matched samples where unmatched observations will be inevitably dropped, Smith (1997) showed that matched samples can increase the efficiency of estimates.<sup>13</sup>

# _(iv) Data Sources_

The sample in this analysis consists of 6,399 children ages 6–9 years from both urban and rural areas of Bangladesh. The data are put together from DHSs 2007, 2011, and 2014, which are nationally representative at the division level. The dependent variable is dichotomous and indicates whether a child aged 6–9 is enrolled (1) or not enrolled (0) in primary school at the time of the survey. The primary variable of interest is the concentration of unimproved sanitation at the baseline within each household cluster. We consider this variable to be reflective of the child’s early exposure to unimproved sanitation. The variable is obtained by geomatching household clusters over a seven-year period.<sup>14</sup> Clusters from DHS 2000 were geomatched with DHS 2007 to estimate the exposure to unimproved sanitation when children in the 2007 sample were 1 or 2 years old.<sup>15</sup> Here we make two assumptions: (i) a household is likely to have unimproved sanitation if the majority of its neighboring households have it; and (ii) the families stayed in the same household and household cluster over the seven-year period. The percentage of children enrolled in primary school at the baseline was also obtained using the geomatching technique. This variable is defined as the proportion of primary schools in a cluster. Finally, the lagged electricity ratio was calculated using the same procedure.

The indicator “URBAN” takes the value of 1 if the household is located in an urban area and 0 otherwise. In our analysis, household wealth quintiles are constructed using a principal component analysis (Filmer & Pritchett, 1999) that accounts for housing conditions, ownership of durable goods, land, etc. Information on the type of water source and sanitation facility used by the household is not included in the calculation since these are considered separate variables in our analysis. The top three quintiles are combined to form the wealth variable, which indicates whether a household is in the top 60 percent of the population in terms of wealth. The analysis takes into account whether water and sanitation facilities are improved or not.<sup>16</sup>

> 13Through theoretical and simulation results in a wide range of scenarios, matched samples can result in substantial bias and variance reduction even if compared with random samples of the same size (Rubin & Thomas, 1992, 1996). 14 The baseline for children in the 2007 DHS is the 2000 DHS, the baseline for children in the 2011 DHS is the 2004 DHS, and the baseline for children in the 2014 survey is the 2007 DHS.

> 15  Of the 6,399 children in our sample, we matched 1,626 children from the 2007 DHS, 2,508 children from the 2011 DHS, and 2,265 children from the 2014 DHS. Figure 1 in the annex shows the geographic distribution of household clusters available before and after geomatching.

> 16 According to the Joint Monitoring Programme (JMP), an improved sanitation facility is defined as “one that hygienically separates human excreta from human contact.” The JMP considers the following categories as improved sanitation: flush to piped sewer system, flush to septic tank, flush to pit (latrine), flush to unknown place, ventilated improved pit latrine, pit latrine with slab, and composting toilet. Shared sanitation is excluded from the improved sanitation category. The following categories are considered as improved water: piped into dwelling; piped into compound, yard, or plot; piped to neighbor; public tap/standpipe; bottled water; tube well/borehole; protected spring; and protected well.

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