3.1.2. Difference-In-Differences (DID)-Based Propensity Score Matching (PSM)

This study employs the PSM-DID method to quantitatively examine whether and to what extent China’s promotion of MSW sorting influences the financing constraints of the waste sorting industry. The difference-in-differences (DID, hereafter) method is widely acknowledged as the best method to evaluate the causal effects of specific external shocks, such as policy implementation [63,64,65,66]. Compared to ordinary regression (e.g., ordinary least square method), the DID method could divide the whole sample into the treatment group and the control group, and clearly identify the difference between the treatment group and the control group before and after the policy [67]. Therefore, the basic regression model in our study is constructed as follows [68,69,70]:

where FCi,t refers to the financing constraints of firm i at time t. We use the Size-Age index (hereinafter referred to as SA Index) to measure FCi,t based on the current previous literature [71,72], and the calculation formula of the SA index is (−0.737 × Size) + (0.043 × Size²) − (0.040 × Age), where Size is the log of total assets and Age is the number of years the enterprise has been listed. The higher the SA index, the more serious the financing constraints are. Treatedi indicates firm i‘s industry, i.e., Treatedi = 1 if firm i is an MSW sorting firm and =0 if firm i is a non-MSW sorting firm. Periodt indicates the post-treatment period, i.e., Periodt = 1 if t ≥ 2019-07-01 and =0 otherwise. εi,t is the error term. Xi,t denotes control variables, according to the available research [73,74]; the control variables in our study are as follows: size (represented by the natural logarithm of total assets), ownership (Ownershipi = 1 if firm i is a state-owned enterprise and =0 otherwise), the proportion of tangible assets to total assets (asset tangibility), the growth rate of business income (growth), Current ratio, Asset-liability ratio (Lev), the ratio of institutional ownership (instinv), the return on assets (hereinafter referred to as ROA, usually calculated by dividing a company’s net income by total assets), the return on stockholders’ equity(hereinafter referred to as ROE, calculated by dividing net income by shareholders’ equity), and the proportion of net cash flow to total assets (cashflow).

However, a concern with the DID approach is that the estimation results can be biased if the treatment group and control group are not stochastically selected. Accordingly, scholars suggest using the propensity score matching (PSM, hereafter) method, which has been widely used in studies on policy effects since its introduction, to handle the endogenous problems caused by selection bias [75,76,77]. The main steps of this method involve: (1) Estimating a logit or other discrete choice model of program participation; (2) Defining the region of common support and balancing tests; (3) Matching pairs; and (4) Calculating the average treatment impact. In this study, the matching model is given by:

where Xi,t denotes matching variables and are chosen from our control variables in Equation (6).