So far, the results have focused on the persistence of water quality impacts in downstream areas by measuring the direct spillover externality imposed by upstream pollution. In Table 3, we provide the estimated impact of the within‐district externality by measuring the impact of pollution on health in the same district using the 2SLS procedure outlined in equations (2) and (3).

The first‐stage is strong across all columns and the upstream concentrations are significant. When local concentrations are instrumented with upstream pollution levels in the second‐ stage, all specifications yield statistically significant estimates of the pollution impact and the effect of nitrogen pollution in water on height is negative, and large in magnitude. Diagnostic statistics for instrument relevance such as the Kleibergen‐Paap F (Kleibergen and Paap, 2006) statistic show that the instrument is very strong. The F‐statistic exceeds the Stock‐Yogo (Stock and Yogo, 2005) weak identification critical value for 10% maximal instrumental variables size.<sup>7</sup> The point estimates from the 2SLS procedure are relatively much larger than the corresponding downstream spillover impact in Table 2, supporting the logic that as water pollution decays with river flow and time, the downstream impacts are likely to be smaller in magnitude than the within‐district health impact. The results show that exceeding the nitrate‐nitrogen safety standards over the entire period decreases height by 2.81 centimeters.

Because adult height is associated with income, this implies a productivity loss of around 7% using decrease in height estimates under full exposure derived from column 1 and using estimates of the economic returns to height assumed in the World Bank Human Capital Project (Kraay, 2018). When using estimates of a decrease in height under mean exposure derived from column 1, this translates into a 1.7% fall in productivity or earning potential.<sup>8</sup>

# 5. Robustness Checks

We carry out several robustness exercises to further corroborate our baseline results.

In order to examine the possibility that these results are driven by spurious spatial or temporal patterns, the analysis is subjected to falsification tests. The first test involves re‐estimating equation (1) while replacing each individual’s exposure condition with exposures that occur for 6 different four‐year periods before or after birth up to age 9. The resulting coefficient estimates are plotted in Figure 3 against the different window periods of exposure. All the

> 7 Baum et al. (2007) and Bazzi and Clemens (2013) provide explanations of these tests.

> 8 As a robustness check, we also make use of the Indian Human Development Survey (IHDS) to measure the  impact of early-life exposure to nitrogen pollution on later-life wages using a similar methodology described in Section 2. The IHDS is a nationally representative survey. The survey provided a more complete recording of men’s earnings that we use as our main variable of interest. In unreported results, we find that full exposure in early-life decreases wages in adult life by 9%, on average, providing direct proof of the impact on labor productivity.

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