become more contaminated, or more turbid (Cunha et al., 2016), which render less effective the point-of-use chlorination that is commonly used by households in low-income countries (Amrose _et al_ 2015).

To estimate the health impacts of forest cover loss via the water channel, we therefore begin by investigating impacts on diarrhea. Our focus on DD is deliberate since different diseases have different disease ecologies and thus different mechanisms of transmission (Pattanayak and Pfaff, 2009; Berazneva and Byker, 2017; Garg, 2019). For our main specification we estimate equation (1) on the pooled sample using Ordinary Least Squares (OLS), where i is a dummy for whether child _i_ experienced DD at the time of survey in year t. For each child we also record its location in cluster _c_ in province _p_ of country _g_ : YY U U i 1∆F F F 2∆F F F + 1 + 2 + γ i<sup>(1)</sup> YY∆F = αα+ ββF F U and ∆Fccii,ii−1F F+ ββU measure annual changes in the share of forest loss in the upstream ccii−1,ii−2 λλ XXccii λλ XXccii−1 ii<sup>+ ρρ</sup> ggii<sup>+ μμ</sup> UU<sup>+ εε</sup> catchment area relative to survey year _t_ and _t-1_ , respectively. These values are measured for upstream ccii,ii−1 ccii−1,ii−2 catchments, exploiting the natural flow of rivers and the fact that water flows downstream. Forest loss upstream is, thus, orthogonal to downstream health. In this way, we exploit quasi-random variation in forest cover loss that originates upstream to estimate the impacts on water quality and health outcomes downstream. Additionally, since DD may vary over time, we also control for country-by-survey year fixed effects ( ) to account for the year when information on the child’s DD condition was collected as well as unobserved national ggii ρρ macroeconomic conditions which might otherwise confound the relationship between forest exposure and DD. Province fixed effects ( ) are included to control for any time-invariant unobservable differences between provinces that could affect health.<sup>13</sup> For example, access to local nutrition programs is one such factor that may UU μμ be constant across individuals residing in the same location. Several other cluster- and household-specific variables are included in the analysis. and are timevarying variables at the cluster level, measuring annual mean temperature and total precipitation within the ccii ccii−1 5km buffer area for survey year _t_ and _t-1_ , respectively. These climate variables are potentially confounding XX XX factors, as they are known predictors of DD (Halpenny et al., 2012; Escamilla et al., 2011). are controls for household characteristics such as age, sex, and birth order of the child, as well as the mother’s age at the time ii γγ of birth. Since access to clean drinking water reduces the incidence of water-borne diseases like diarrhea, in some specifications we also control for whether a household has access to an improved water source at the time of the survey using the WHO/JMP definition.<sup>14</sup> Lastly, we cluster robust standard errors at the province level to account for arbitrary correlation of observations across time and within provinces.

To estimate stunting impacts of childhood exposure to forest cover loss via the water channel, we use a similar research design but modify the timing of exposure. Specifically, we exploit quasi-random variation in upstream forest cover loss experienced by different birth cohorts and compare height outcomes between exposed and non-exposed cohorts, controlling for average differences in these outcomes across birth years and across clusters. For our main specification we estimate equation (2) on the pooled sample where i is a dummy for whether child _i_ was severely stunted at the time of survey in year _t_ and was born in year _b_ : YY U i F F c + 1 c + + 2 c −1 γ i<sup>(2)</sup> ,cc−3 ii<sup>+ ρρ</sup> ggcc<sup>+ μμ</sup> UU<sup>+ εε</sup> YY = αα+ ββ∆F λλ XX λλ XX

> 13 When estimating equation (1) for the Peru sample, we control for district fixed effects, as access to public health facilities and local nutrition programs is constant across individuals residing in the same district.

> 14 The WHO/JMP definition of improved drinking water sources includes piped water, boreholes or tube wells, protected dug wells, protected springs, rainwater, and packaged or delivered water.

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