We assumed that people living within 10 km of a PA were near enough to be affected by its presence, while those further than 10 km were unlikely to be. While there is strong empirical and theoretical evidence for the validity of this threshold (10), we also tested for impacts at two alternative distance thresholds. We reran all of our matching models and subsequent impact estimation regressions using 5 and 20 km, respectively, as alternate distance-to-PA thresholds. The resulting impact estimation models showed few differences in regression coefficient values (fig. S3). The 95% Bayesian credible intervals for coefficients of all predictor variables overlapped with one another regardless of the proximity-to-PA distance threshold used. When examining impacts of PAs on well-being outcomes using these different thresholds (fig. S4), we saw that despite a greater sample size and therefore greater power to detect impacts, all well-being impacts at a distance of 20 km are no longer statistically greater than zero except for those associated with household wealth scores, and even these have declined in absolute value relative to estimates at 10 km. This suggests that a distance of 20 km from a PA may be too great for PA impacts to extend out to. On the other hand, at a distance of 5 km, household wealth and poverty impacts increase, but height-for-age and stunting impacts decrease and are no longer statistically greater than zero. This may be a function of reduced sample size and power; 95% Bayesian credible intervals are larger at the 5-km versus 10-km threshold, reflecting increased variability of estimates. However, it also suggests that potential impacts at a 5-km threshold are being dampened because of the presence in the control group of households that are between 5 and 10 km from a PA and yet are seeing well-being improvements, as per the analysis presented in Results. Note that the well-being impacts associated with changes in socioeconomic variables (Fig. 4) remain relatively robust to PA-proximity threshold changes.

We also assessed how sensitive our model results were to the presence of hidden bias via an unobserved covariate that might strongly affect selection into the treatment. We used the Rosenbaum bounds approach as implemented in the “sensitivitymult” package in R (52), which calculates whether differences in outcomes between treated and untreated observations remain statistically significant as the value Γ, which represents the odds of an observed covariate affecting differences between treated and untreated, increases. Lower values of Γ (i.e., close to 1) indicate models that are highly sensitive to the presence of hidden bias, with greater values of Γ indicating models that are more robust to such bias. In our case, the values of Γ at which treatment differences are no longer significant due to hidden bias (table S3) are similar to those from other studies that have looked at PA impacts on poverty (13, 53, 54) and can be characterized as emanating from models that are moderately sensitive to possible hidden bias. Note that this test does not imply that a powerful and unobserved confounding variable does exist; it merely assesses the sensitivity of matching models to hidden bias if such a variable were in existence.

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