The Economic Impact of Payments for Water-related Ecosystem Services on Protected Areas: a Synthetic Control Analysis

Payments for Water-Related Ecosystem Services (PWES) are increasingly popular for promoting water ecological conservation, and their impact on development is of considerable interest. This study estimates the economic impact of PWES on protected areas using the synthetic control method. Taking the Middle Route of the South to North Water Diversion Project in China as a case study, we find that the per capita GDP in protected areas increased markedly relative to synthetic control regions, and PWES had a positive economic impact. Additionally, we conducted many placebo tests to verify the validity and robustness of the results. We believe that the main factor responsible for the positive effect lies in developing the ecological-economic industrial system. This study provides a baseline for synthetic control analysis of PWES to compare regions of interest with their counterfactuals. The case study findings provide reference for the economic development of protected areas.


Introduction
Water ecosystems provide a wide range of environmental services that contribute to human wellbeing, such as water supply, water purification, and biodiversity maintenance (Lv et al. 2021). Payments for Water-related Ecosystem Services (PWES), a branch of Payments for Ecosystem Services (PES), is an institutional arrangement for regulating stakeholders' interests through economic instruments for the sustainable utilization of water ecosystems (Wunder 2015). Protected areas, that is, service providers, need to protect and restore the ecosystem and restrict socioeconomic activities, which has significant impacts on protected areas (Kaplowitz et al. 2012). With PWES schemes being increasingly implemented in various countries (Salzman et al. 2018), their impacts on protected areas have received extensive attention.
Literature on the impacts of PES on protected areas focuses on: (1) socioeconomic impact and the effect on poverty alleviation (Dang Do and NaRanong 2019); (2) ecological and environmental impacts (de Melo et al. 2021); and (3) cultural and institutional impacts (Hayes et al. 2019). However, there are two limitations: (1) Studies often focus on microscales, such as individuals, families, or communities with the emphasis placed on changes in family livelihoods, farm productivity, and community factories (Ola et al. 2019); for larger regions, land-use changes are studied. Few studies have concentrated on the overall economic impact of protected cities (Benra et al. 2022).
(2) Econometric approaches such as multiple regression analysis and propensity score matching are applied to estimate socioeconomic outcomes (Duong and De Groot 2020;Ezzine-de-Blas et al. 2016), but these methods have some shortcomings such as large errors and strict preconditions. Besides, remote sensing data are primarily used to analyse land-use changes, while rigorous evaluations of PES additionality remain scarce (Pagiola et al. 2020). Appropriate and universal quantitative estimation methods for impacts research are lacking.
An in-depth analysis of whether the PWES policy hinders or facilitates the economic growth of protected areas remains to be conducted. In the context of sustainable development, particularly in developing countries, it is necessary to explore the impact of water protection on economic development (Jia et al. 2021). Many intuitively believe that the closure of industrial enterprises for environmental purposes may hinder economic development . Therefore, from the perspective of the aggregate level of the protected area, we investigate the impact of PWES on the macro-economy by applying a policy evaluation method.
As the largest water diversion project in the world, the South to North Water Diversion Project (SNWD) in China aims to provide water resources for Beijing, Tianjin and other important regions (NDRC et al. 2017). Hence, cities in the headwater areas have protected water through restoration and conservation measures and have reduced water pollution by limiting the development of highly polluting industries. These measures have direct and indirect economic effects. Thus, the central and local water-receiving governments pay headwater cities subsidies. Therefore, taking the SNWD as a case study, we discuss the impact of PWES on economic growth in headwater areas and estimate the effect value.
Many socioeconomic approaches can evaluate the impacts of specific policies on specific regions. The synthetic control method, a relatively new approach, regards policy implementation as an experiment performed on the treatment unit. By summing up multiple control units with corresponding weights, an artificial unit with characteristics similar to the treatment unit is obtained. The policy effects are evaluated by comparing the differences between the treatment and synthetic units. Because of its attractive features of transparency in choosing synthetic control units and safeguarding against extrapolation (Abadie et al. 2010), the synthetic control method is being increasingly applied (Ando 2015;Peng et al. 2020); however, there are few applications in the PES field. Thus, we use the synthetic control method to estimate the economic impact of PWES to avoid the shortcomings of the above econometric approaches.
The main innovations of this study are as follows. First, taking the national-level and large-scale PWES scheme of SNWD as an example, we systematically study the aggregate economic impact of PWES on headwater cities, quantitatively estimate the effect, and precisely analyse the leading causes to provide a basis for ecological protection and economic transition. Second, the study pioneers the use of the synthetic control method in the field of PES, providing a general and rigorous method for studying the socioeconomic and ecological impacts of PES.

Methods
We regard the intervention of the PWES scheme as a policy experiment conducted in protected areas. Let t = T 0 be the intervention time. Y it (1) and Y it (0) represent the outcome variables with and without intervention, respectively. The experimental effect it of implementing the PWES policy is For the treatment region (i = J + 1) , when t ≥ T 0 , Y it (1) can be observed and Y it (0) is an unobservable value. When t < T 0 , only Y it (0) can be observed. For potential control regions (i ∈ {1, ..., J}) , Y it (0) can be continuously observed. Suppose Y it (0) is given by where Y it is an indicator of economic growth, Z i , a predictive variable, is a set of factors that influence economic growth, t represents a time fixed effect, t represents a common shock, i is an individual fixed effect, it represents random shocks. We denote a (J × 1) vector of weights as W = ( 1 , ..., J ) ′ , where i represents the relative contribution of each control unit to the synthetic region. For any i ∈ W , 0≤ i ≤ 1 , and 1 + 2 ...
i Y it → 0 during the pre-intervention period, then the unbiased estimate of the economic effect after the intervention is To choose the optimal W * , let X 1 be a (k × 1) vector of pre-intervention predictors for the treatment region and X 0 be a (k × J) matrix of the corresponding predictors of the potential control regions. We hope X 0 W * could best approximate X 1 , and thus W * minimizes where V is a (k × k) symmetric matrix with diagonal element representing the contribution of each predictor to the outcome. Furthermore, we select the optimal V * such that U 1 , the treated outcome, best resembled by U 0 , the corresponding synthetic outcome during the pre-intervention period. Therefore, V * minimizes the mean square prediction error (MSPE).
By solving the nested optimization problem, we can estimate the value of the economic effect τ J+1,t for the post-treatment period.

Study Area
The Middle Route of the South-to-North Water Diversion Project (SNWD-MR) discharges water from the Danjiangkou Reservoir located in the upper reaches of the Hanjiang River. The headwater areas include 49 counties distributed in 11 cities in Shaanxi, Hubei, Henan, Gansu, Sichuan provinces, and Chongqing municipality (see Fig. 1). Among the cities involved, Hanzhong, Ankang, and Shangluo in Shaanxi account for 70% of the annual water inflow to the Danjiangkou Reservoir, which plays a prominent role in ensuring the water quality of SNWD-MR (NDRC et al. 2017).
To protect water resources, Hanzhong, Ankang, and Shangluo have continuously adjusted their economic structure and development mode, controlled pollutant emissions, and shut down enterprises and mineral operations that caused serious pollution, which has a considerable impact on the economy. To compensate for the direct and opportunity costs, the central government, Shaanxi, and the water-receiving regions have given the three cities numerous protection funds and subsidies. In 2008, the three cities received the first transfer payment of 1.09 billion yuan (Li 2021). These funds are used to improve people's livelihoods and protect the ecological environment.
However, 24 of the 28 counties are national poverty counties with relatively low economic level. There is a notable conflict between the three cities' strict water protection requirements and strong economic development demands. Therefore, this study takes Hanzhong, Ankang, and Shangluo as study sites and focuses on the economic impact of water protection.

Data and Variables
Under the synthetic control method guidelines, after choosing the treatment cities, it is necessary to select the potential control cities. Subsequently, the pre-intervention period and the total duration of the policy impact should be clarified. Relevant predictive variables that significantly influence economic growth should be identified. Using specific data, we estimate the economic impact of PWES during the post-intervention period.
Hanzhong, Ankang, and Shangluo are the treatment cities. Potential control cities should be similar to the treatment cities in terms of economic characteristics. The cities are chosen following these steps: (1) preliminary selection of non-provincial-capital cities in other provinces similar to the treatment cities and other cities in Shaanxi Province; (2) removal of cities exposed to the PWES policy, with severe missing data, with shorter prefecture-level history, and with large differences in geographical features and folk customs. In total, 62 potential control cities were identified.
We set 2008 as the time of PWES intervention. The method requires a sufficiently large number of pre-and post-intervention periods. Considering the changes in the statistical caliber and availability of data, we determine that the sample period begins in 2000 and ends in 2017. The PWES policy has been implemented nationwide since 2017, invalidating many cities as potential control units.
The main factors that enable economic growth include structural change, capital input, labor input, human capital level, and infrastructure status (Thirlwall and Pacheco-López 2017). Referring to Borrego-Marín et al. (2015) and Zhang et al. (2020), our predictors of economic growth are: (1) the respective proportions of the secondary and tertiary industries output in GDP to reflect local industrial structure, (2) gross industrial output above scale to indicate economic development achievements, (3) population density to reflect labor conditions, (4) ratio of fixed asset investment to GDP to characterize capital input, (5) education expenditure to reflect human capital level, and (6) road density to measure infrastructure status. As for the outcomes, concerning Ando (2015) and Kahia et al. (2017), we select real per capita GDP, a comprehensive indicator that can reflect the degree of local economic development and residents' affluence, as the outcome of interest, with 2000 as the base year, and yuan as the unit. Some special -The onomic Impact of Pa … yments for Water related cosystem c E E 1539 predictors in specific years are added to improve the fitting accuracy, such as the real per capita GDP values in 2000, 2004, and 2006. We obtain these data from the "China City Statistical Yearbook."

The Need for Synthetic Control Analysis
It is important to note that the synthetic control simulation of pretreatment cities is superior to simpler controls. As Fig. 2 shows, the real per capita GDP of the three cities is far lower than the national average. Similarly, the trend in the average of the controls differs notably from that of the three cities. The indicators for each control city are also not well-matched. None of them are appropriate controls. Therefore, we construct a suitable counterfactual using the synthetic control method to better fit economic characteristics, while the higher average value of these controls reduces synthetic error.

Result and Analysis
In this section, we discuss the fitting degree between each treated city and its synthetic counterpart in the pre-PWES period and then analyse the policy effects based on the discrepancy between the actual value and the counterfactual outcome in the post-PWES period. Lastly, we conduct placebo tests and robustness tests of the empirical results. We use the R package Synth to perform these calculations based on this method.

The Pre-PWES Fit
As explained above, we construct synthetic cities that approximate the three cities in terms of pre-PWES economic growth predictors. Table 1 compares the three cities and their synthetic counterparts using predictive variables in the pre-PWES period. This study uses the logarithm of the absolute values to reduce multicollinearity and heteroscedasticity. Table 1 shows there is not much difference in predictor values. Although the population density of Shangluo and Hanzhong and the sectoral ratio of Ankang are slightly different, they are all within a reasonable range of 10%. Furthermore, Shangluo has the lowest MSPE (0.0002), indicating that the fit is quite good, followed by Ankang, which has an MSPE of 0.0008, and Hanzhong, which has an MSPE of 0.0037. Overall, the synthetic method provides an excellent fit for the economic growth determinants in the three cities before implementing PWES. The good fit during the pre-PWES period provides a basis for synthetic analysis of the post-PWES period.

Economic Impact of PWES
As the left graphs in Fig. 3 show, before the implementation of PWES, the actual curves of the three cities overlapped or resembled the synthetic versions. After implementing PWES, the actual path is higher than the synthetic path, indicating that the actual value is greater than the synthetic value; that is, PWES positively impacts on per capita GDP and thus significantly affects the economic growth of the three cities.
The right column of Fig. 3 plots the gap between the actual and synthetic values, while the gap after policy implementation represents the net policy effect. After the implementation, the gaps in the three cities are above zero, suggesting that the policy effect is positive. In comparison, Shangluo's policy effect was the most significant. The policy effects of Ankang and Hanzhong were also apparent, but the two cities were not comparable because differences between them were present before the intervention. The policy effects of Shangluo and Ankang was positive in 2007 partly due to previous large-scale water resource protection activities and related industrial structural adjustments.

Validity Test
This study draws on the placebo test proposed by Abadie et al. (2010).

Placebo Test for Single Control City
The basic process of the placebo test is as follows: first, select a control city that has not implemented PWES, assuming that the city was affected by PWES in 2008, and then construct a synthetic control counterpart of this city by using other control cities, and estimate the policy effect. If the effect value is greatly inferior to that of the treatment cities, it means that the economic growth effect of the treatment cities is indeed derived from PWES; that is, the results of the empirical analysis are valid. Otherwise, the results are considered invalid. Table 2 lists the synthetic control weights corresponding to each treatment city. After many trials, the estimated MSPE is relatively minimum, and the synthetic predictors are closest to the actual values. However, the increase or decrease of the control numbers will lead to larger MSPE, indicating that the combination of these 62 cities is a much better choice. We can see that for the synthetic Shangluo, Dingxi, Lijiang, Pingliang, and Tianshui have relatively larger weights, 0.249, 0.238, 0.200, and 0.159, respectively. For the synthetic Ankang, Baoshan, Wuwei, and Dingxi account for relatively larger weights, 0.415, 0.145, and 0.142, respectively. For the synthetic Hanzhong, Huaihua, Tianshui, and Qujing have larger weights, 0.374, 0.219, and 0.130, respectively. Therefore, this study uses the eight cities with higher weights as examples to illustrate the effect of the placebo cities. Figure 4 presents the evolution paths of the actual and synthetic real per capita GDP logarithms for the eight cities. The policy effects of the placebo test are divided into three categories: (1) before the intervention, the two lines almost overlap; then, the real path is lower than the synthetic path, such as Tianshui, Wuwei, Pingliang, and Qujing, indicating that the city's policy effect is negative; (2) the actual path and the synthetic path almost coincide both before and after the intervention, such as Baoshan, Lijiang, and Huaihua, suggesting that the city's policy effect is almost zero; and (3) the gap between the true path and the synthetic path is vast during the whole period, such as Dingxi, implying that the city has a poor fit. We know from the above analysis that control cities with higher similarity to the treatment cities did not show positive policy effects, indicating that the positive policy effect of the treatment cities is caused not by accidental factors but by the implementation of PWES.  The sum of the weights of the control cities corresponding to each treatment city is 1, and the cities with larger weights are highlighted 1 3

Permutation Tests for Multiple Control Cities
Permutation tests are used to assess whether the policy effect is statistically significant. We select a series of control cities to conduct placebo tests one by one. If these placebo effects are smaller than that of the treatment city, the policy effect of the treatment city is demonstrated to be significant. It is difficult to judge whether the gap in the post-PWES is due to calculating bias or policy intervention; therefore, we need to exclude cities with poor fit during the pre-PWES. This study excludes cities with a pre-PWES MSPE over twice bigger than that of the treatment city. Ultimately, 19, 39, and 57 control cities were retained in Shangluo, Ankang, and Hanzhong. In Fig. 5, each gray line represents the gap of the control city. Before implementation, Shangluo and the control cities roughly share a close-to-zero gap. However, after implementation, the estimated policy effect of Shangluo is substantial. The probability of such an unusual gap is 1/20, at an exact 5% significance level. For Ankang and Hanzhong, the effects in the post-PWES period are much bigger than those of all the controls, which means that it is a small probability event. In summary, the implementation of PWES has markedly promoted the economic growth of the three treatment cities.

Robustness Test
Additionally, to exclude economic growth effects caused by other policies and related predictive variables, we use time-based placebo tests and change predictors to assess whether the policy effects are robust.

Time-based Placebo Test
We assume that the policy intervention time is advanced by three years to 2005. The left column in Fig. 6 shows the time-based placebo test results. Around 2005, the actual trajectory of the logarithm of per capita GDP is reasonably close to its synthetic counterpart. It was not until 2007 or 2008 that there was an apparent deviation between these two lines, indicating that the hypothetical implementation of PWES in 2005 had no perceivable effect, and excluding the possibility of economic growth caused by other policies.

Placebo Test of Changing Predictors
To test whether the above results vary with the change in predictors, we refer to Opatrny (2020) and Nannicini and Billmeier (2011) and use the urbanization rate and openness as additional predictors. A high urbanization rate can provide a considerable impetus, and openness can accelerate the reform process for economic growth. We use the proportion of the non-agricultural population in the total amount to measure the urbanization rate and the logarithm of the total export-import volume to measure the openness. The right column in Fig. 6 illustrates the evolutionary path of economic growth by adding predictors of urbanization rate and openness. Similarly, the fit of Shangluo is the best, followed by Ankang and Hanzhong; the actual and synthetic paths of Shangluo and Ankang began to diverge in 2007, and Hanzhong in 2008, meaning that PWES has gradually played a role in promoting economic growth.
We obtain similar results by substituting the ratio of employed population to total population for population density and removing gross industrial output above the scale, with other predictors unchanged. In general, the test results show that the core conclusion that PWES promotes economic growth in protected areas is robust.

Discussion
This section further analyses the sources of PWES's positive impact and compares our study with others.

Industrial Structure and Pillar Industries
In 2008, the three industrial structures in Shangluo, Ankang, and Hanzhong were 25.6:39.0:35.4, 27.3:32.5:40.2, and 24.9:38.6:36, respectively. According to Huang (2013), all three cities were in the early stages of industrialization. After implementing PWES, the three cities complied with the economic laws to develop the secondary industry. They significantly promoted the circular economy and ecological economy with a firm commitment to water protection.
Taking Ankang as an example, the secondary industry has developed rapidly since 2000. By 2018, it was 55.28% of the entire industry, 22.78% higher than in 2008. Relying on selenium-rich resources, Ankang has developed distinctive products such as tea, konjac, and livestock pigs. The proportion of selenium-enriched industry increased from 16.5% in 2010 to 41.2% in 2020, ranking it as the leading pillar industry. Additionally, Ankang has developed agri-tourism and promoted the integrated development of primary, secondary, and tertiary industries. Eco-friendly industries accounted for more than 65% of Ankang's GDP. More than 60% of farmers' per capita net income came from selenium-rich characteristic farming (Ankang MPCPRO 2017), showing that the green industry system based on "eco-economy" has become a strong support for Ankang's economic growth, and economic development is not in conflict with ecological protection.

Comparison with Similar Cities
There is confusion that the rapid economic growth in the protected areas may be caused by the development of secondary industry rather than the ecological protection effect caused by PWES. To eliminate this possibility, we compare Ankang and cities with the same level of industrialization and a similar trend in industrial structure.
Recall that Baoshan in Yunnan Province makes the largest contribution to synthetic Ankang. The three industrial structures of Baoshan in 2008 were 31.8:28.5:39.7, indicating that Baoshan was also in the early stages of industrialization. The proportion of the secondary industry rose to 38.1% in 2018, indicating its increasingly dominant role in economic growth. However, the ecological economy is not prominent in the industrial system, and plays a humble role in promoting the economy, demonstrating Baoshan's placebo test result that no significant economic growth can be observed if PWES is applied to Baoshan.

Comparison with Other Studies
Synthetic control methods are primarily used in socioeconomic, environmental, and medical fields. In the economic field, the research mainly involves the impacts of specific policies or events, such as economic liberalization, trade openness, and agricultural policy (Nannicini and Billmeier 2011;Opatrny 2020), while in the environmental field, the research focuses on the impacts of resource businesses, and the atmospheric environment (Pellegrini et al. 2021;Peng et al. 2020). Therefore, applying this method to the study of PWES impacts opens a broad field for research on PES.
The disadvantage is that when evaluating the contribution to economic growth, this study uses the treatment predictors during the pre-intervention period without considering the post-intervention period (Xu 2017), which leaves much room for further improvement in follow-up studies. Furthermore, we can draw on Liu (2021) and Alola and Yildirim (2019), and use green GDP and per capita disposable income as outcome variables to reflect the net effect of economic growth and the impact of PES on residents' well-being, respectively.

Conclusion
The economic impact of PWES on protected areas should be assessed by using scientific methods to conduct specific analyses. We take the headwater areas in SNWD-MR as an example, construct appropriate counterfactuals using the synthetic control method, and compare the real per capita GDP with their synthetic values. The conclusions are as follows.
1. The per capita GDP of treatment cities increased markedly relative to the synthetic regions, and the policy effect of PWES was positive; that is, the policy promoted the economic development of the protected cities. 2. The validity of the estimation is demonstrated by the placebo tests of single cities and permutation tests of multiple cities; the robustness is proved by placebo tests with changing time and predictors. 3. Economic growth is primarily attributed to developing the ecological-economic industrial system.
This study provides an integrated synthetic analysis of PES impacts research that can be generalized to study the ecological and social impacts of PES on areas of interest. The synthetic control method can be used to construct the counterfactual control group. The difference between the actual outcome and the corresponding synthetic value can be compared to reflect the PES effect. Various placebo tests can be carried out to determine whether the results are valid, robust, and statistically significant.
This economic development pattern can be used by other protected cities; by relying on natural resources, the protected cities can take advantage of the ecological environment, ecologicalize the industry, develop a green and ecological economy to achieve coordinated economic development and environmental protection and realize sustainable development.