Supply chain resilience and digital transformation: perspectives from a supply chain network

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Supply chain resilience and digital transformation: perspectives from a supply chain network

Regression-based DID

Table 2 presents the results of a DID estimation model analyzing the impact of supply chain digitalization pilots on the resilience and out-degree of nodes in the supply chain network. Columns (1) and (2) indicate that the impact of the supply chain digitalization pilots on the network nodes’ centrality is statistically significant. Specifically, conditioning on controls, the estimated coefficient implies an increase of 0.032 in weighted degree for firms in pilot cities relative to non-pilot cities (column (2)). Given that the average pre-treatment resilience of the supply chain network in pilot cities was 0.16 (based on sample means), the estimated coefficient of 0.032 implies an ~20% relative increase in resilience (0.032/0.16), significant at the 95% confidence level.

Table 2 Baseline regression.

Furthermore, results in columns (3) and (4) indicate that this increase is primarily driven by a rise in out-degree, which accounts for over 34% of the total centrality change and is statistically significant at the 99% confidence level. However, due to potential issues of endogenous, the estimates in Table 2 might be biased. We therefore turn to an IV approach in Section “IV method”.

IV method

To correct the estimation bias in the DID model, we adopted the instrumental variable method. The constructed instrumental variable is the interaction term between the standard deviation of city altitudes (\({altitude}\)) and the dummy variable for cities piloting supply chain digitization. The rationality of this instrumental variable has been fully justified in the previous text. Here, its effectiveness is tested. In terms of relevance, columns (1) and (2) of Table 3 report the first-stage regression results of the instrumental variable method. The results show that the instrumental variable is highly positively correlated with the supply chain digitization pilot dummy variable, meeting the relevance requirement (the Kleibergen–Paap rk Lm statistic values provided in Table 3 are all above 10, indicating no weak instrumental variable issue); moreover, the results are consistent with our expectations—that implementing pilot, cities with flatter terrain are more likely to be selected as pilot cities.

Table 3 Endogeneity test.

Regarding exogeneity, as previously pointed out, the probability that this instrumental variable directly affects the centrality of supply chain network nodes, other than through influencing the supply chain digitization pilot dummy variable, is small, thus satisfying the condition for the exogeneity of the instrumental variable. To verify this, our study follows the method of Dinkelman (2011), constructing a placebo test. We took the period from 2010 to 2017, when supply chain digitization pilots had not yet been implemented, as the sample period and included the interaction term between the standard deviation of city altitudes and the supply chain digitization pilot dummy variable in regression Eq. (1). If this interaction term satisfies the condition of exogeneity, i.e. it only affects the dependent variable by influencing the selection of pilot cities and does not have a direct impact on the dependent variable, then during the years from 2010 to 2017, when pilot had not yet been implemented, it should have no significant effect on the dependent variable. Columns (7) and (8) of Table 3 show that the coefficient of this interaction term is small and statistically insignificant, indicating that the instrumental variable satisfactorily meets the condition of exogeneity.

After ensuring the validity of the instrumental variable, we present the estimation results of the instrumental variable method in Table 3. Consistent with the estimation results of the DID model, the supply chain digitization pilot has a significant positive impact on the centrality of supply chain network nodes, but the absolute value of the impact coefficient is larger. This suggests that the endogeneity problem tends to cause a downward bias in the estimation results. Specifically, after effectively correcting for endogeneity, the supply chain digitization pilot led to a 33.4% increase in the pilot of firms in pilot cities (see column (4) of Table 3) and a 60% increase in out-degree (see column (6) of Table 3). Therefore, the supply chain digitization pilot significantly enhanced the \({SCR}\) of firms in pilot cities, consistent with the original intent of the pilot. At the same time, it also increases the influence of these firms in the supply chain network (see columns (5) and (6) of Table 3). These findings support H1.

Dynamic analysis

The parallel trend assumption is one of the fundamental conditions for applying the DID method. In this study, following the approach of Jacobson et al. (1993), we employ an event study that spans from three years before to three years after the event, using the year prior to the event as the base year. This analysis reinforces the argument that the supply chain digitalization pilot serves as an external shock for the firm, making it unlikely that our results are influenced by reverse causality. We construct the model as follows:

$$\begin{array}{l}{{SCR}}_{i,t}={\alpha }_{0}+{\sum }_{u\ge -3}^{3}{\beta }_{i}{{Treat}}_{i}\times {T}_{i,u}+{\sum }_{k}{\alpha }_{k}{{Control}s}_{i,t}^{k}\\\qquad\qquad+{\mu }_{i}+{\delta }_{t}+{\varepsilon }_{i,t}\end{array}$$

(2)

Where, \({{Treat}}_{i}\) is a dummy variable used to classify firms into treatment and control groups; \({T}_{i,u}\) represents a series of time dummy variables. We set the year when the treatment group cities first launched the policy during the sample period as period 0. For each year that is the \(u\) period relative to the treatment cities’ policy launch, \({T}_{i,u}\) takes a value of 1; otherwise, it is 0. The coefficients of interest are \({\beta }_{-3}\), \({\beta }_{-2}\), and \({\beta }_{-1}\). If there were any nonparallel trends between the treatment and control groups, then we would obtain statistically significant estimates of \({\beta }_{-3}\), \({\beta }_{-2}\), and \({\beta }_{-1}\).

We report the dynamic DID results in Table 4. Consistent with the parallel trend assumption, the coefficients of \({\beta }_{-3}\), \({\beta }_{-2}\), and \({\beta }_{-1}\) are not statistically significant in all regressions. This also implies that the positive effect of participation in supply chain digitalization pilots on supply chain resilience is unlikely to result from policymakers selectively including firms based on pre-existing or expected differences in supply chain resilience between treated and control firms. Thus, it helps address the reverse causality concern and further strengthens our previous findings. Moreover, by examining the coefficients associated with post-event time dummies, we find that the positive effect of supply chain digitalization pilots generally begins to materialize in the second year (column (1)) and persists beyond. This is consistent with our hypothesis that improvements in supply chain resilience, driven by digitalization efforts, take time to manifest as firms adapt and integrate digital technologies into their supply chain operations.

Table 4 Dynamic analysis.

Meanwhile, the dynamic coefficients in Table 4 enable us to distinguish between short-term adaptive responses and long-term structural effects. In the first year after the policy was introduced (\({T}_{1}\)), the impact already becomes apparent—especially for the output-based resilience measure (column (2))—indicating that treated firms initiated preliminary adaptive adjustments. Notably, the coefficients continue to rise and reach statistical significance in the second and third years (\({T}_{2}\) and \({T}_{3}\)) for both the SCR and output measures. This growing effect over time suggests that the policy’s influence is far from transitory; instead, it reflects a sustained, structural enhancement of supply-chain resilience, likely driven by the progressive build-up of digital infrastructure and the deepening of inter-organizational coordination mechanisms.

We also provide a graphical illustration of the relative changes in supply chain resilience between the treated and control groups around the initiation of the supply chain digitalization pilot. We plot the coefficients of the interaction terms between the treatment dummy and time dummies estimated from regression Eq. (2).

Figure 2 shows the estimated coefficients and 95% confidence intervals from the dynamic analysis. The results indicate that before the implementation of the policy, the estimated coefficients of the interaction terms remained relatively stable, suggesting no significant statistical differences in \({SCR}\)(\({Out}\)) between the treatment and control groups. After the implementation of the policy, however, the \({SCR}\) (\({Out}\)) of firms in the treatment group exhibited a clear upward trend. Overall, our findings demonstrate that dynamic analysis supports our model.

Fig. 2: Parallel trend.
figure 2

Shows the parallel trend test of the policy in the years before and after 2018 (Duration 0). The left part of the picture shows the test of the SCR specification, and the right side shows Out specification.

Heterogeneity analysis

In this subsection, we examine the potential mechanisms through which supply chain digitization enhances resilience. Theoretically, if digitization policies foster greater resilience—by promoting better data integration, advanced monitoring capabilities, and improved adaptability, then their impact should be stronger under conditions that favor the absorption of these benefits. Specifically, we focus on three potential channels: (1) geographical distribution diversity of the supply chain, (2) hierarchy of supply chain, and (3) operations transparency of supply chain. To test these proposed channels, we use the following regression equation:

$${{SCR}}_{i,t}={\beta }_{0}+{\beta }_{1}{{Treat}}_{i}\times {{Pos}{t}_{\_H}}_{i,t}+{\beta }_{2}{{Treat}}_{i}\times {{Pos}{t}_{\_L}}_{i,t}$$

$$+\,\,{\sum }_{k}{\alpha }_{k}{{Control}s}_{i,t}^{k}+{\mu }_{i}+{\delta }_{t}+{\varepsilon }_{i,t}$$

(3)

Where, \({{SCR}}_{i,t}\), \({{Treat}}_{i}\), and \({{Control}s}_{i,t}^{k}\) are the same as in Eq. (1). \({{Post\_H}}_{i,t}\) and \({{Post\_L}}_{i,t}\) are indicator variables equal to 1 if firm \(i\)’s value of the grouping variable is above or below the cross-sectional average prior to the policy, respectively, and 0 otherwise. These group indicators are used in Eq. (3) to examine the heterogeneous effects across high and low groups. These high and low groups are based on the three partition variables: geographical distribution diversity of supply chain, supply chain hierarchy, and operational transparency. By comparing the differences in resilience outcomes between these groups, we aim to identify which conditions amplify or attenuate the positive effects of supply chain digitization.

The role of geographic dispersion of supply chain

de Moura et al. (2021) highlighted that dispersed supply chains rely on the integration of operational technology (OT) and information technology (IT). Digitization enhances transparency and responsiveness through real-time data sharing, converting data from dispersed facilities into valuable information, optimizing logistics, production, and inventory management, and thus mitigating complexity and enhancing supply chain resilience. We use whether a firm has cross-province subsidiaries to measure the geographical dispersion of its supply chain. Based on the cross-province subsidiaries, firms are divided into high and low groups, defined as \({Post\_H}\) and \({Post\_L}\), respectively. We then analyze the changes in firms’ supply chain resilience using Eq. (3), with the results presented in Table 5.

Table 5 Mechanisms analysis of geographic dispersion of supply chain.

The results show that supply chain digitization policies significantly enhance \({{SCR}}_{i,t}\) and \({{Out}}_{i,t}\) for firms with higher geographical dispersion (\({Post\_H}\)), with positive and significant coefficients for \({Treat}\times P{ost\_}H\) (0.034, p < 0.05 in column (1); 0.033, p < 0.01 in column (2)). In contrast, the coefficients for \({Treat}\times P{ost\_}L\) are small and not significant. The significant differences between the two groups, as shown by \({Treat}\times ({Post\_H}-{Post\_L})\) (0.034, p < 0.1 in column (1); 0.028, p < 0.1 in column (2)), suggest that digitization policies are particularly effective for firms with dispersed supply chains.

The role of hierarchy of supply chain

Following the methodology of Hu et al. (2022), we employ social network analysis techniques to determine each firm’s hierarchical position within the supply chain. Specifically, this approach assigns a metric, referred to as the hierarchical value, to each firm. The hierarchical value reflects a firm’s position in the supply chain network and its susceptibility to demand fluctuations.

Theoretically, firms with lower hierarchical values, those closer to the end consumer, are more likely to directly benefit from the adoption of supply chain digitization technologies. This is because digitization enhances information transparency and real-time responsiveness, enabling downstream firms to manage inventory, address fulfillment pressures, and adapt to market fluctuations more effectively, thereby significantly enhancing supply chain resilience.

To determine the hierarchical value, we first identify the outermost firms in the supply chain network, those without any suppliers of their own. These firms, which are closest to the end consumer, are assigned a hierarchical value of 1. These firms are then removed from the network, and the structure is reevaluated. The firms that emerge as the new outermost layer after this removal are assigned a hierarchical value of 2. This iterative process continues until every firm in the network is assigned a hierarchical value, reflecting its position relative to the ultimate consumer.

Based on hierarchical values, we classify firms into two groups: \({Post\_H}\) and \({Post\_L}\). Firms in the \({Post\_H}\) group have lower hierarchical values, meaning they are closer to the end consumer, while firms in the \({Post\_L}\) group have higher hierarchical values, indicating their position further upstream in the supply chain. This classification allows us to analyze the differentiated impact of digitization policies on firms at varying hierarchical levels within the supply chain. We then analyze the changes in supply chain resilience using Eq. (3), with the results presented in Table 6.

Table 6 Mechanisms analysis of hierarchy of supply chain.

The results indicate that supply chain digitization policies significantly enhance \({{SCR}}_{i,t}\) and \({{Out}}_{i,t}\) for firms closer to the end consumer (\({Post\_H}\)), while having little to no significant impact on firms further upstream (\({Post\_L}\)). The coefficients for \({Treat}\times {Post\_H}\) are positive and highly significant (0.060, p < 0.01 in column (1); 0.046, p < 0.01 in column (2)), suggesting that firms in the \(P{ost\_H}\) group benefit significantly from digitization policies. In contrast, the coefficients for \({Treat}\times P{ost\_}L\) are small and not significant for \({{SCR}}_{i,t}\) (0.010, p > 0.1 in column (1)) and only marginally significant for \({{Out}}_{i,t}\) (0.016, p < 0.1 in column (2)). These findings highlight that supply chain digitization policies have a more pronounced effect on firms positioned closer to the end consumer.

The role of operation transparency of supply chain

Corporate transparency enhances supply chain resilience by facilitating smooth information flow and collaboration among partners (Liu et al. 2024a). High transparency helps in the rapid identification and communication of risks (Wong et al. 2011), reduces uncertainty, and fosters trust through informal collaboration, minimizing reliance on independent risk management practices (Bubicz et al. 2019). This environment of trust and collaboration enables the supply chain to respond more effectively to disruptions and improves its recovery capability (Wieteska 2020).

Following Sodhi and Tang (2019) and Hutton et al. (2009), we measure corporate transparency based on firms’ disclosures related to supply chains (SCT) and financial reporting (Opaque). Specifically, SCT represents the proportion of transaction value with major suppliers and customers whose names are explicitly disclosed in annual reports, relative to the total transaction value of the top five suppliers and customers. Opaque, in line with Hutton et al. (2009), is proxied by the magnitude of earnings management, measured using discretionary accruals estimated from a modified Jones model. Greater discretionary accruals reflect higher financial opacity due to reduced reliability of reported earnings.

Based on the level in the sample, companies are divided into high transparency and low transparency groups, defined as \({Post\_H}\) and \({Post\_L}\), respectively. We then analyze the changes in supply chain resilience using Eq. (3), with the results presented in Table 7.

Table 7 Mechanisms analysis of operation transparency of supply chain.

Columns (1) and (2) present results based on firms’ supply chain transparency. We find that supply chain digitization policies significantly enhance both \({{SCR}}_{i,t}\) and \({{Out}}_{i,t}\) for firms with higher supply chain transparency, with effect sizes of 0.072 and 0.054, respectively (both significant at the 1% level). In contrast, the impact is notably weaker for firms with lower transparency—0.011 (not significant) for \({{SCR}}_{i,t}\) and 0.019 (\(p < 0.1\)) for \({{Out}}_{i,t}\) The difference between high and low transparency groups is statistically significant, as indicated by the interaction term \({Treat}\times (P{ost\_H}-P{ost\_}L\)), with effect sizes of 0.061 (\(p < 0.01\)) and 0.034 (\(p < 0.05\)), respectively.

Columns (3) and (4) report results based on financial reporting transparency. Again, the policy effect is more pronounced among firms with greater transparency in financial disclosures. High-transparency firms exhibit significant improvements in both \({{SCR}}_{i,t}\) (0.032, \(p < 0.05\)) and \({{Out}}_{i,t}\) (0.032, \(p < 0.01\)), whereas the effects for low-transparency firms are negative and statistically insignificant. The interaction term capturing the differential effect, \({Treat}\times (P{ost\_H}-P{ost\_}L\)) shows a significant gap of 0.040 (\(p < 0.1\)) for \({{SCR}}_{i,t}\) and 0.043 (\(p < 0.01\)) for \({{Out}}_{i,t}\)

These findings consistently suggest that transparency serves as an important amplifier of the policy’s effectiveness. Specifically, after the policy implementation, high-transparency firms improved their supply chain resilience more significantly than low-transparency firms, highlighting the amplifying role of transparency in enhancing the effectiveness of supply chain digitization policies.

Mechanism analysis

Next, we further investigate the mechanism through which supply-chain digitalization policies enhance supply-chain resilience. Section “Theoretical framework” has already provided a comprehensive theoretical discussion; therefore, this section concentrates on examining how the digitalization pilot policy affects the key mechanism variables. To that end, we specify the following regression model:

$${M}_{i,t}={\alpha }_{0}+{\beta }_{1}{{Treat}}_{i}\times {{Post}}_{t}+\mathop{\sum }\limits_{k}{\alpha }_{k}{{Control}s}_{i,t}^{k}+{\mu }_{i}+{\delta }_{t}+{\varepsilon }_{i,t}$$

(4)

where \({M}_{i,t}\) represents the mechanism variables of supply-chain resilience, including dimensions such as recovery capability and operational efficiency; \({{Treat}}_{i}\times {{Post}}_{t}\) is a dummy variable that equals one for firms covered by the digital-transformation pilot policy. The definitions of the remaining covariates are identical to those in the baseline regression. This model is designed to test whether the pilot program indirectly enhances firms’ supply-chain resilience by improving their information-processing capacity and recovery capability.

Information processing capacity

Based on the definition provided in Premkumar et al. (2005), which assesses information processing capacity as “the level of information technology support for various activities in the procurement life cycle,” we use digital information disclosure (\({Digital\_dis}\)) and digital intangible assets (\({Digital\_asset}\)) as proxies. Digital information disclosure through MD&A reflects the cognitive framing and agenda-setting function of top management regarding digital strategies, while digital intangible assets more directly indicate a firm’s operational capacity to manage high volumes of supply chain information efficiently.

First, \({Digital\_dis}\) captures the salience of digital strategies in top management narratives by analyzing the MD&A sections of annual reports issued by publicly listed firms. We identify and count the frequency of digitalization-related terms—such as “digital transformation,” “blockchain,” “cloud computing,” “big data,” “AI,” “platform,” and “smart manufacturing”—and normalize this count by the total word count of the MD&A to account for variation in document length. Second, \({Digital\_asset}\) reflects a firm’s internal investment in digital capabilities. We extract the year-end value of intangible assets from the financial report footnotes that include keywords such as “software,” “network,” “client,” “management system,” “intelligent platform,” or digital-related patents. These components are aggregated and log-transformed to produce a firm-level digitalization indicator. All identified items undergo manual verification to ensure consistency with digital transformation efforts. We then examine the mechanism through which supply-chain digitalization policies influence supply chain resilience by estimating Eq. (4), with the results reported in Table 8.

Table 8 Information processing capacity.

The results reported in Table 8 provide empirical support for H2a, which suggests that pilot policy enhance firms’ information processing capacity. Specifically, column (1) shows that the coefficient on \({Digital\_dis}\) is statistically significant. (coefficient = 9.875, \(p < 0.01\)), indicating that managers in pilot firms placed greater emphasis on digital transformation in their strategic communications. Column (2) shows that the coefficient on \({Digital\_asset}\) is also statistically significant (coefficient = 3.275, p < 0.01), suggesting greater investment in internal IT infrastructure. Together, these results confirm that the policy intervention bolstered the cognitive and technical dimensions of firms’ information processing capability, thereby validating H2a.

Recovering capability

Based on the conceptual framework established by DuHadway et al. (2019) and Sheffi and Rice (2005), we define recovery ability as a firm’s capacity to return to expected operational performance following a disruption. Specifically, we measure this construction using the natural logarithm of the residual from a firm-level performance regression, where the residual captures deviations from expected outcomes and thus reflects latent recovery capability. We then examine the mechanism through which supply-chain digitalization policies influence supply chain resilience by estimating Eq. (4), with the results reported in Table 9.

Table 9 Recovering capability and inventory turnover efficiency.

Consistent with H2b, the results in Column (1) of Table 9 confirm that pilot policy significantly enhances firm’s recovery ability. The estimated coefficient on the treatment indicator is positive and significant at the 5% level, indicating that pilot firms are better able to respond to and recover from operational disruptions after policy. This supports the argument that digital technologies improve firms’ supply chain resilience by enabling faster recovery capability.

Inventory turnover efficiency

Following operational literature, inventory turnover efficiency reflects a firm’s capacity to align supply with demand and respond swiftly to market fluctuations. It is calculated as the natural logarithm of the inventory turnover ratio, where:

$${Inventory\; Turnover\; Ratio}=\frac{{Net\; Sales}}{{Average\; Inventory}}$$

This metric captures how frequently a firm replenishes its inventory over a given period. Higher turnover indicates more efficient inventory utilization, and less capital tied up in stock, which contributes to enhanced operational agility and supply chain resilience. We then examine the mechanism through which supply-chain digitalization policies influence supply chain resilience by estimating Eq. (4), with the results reported in Table 9.

The findings in Column (2) support H2c, showing that pilot policy improves inventory turnover efficiency. The positive significant coefficient suggests that firms in the pilot program manage inventory more effectively post-policy. This lends empirical support to the theoretical expectation that digital infrastructure improves information flow and forecasting accuracy, which in turn facilitates learner and more responsive inventory management practices.

Robust test

Excluding omitted variable bias

To ensure the credibility of our baseline conclusions, we conduct a series of robust tests addressing potential sources of bias. First, to mitigate the influence of unobserved heterogeneity at the regional and sectoral levels, we incorporate fixed effects for cities and industries. This approach controls for time-invariant characteristics that may simultaneously affect a firm’s supply chain centrality and its likelihood of being selected for digital transformation pilots, thus helping isolate the net effect of the policy intervention.

Second, to reduce potential omitted variable bias at the firm level, we include a comprehensive set of control variables informed by prior literature. Specifically, we account for SOE status, given that state-owned enterprises tend to differ in resource access and strategic priorities (Musacchio and Lazzarini 2014); high-tech designation, which reflects innovation capacity and technological adaptability (Kamalahmadi and Parast 2016); and the volume of digital-related patents, a proxy for internal digital capability (Ivanov 2021). Additionally, we control firm age (Tang 2006), CEO gender (Faccio et al. 2016), overseas managerial experience (Nielsen and Nielsen 2013), and academic background (Zhang and Rajagopalan 2004), all of which may influence firms’ risk management behavior and responsiveness to digital initiatives. By accounting for these factors, we strengthen the credibility of our identification strategy and bolster the robustness of our empirical findings.

Across columns (1)–(4) of Table 10, coefficients on the pilot indicator remain positive and statistically significant, and magnitudes are very similar to the baseline, indicating strong robustness.

Table 10 Excluding omitted variable bias.

Excluding selection bias

Second, we also try to use other methods to correct the endogenous selection bias problem to test the reliability of the baseline conclusions. Specifically, this paper adopts the PSM-DID method: firstly, based on the mean data of the matching variables of the sample cities before the pilot implementation (2010–2017), the propensity score is estimated using the Probit model; then, the treated group (sample cities that have implemented the pilot by 2018) and the control group (sample cities that have not implemented the pilot) are matched using the 1-to-1 nearest neighbor matching method; then, based on the panel data of the matched sample counties from 2010 to 2021, the pilot effect is estimated using the DID method.

Supplementary Appendix Table A2 reports pre- vs. post-match t-tests of covariate balance; Supplementary Appendix Fig. A.1 presents covariance-balance plots. Post-matching standardized biases lie well below the 10% threshold and cluster near zero, indicating satisfactory balance. As shown in columns (1)–(4) of Table 11, the PSM–DID estimates remain positive and significant, closely tracking the baseline results and supporting robustness to selection on observables.

Table 11 Excluding selection bias.

Placebo test

To further verify the validity of our baseline estimates, we conduct a placebo test based on the permutation approach proposed by Abadie et al. (2010). Specifically, we randomly reassign the treatment indicator, \({{Treat}}_{i}\times {{Post}}_{t}\), 500 times. After each reshuffle, we re-estimate the DID model, recording the coefficient, its standard error, and the degrees of freedom, while continuing to control for firm characteristics as well as industry, year, and firm fixed effects.

We then plot the empirical distribution of the 500 placebo coefficients alongside the null line (\(\beta =0\)) and the actual DID estimate (dashed line). In Fig. 3 (\({SCR}\) as outcome) and Fig. 4 (Out as outcome), the vast majority of placebo coefficients cluster tightly around zero, with only a small fraction approaching the observed estimate (\(\beta =0.031\) in Fig. 3; \(\beta =0.032\) in Fig. 4). This pattern indicates that the main results are unlikely to be driven by random assignments or model artifacts.

Fig. 3: Placebo test of SCR.
figure 3

This figure presents the results of 500 placebo simulations where the treatment indicator is randomly reassigned. The scatterplot shows simulated p-values against estimated treatment effects, while the kernel density on the right axis illustrates the distribution of β. The black solid line marks the null hypothesis (β = 0), and the red dashed line indicates the actual estimate from the main regression (β = 0.031). The concentration of simulated estimates around zero, with the actual estimate lying in the far tail, supports the robustness of the policy effect.

Fig. 4: Placebo test of out degree.
figure 4

This figure presents the results of 500 placebo simulations where the treatment indicator is randomly reassigned. The scatterplot shows simulated p-values against estimated treatment effects, while the kernel density on the right axis illustrates the distribution of β. The black solid line marks the null hypothesis (β = 0), and the red dashed line indicates the actual estimate from the main regression (β = 0.032). The concentration of simulated estimates around zero, with the actual estimate lying in the far tail, supports the robustness of the policy effect.

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