*3.4. Methodology*

**Difference-in-Differences.** To explore how MSER affect firm innovation, we adopted a DID approach based on the exogenous regulations in China. The logic here was to compare the relative difference between the treatment group and the control group before and after the exogenous shock. One important presumption for this estimation is the satisfaction of "parallel trends" between the treatment and control groups (we discuss this later). In this way, we can control for unobservable sources of heterogeneity across groups. If MSER facilitate firm innovation, we expect to observe that the difference in the increase in innovation between the treatment and control firms was more salient in the post-regulation period than in the pre-regulation period.

Given that the MSER were announced at the end of 2008 (30 December 2008 for SSH and 31 December 2008 for SZSH), we set 2009 as the first year the policy began to influence the treatment firms' behavior. Thus, we selected 2009 to 2011 as the post-regulation period and 2006 to 2008 as the pre-regulation period. We opted for a three-year window for two reasons: (i) the range should not be too short because time is necessary to determine the effect of the event on the innovation outputs; and (ii) it should not be too long to avoid confounding events. We also varied the length of the observation window in robustness analyses. Our specification model is as follows:

$$Innovation\_{it} = a\_0 + a\_1 Treated + a\_2 Post + a\_3 Treated \times Post + \gamma \mathbf{X}\_{it} + I\_j + \varepsilon\_{it\prime} \tag{1}$$

where *i* denotes firms; *t* denotes years; and *j* denotes industries. The dependent variable in this model is our measure of a firm's innovation output (i.e., *LnPatents* and *LnInventions*). *Treated* is a dummy variable that is equal to one for the treatment firms and zero for the control firms. *Post* is a dummy variable that equals one if a firm year belonged to the post-regulation period (2009–2011) and zero if a firm year belonged to the pre-regulation period (2006–2008). **X** is the vector of the control variables, which included firm size, firm age, ROA, leverage, cash holdings, and R&D intensity. We also included the industry fixed effects (*Ij*) to absorb the industrially time-invariant differences that were not captured by firm characteristics. *ε* is the error term. To account for the serial correlation of the error

term, we clustered standard errors at the firm level. The coefficient of interest is *α*3, which measures the effect of MSER on innovation.

**Propensity-Score Matching.** To mitigate the differences between the treatment and control firms, we generated a matched control sample using the PSM approach with respect to the observed characteristics. The basic logic was that each treated firm was matched with "control" firms, which were otherwise similar to the treated firm in terms of the propensity for being treated. A matching method can reduce the bias between two groups and allow for more accurate comparisons of innovation trends between the pre- and post-regulation periods. This approach enabled us to make stronger causal claims about the effect of MSER on firm innovation.

The PSM approach is based on the conditional probability of assignment to a particular treatment given a vector of observed covariates [44]. We adopted a probit regression to determine whether or not a particular firm was "treated" (included in the regulation list). Specifically, we included the firm size, return on equity, share turnover, stock returns, state ownership, and R&D intensity as the determinants that have been closely linked with the entry of regulation lists [3,4]. We selected the pre-regulation period as the matching window. Thus, all the covariates included in the probit regression were averages over the pre-regulation period (2006–2008). Additionally, we incorporated the growth measure of innovation (*patent growth*), which is measured by the growth ratio of the number of a firm's patents over the pre-regulation period, to ensure that the parallel trends assumption was satisfied. We then used the one-to-two nearest-neighbor matching algorithm with replacements to identify the control units. To ensure that the matching procedures improved the balance, we compared the differences in the means between the treatment and control firms (before and after matched) for these covariates. As shown in Table A2, the results revealed that the PSM procedures effectively reduced the differences between our treatment and control firms before the regulations. This procedure resulted in a matching sample of 2958 firm-year observations, 1589 of which were treatment firm years and 1369 of which were control firm years. Table A1 presents the distribution of the matched sample firms across the industry. We found that most observations in our sample came from the manufacturing industry, accounting for 54%, which is similar to the actual distribution of Chinese public firms.

#### **4. Results**
