2.1 Methods
We regard the intervention of the PWES scheme as a policy experiment carried out by the government in protected areas. Let \({Y}_{it}\) be the outcome of economic growth for region i at time t; thus, \({Y}_{it}\left(1\right)\) and \({Y}_{it}\left(0\right)\) represent the outcome variables with and without intervention, respectively. Concerning Abadie et al. (2010, 2015), \({Y}_{it}\left(1\right)\) and \({Y}_{it}\left(0\right)\) can be
$${Y}_{it}\left(1\right)={Y}_{it}\left(0\right)+{\tau }_{it}{D}_{it}$$
2
where Zi, also known as a predictive variable, is a set of factors that influence economic growth, δt represents a time fixed effect, λt represents a common shock, μi is an individual fixed effect, εit represents random shocks. Dit is a dummy variable that indicates whether region i is exposed to the policy. For the treatment region i=J+1, when T≥T0 (the timing of intervention), Dit is 1, while the rest are 0.
\({Y}_{it}\left(0\right)\) of the treatment region \((i=J+1)\) can be approximated by the weighted average of \({Y}_{it}\left(1\right)\) of the control regions \((i\in \left\{1,...,J\right\})\), which can be observed. Define as a \((J\times 1)\) vector of weights W=(ω1,...,ωj)', \({\omega }_{i}\) represents the relative contribution of each control unit to the synthetic region. For any \({\omega }_{1}\in {W}\), \(0{\le \omega }_{i}\le 1\), and \({\omega }_{1}+{\omega }_{2}...+{\omega }_{J}=1\). The synthetic outcome is
$$\sum _{i=1}^{J}{\omega }_{i}{Y}_{it}={\delta }_{t}+{{\theta }}_{t}\sum _{i=1}^{J}{\omega }_{i}{Z}_{i}+{{\lambda }}_{t}\sum _{i=1}^{J}{\omega }_{i}{\mu }_{i}+\sum _{i=1}^{J}{\omega }_{i}{\epsilon }_{it}$$
3
The unbiased estimate of the economic effect after the intervention is
$$\widehat{{{\tau }}_{\text{J}+1,\text{t}}}{ =Y}_{J+1,t}\left(1\right)-{Y}_{J+1,t}\left(0\right)={Y}_{J+1,t}\left(1\right)-\sum _{i=1}^{J}{\omega }_{i}^{*}{Y}_{it} , t\in \{{T}_{0},...T\}$$
4
To choose the optimal W*, let \({X}_{1}\) be a \((k\times 1)\) vector of preintervention predictors for the treatment region and \({X}_{0}\) be a \((k\times J)\) matrix of the corresponding predictors of the potential control regions. We hope \({X}_{0}{W}^{*}\)could best approximate \({X}_{1}\), so \({W}^{*}\) minimizes
$${min}_{W}\sqrt{{({X}_{1}-{X}_{0}W)}^{\text{'}}V({X}_{1}-{X}_{0}W)}$$
5
where \(V\) is some \((k\times k)\) symmetry, with the non-negative diagonal element representing the contribution of each predictor to the outcome.
Furthermore, we select the optimal \({V}^{*}\) such that during the preintervention period, \({Z}_{1}\), the outcome of the treated region is best resembled by \({Z}_{0}\), corresponding to the outcome of the synthetic region. Therefore, \({V}^{*}\) minimizes the mean square prediction error (MSPE).
$${\text{V}}^{\text{*}}=\text{a}\text{r}\text{g}{min}_{V}\frac{1}{{T}_{p}}{({Z}_{1}-{Z}_{0}{W}^{*}(V\left)\right)}^{\text{'}}({Z}_{1}-{Z}_{0}{W}^{*}(V\left)\right)$$
6
The nested optimization problem that minimizes equation (6) can be solved for \({W}^{*}\left(V\right)\) given by Equation (5). By substituting \({W}^{*}\left(V\right)\) into equation (4), we can estimate the value of the economic effect \(\widehat{{{\tau }}_{\text{J}+1,\text{t}}}\) for the post-treatment period.
2.2 Case description
2.2.1 Study Area
The Middle Route of the South-to-North Water Diversion Project (SNWD-MR) discharges water from the Danjiangkou Reservoir in the upper and middle reaches of the Hanjiang River (Zhao et al. 2017). The headwater areas are distributed in Shaanxi, Hubei, Henan, Gansu, Sichuan provinces, and Chongqing municipality, involving 11 cities or 49 counties (see Figure 1). Among the cities involved, Hanzhong, Ankang, and Shangluo in Shaanxi, as the origin of the Hanjiang and Danjiang rivers, account for 70% of the annual water inflow to the Danjiangkou Reservoir, which plays a prominent role in ensuring the water quality in SNWD-MR (NDRC et al. 2017).
To protect water resources, the three cities of Hanzhong, Ankang, and Shangluo have continuously adjusted their economic structure and development mode, controlled pollutant emissions, and shut down enterprises and mineral operations with serious pollution, which has a huge impact on economic development. To compensate for the direct cost and opportunity cost, the central government, Shaanxi, and the water-receiving regions’ government have given the three cities a large number of ecological funds and other forms of compensation. In 2008, the three cities received the first transfer payments from the central government, with a total of 1.09 billion yuan (Li 2021). Since 2014, Tianjin, a water-receiving region, has paid counterpart cooperation funds to the three cities. All these funds are used to improve people’s livelihoods and protect the ecological environment.
However, 24 of the 28 counties in the three cities are national poverty counties, and the economic level in the three cities is relatively low. There is a notable conflict between the strict water counterpart requirements and strong economic development demands in the three cities. Therefore, this study uses the three cities of Hanzhong, Ankang, and Shangluo as the study sites and focuses on the impact of water protection on their economic development.
2.2.2 Data and Variables
Under the guideline of the synthetic control method, after choosing the treatment cities, it is necessary to select the potential control cities. Subsequently, the preintervention period should be clarified, as well as the total duration of policy impact. Relevant predictive variables with a significant influence on economic growth should be identified. With the specific data, we can estimate the economic impact of the PWES policy during the postintervention period.
Recall that Hanzhong, Ankang, and Shangluo are our study sites; that is, the treatment cities. Potential control cities should be similar to the treatment cities in terms of economic characteristics and not exposed to the PWES policy. The steps for choosing potential control cities are as follows: (1) initially select non-provincial-capital cities in other provinces (autonomous regions), as well as other cities in Shaanxi Province, which are similar to the treatment cities in terms of GDP or per capita GDP; (2) Remove cities exposed to the PWES policy but excluded from the treatment group (such as Shiyan in Hubei and Huangshan in Anhui); cities with severe missing data (such as Longnan in Gansu and Wuzhong in Ningxia); cities with shorter prefecture-level history (such as Bijie in Guizhou); and cities with large differences in geographical features and folk customs (such as Aba Tibetan Autonomous Prefecture in Sichuan). Finally, we identified 62 potential control cities.
We use annual city-level panel data for 2000–2017. We set 2008 as the timing of the PWES policy intervention. The synthetic control method requires a sufficiently large number of preintervention and postintervention periods. Considering the changes in the statistical caliber and the availability of data, we determine that the sample period begins in 2000 and ends in 2017. Since 2017, the PWES policy has been implemented nationwide, invalidating many cities as potential control units.
Concerning Abadie (2003) and Ando (2015), our outcome variable of interest is real per capita GDP, measured in yuan, with 2000 as the base year. Referring to Borrego-Marín (2015), and Zhang (2020), our predictors of economic growth are: (1) secondary and tertiary industries accounting for 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. In addition, some special predictors in specific years are added to improve the fitting accuracy, such as real per capita GDP values in 2000, 2004, and 2006. We obtain these data from the “China City Statistical Yearbook”, with some missing data supplemented by the statistical yearbooks and bulletins of national economic and social development in relevant provinces and cities.
2.2.3 The Need for Synthetic Control Analysis
It is important to note that the synthetic control mimics the pre-treatment cities much better than simpler types of controls. Figure 2 plots the trends in real per capita GDP of the three cities, the national average, and the average of the control cities. As can be seen, the real per capita GDP of the three cities is far lower than the national average. Similarly, the trend for the average of the control cities differs notably from that of the three cities. The indicators of 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.