attending school). **Appendix Figure A3** describes the composition of the different household wealth measures used.

As described in Alix-Garcia et al. (2018), our social capital measures included elements generally considered to be relevant both globally (Grootaert, 2004) and locally (Merino and Martinez, 2014). We included actions that indicate cooperation (participation), investments that benefit the whole community (infrastructure), and attitudes demonstrating the foundations of social capital (trust or functions). We also measured institutional structures that support social capital, including the range of decisions made by the community assembly (governance), and whether a wide variety of community members participated in decisions (inclusion). **Appendix Figure A4** describes the composition of the social capital indices. The full survey instruments are published as part of the supplemental information in Alix-Garcia et al. (2018).

To reduce dimensionality and multiple-hypothesis testing concerns due to the large number of outcomes, we aggregated into indices the land-cover management activities, the household-level socio-economic measures, and the community-level social capital measures. We used a variety of methods, including simple summation of the presence or absence of particular characteristics, principal components, polychoric principal components (which takes into account categorical variables), and inverse proportion weighting (which applies higher weight to rare items). The results were similar across different aggregating methods. We report the results of simple aggregation, but other results are available upon request.

This paper also explores impact heterogeneity for a series of time-invariant covariates where theory suggests there may be differential impacts. In particular, we expect greater program impact where there is higher deforestation risk. Risk may also be (but is not necessarily) indicative of higher participation costs and hence lower economic gains. We also test for differential impacts across regions for similar reasons.

# _Comparison between Study Samples and Universe of Applicants_

A key concern for external validity is the extent to which the studied samples are representative of the population from which they were drawn. In the environmental analysis, we analyzed the universe of polygons within 25 points of the cutoff, which includes 97% of the applicants. However, to examine deforestation, we begin with applicant polygons that include more than 50% forest cover in 2000, which eliminates 43% of the area submitted for consideration during our study period. Therefore, our results cannot shed light on program impacts in areas without land that is easily classified as forest, which includes many types of vegetation important for the biodiversity program, such as the low shrubs and cacti characteristic of arid regions. This is a fundamental limitation of having to fall back on the Hansen et al. data set.

With regards to the survey data, survey participant characteristics indicate they are very similar to the universe of eligible applicants to the program for the years studied. **Table 2** compares environmental and social characteristics of the communities that were surveyed with the rest of the population of properties that applied in 2011-2014. Our survey sample of 862 properties represents 30% of the available universe of 2,839 _ejidos_ and _communidades_ that met the minimum program requirements in these years (after dropping repeat applications and 52 properties without a matching code for the _Sistema Padrón e Historial de Núcleos Agrarios-PHINA_ ). To assess differences between our survey 12