metadata: authors: 0: author: Coffey, Diane
1: author: Haque,Sabrina Sharmin
2: author: Hathi,Payal Jayant
3: author: Pant, Lovey
4: author: Spears,Dean Edwin
count: World
docna: 0: docna: Place and child health : the interaction of
            population density and sanitation in developing countries
docty: Policy Research Working Paper
subtopic: Health Care Services Industry,Sanitation and Sewerage,Engineering,Reproductive Health,Early Child and Children's Health,Water and Human Health,Water Supply and Sanitation Economics,Sanitary Environmental Engineering,Small Private Water Supply Providers,Environmental Engineering,Health and Sanitation,Law and Justice Institutions,Town Water Supply and Sanitation
teratopic: Water Supply and Sanitation,Water Resources
abstracts: cdata!: A long literature in demography debates
            the importance of place for health. This paper assesses
            whether the importance of dense settlement for child
            mortality and child height is moderated by exposure to local
            sanitation behavior. Is open defecation, without a toilet or
            latrine, worse for infant mortality and child height where
            population density is greater? Is poor sanitation an
            important mechanism by which population density in?uences
            health outcomes? The paper uses newly assembled data sets to
            present two complementary analyses, which represent di?erent
            points in a trade-o? between external and internal validity.
            The first analysis concentrates on external validity by
            studying infant mortality and child height in a large,
            international child-level data set of 172 Demographic and
            Health Surveys, matched to census population density data
            for 1,800 subnational regions. The second analysis
            concentrates on internal validity by studying child height
            in Bangladeshi districts, with a new data set constructed
            with Geographic Information System techniques, and controls
            for ?xed e?ects at a high level of geographic resolution.
            The paper ?nds a statistically robust and quantitatively
            comparable interaction between sanitation and population
            density with both approaches: open defecation externalities
            are more important for child health outcomes where people
            live more closely together.
repnme: repnme: Place and child health : the interaction of
            population density and sanitation in developing countries
display_title: Place and child health : the
            interaction of population density and sanitation in
            developing countries
listing_relative_url: /research/2014/11/20426961/place-child-health-interaction-population-density-sanitation-developing-countries
topicv3: Sanitation m1326453 2000,Infant and Child Mortality m1326544 1446,Population, Aging and Health m1327736 640,Mortality m1504365 3661,Health m1504661 3480
publishtoextweb_dt: 2014-11-01T00:00:00Z
historic_topic: Water Supply and Sanitation,Water Resources
no_of_pages: 47
author_keys: 0: author_key: 1276316
1: author_key: 1247771
2: author_key: 1232196
model_extractions: WPS7124 Policy Research Working Paper 7124

# Place and Child Health

The Interaction of Population Density and Sanitation in Developing Countries _Payal Hathi Sabrina Haque Lovey Pant Diane Coffey Dean Spears_ Water Global Practice Group November 2014
Policy Research Working Paper 7124

# **Abstract**

A long literature in demography debates the importance of place for health. This paper assesses whether the importance of dense settlement for child mortality and child height is moderated by exposure to local sanitation behavior. Is open defecation, without a toilet or latrine, worse for infant mortality and child height where population density is greater? Is poor sanitation an important mechanism by which population density influences health outcomes? The paper uses newly assembled data sets to present two complementary analyses, which represent different points in a trade-off between external and internal validity. The first analysis concentrates on external validity by studying infant mortality and child height in a large, international child-level data set of 172 Demographic and Health Surveys, matched to census population density data for 1,800 subnational regions. The second analysis concentrates on internal validity by studying child height in Bangladeshi districts, with a new data set constructed with Geographic Information System techniques, and controls for fixed effects at a high level of geographic resolution. The paper finds a statistically robust and quantitatively comparable interaction between sanitation and population density with both approaches: open defecation externalities are more important for child health outcomes where people live more closely together.

This paper is a product of the Water Global Practice Group. It is part of a larger effort by the World Bank to provide open access to its research and make a contribution to development policy discussions around the world. Policy Research Working Papers are also posted on the Web at http://econ.worldbank.org. The authors may be contacted at dean@riceinstitute.org.

_The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent._ Produced by the Research Support Team
Place and child health: The interaction of population density and sanitation in developing countries Payal Hathi, Sabrina Haque, Lovey Pant, Diane Coffey, and Dean Spears<sup>_∗_</sup> JEL classification: J00, I1 keywords: sanitation, infant mortality, height, population density, developing countries

> _∗_ Hathi: r.i.c.e.. Haque: World Bank Water and Sanitation Program. Pant: r.i.c.e. Coffey: Princeton University Office of Population Research, Centre for Development Economics at Delhi School of Economics, and r.i.c.e. Spears: Centre for Development Economics at Delhi School of Economics and r.i.c.e. (Corresponding author: dean@riceinstitute.org) We are grateful for comments from seminar participants at the World Bank in Delhi. This project would not have been possible without the support from and dedicated work of the World Bank WSP in Bangladesh, and especially Ahasan Hoque, to facilitate the GIS matching. Part of the work of r.i.c.e. on this study was funded by the United States Agency for International Development under Translating Research into Action, Cooperative Agreement No. GHS-A-00-09-00015-00. This study was made possible by the support of the American people through the United States Agency for International Development (USAID). The findings of this study are the sole responsibility of the authors, and do not necessarily reflect the views of USAID or the United States Government.
# **1 Introduction**

A long literature in demography explores the importance of place for health (Entwisle, 2007). In many cases, this has been characterized as a debate over the health consequences of living in urban settings versus rural settings (Woods, 2004; Dye, 2008; Sastry, 1997). Although many demographers who study the effects of urban residence on health in developed countries today find a strong urban advantage (Eberhardt et al., 2001; Hartley, 2004), historically, discussions of urban health have often begun with the history of poor sanitation and high infectious disease burdens that plagued the cities of now-rich countries while they were developing (Preston, 1975; Cutler and Miller, 2005).

In modern developing countries, there is active debate about what defines “urbanness” (Hugo et al., 2003; Dor ́elien et al., 2013) and when and why urban advantages in child and infant health exist (Fink et al., 2014; G ̈unther and Harttgen, 2012; Van de Poel et al., 2007; Smith et al., 2005; Montgomery and Hewett, 2005; Jankowska et al., 2013). Bocquier et al. (2011) point out that urban advantages depend on the services and economic opportunities that a city provides, while Sastry (1996) points out that the effects of community-level variables on child health often depend on context; that is, that when exploring the effects of place on health, interactions are often important.

In developing countries today, dense settlement often implies a number of health advantages for children. It is correlated with more wealth, which buys better housing and food, and with more schooling, which leads to better educated mothers. Additionally, people in densely populated areas are more likely to have access to health services that matter for child survival and development, such as trained doctors, maternal care and medicines (Magadi et al., 2003; Matthews et al., 2010).

However, scholars have also hypothesized that one important reason why place matters for health in developing countries today, and why it mattered in developed countries historically, is variation in sanitation and the disease environment (Mosley and Chen, 1984; Preston and 2
Haines, 1991). Recent research in economics, epidemiology and public health suggests that open defecation, the practice of defecating in the open without using a toilet or latrine, is an important cause of infant mortality and stunting in both rural and urban settings (Humphrey, 2009a; Fink et al., 2011; Cameron et al., 2013; Spears, 2013, 2012).

In this paper we assess whether the importance of dense settlement for infant mortality and child height is moderated by exposure to local sanitation behavior. We ask: does sanitation interact with population density to produce these child health outcomes? Such an interaction would be consistent with facts and theories in the literature. If open defecation reduces human capital by releasing germs into children’s environments, then it is plausible that the consequences of open defecation would be worse where people live more closely together and are more likely to encounter their neighbor’s germs.

Documenting and measuring the magnitude of the interaction between open defecation and population density is important for several reasons. First, it moves beyond dichotomous rural and urban distinctions and clarifies the circumstances under which population density is positively associated with health, and the circumstances under which poor sanitation is particularly harmful. Second, it contributes to understanding the importance of externalities or “spillover effects” of sanitation: one household’s toilet use or open defecation has consequences for neighboring households’ children. Such externalities are recognized in public economics as a central rationale for policy action. Finally, documenting and measuring such an interaction could guide policy decisions. Open defecation is increasingly concentrated in South Asia, a region where even rural areas are very densely populated.

We present two complementary analyses: the first establishes the broad importance of the interaction between sanitation behavior and population density for predicting infant mortality and child height in developing countries, and the second provides evidence to support the internal validity of this interaction. For the first analysis, we construct a new international dataset from 172 Demographic and Health Surveys (hereafter DHS surveys) collected in 69 developing countries between 1990 and 2012. Child level health data are 3
matched with estimates of community open defecation rates and census population density data for 1,800 sub-national regions. For the second analysis, we use Geographic Information System (GIS) codes to create a new dataset of children in Bangladesh that allows us to identify the effect of the interaction of population density with local sanitation on child height. These new data allow our measure of population density to be more precise than is possible in the international dataset, and they allow us to control for higher-resolution geographic fixed effects.

We motivate the international analysis by confirming the results of prior papers which find that urban children in developing countries are less likely to die in the first year of life than rural children. Using the dataset of 172 DHS surveys, we find that part of this difference is explained by the fact that rural children are exposed to more open defecation, on average, than urban children. However, a positive interaction of urban place with local open defecation suggests that the urban survival advantage is less pronounced where open defecation is high. Further controlling for the interaction of population density and local sanitation clarifies that higher average population density in urban areas is the mechanism through which urban residence likely moderates the effect of sanitation on infant mortality.

We then focus directly on the population density–sanitation interaction and show that it is robust to a variety of respecifications. We also perform falsification tests to show that other variables do not similarly interact with population density to predict infant mortality in these data. Finally, we plot the shape of the interaction between local open defecation and population density and find that it is steeper at higher population densities.

The second analysis seeks to further test the internal validity of the interaction between sanitation and population density in predicting child height. We use GIS codes to match children in the Bangladesh DHS to the population density for their area of residence using highly disaggregated census data. This allows us to construct an interaction of population density and local sanitation that provides a more precise measure of exposure to density of open defecation than we are able to use in the international dataset. We then regress 4
child height on these more precise measures of exposure to density of open defecation using district and survey round fixed effects. As in Sastry and Hussey (2003), we use geographic fixed effects because they control for time-invariant properties of place at the level of the fixed effect, in this case the district.<sup>1</sup> The magnitude of the interaction that we identify in the Bangladesh dataset is quantitatively similar to what is predicted for Bangladesh by a semi-parametric model fit to the international data.

This paper proceeds in three sections. First, section 2 presents background on global sanitation and summarizes evidence from the literature about why poor sanitation would be expected to have a larger effect on infant mortality and child height where population density is higher. Section 3 describes the analysis and presents results from the international dataset. Section 4 describes the analysis and presents results from the Bangladesh dataset. Section 5 discusses the findings. We point out that although, taken at face value, our results might seem to recommend concentrating policy efforts on improving sanitation in urban areas, the distributions of sanitation coverage and population density in the world today show that many of the places on earth where open defecation is most densely practiced are actually classified as rural. Indeed, our findings, combined with these empirical distributions, highlight the threats to child health posed by the enduring density of open defecation in _rural_ South Asia.

# **2 Background: Population density, sanitation and**

# **disease externalities**

Rural places have lower population density than urban places on average, but also have more open defecation than urban places and lower quality sanitation, on average. Although

> 1We do not present multi-level models because, as explained by Sastry and Hussey (2003), these models require the assumption that the random effects that are used in the models be independent of measured covariates. This independence criterion is not met in this case; for example, more urbanized districts have higher population density, on average.

5
developing countries are making progress in improving sanitation, over one billion people still defecate in the open, without using a toilet or latrine (WHO and UNICEF, 2012). Increasingly, open defecation is concentrated in rural areas, but it is also becoming increasingly concentrated in countries with high rural population densities, such as Indonesia, Pakistan, and especially India, where the 2011 census finds that 90 percent of households without a toilet or latrine live in rural areas.

Open defecation is a practice with strong negative health externalities: it spreads infectious diseases such as diarrhea, polio, cholera and parasites. Greater population density could exacerbate these negative externalities by providing more opportunities for disease transmission. Although there are several examples of population density-health interactions in present-day developing countries in the literature,<sup>2</sup> and there is some evidence from present-day developed countries,<sup>3</sup> discussion of the evidence that population density can intensify an epidemiological externality often begins with the history of urbanization in now-rich countries.

Much has been written about the lethal combination of population density and poor sanitation in 19th century London. To illustrate an exemplary use of observational statistics, Freedman (1991) recounts John Snow’s investigation of the 1853-54 cholera epidemic. By tracing deaths to the supply of their households’ water, he demonstrated the nature of the epidemic, and is widely credited for establishing the infectious mechanism of the disease.

2For example, Root (1997) finds that population density is correlated with child mortality across provinces of Zimbabwe. A study of typhoid in Dhaka showed that crowdednesss has a considerable impact on the transmission and distribution of the disease: areas with low risk of typhoid were those with the lowest population density and those with the highest risk had the highest population density (Corner et al., 2013). Ali et al. (2002) show that higher population density is associated with a greater risk of cholera in a rural part of Bangladesh. Grassly et al. (2006) describe challenges to polio eradication in densely populated Uttar Pradesh and Bihar: “high population density and poor sanitation can lead to more frequent infectious contacts and increase levels of excreted polio-virus in the environment.”

> 3An observational study in rural Wisconsin in the U.S. found that a higher density of septic tanks was associated with an increased prevalence of diarrhea (Borchardt et al., 1979). Studies of the Tama River in Tokyo and the Cumberland River in Nashville showed that fecal bacteria concentrations, possibly originating from sewer overflows, were significantly affected by population density (Ham et al., 2009) and (Young and Thackston, 1999). An aggregated (or “ecological”) study across three developed countries also found suggestive evidence that higher population density may be related to increased antibiotic resistance, because higher interpersonal contact can lead to the spread of resistant bacteria (Bruinsma et al., 2003).

6
A large medical and epidemiological literature documents that poor sanitation continues to cause death and disease, particularly among children in developing countries today. Ingestion of fecal pathogens as a result of living near poor sanitation is well-known to cause diarrhea (Esrey et al., 1991). Checkley et al. (2008) use detailed, high-frequency longitudinal data from five countries to demonstrate effects of childhood diarrhea on subsequent height. Humphrey (2009b) posits that chronic but subclinical “environmental enteropathy,” caused by ingestion of fecal pathogens, may also lead to slowed growth. Lin et al. (2013) find associations among fecal environmental contamination, enteropathy and child height in Bangladesh. Several papers in economics have also identified large effects of sanitationrelated diseases on early-life mortality ( _e.g._ Galiani et al., 2005; Cutler and Miller, 2005; Watson, 2006), as well as effects on subsequent human capital accumulation ( _e.g._ Bleakley, 2007; Baird et al., 2011).

Recent econometric studies suggest an interaction between sanitation and population density in predicting health outcomes in developing countries. Spears (2012) finds that infant mortality improved by more and child height increased by more in Indian districts where a government rural sanitation program was more intensively implemented, and that this effect was larger in districts with greater population density. Spears (2013) observes that heterogeneity across developing countries in open defecation can account for a large fraction of international differences in average child height, and that this fraction is further increased when the density of open defecation is used as the explanatory variable. However, unlike this paper, neither of these studies focuses on understanding the interaction of population density with sanitation; instead, interactions have been used as supporting evidence that sanitation indeed has important implications for health.

7
# **3 Population density, sanitation and child health in developing countries: Evidence from 172 DHS**

In these analyses, we use a dataset of 172 DHS surveys collected between 1990 and 2012 in 69 developing countries to assess whether the importance of dense settlement for infant mortality and child height in developing countries is moderated by exposure to local sanitation behavior. As motivation, we begin with a description of how urban place, sanitation, and population density predict infant mortality. We find that the urban infant survival advantage is importantly diminished after controlling for local sanitation, population density, and their interaction.

We then focus directly on the interaction of population density with local open defecation in predicting height and infant mortality. Although this multi-country analysis is not intended to precisely identify a causal effect, we demonstrate that the effect of population density on the sanitation-health gradient is quantitatively robust to model respecifications, including the introduction of a range of fixed effects and controls, suggesting that the interaction we document is unlikely to reflect omitted variables. To provide additional evidence that this relationship is not due to omitted variables, we conduct falsification tests that demonstrate that other measures of socioeconomic status do not similarly interact with population density to predict infant mortality. Finally, we model the shape of the dependence of the sanitation-mortality gradient, and the sanitation-height gradient on population density.

## **3.1 Data & summary statistics**

These analyses combine data from two sources: population density from census or other aggregate demographic data, and sanitation, health, and other covariate data from DHS surveys collected between 1990 and 2012. DHS surveys are internationally comparable, nationally representative surveys collected in poor and middle income countries. We append 8
all available DHS surveys to make a large dataset where each observation is an individual child. We merge to the child level data a new dataset on population density at the level of DHS sub-national regions (hereafter regions). For each of the over 1,800 regions, we manually matched the region to publicly available, published demographic data for the closest available year to the year of the survey. Appendix table 8 lists all of the countries and years in the international sample as well as the source of the region level data on population density.

**Independent variable.** Our independent variable is the interaction of the log of population density at the region level with local prevalence of open defecation near a child. We estimate local prevalence of open defecation near a child by estimating the fraction of the households in a child’s primary sampling unit (PSU)<sup>4</sup> that defecate in the open rather than using a toilet or latrine. We do this by computing the fraction of households in each PSU in the sample that report open defecation.<sup>5</sup> This is a local (neighborhood-level) measure of exposure to open defecation, and not merely a property of the child’s own household (Montgomery and Hewett, 2005). To isolate and emphasize the negative externality of neighbors’ open defecation, we also control for whether a child’s own household defecates in the open in all of the regressions we present.

**Dependent variables.** Our dependent variables are infant mortality and height-for-age. Infant mortality is a child level indicator, which we define for all live births that occurred at least one year before the date of the survey and no more than ten years before the date of the survey. Infant mortality is coded as 0 if the child survived her first year of life, and 1,000 if the child died within the first year. This scaling of the indicator by 1,000 makes our infant mortality estimates consistent with published population-level infant mortality rate (IMR) statistics. The second dependent variable is a child’s height-for-age _z_ -score.<sup>6</sup> A

> 4 DHS surveys use two-stage random sampling. First, a PSU, which is either a rural village or a small set of urban blocks, is selected; second, households within the PSU are randomly selected.

> 5Because the fraction of households in a PSU that defecates in the open is estimated from a sample, and not from data on every household in the neighborhood, this is a noisy measure of the true fraction of households in a child’s local area who defecate in the open; this random measurement error will attenuate our coefficients, so any sanitation gradient we uncover may be a lower bound.

> 6Following standard practice using these WHO _z_ -scores, we omit any child beyond _±_ 6.

9
height-for-age _z_ -score scales a child’s height relative to a healthy population of that child’s age and sex. We use the 2006 WHO international reference population of healthy children.

**Summary statistics.** Table 1 presents summary statistics about the international dataset. Over 6 percent of children in the data died before their first birthday. The average child in our data is notably shorter than children in the healthy reference population. About one-third of the average child’s neighbors defecate in the open. Although it is not used in the regressions (because it would be a country-year fixed effect, which we use as a control), we include GDP per capita from the Penn World Tables in table 1 for illustration. The median child in this dataset is poor; she is growing up in a country-year with a GDP per capita per day of $1.44.

Population density varies widely in our sample, with an interquartile range from 31 to 239 people per square kilometer. Appendix figure 3 plots a kernel density estimate of the distribution of population density among children in our international sample. Throughout our analysis, we transform population density to a log scale. A normal distribution with the same mean and standard deviation is included for comparison; population density appears to match a lognormal distribution.

# **3.2 Motivation: Urban place, sanitation and infant mortality**

Urban places have higher population density on average, but also lower open defecation rates, on average. How do these three factors interact to predict infant mortality? In this section, we motivate the analyses that follow by using the international dataset to present results from regressions of the form: where _mortality_ for child _i_ living in place _p_ is scaled for infant deaths per 1,000; _sanitation_ is open defecation in the child’s local area (PSU); and _place_ will be implemented either as 10
a dummy for urban residence, as defined by the DHS,<sup>7</sup> as population density of the child’s sub-national region, or with both in the same regression.

Table 2 presents estimates of the descriptive regression in equation 1. As the literature suggests, column 1 finds that averaging over the combined dataset, children in urban places, as defined by the DHS, are 16 per 1,000 more likely to survive their first year of life than children in rural places. Part of this apparently large urban advantage reflects the better sanitation environment in urban areas. Column 2 adds local open defecation, and an interaction with the urban indicator. The coefficient on urban in this regression declines in absolute magnitude by almost two-thirds relative to the magnitude of its coefficient in column 1, which does not include sanitation. As expected, open defecation and urban residence interact, such that open defecation is more steeply associated with mortality in urban rather than rural places. The results predict that the average urban child is only 2.4 per 1,000 less likely to die in infancy in places where everyone defecates in the open, compared with 8.0 per – – 1,000 or more than triple the advantage in places where nobody defecates in the open. This suggests that, on average, urban places combine the advantages of available resources and better sanitation with the disadvantages of population density.

To check this interpretation, column 3 documents that infant mortality is lower, on average, in more densely populated places, and column 4 adds the interaction of population density with sanitation. We find that open defecation is more steeply associated with mortality in more densely populated places, and that once differences in sanitation are accounted for, population density itself is associated with neither a mortality advantage nor a mortality disadvantage at the average level of open defecation.

Finally, the regression results in column 5 include the interactions of both population density and local sanitation, as well as urban residence and local sanitation. We find that infant mortality is higher where open defecation is more common, and lower, on average, in urban places. However, the urban advantage documented in column 5 is only one-third as 7The DHS defines urban residence based on the definitions used by countries’ national statistical offices.

11
much as appeared to be the case in column 1. Once the interaction of population density and open defecation is accounted for, there is no longer an apparent interaction between urban place and sanitation – which is consistent with a large effect of sanitation on infant mortality even in densely populated rural places. Moreover, population density _per se_ appears neither associated with greater nor lesser mortality.

Table 2 suggests that in developing countries, an interaction between sanitation and population density importantly moderates the relationship between place and early-life health and mortality. The following analyses sharpen our understanding of this interaction, and investigate its external and internal validity.

# **3.3 The interaction of sanitation and population density in 172 DHS**

We have seen that the relationship between urban place and health depends importantly on population density and on open defecation. In this section we focus directly on establishing and interaction between population density and sanitation, and assess the robustness of the estimate.

## **3.3.1 Empirical strategy**

For each dependent variable, we regress health on a linear interaction of local sanitation and population density, controlling for household sanitation and one of three levels of fixed _α_ :

- _country_ : for example, a fixed effect for India, pooling over the 1992, 1998, and 2005 DHS surveys

- _survey_ : a partition of _country_ , for example, a fixed effect for India in each surveyed year

12
- _region_ : a partition of _survey_ into the sub-national region level at which population density is matched, for example, the Indian state of Bihar in 2005

Note that adding fixed effects means our identification is derived from heterogeneity within these regions. Depending on the question we seek to answer, this may be _over_ controlling. For example, in the case of the region fixed effects, the difference in population density between regions within the same country may be of policy relevance.

Our regression specification is: where _i_ indexes individual children, _p_ is the region for which population density is matched, _s_ indicates a DHS survey, and _c_ is a country. _X_ is an extensive set of controls which we use throughout the analysis of the international dataset. It includes six indicators for the child’s household owning the six common DHS assets (electricity, radio, TV, motorcycle, car, refrigerator); indicators for sex, birth calendar month, and multiple births; year of birth entered linearly; indicators for first, second, or third birth order; an indicator for household education; and the mother’s age entered linearly.<sup>8</sup> We also control for whether or not the child’s own household defecates in the open. When child height is the dependent variable, we always add a vector of 120 age-in-months by sex indicators. Standard errors are conservatively clustered at the level of 172 DHS surveys (thus, India’s entire 2005 DHS is one cluster), except in specifications with country fixed effects, where standard errors are even more conservatively clustered at the country level.

# **3.3.2 Results**

Table 3 reports estimates of equation 2, for infant mortality in panel A and for height-forage in panel B. It reports results using several combinations of fixed effects and controls.

> 8We are constrained to use variables that are available in all of the DHS surveys.

13
The result is quantitatively robust as the estimates remain in a stable range: a one logunit increase in population density increases the change in infant mortality associated with moving from no neighbors defecating in the open to all neighbors defecating in the open by about 2 deaths per 1,000 live births, and increases the corresponding decline in height-for-age by about 0.04 of a height-for-age standard deviation.

Results are similar if we use fixed effects for countries (64 for height and 69 for infant mortality) or if we instead use over 1,800 disaggregated fixed effects by region within each survey year, with or without a long vector of controls. Indeed, the regional fixed effects may represent over-controlling if part of what is important for child health in differences across region-years is differences in the density of open defecation across space and time. Two of the twelve coefficient estimates are not statistically significantly different from zero; we include them for completeness and note that their coefficients are of important magnitude and not statistically distinguishable from the other coefficient estimates. Moreover, this lack of statistical significance is only because we have conservatively clustered standard errors at country or country-year levels; if standard errors were clustered by sub-national region or survey PSU (as is common in use of DHS surveys) then both of these coefficients would be highly statistically significant in our very large dataset.

# **3.4 Falsification: Other measures of SES do not interact to predict infant mortality**

In this section, we conduct falsification tests: we interact open defecation with other “placebo” measures of community socioeconomic status. If the interaction documented in table 3 merely reflects some unobserved spurious correlation between population density and health, rather than an effect of population density on the consequences of open defecation, then we would expect many other measures of community socioeconomic status to similarly apparently interact with population density.

14
Figure 2 plots _t_ -statistics on _β_<sup>ˆ</sup> 3 from estimates of regression equation (3) with various community-level socioeconomic status variables substituted in place of sanitation, with and without a vector of controls _X_ , including the household’s own open defecation, as described above. Regressions take the following form: In all cases, the SES variables are community (survey PSU) averages, computed from the household recode, as in our estimated local open defecation variable. So, for example, open defecation is the fraction of households in the PSU which defecate in the open, radio is the fraction of households in the PSU which have a radio, and bottom fifth is the fraction of the PSU whom the DHS asset index sorts into the bottom fifth of their survey round. The one exception is GDP, which is a country-year level variable.

The dotted lines in figure 2 indicate the threshold for statistical significance. Figure 2 shows that only local open defecation robustly statistically significantly interacts with population density to predict infant mortality, with and without controls.<sup>9</sup> This specificity of the sanitation-density interaction increases our confidence that the result is indeed due to a greater effect of sanitation on height where population density is greater.

# **3.5 Extension: The shape of the sanitation-population density**

# **interaction**

For tractability, the regressions in section 3.2 assumed a linear association between population density and the sanitation-health gradient: each log-unit increase in population density

> 9A high fraction of the local area being in the bottom fifth of the country-year’s asset index statistically significantly interacts with population density _without_ controls, although not _with_ ; although it is beyond the scope of this paper, it is plausible that there is a special effect on health of poor people living densely close together. Note, however, that this cannot be an omitted variable in our results: our extended controls include indicators for the individual assets used to construct the asset index.

15
was assumed to be associated with the same steepening of the relationship between sanitation and health. However, with such a large dataset, we can model this relationship more flexibly to show the shape of the sanitation-population density interaction.

In this section, we allow the interaction between population density and the healthsanitation gradient to be a fifth-order polynomial. We use an odd-ordered polynomial to capture flexibility in the increasing relationship between population density and the sanitation-infant mortality gradient. We use a 5th order polynomial because of the statistical significance of these terms (F = 5.6; p ¡ 0.01) and the failure of the extra 6th and 7th terms to be jointly significant additions to the model (F = 0.4; p = 0.79).

For both infant mortality and height-for-age, we estimate: As before, we are estimating health outcomes for child _i_ , in region _p_ , in DHS survey _s_ , and in country _c_ . As described above, we introduce fixed effects _α_ at country, survey, and region levels, in stages. We also include the same vector of extended controls _X_ , as well as the household’s own open defecation, as described above.

This functional form implies that the change in health associated with a change from 0% to 100% local open defecation is: Panel A of figure 1 plots the dependence of the infant mortality-open defecation gradient on population density; panel B plots the height-open defecation gradient as a function of population density. In both cases, the same six specifications that were used in section 3.3’s table 3 are plotted: fixed effects at the country, survey, and region level, with and without an 16
extended vector of controls. _F_ -tests with eight degrees of freedom show that the higher-order interaction does not improve the fit – that is, that _β_ 2 _,_ 2 through _β_ 2 _,_ 5 and _β_ 3 _,_ 2 through _β_ 3 _,_ 5 are all zero – are rejected, for example with _F_ = 8 _._ 50, _p <_ 0 _._ 0001 in the case of country fixed with no controls.

Figure 1 shows that although adding controls and changing the fineness of fixed effects shifts the estimated function vertically, which changes the _level_ of the sanitation-health – gradient, the shape of the function that is, the dependence of the health-open defecation gradient on population density – remains similar. Across model specifications, the association between open defecation and infant mortality, for example, is about twice as steep in places with the average population density of Bangladesh (or in the similarly dense, largely rural Indian states of Uttar Pradesh and Bihar) as it is in places with the average population density of sub-Saharan Africa. Moreover, the function curves convexly, so the effect of population density is even greater at higher levels of population density. Because the average population density in the Bangladesh data used in section 4 is especially high, these estimates predict a particularly steep sanitation-health gradient and large interaction with population density in that context.

# **4 Population density, sanitation and child height in Bangladesh**

Section 3 showed that higher population density is robustly and uniquely associated with a steeper sanitation-health gradient. This section uses variation across time and place in local – open defecation within Bangladesh a country where open defecation has fallen sharply – over recent decades in order to provide further evidence for the internal validity of the sanitation-population density interaction.

Bangladesh is an apt case study to further interrogate the sanitation-population density interaction for two reasons. First, unlike many DHS surveys, the Bangladesh DHS surveys 17
report GIS codes for primary sampling units (PSUs). This permits us to create a more precise measure of the density of open defecation to which an individual child is exposed than we were able to use in the international data, and to control for fixed effects at the district level, which is a much smaller geographic area than the region that was used in the international analysis. Second, Bangladesh experienced a rapid decline in open defecation over the period we study. According to WHO-Unicef statistics, national open defecation declined from 20.6 percent in 1999 to 3.9 percent in 2011 (UNICEF & WHO, 2012). As a result, much of the variation we use to identify the effect of the interaction of sanitation and population density on child height results from a reduction in the density of open defecation over time.

# **4.1 Data and summary statistics**

We combine data from the 1999, 2004, and 2011 Bangladeshi DHS surveys, as well as from two Bangladesh censuses, to investigate the relationship among open defecation, population density, and child height. To do this, we match the PSUs of children in the DHS to political boundaries using GIS codes.

There are three levels of political disaggregation within Bangladesh. Most coarsely, Bangladesh is divided into 7 divisons. Divisions are the sub-national region coded in DHS data; we refer to these as regions for consistency with section 3. Regions are divided into districts, which are not reported in the DHS. There are a total of 64 districts in Bangladesh; the average district has a population of about 2 million people. Districts are divided into subdistricts, which are then divided into Unions (rural), Wards (parts of cities), or Pourashava (towns), which we abbreviate UWP. The average UWP had 339,906 people in the 2011 census.

Each PSU in the Bangladesh DHS surveys is accompanied by a GIS code, which is publicly available on request, which includes the latitude and longitude of the PSU.<sup>10</sup> We used ArcGIS

> 10We drop two PSUs from the 2004 DHS where GIS information was not reported.

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10 software and a polygon overlay technique to match PSUs from the DHS to districts and UWPs from the 2009 Local Government Engineering Department (LEGD) UWP-level map. After identifying each PSU’s UWP, we matched it with a UWP-level population density from census data from Bangladesh Bureau of Statistics (2002) and Bangladesh Bureau of Statistics (2012) to create our independent variable, the interaction of PSU-level open defecation with the log of UWP-level population density. The 1999 and 2004 DHS were matched to the 2001 population census of Bangladesh; the 2011 DHS was matched to the 2011 population census.<sup>11</sup> Thus, each PSU is matched to a highly disaggregated measure of population density. Because the DHS surveys are repeated, nationally representative cross sections that do not form a panel of PSUs, it is often the case that a given UWP is not represented in more than one round of the DHS surveys. Therefore, the smallest geographic unit for which we can include a is the district.

**Independent variable.** Our independent variable of interest is the interaction of the log of UWP-level population density with the fraction of households in a PSU that defecates in the open; this is the same for each child in a given survey round and PSU.

**Dependent variable.** The dependent variable in this analysis is the height-for-age _z_ - score of children under five, using the WHO 2006 reference of healthy children. For the Bangladesh analysis, we no longer use infant mortality as a dependent variable. With a sample less than four percent as large as in the international analysis of section 3, we are unable to precisely identify effects on infant mortality, a low probability binary outcome, using district fixed effects. Sample size is less of a constraint for continuously-distributed, normalized height-for-age, which is routinely studied in samples of this size (e.g. Spears, 2013). The appendix presents evidence that supports an interactive effect of sanitation and population density on infant mortality. Appendix table 7 presents results for infant mortality that use fixed effects for region, rather than district fixed effects, and repeats falsification

> 11In a small number of cases, area was not available from the census, so we computed population density by dividing census population by area from LEGD data.

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tests showing that there is no similar interaction with electrification or radio ownership.

**Summary statistics.** Table 4 reports summary statistics for the Bangladesh dataset. Observations are infants and children, so averages do not, in general, correspond to published summary statistics representative of the population of Bangladesh. For example, if young children are disproportionately found in poorer households, our summary statistics will present a worse picture of human development. Indeed, the summary statistics reflect a poor, mainly rural population with high mortality and low maternal nutrition. However, child height, infant mortality, sanitation, maternal nutrition, and electrification all show clear improvements over the three survey rounds.

# **4.2 Empirical strategy**

We identify the association between local sanitation density and child height from crosssectional and over-time variation within districts. The GIS matching described above allows us to use fixed effects that are approximately 10 times finer than the seven regional fixed effects used in the international analysis. We estimate regressions with district and survey round fixed effects for children under 5 years old of the following form: where _i_ indexes individual children, _d_ indexes districts, and _t_ indexes survey rounds. Standard errors are clustered at the district level (that is, pooling all survey rounds within a district). As with prior regressions in which height-for-age is the dependent variable, we include 120 age-in-months by sex indicators _Aidt × sexidt_ . We also add fixed effects for the year in which a child was born, _yearidt_ , to account for overall time trends. As before, we control for an indicator for whether the child’s own household defecates in the open. _δd_ is a district fixed effect and _γt_ is a survey round fixed effect. This strategy allows us to control 20
for everything about a child’s district, for any potential time trends affecting height, as well as any potential survey round specific measurement issues.

In order to demonstrate the robustness of our result to individual and household regression controls, we add controls, _Xidt_ , which are more comprehensive than those included in the international analysis, in stages:

- Birth demography: mother’s age at the child’s birth as a quadratic polynomial, indicators for multiple birth, indicators for calendar month of birth, and an indicator for being the first born to a mother.

- Household wealth: indicators for the household having electricity, a radio, a television, a bicycle, and a motorcycle or scooter.

- Maternal nutrition, anthropometry, & care: mother’s body mass index (BMI) and height in centimeters; indicator for mother’s literacy; indicator for breastfeeding beginning on the first day.

# **4.3 Results**

Table 5 presents estimates of regression equation 6. We find that local sanitation statistically significantly and robustly interacts with local population density to predict average child height. Adding fixed effects and controls does little to change the magnitude of the coefficient on the interaction; none of the six estimates is statistically distinguishable from the others. These coefficients suggest that a doubling of population density is approximately associated with a 0.2 height-for-age standard deviation increase in the difference in average child height between places where there is no open defecation and where there is 100% open defecation. The stability of the coefficient on the interaction suggests that it is unlikely to be driven by an omitted variable uncorrelated with all of these controls. In particular, mother’s BMI may well be over-controlling, as weight-for-height is a short-term net nutritional outcome that, 21
in part, depends on the infectious disease environment.<sup>12</sup> The average linear interaction in table 5 for Bangladesh is approximately 10 times the size of the international average linear interaction in table 3. This best linear approximation to the interaction is useful because it allows our fixed effects identification strategy and – permits simple statistical significance tests with controls. However, figure 1 suggests that over the entire global range of variation in population density – the interaction is not linear. Instead, the dependence of the health-sanitation gradient on population density appears to be steeper at greater population densities; in other words, the effect of sanitation on health is more quickly changing in population density where population density is greater.

Average population density in Bangladesh is very high in international comparison. Bangladeshi children, therefore, would be on the far right side of panel B of figure 1, which would predict a particularly steep linearized interaction between sanitation and open defecation. Table 6 reports the six linear interaction gradients at the average population density of children in our Bangladeshi sample, computed from the six models estimated in panel B of figure 1. The numerical predictions in table 6 are larger than the global average linear interaction in table 3 and similar to what our fixed effects identification strategy finds within Bangladesh in table 5.

# **5 Discussion and conclusion**

Our paper was motivated by the observation that an interaction between sanitation and population density importantly moderates the relationship between place and early-life health outcomes. The results presented in this paper sharpen our understanding of this interaction, – and investigated its external and internal validity. In two separate analyses representing – two different points in a trade-off between external validity and internal validity we find that poor sanitation is more detrimental for early life health where population density is

> 12Duh and Spears (2013) have shown that a similar local open defecation variable in India is robustly associated with lower BMI for childbearing age women.

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greater, or stated differently, that population density does not have the same benefits for health where sanitation is poor. These results are biologically plausible because open defecation leads to environmental contamination with germs from feces, and these germs are more likely to cause disease where people are more likely to come in contact with them.

Although resolving longstanding debates about the health advantages or penalties of living in urban or densely-populated areas is well beyond the scope of this paper, our results suggest some clarifications about the importance of place for child health in developing countries. We have isolated that high population density and poor sanitation _in combination_ are particularly threatening to early life health. Our results suggest that high density _without_ poor sanitation is substantially less dangerous, such that the advantages of access to health care and other resources might dominate the disadvantages of disease externalities, yielding a net health benefit of living in dense cities (Leon, 2008). Additionally, urban settings with low population density may not be disadvantaged relative to rural settings with high population density.

Our result has an important implication for policy-makers: for a given level of open defection, concentrate attention on improving sanitation where population density is high, or at minimum include population density as a factor in allocation decisions. To emphasize, this does not exclusively or even necessarily recommend that sanitation policy attend to urban places. Population density is a continuous variable, and many parts of the developing world that are classified as rural have higher population densities than places classified as urban. The latest estimates of open defecation and population density in the developing world suggest an increasing concentration of open defecation in densely populated parts of rural India, which poses a significant threat to the health of children in these regions, despite their “rural”<sup>13</sup>

> 13According to the Unicef-WHO statistics, open defecation is increasingly a South Asian, and particularly an Indian, problem. Although Bangladesh has drastically reduced open defecation, and Pakistan has seen marked improvements, there continues to be more open defecation in India than there is toilet or latrine use. 60% of open defecation in the world occurs in India, a country where 70% of households live in rural areas, and 70% of rural households defecate in the open. Primarily rural Indian states like Uttar Pradesh and Bihar, home to about 300 million people, have population densities that exceed 800 persons per square

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