Appendix: Methodological Approach

Sample of Analysis

The 30 Italian cities were selected on an equal basis within the territory to guarantee the high heterogeneity of the sample. To set the final sample, we based it on several constructs. First, we based on the homogeneity of the variables included in our model that has been considered uniform to assure the model approach. Second, we construct the sample of analysis based on the reference context as it is characterized by a different city size with a population ranging from 67,200 to 285,200. Finally, to guarantee the robustness of our sample, we apply the probability-proportional-to-size sampling in each stratum of the medium and large cities. This distinction between large and medium size has also been used as a control variable in our model.

Using this approach, the city with the largest population in each stratum emerges as a representative sample to be considered (Levy & Lemeshow, 2011). As a result, the final sample of analysis considered 30 of the 46 most populated Italian cities to guarantee the heterogeneity of the analysis sample. Thus, we use geo-software to draw the Italian map with our sample of analysis emerging from the sampling based on average from 2010 to 2021 (See Fig. A1), which shows the distribution and size of the cities under consideration. This empirical investigation focus on the Italian context as it currently is at the center of the academic and political debate on firms' green transformation, social policies and the current trends in sustainable advance, constituting a prominent empirical focus for the debates on sustainable development in Europe compared to other countries (i.e., Asia, US and Latin America).

Estimation Model

Due to the intrinsic characteristics of the panel dataset, which consists of a wide cross-section and a relatively short time period of 11 years, the dynamic Generalized Methods of Moments (GMM) estimation technique was employed in this article. By including time and city-fixed effects, the time-varying nature of the data was accounted for, and unobserved heterogeneity across cities was controlled. Following Roodman's approach (Roodman, 2009a, 2009b, 2009c) to the estimation model, internal instruments from lagged variables were also utilized to address the issue of over-identification (Windmeijer, 2005).

Roodman's approach (Roodman, 2009a, 2009b, 2009c) was employed in our estimation model to address the critical issue of identification and ensure the validity of our results. This approach relies on the use of internal instruments derived from lagged variables, and it was chosen for several reasons. Firstly, identification is a crucial aspect in estimating econometric models as it allows for the unique attribution of the effects of independent variables on the dependent variable. However, in the presence of endogenous or correlated variables, identification can become challenging. The use of internal instruments, such as lagged variables, helps overcome this issue by providing additional information that aids in the identification process. Roodman's approach offers a robust solution for addressing over-identification, a common concern in econometric analysis. Over-identification occurs when there are more instruments than necessary to identify the parameters of interest, leading to inefficient estimates and potential biases. By employing internal instruments from lagged variables, we ensure that the model is neither under-identified nor over-identified, striking a balance that promotes accurate and reliable estimation (Wooldridge, 2002). The inclusion of lagged variables as instruments is particularly valuable in dynamic models, where the dependent variable's past values can serve as relevant predictors. By capturing the persistence and lagged effects of the dependent variable, the lagged variables act as valid instruments, allowing us to account for the dynamic nature of the relationship under investigation. Furthermore, Roodman's approach is well-suited for panel datasets with a wide cross-section and a relatively short time period, as is the case in our study (Roodman, 2009c). By incorporating time and city-fixed effects, we account for the time-varying characteristics of the data and control for unobserved heterogeneity across cities. This helps mitigate potential biases and provides a more accurate estimation of the effects of interest.

To ensure the validity of the dynamic GMM estimations and assess the robustness of the results, various diagnostic tests were conducted. Specifically, the Arellano and Bond test, the Sargan test, and the Wald Chi-Square test were employed (Bond & Arellano, 2012; Magazzini & Calzolari, 2020; Roodman, 2009b; Sargan, 1958).

The Sargan test was used to examine the joint validity of the instruments and detect over-identification in the model (Sargan, 1958). The choice of using the Sargan test instead of the Hausmann test was made, as it is known to be more effective in detecting over-identification and less susceptible to the instrument proliferation problem, as noted by Roodman (Roodman, 2009c). Specifically, unlike the Hausmann test, the Sargan test is known to be more effective in detecting over-identification and less susceptible to the instrument proliferation problem (Bond & Arellano, 2012; Breitung & Salish, 2021; Debarsy, 2012). By conducting the Sargan test, we ensured that our instruments were not correlated with the error term and that the model was properly identified. This test further enhanced the validity and reliability of our estimation results, contributing to the robustness of our analysis.

In addition, the Arellano and Bond test (Bond & Arellano, 2012; Lee & Yu, 2014) was applied to assess any autocorrelation in the idiosyncratic disturbance term. Further investigation of potential autocorrelation issues was conducted through the AR(1) and AR(2) tests. These tests helped evaluate the presence of autocorrelation and address it appropriately.

The Arellano and Bond test is a widely used method to detect autocorrelation in dynamic panel data models. It is based on the first-differenced transformation of the model equation and compares the coefficient estimates of lagged dependent variables with their predicted values. The test examines whether the lagged dependent variables are correlated with the first-differenced residuals, indicating the presence of autocorrelation. To further investigate potential autocorrelation issues, we conducted the AR(1) and AR(2) tests. The AR(1) test examines first-order autocorrelation by regressing the residuals on lagged residuals from the previous time period. Similarly, the AR(2) test examines second-order autocorrelation by regressing the residuals on two lags of residuals. These tests help us evaluate the presence and magnitude of autocorrelation in the error terms. If significant autocorrelation is detected, it suggests that the error terms are correlated over time, violating the assumption of independence. To address autocorrelation, we can employ various techniques such as adding lagged dependent variables, including additional lagged independent variables, or using alternative estimation methods such as Generalized Method of Moments (GMM) or Fixed Effects (FE) models (Allison, 1994; Elhorst, 2003; Wooldridge, 2002). By applying the Arellano and Bond test, along with the AR(1) and AR(2) tests, we can identify and address autocorrelation in our model. This ensures that our estimations account for the time-dependent patterns and improves the reliability of our results. By taking these rigorous steps to detect and mitigate autocorrelation, we enhance the validity and robustness of our analysis, providing more accurate insights into the relationship between variables in our dynamic panel data model.

Finally, to ensure the validity of the model and address heteroskedasticity, the Wald Chi-square test was conducted along with additional checks. Heteroskedasticity refers to the presence of unequal variances in the error terms, which can affect the efficiency and accuracy of the estimations (Lee & Yu, 2014; Roodman, 2009c). The Wald Chi-square test is a statistical test that examines whether the coefficients in the model are jointly significant. It assesses the overall validity of the model and helps determine if the estimated relationships between variables are statistically meaningful. To mitigate the effects of unobserved heterogeneity and endogeneity issues, the Roodman GMM dynamic approach (Roodman, 2009c) was adopted. This approach is a robust estimation method that addresses endogeneity and unobserved heterogeneity by using instrumental variables. In this case, the lagged-dependent variable was utilized as an instrument to capture the persistence of the dependent variable. By including the lagged-dependent variable as an instrument, potential biases caused by the endogeneity of the dependent variable and the presence of unobserved factors that may affect the relationship between variables are controlled. By employing the Wald Chi-square test, implementing additional checks, and adopting the Roodman GMM dynamic approach, the validity and reliability of the model are enhanced. These methodological approach enable the control of heteroskedasticity, address endogeneity and unobserved heterogeneity, and provide more accurate and robust estimations (Lee & Yu, 2014; Magazzini & Calzolari, 2020; Roodman, 2009a). As a result, meaningful conclusions can be drawn, and reliable inferences about the relationships and dynamics within the model can be made.

As a last check, the presence of multicollinearity, which refers to high correlation among independent variables in a regression model, was assessed using the Variance Inflation Factor (VIF). The VIF measures the extent to which the variance of an estimated regression coefficient is inflated due to multicollinearity (Akinwande, Dikko, & Samson, 2015). In our analysis, a VIF value of less than four is generally considered acceptable, indicating that the independent variables in the model are not highly correlated with each other. This suggests that multicollinearity is not a significant issue in our model. By ensuring low levels of multicollinearity, we enhance the stability and reliability of the results. High levels of multicollinearity can lead to unreliable coefficient estimates, making it difficult to interpret the impact of individual variables on the dependent variable. However, in our case, the VIF values below four indicate that the variables in our model are relatively independent and do not suffer from multicollinearity issues. Having a stable and reliable model allows us to make accurate inferences and draw meaningful conclusions from our analysis. It ensures that the estimated coefficients are more robust and the relationships between variables are accurately represented. Therefore, by assessing and addressing multicollinearity, we can have greater confidence in the validity and accuracy of our results.

By employing these rigorous statistical techniques and diagnostic tests, the robustness of the analysis was enhanced, and potential biases were minimized. These methodological choices strengthen the validity of the findings and provide a solid foundation for drawing meaningful conclusions from the research.

Data Collection and Variables

This research uses city-level variables and collects data from databases at the national (ANPR, AGCOM, ISTAT, GreenItaly, GSE, OECD, MIUR CoC and IBS) and international (EUROSTAT and OECD) levels. Specifically, in Tables A1 and A2, describe the variables adopted in the empirical analysis showing the source, type of variables, operationalization, and short description. Table A3 displays the results of the GMM model.

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Fig. A1.

Sample of Analysis.