petra Todd and Eric Weese for helpful comments and discussion as well as seminar participants at the University of Tokyo, the Institute of Developing Economies (IDEJETRO), Autonoma Universitat de Barcelona and the University of Hawaii. I would also like to thank the editor

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and four anonymous referees for comments that greatly improved the paper. I gratefully acknowledge financial support from the Grand Challenges Canada Grant 0072-03 to the Grantee, The Trustees of University of Pennsylvania. Appendix A

Table 1 Descriptive statistics by treatment (atole) vs. control (fresco).

Children’s height (cm) Average daily total calories Average daily home calories Average daily supplement calories Days sick with diarrhea (per month) Child’s age (months) Percent male N

atole

fresco

Difference

94.01 (10.52)

92.2 (10.48)

1032.35 (347.01)

993.74 (360.82)

884.29 (331.26)

941.19 (347.29)

148.07 (114.02)

52.55 (44.01)

95.52

z

5.46 (10.4)

6.47 (11.04)

1.01

z

49.91 (17.13)

49.84 (16.88)

.53 (.5) 1403

.57 (.5) 1297

1.82

z

38.61

z

56.9

z

.07 .04

z

Notes: Standard deviations are reported in parentheses. The models estimated using instrument sets IV-2 and IV-3 (see below) have slightly fewer observations because of missing distance data but the patterns are very similar in the smaller samples. * p < 0.1. y p < 0.05. z p < 0.01.

Table 2a First-stage regressions dependent variable: calories.

Atole

IV-1

IV-2

IV-3

(2)

(3)

(4)

39.83y (17.812)

1.00 (0.648) 9.00z (0.379) 75.56z (17.748) 508.91z (25.344)

29.93 (23.429) 28.94z (10.564) 1.09 (0.760) 10.99z (0.480) 98.56z (22.999) 498.53z (41.636)

30.76z (10.364) 1.11 (0.767) 10.99z (0.476) 96.84z (22.865) 519.93z (36.574)

2700 0.202 5.00

1808 0.283 5.34

1808 0.282 8.81

Distance to feeding center Days with diarrhea Age Male Constant

N R2 Kleibergen-Paap F-stat

Notes: First-stage regressions corresponding to the change in height IV regressions in Table 2b. For the excluded exogenous variables, IV-1 uses exposure to atole, IV-2 uses both distance to the feeding center and atole as instruments and IV-3 uses distance to the feeding center as an instrument. * p < 0.1. y p < 0.05. z p < 0.01.

A.S. Griffen / Economics and Human Biology 20 (2016) 55–69

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Table 3 (Continued )

Table 2b Dependent variable: change in height.

Calories Days with diarrhea Age Male Constant

N R2 Durbin–Wu– Hausman p-value IV/OLS Hansen’s J p-value

OLS

IV-1

IV-2

IV-3

(1)

(2)

(3)

(4)

0.0003z (0.000) 0.0133z

0.0051* (0.003) 0.0082

0.0028y (0.001) 0.0127z

0.0015 (0.001) 0.0139z

(0.003) 0.0677z (0.002) 0.2718z (0.063) 10.5655z (0.129)

(0.005) 0.1106z (0.024) 0.6259z (0.221) 8.0300z (1.428)

(0.004) 0.0978z (0.014) 0.5313z (0.146) 9.5604z (0.559)

(0.004) 0.0840z (0.013) 0.4109z (0.137) 10.1148z (0.536)

2700 0.311

2700 0.277 0.00

1808 0.208 0.02

1808 0.302 0.39

17.57

9.64 0.03

5.28

Notes: Standard errors reported in parentheses are cluster-robust at the individual level. IV-1 uses exposure to atole as an instrument, IV-2 uses distance to the feeding center and atole as instruments and IV-3 uses distance as an instrument. Durbin–Wu–Hausman is a test of the difference between the IV estimates and the OLS estimate. Hansen’s J tests the exogeneity of overidentifying instruments in regression (3) only. * p < 0.1. y p < 0.05. z p < 0.01.

Male Constant N R2 Kleibergen–Paap F-stat Durbin–Wu– Hausman b1,a = b1 Hansen’s J p-value

OLS

IV-1

IV-2

IV-3

(1)

(2)

(3)

(4)

0.2749z (0.063) 9.1259z (0.358) 2700 0.320

0.0634 (1.395) 16.5503 (55.609) 2700 2.778 0.0159

0.5345z (0.137) 0.1729 (3.118) 1808 0.000 2.4586

0.4076z (0.156) 1.0616 (4.706) 1808 0.122 0.8039

0.0022

0.0387

0.6647

0.0321

0.0004 0.3627

0.0137

Notes: Standard errors reported in parentheses are cluster-robust at the individual level. IV-1 uses exposure to atole interacted with age dummies as instruments, IV-2 uses distance to the feeding center and atole interacted with age dummies as instruments and IV-3 uses distance interacted with age dummies as instruments. Durbin–Wu–Hausman is a test of the difference between the IV estimates and the OLS estimates. Test b1,a = b1 reports the p-values for a joint test of the equality of the marginal impacts of calories by age. Hansen’s J tests the exogeneity of overidentifying instruments in regression (3) only. * p < 0.1. y p < 0.05. z p < 0.01.

Table 4 Calorie gap: US vs. Guatemala. Table 3 Change in height, parameter heterogeneity by age.

Dependent variable: daily calorie intake (2)

(1)

Calories 12–24 months Calories 24–36 months Calories 36–48 months Calories 48–60 months Calories 60–72 months Calories 72–84 months Days with diarrhea Age

OLS

IV-1

IV-2

IV-3

(1)

(2)

(3)

(4)

0.0012z

0.0173

0.0097z

0.0077*

(0.000) 0.0010z

(0.025) 0.0056y

(0.003) 0.0055z

(0.004) 0.0040*

Age

(0.000) 0.0003z

(0.002) 0.0023

(0.001) 0.0025z

(0.002) 0.0013

Age-squared

(0.000) 0.0000

(0.018) 0.0089

(0.001) 0.0004

(0.001) -0.0008

US  age

(0.000) 0.0002

(0.034) 0.0147

(0.001) 0.0013

(0.001) 0.0024

US  height

(0.000) 0.0003

(0.048) 0.0197

(0.001) 0.0025

(0.002) 0.0036*

N R2

(0.000) 0.0132z

(0.061) 0.0025

(0.002) 0.0087*

(0.002) 0.0096*

(0.003) 0.0396z (0.007)

(0.022) 0.5509 (1.541)

(0.005) 0.1075* (0.058)

(0.005) 0.1091 (0.086)

Indicator US

z

592 (12)

Height

(3) z

(4) z

(5) z

(6) z

430 (12)

442 (19)

462 (21)

471 (32)

348y (169)

16z (0)

15z (1)

15z (1)

15z (1)

13z (1)

7 (10)

66z (21)

68z (22)

75z (22)

7z (2)

7z (2)

7z (2)

2 (6)

15 (18) 2 (2)

6838 0.253

6,838 0.377

6838 0.377

6838 0.378

6838 0.378

6838 0.378

Notes: Robust standard errors reported in parentheses. US is an indicator variable that equals 1 if the observation comes from the NHANES-I and 0 from the INCAP. In this pooled regression, 3225 observations come from the INCAP data and 3613 observations come from the NHANES-I data. * p < 0.1. y p < 0.05. z p < 0.01.

A.S. Griffen / Economics and Human Biology 20 (2016) 55–69 Table 5 Cross study average heights (cm): USA vs. Guatemala.

Table 6 Production function counterfactuals: baseline model.

Bogin et al. (2002)

Age 5 Age 6 Age 7

67

USA1992

USA2000

Guate1998

INCAP 1969–1977

NHANES I 1971–1975

111.3 113.2 118.5

111.5 115.8 119.7

102.2 105.0 109.3

99.1 104.9 110.5

112.8 118.9 124.9

OLS Adjusted OLS IV1 IV2 IV3

D Average height

% Height gap

0.74 1.49 13.06 7.16 3.93

8% 15% 133% 73% 40%

Notes: Height statistics reported in centimeters. Adjusted OLS is the OLS estimates adjusted for attenuation bias. D Average Height refers to the predicted counterfactual change in average height at 7 years old and % Height Gap refers to the percent of the actual 9.8 cm height gap.

Notes: Average population height reported in centimeters. Bogin et al. (2002) samples are USA-1992 and USA-2000, from the children of Maya immigrants born and living in the US, and Guate-1998, a sample of Maya Guatemala school children. The Bogin samples were collected in 1992, 2000 and 1998, respectively, and the sample size varied by age and sample but averaged 70 children per group. INCAP 1969–1977 is from a sample of four ladino villages in the INCAP Longitudinal Study 1969– 1977. NHANES I 1971–1975 is a nationally representative sample from the USA.

Table 7 Production function counterfactuals: model with parameter heterogeneity by age.

Intervention timing

1–2 1–3 1–4 1–5 1–6 1–7

OLS

years years years years years years

IV1

IV2

IV3

D Height

%Gap

D Height

%Gap

IV/OLS

D Height

%Gap

IV/OLS

D Height

%Gap

IV/OLS

.53 .94 1.08 1.08 1.08 1.08

5.4% 9.6% 11% 11% 11% 11%

7.42 9.82 9.82 9.82 9.82 9.82

75.8% 100.2% 100.2% 100.2% 100.2% 100.2%

14.1 10.4 9.1 9.1 9.1 9.1

4.16 6.5 7.58 7.76 7.76 7.76

42.4% 66.3% 77.3% 79.2% 79.2% 79.2%

7.9 5.3 7 7.2 7.2 7.2

3.31 5.03 5.57 5.57 5.57 5.57

33.8% 51.4% 56.9% 56.9% 56.9% 56.9%

6.3 5.3 5.2 5.2 5.2 5.2

Notes: D Height refers to the predicted counterfactual change in height in centimeters given the length of the intervention in the far left column. %Gap refers to the percent of the actual 9.8 cm height gap and IV/OLS divides each IV counterfactual by the OLS counterfactual result.

Appendix B Let Y be the outcome of interest (change in height DH in this case). For calories, following the notation in the paper, let total observed calories be given by CT,o = CT + U where CT is total calories and U is a random variable with E[U] = E[(Y S E[Y])U] = E[(CT S E[CT])U] = 0 and E½U 2  ¼ s 2u . The OLS estimate of the true marginal impact of calories, b1, is attenuated according to: T;o

T

CovðY; C Þ CovðY; C þ UÞ ¼ E½b1;OLS  ¼ ˆ VarðC T;o Þ VarðC T þ UÞ

¼

CovðY; C Þ þ CovðH; UÞ T

VarðC Þ þ VarðUÞ CovðY; C T Þ

VarðC T Þ

VarðC T Þ VarðC T Þ þ VarðUÞ

¼ b1

s 2c s 2c þ s 2u

CovðY; ZÞ CovðY; ZÞ E½b1;IV  ¼ ¼ ˆ CovðC T;o ; ZÞ CovðC T þ U; ZÞ CovðY; ZÞ T

CovðC ; ZÞ þ CovðU; ZÞ

CovðH; P ðC h þ UÞ þ ð1PÞ C c Þ h

c

VarðP ðC þ UÞ þ ð1PÞ C Þ

¼

CovðH; C T þ PUÞ VarðC T þ PUÞ

T

Instrumental variables can remove the attenuating effects of measurement error. If the instrument Z is exogenous, correlated with total calories and uncorrelated with the measurement error U according to E[(Z S E[Z])U] = 0, then:

¼

CovðH; C T;o Þ CovðH; P C h;o þ ð1PÞ C c Þ E½b1;OLS  ¼ ¼ ˆ VarðC T;o Þ VarðP C h;o þ ð1PÞ C c Þ ¼

T

¼

In the INCAP experiment, instead of observing CT,o = CT + U, we actually observe CT,o = P Ch,o + (1 S P) Cc with potential observed home calories given by Ch,o = Ch + U, where I assume U has the same properties as previously. P is a random variable that takes values in [0, 1] and if I assume that U and P are independent, then the attenuation bias is given by:

¼

¼ ¼ ¼

CovðH; C Þ þ CovðH; PUÞ VarðC T Þ þ 2CovðC T ; PUÞ þ E½P2 U 2  CovðH; C T Þ VarðC T Þ þ E½P 2 s 2u CovðH; C T Þ T

VarðC T Þ T

2

VarðC Þ VarðC Þ þ E½P s 2u

¼ b1

s 2c s 2c þ E½P2 s 2u

Because the range of P is [0, 1] then 0 = P2 = 1 and so:

CovðY; ZÞ T

CovðC ; ZÞ

¼ b1

Z 0 P2 fðPÞdP ¼ E½P2 1

A.S. Griffen / Economics and Human Biology 20 (2016) 55–69

68

In the INCAP measurement error, the attenuation bias is less severe than the attenuation bias in the classical measurement error case: E½P 2 s 2u s 2u s 2c þ E½P2 s 2u s 2c þ s 2u 

s 2c 2 c

s þs

2 u



1

s 2c þ s 2u



1

s 2c þ E½P2 s 2u

s 2c s 2c þ E½P2 s 2u

The inequality holds with equality if P is distributed degenerately at 1, which is exactly the case where all calories are measured with error. Notice also that if P is distributed degenerately at 0, which is the case of no measurement error in calories, then the right-hand side equals 1 so that there is no attenuation bias. Essentially the INCAP attenuation bias is bounded between the traditional measurement error case and the true coefficient:

b1

s 2c 2 c

s þs

2 u

b1

s 2c s 2c þ E½P2 s 2u

b1

In the measurement error process given above, an instrumental variable that decontaminates classical measurement error also decontaminates the INCAP measurement error: CovðH; ZÞ CovðH; ZÞ ¼ E½b1;IV  ¼ ˆ CovðC T;o ; ZÞ CovðP C h;o þ ð1PÞ C c ; ZÞ CovðH; ZÞ CovðH; ZÞ ¼ T CovðP ðC h þ UÞ þ ð1PÞ C c ; ZÞ CovðC þ P U; ZÞ CovðH; ZÞ CovðH; ZÞ ¼ ¼ b1 ¼ CovðC T ; ZÞ þ CovðP U; ZÞ CovðC T ; ZÞ

¼

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