Estimating the impacts of conservation on ecosystem services and poverty by integrating modeling and evaluation Paul J. Ferraroa,1, Merlin M. Hanauerb,1, Daniela A. Mitevac,d, Joanna L. Nelsone,f, Subhrendu K. Pattanayakg, Christoph Nolteh, and Katharine R. E. Simsi,j a Department of Economics, Andrew Young School of Policy Studies, Georgia State University, Atlanta, GA 30319; bDepartment of Economics, Sonoma State University, Rohnert Park, CA 94928; cThe Nature Conservancy, Fort Collins, CO 80524; dInstitute on the Environment, University of Minnesota, St. Paul, MN 55108; eThe Nature Conservancy, Arlington, VA 22203; fStanford Woods Institute for the Environment, Stanford, CA 94305; gSanford School of Public Policy and Nicholas School of the Environment, Duke University, Durham, NC 27708; hSchool of Natural Resources and Environment, University of Michigan, Ann Arbor, MI 48109; and Departments of iEconomics and jEnvironmental Studies, Amherst College, Amherst, MA 01002

Edited by Stephen Polasky, University of Minnesota, St. Paul, MN, and approved February 4, 2015 (received for review May 5, 2014)

Scholars have made great advances in modeling and mapping ecosystem services, and in assigning economic values to these services. This modeling and valuation scholarship is often disconnected from evidence about how actual conservation programs have affected ecosystem services, however. Without a stronger evidence base, decision makers find it difficult to use the insights from modeling and valuation to design effective policies and programs. To strengthen the evidence base, scholars have advanced our understanding of the causal pathways between conservation actions and environmental outcomes, but their studies measure impacts on imperfect proxies for ecosystem services (e.g., avoidance of deforestation). To be useful to decision makers, these impacts must be translated into changes in ecosystem services and values. To illustrate how this translation can be done, we estimated the impacts of protected areas in Brazil, Costa Rica, Indonesia, and Thailand on carbon storage in forests. We found that protected areas in these conservation hotspots have stored at least an additional 1,000 Mt of CO2 in forests and have delivered ecosystem services worth at least $5 billion. This aggregate impact masks important spatial heterogeneity, however. Moreover, the spatial variability of impacts on carbon storage is the not the same as the spatial variability of impacts on avoided deforestation. These findings lead us to describe a research program that extends our framework to study other ecosystem services, to uncover the mechanisms by which ecosystem protection benefits humans, and to tie cost-benefit analyses to conservation planning so that we can obtain the greatest return on scarce conservation funds.

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correlations between programs and outcomes can be confidently attributed to causal relationships; however, these studies do not estimate impacts on ecosystem services, but rather estimate impacts on human behaviors (e.g., deforestation, fire, resource extraction) assumed to be correlated with ecosystem service stocks and flows. In other words, they focus on intermediate variables on the assumed causal chain between the policy interventions and subsequent changes in ecosystem services. Given the substantial evidence that ecosystem service stocks and flows are highly spatially variable and nonlinear, a close correlation between behavioral impacts and ecosystem service impacts cannot be assumed. For example, interventions that generate the most avoided deforestation or avoided fires might not be the same ones that generate the most additional carbon storage or hydrological services, or generate the highest economic return on investment. We need direct empirical estimates of program impacts on ecosystem services and their economic values. Scholars in these two literatures—impact evaluation and ecosystem service modeling and monetization—need to collaborate (12). This paper illustrates how impact evaluators have an intellectual architecture for estimating policy and program impacts on human behaviors like land conversion, and also for explaining how these effects are moderated by time-varying and time-invariant (i.e., fixed) site characteristics. Ecosystem Significance Research shows how the potential services from ecosystem conservation can be modeled, mapped, and valued; however, this integrative research has not been systematically applied to estimate the actual impacts of programs on the delivery of ecosystem services. We bridge this divide by showing how protected areas in Brazil, Costa Rica, Indonesia, and Thailand store carbon and deliver ecosystem services worth at least $5 billion. Impacts on carbon are associated with poverty exacerbation in some settings and with poverty reduction in others. We describe an agenda to improve conservation planning by (i) studying impacts on other ecosystem services, (ii) uncovering the mechanisms through which conservation programs affect human welfare, and (iii) more comprehensively comparing costs and benefits of conservation impacts.

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o inform decision makers about how they can best allocate resources to maintain and enhance ecosystem services, scholars need to develop a better understanding of how policy interventions actually affect the supply of ecosystem services. In the last two decades, scholars have made important advances in defining, measuring, and valuing ecosystem services across time and space (1–7). These measures and values have in turn been used as conservation planning and resource management decision tools (8–11). The degree to which policies and programs have affected these services and values in the past remains poorly understood, however (12, 13). Without an evidence base for the impacts of real policies and programs on ecosystem services, the insights from modeling and valuation are not as informative to decision makers as they could be. A separate and more recent literature focuses on estimating the impacts of conservation policies and programs on environmental and social outcomes (reviewed in refs. 14 and 15). Scholars working in this impact evaluation literature strive to eliminate rival explanations for the empirical patterns observed, so that any

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Author contributions: P.J.F., M.M.H., and J.L.N. designed research; P.J.F., M.M.H., D.A.M., J.L.N., S.K.P., C.N., and K.R.E.S. performed research; P.J.F., M.M.H., and D.A.M. analyzed data; and P.J. F., M.M.H., and S.K.P. wrote the paper. The authors declare no conflict of interest. This article is a PNAS Direct Submission. 1

To whom correspondence may be addressed. E-mail: [email protected] or pferraro@ gsu.edu.

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10. 1073/pnas.1406487112/-/DCSupplemental.

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Study Design To measure carbon consistently across all four countries, we used new data on the global distribution of aboveground woody biomass in the tropics in 2008 (18) and published formulas for converting biomass into carbon stocks (34). To estimate the impact of protection on carbon storage in the protected units, known as the “average treatment effect on the treated” (ATT), one must establish what carbon storage would have been in the absence of protection. To estimate this counterfactual outcome, we used matching to select unprotected control units that are similar at baseline to protected units in terms of distributions of key covariates believed to affect both carbon density and selection into protection (Materials and Methods and SI Appendix, Tables S1–S10 and Figs. S1–S6). For example, protected areas are often placed on land less suited for agriculture (35), which also might have lower carbon density (18). Protected areas can affect carbon storage in two ways: by preventing the loss of biomass (avoided emissions) and by permitting the growth of biomass (additional storage, or sequestration). We estimated the effect of both pathways (described formally in SI Appendix). In developing countries, efforts to use protected areas to reduce carbon emissions from forests are

*The most recent definition of REDD+ refers to “reducing emissions from deforestation and forest degradation in developing countries, and the role of conservation, sustainable management of forests, and enhancement of forest carbon stocks in developing countries” (16th edition of Conference of the Parties of the United Nations Framework Convention on Climate Change).

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controversial because of concerns about negative impacts on the rural poor (31); thus, we also contrasted the estimated effects of protected areas on carbon with their estimated effects on poverty in the same countries. We estimated the impacts for the protected area networks established before 1997 in Costa Rica, before 1985 in Thailand, between 1988 and 2008 in Indonesia, and between 2000 and 2008 in the Brazilian Amazon (Materials and Methods and SI Appendix). We selected these four countries for two reasons. First, Brazil and Indonesia contain 35% of the total carbon stored in tropical forests and produce the largest emissions from forest loss (18, 36). Second, our interdisciplinary team had the requisite data to credibly estimate the effects of protected areas on carbon in all four countries, and to contrast those effects with the effects on poverty in neighboring communities in three of the four countries. All four countries have been the subjects of previous studies on the impact of protected areas on deforestation and regrowth (23, 25, 29, 32). Two of them have been the subjects of published studies on the impact of protected areas on poverty in neighboring communities (31, 32), and on the moderators of the forest and poverty impacts (26, 37). The greatest challenge in retrospective studies of program impacts on ecosystem services is the lack of preprotection measures of ecosystem services. In our context, we cannot measure preprotection carbon densities. As is the case for most ecosystem services, widespread and accurate mapping of carbon densities has become available only recently. To address the challenge of missing carbon baselines, we have developed an approach that permits temporal variation in carbon density, which has been reported elsewhere (33). We assumed that after matching on observable characteristics that affect both land use and where protected areas are assigned, the unobservable, baseline carbon values of matched protected and unprotected forest parcels were the same, on average. Under this assumption, the current average carbon density of the matched unprotected parcels provides a good estimate of the counterfactual average carbon density of the protected parcels had they not been protected. In contrast to approaches that assume no temporal variation in carbon, or require imputation of missing baseline carbon values, our approach provides an indirect test (i.e., a “placebo test”) to reject the key untestable assumption on which the approach relies. If matching were effective in making baseline carbon densities similar among protected and unprotected parcels, then it also should be effective in making current carbon values similar among unprotected parcels. In other words, we took the matched unprotected parcels (i.e., the control parcels matched to the protected parcels) and match them to other unprotected parcels. We then tested the null hypothesis that the mean carbon values are equal in these two groups. Large and statistically significant differences would cast doubt on our assumption that the distributions of baseline carbon densities of protected and unprotected parcels are equivalent after matching (SI Appendix, Table S11). Carbon storage is a global service (i.e., contribution to climate change mitigation), and thus offers a relatively straightforward case for calculating its value, or shadow price. The “social cost of carbon” (SCC) provides an estimate of the monetized damages from an incremental increase in carbon emissions in a given year. SCC estimates vary widely, depending on the discount rate applied and the particular integrated assessment model and parameterization used (38, 39). Because we do not have repeated observations of carbon density over time, we cannot know the exact year when a particular avoided ton of CO2 emissions from protection would have been emitted, or when a particular additional ton of CO2 would have been sequestered. Impacts achieved earlier in the study periods would be worth less than impacts achieved later. Moreover, we cannot predict whether these impacts are permanent (i.e., the stored carbon will not be

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service modelers have another intellectual architecture for modeling and mapping the relationships between ecosystem service flows and time-varying attributes, such as land use change. Economists doing monetization and valuation have a third architecture for estimating the value of changes in ecosystem services. An integrated architecture would trace causal relationships between policies and ecosystem services, and include the option to conduct an economic valuation of the impacts as an estimate of the societal benefits from the policies. By integrating these architectures in single studies of real policies, scholars would be able to produce far more policy-relevant scientific evidence than that currently produced in their separate scientific spheres. Here we provide an illustration of such an integration, and the insights that it can provide, by examining the impacts of protected area networks on carbon storage in forested ecosystems of the Brazilian Amazon, Costa Rica, Indonesia, and northern and northeastern Thailand. We focus on forests because the proportion of carbon stored in forests composes 70–80% of total terrestrial carbon (16). More critically, great strides have been made in measuring and monitoring carbon stocks and carbon emissions from forests (17, 18), but the degree to which these stocks and emissions have been affected by environmental policies and programs is poorly understood (19). Governments often use protected areas to protect ecosystems and their services (20). Protected areas are also integral parts of strategies to reduce carbon emissions from deforestation and degradation, such as the REDD+* program (21, 22). Recent studies have estimated the effects of terrestrial protected area networks on deforestation (23–27), fire (28), regrowth (29), and poverty (30–32), but not their effects on ecosystem services. Explicitly estimating effects on ecosystem services is important, because there is no reason to assume that the spatial variability of effects on ecosystem services matches the spatial variability of effects on human behaviors; for example, the spatial variability of carbon is highly heterogeneous (18, 33), and the locations where carbon density is highest might not be the same locations where protected areas have the greatest effects on land use.

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emitted back into the atmosphere). Thus, to be conservative, we used a value of $5/ton of CO2, similar to payments in current REDD+ arrangements (40). For readers who believe that the SCC should be much higher, we also present results using $100/ton. Results Estimated Impacts. In Fig. 1, the estimated ATTs are measures of additional storage per hectare inside protected areas. Based on t tests of the null hypothesis of zero impact, the estimates are significantly different from zero in all four countries (SI Appendix, Table S12). The bars in Fig. 1 represent the total estimated additional amount of CO2 storage induced by the protected areas. For comparison, we used a recent study (36) to estimate the median annual gross CO2 emissions from deforestation in these four countries for the period 2000–2005 (includes losses from belowground biomass): 1,247.8 Mt CO2 y−1 for Brazil, 3.67 Mt CO2 y−1 for Costa Rica, 385.4 Mt CO2 y−1 for Indonesia, and 58.7 Mt CO2 y−1 for Thailand. Thus, for example, Brazil’s post-2000 protected areas induced additional CO2 storage by 2008 that was equivalent to approximately two-thirds of 1 year’s emissions from deforestation in the early 2000s. Fig. 1 also presents monetary values of the total additional amount of CO2 stored. The aggregate amounts on the left axis could instead be multiplied by a different estimate of the SCC, if so desired. In all four countries, the placebo test results are consistent with our implicit assumption that the distributions of baseline carbon densities of protected and unprotected parcels are equivalent after matching (SI Appendix, Table S11). We tested for local displacement (i.e., local leakage to nearby unprotected areas) and were unable to detect any (SI Appendix, Table S13). The most likely sources of measurement error would hinder detection of any treatment effects, and thus measurement error is unlikely to be a rival explanation for our results (SI Appendix). Finally, we conducted tests to assess the sensitivity of our results to potential hidden bias from a potential unobserved confounder (SI Appendix, Table S12). 7422 | www.pnas.org/cgi/doi/10.1073/pnas.1406487112

Moderators of Impacts. To illustrate the heterogeneity of the impacts of protected areas on CO2 storage, and how this heterogeneity may differ from the heterogeneity of impacts on avoided deforestation, Fig. 2 shows how impacts vary conditional on slope and distance to major cities, holding other factors constant. These two covariates have been used in a previous analysis of moderators of protected areas’ impacts on avoided deforestation (26) because they are globally available and capture landscape features that affect the returns to agriculture and logging, the primary drivers of land use change in our four countries. A gentle slope facilitates land use, as does proximity to urban markets. Slope also has been identified as an important predictor of carbon density (41). As noted above, we also sought to contrast the effects of protection on carbon and on poverty. Because we did not have poverty data for Brazil, we do not include its analysis of heterogeneity in Fig. 2; the shapes of its carbon storage graphs are similar to those of Costa Rica and Thailand (SI Appendix, Figs. S7 and S8). In Fig. 2, the ways in which slope and distance to cities moderate carbon and poverty impacts are not the same across the countries. These results highlight how global-level analyses may miss important heterogeneity of program impacts on ecosystem services. Moreover, the slopes and distances associated with the greatest poverty alleviation are not necessarily those associated with the most additional carbon storage. Comparisons with similar figures for avoided deforestation in Costa Rica, Thailand (fig.1 in ref. 26), and Indonesia (SI Appendix, Fig. S9) demonstrate that how impacts vary across space depends on whether the outcome is measured in terms of avoided deforestation or additional carbon storage. For example, in Thailand, protected areas’ impacts on avoided deforestation are lowest at approximately 100 km from cities, but their impacts on CO2 storage are greatest at that distance. Thus, impacts estimated in terms of avoided deforestation are imperfect proxies for CO2 storage impacts. In each country, the locations where protected areas generate the most avoided deforestation are not necessarily the areas with the highest carbon densities.

Discussion Research on forest carbon, like research on ecosystem services in general, emphasizes measurement and monitoring (e.g., to facilitate emissions reporting requirements); however, understanding which policies and programs work best to reduce carbon emissions from land use change, and under what conditions they work best, is important as well. Much of the policy-related science on ecosystem services evaluates how modeled (and usually hypothetical) changes in a generic conservation action would affect the quantity of one or more services, or people’s willingness to pay for changes in these services (42, 43). In these hypothetical scenarios, decision makers often are assumed to know where ecosystem conversion will occur and then can assign “protection” that stops this conversion. Real conservation programs are quite different, however. For example, there is ample evidence that protected areas and payments for environment services are assigned to areas with belowaverage probability of conversion (35, 44). In addition, compliance with these programs might not be perfect. Moreover, the mechanisms through which a conservation program achieves impacts, the moderators of those impacts, and the costs of achieving those impacts likely differ depending on the kind of conservation program and its location. Thus, assuming a homogenous intervention labeled “protection” may mislead us regarding how to allocate scarce conservation resources. Scientists need to move beyond hypothetical scenarios and undertake impact evaluations of real-world policies aimed at delivering ecosystem services. Even the most sophisticated scenario modeling that incorporates behavioral models of land user responses to policies Ferraro et al.

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(11) could be improved by incorporating insights from estimates of actual behavioral responses to real conservation programs. Although the protected areas in our study were not established with the intent of protecting carbon, they contributed to at least an additional 1,000 Mt of CO2 stored. (The estimates ignore below-ground carbon and do not cover all protected areas; Materials and Methods.) The locations where protected areas generated the most additional carbon storage were not necessarily the areas where they generated the most avoided deforestation. Moreover, although protected areas can reduce poverty in neighboring communities, our analysis highlights trade-offs if decision makers wish to use protected areas to attain more carbon additionality or poverty reduction. To visualize these trade-offs, planners can use suitability maps (26) like the one for Costa Rica shown in Fig. 3. Although there are locations where, based on past patterns of impacts, one would expect protected areas to contribute to relatively high amounts of additional carbon storage and poverty reduction (yellow in Fig. 3), these locations are not abundant; however, there are many areas where carbon storage goals may be achieved without exacerbating poverty (blue). These areas with the greatest expected additionality from protection are not necessarily the areas with the greatest carbon density, however (SI Ferraro et al.

Appendix, Fig. S10). Suitability maps like these could be used in the design of REDD+ programs aimed at reducing emissions from forest degradation and deforestation while maintaining livelihoods and reducing poverty. (More details on creating suitability maps are provided in SI Appendix.) Estimates like those in Fig. 1 also can contribute to an important debate in negotiations over the design of REDD+ programs: how, if at all, to acknowledge past investments to reduce deforestation and degradation. Most proposed REDD+ designs reward a country if it reduces its deforestation rate below a reference level. The most commonly suggested reference level is a country’s recent national deforestation rate (45). Some have argued that this design rewards historically “prolific deforesters” and punishes good stewards (46). Countries like Costa Rica have argued that they should receive credit for protecting their forests over the years (47). To adjust reference levels to take into account past conservation investments, decision makers must be able to distinguish countries that have low historical deforestation rates for economic reasons from countries with low historical deforestation rates because of conservation actions. Impact estimates like those shown in Fig. 1 can assist efforts to adjust REDD+ reference levels based on pre-REDD+ conservation actions. PNAS | June 16, 2015 | vol. 112 | no. 24 | 7423

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Our study is a first step in a much broader research program for integrating the growing literatures on impact evaluation and on ecosystem service modeling, mapping, and monetization. Ultimately, a focus on an array of services, contexts, and values will permit better integration of two key decision making tools: conservation planning (48, 49) and cost-benefit analyses. Below we highlight several extensions: i) More services. Carbon storage in forests is arguably the simplest case for integration, because storage is immobile and a global public good. For such services as hydrological or pollination services, spatial interactions are much more important, and the demands on the impact evaluation and modeling team will be more substantial. For similar reasons, the valuation of regional services, such as water quality and quantity, or local services, such as nontimber forest products and ecotourism, will require the use of nonmarket valuation designs that incorporate the characteristics of the beneficiary populations (2, 50). Extending this research to examining how programs affect biodiversity, which may then affect ecosystem services, also would be fruitful, and informative for the contentious debate about the appropriate focus of conservation investments: biodiversity versus ecosystem services (51–53). ii) More places. More evidence from more countries is needed. Although carbon data exist at a global level, we believe that a single global-level study is ill-advised. Controlling for the country-specific selection processes through which some areas come to be protected cannot be accomplished with just a few covariates available at a global level. Moreover, as observed in our study, analyses at smaller scales reveal important policy-relevant patterns of heterogeneity. iii) More policies. Protected areas are not the sole available tools for ecosystem conservation. Similar studies should be done on other types of conservation interventions, particularly payments for ecosystem services, which are explicitly aimed at supplying ecosystem services. iv) Linking conservation actions and human well being. Conservation actions can improve human welfare through various mechanisms, including the maintenance and enhancement of ecosystem services. A recent study of these mechanisms could only estimate how protected areas affected poverty through changes in land cover, rather than through changes in specific services that arose from the changes in land cover (54). Future attempts to quantify these mechanisms could 7424 | www.pnas.org/cgi/doi/10.1073/pnas.1406487112

benefit from more careful and rigorous connections to the modeling and monetization literature. Clarifying the mechanisms through which protected areas operate in each country also could shed light on why we observe trade-offs in some locations between poverty reduction and carbon storage, and how we may reduce the magnitude of these tradeoffs in the future through better program design. Both conservation planning and cost-benefit analyses can use better information on the extent, type, and value of services from past policies to forecast expected impacts in the future. For example, carbon values from Fig. 1 could be added to values from other ecosystem services and then compared with the opportunity costs of foregone land uses (including effects on livelihoods and local cultures) and protected area management costs (55, 56). Similarly, more elaborate versions of our suitability maps can be used to improve conservation planning efforts to maximize expected impacts of conservation programs, subject to budget constraints. Ultimately, decision makers and ecosystem service scientists want a strong evidence base to guide conservation actions. This evidence base can be built by combining the strengths of existing research areas in impact evaluation and in the modeling, mapping, and monetization of ecosystem services. With stronger evidence and theories about how conservation programs affect coupled natural–human systems, scientists, policymakers, and practitioners can determine how to best design policies for enhancing human welfare, while conserving species and habitats. Materials and Methods Carbon and CO2. Our data on carbon stocks came from the Pantropical National Level Carbon Stock Dataset of Woods Hole Research Center (18), which was created using a fusion of MODIS and LiDAR data calibrated with field measurements. Each 500-m2 pixel contains a measure of aboveground live woody biomass in milligrams per hectare. We converted measurements of aboveground live woody biomass (biomass) per hectare to CO2 storage per hectare by (i) converting biomass per hectare to tons of carbon per hectare (mg C ha−1 = mg biomass ha−1 · 0.5) (34) and (ii) converting tons of carbon per hectare to tons of CO2 per hectare (mg CO2 ha−1 = mg C ha−1 · 3.67). The final conversion is based on the atomic mass of carbon as a fraction of CO2: 44/12 = 3.67. We assumed that all carbon is released into the atmosphere on biomass removal, so that differences in observed and counterfactual levels of CO2 are interpreted as the additional CO2 storage due to protection; a similar assumption has been used by other investigators (36). Our study does not include protected area impacts on below-ground biomass, on soil carbon, or on peat drainage and burning. Below-ground biomass in tropical forests is much less than the aboveground biomass (6–33%) (57), but peat drainage and burning is an important source of carbon emissions in Indonesia (58). More details are provided in SI Appendix. Units of Analysis. Brazil, carbon: 1-km2 parcels selected at random from land that was forested in 2000. Costa Rica, carbon: 3-ha parcels selected at random from either forested or unforested land at the relevant baseline year (1960 or 1986). Costa Rica, poverty: 1973 census tracts (average area of 9 km2); poverty data from the 1973 and 2000 censuses. Indonesia, carbon: 463-m forest or peatland parcels selected at random from a 1988 land cover map. Indonesia, poverty: Villages (average area of 22 km2); poverty data from the 2006 village census (PODES). Thailand, carbon: 3-ha parcels selected at random from land that was forested in 1973 in northern and northeastern Thailand, where the majority of the protected areas are located. Thailand, poverty: subdistricts (tambons; average area, 74 km2). More details are provided in SI Appendix. Protection. Carbon analyses: A parcel is defined as protected if the parcel’s centroid lies within a national protected area. Poverty analyses: In Costa Rica and Thailand, a unit (census tract, subdistrict) is protected if at least 10% of the unit is covered by a protected area. (Units with coverage between 1% and 10% are excluded from the sample.) In Indonesia, a village is protected if it intersects with a protected area. More details are provided in SI Appendix.

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SI Appendix provides more details on matching covariates, matching metrics, and balance metrics.

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ANNIVERSARY SPECIAL FEATURE

Matching. We used one-to-one nearest-neighbor matching with replacement to select unprotected units that are similar to protected units on average, based on observable covariates. For the carbon analyses, the selected covariates are joint predictors of land use and location of protected areas. For the poverty analyses, the covariates are joint predictors of poverty and location of protected areas. The specific covariates differ among the four countries, but common covariates include slope, distance to forest edge, and distance to major cities. Each country analysis used the matching metric that provides that the best postmatch covariate balance. A postmatching adjustment was applied to control for residual bias in finite samples (59).

PNAS | June 16, 2015 | vol. 112 | no. 24 | 7425

SUSTAINABILITY SCIENCE

Analysis of Heterogeneity. To isolate the moderating effects of slope and distance to cities on carbon storage and poverty (net of other influences), we used a semiparametric partial linear model on the matched data (60). This two-stage estimator controls linearly for other covariates in the first stage and then, in the second stage, estimates the outcome as a nonparametric function of the moderator of interest using nonparametric locally weighted scatterplot smoothing. More details are provided in SI Appendix.