wealth proxy over the wealth proxy given in the DHS dataset. Finally, most assets that are part of the DHS questionnaire are owned by only a very small fraction of the rural population in the very poor contexts that we analyze. It is difficult to understand why the wealth-related questions chosen for the DHS have such a strong urban bias.

# _Descriptive statistics_

Summary statistics for the share of children who died in the five years preceding the survey and selected explanatory variables are provided in Table A2. The share of children who died of course reflects the child mortality rate estimates reported above, with the highest share in Niger in 1998 and the lowest in Madagascar in 2003. Mean mother’s age at birth is surprisingly similar across countries fluctuating around 27 with the lowest average for Uganda in 2000 with 25.9 years and the highest for Senegal with 27.9 in 1997. In terms of mother’s education however there are considerable differences between the countries that we have already discussed above. Birth intervals of less than 2 years are fairly common in most of the countries and the share of births with short intervals is around one fifth with quite some variation between countries, but also over time. Madagascar and Uganda exhibit high shares of more than 27 percent in the early survey year, while this share stands at around 15 percent in Mozambique, Guinea, and Senegal. Average household size varies considerably between countries from around 6 members in Madagascar and Kenya to more than 13 in Senegal. Households are generally larger in Western than in Eastern Africa, certainly reflecting sociocultural differences in the formation of households, as defined by the DHS. Finally, the descriptive statistics again show the deficiencies of the water supply variables in the DHS survey, as somewhat implausible variations appear over time for example for Mali, Niger, and Senegal. The corresponding results should hence be taken with caution.

Table A3 reports summary statistics for the vaccination rates. These statistics originate from the STATcompiler of http://www.measuredhs.com/ and are averages of (surviving) children aged 12-23 months who had received a specific vaccine at any time survey. Earlier DHS surveys only record vaccination information for children up to the age 2 years. The recent ones collect this information also for older children up to the 60<sup>th</sup> month and can hence be used in the micro analysis.<sup>8</sup> Table A3 shows considerable variation in vaccination rates.

> 8 As just mentioned, the statistics are computed only for surviving children, since the surveys do not have vaccination records for dead children. Hence, the reported figures only partially reflect the averages of the relevant ‘true’ vaccination rates. While these average rates among surviving children can provide a reasonable approximation about actual vaccination rates among all children, we do need the child-level vaccination information for our analysis. We achieve this by a very simple imputation procedure: We assume that each (dead) child has received the same vaccinations as other children (at least one other child) in the same household.

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