*2.4. Statistical Analysis*

We have specified five linear regression models with the actual budget balance as the dependent variable. In what follows (Section 3), results of these models were presented and commented in the order they are listed in Table 1, reporting the regression coefficients of each model in separated tables. All models were checked against the basic assumptions of Ordinary Least Square (OLS) model fitting, i.e., testing for linearity, homoscedasticity, independence, and normality assumptions (Ciommi et al. 2019). Results of statistical checks were presented in a graphical form (Lamonica et al. 2020).

**Table 1.** Specification of econometric models used in our analysis (Acronyms in Section 2.3).


#### **3. Results and Discussion**

*3.1. Outcomes of Model 1*

Model 1 provided the simplest specification of the variability in the actual budget balances of Greece (1974–2020) using only four variables. Since the lagged dependent variable is included in the explanatory variables, residuals are independently distributed (Salvati 2022). Plotting the residuals versus the fit, we verify that the linearity and homoscedasticity assumptions hold (Figure 1). Finally, a QQ plot and histogram of the residuals reveal no serious departures from normality (Ciommi et al. 2018). ABB-1 and UNR are significant at α = 0.01, ELE is significant at α = 0.05, and TYGR is significant at α = 0.1. Low Variance Inflation Factors (VIF) values indicate no evidence of multicollinearity (Table 2). The proportion of explained variance is relatively high (adjusted-R2 = 0.70).

**Figure 1.** Residual plots for Model 1 with Actual Budget Balance as dependent variable.



#### *3.2. Outcomes of Model 2*

EXPO and IMPO were introduced in Model 2 together with the predictors already considered in Model 1. Residual plots in Figure 2 document how results of Model 2 fully adhere to linearity, homoscedasticity, independence, and normality assumptions. ABB-1, TYGR, and EXPO are significant at α = 0.01, while ELE and IMPO are significant at α = 0.05. VIF values indicate evidence of a residual multi-collinearity in Model 2, mainly attributable to IMPO and EXPO variables (Table 3). The proportion of explained variance is rather high (adjusted-R<sup>2</sup> = 0.74).

**Figure 2.** Residual plots for Model 2 with Actual Budget Balance as the dependent variable.

**Table 3.** Regression coefficients of Model 2 (see Table 1 and Section 2 for the model description).


#### *3.3. Outcomes of Model 3*

The lagged variable ABB-2 was introduced as a predictor in Model 3 and accounted for a particularly high proportion of the explained variance (adjusted-R2 = 0.75). The residual plots in Figure 3 indicate no deviations from the basic regression assumptions. EXPO was significant at α = 0.01, ELE, IMPO, TYGR, and ABB-1 were all significant at α = 0.05, and ABB-2 was significant at α = 0.1 (Table 4). A weak multi-collinearity issue (VIF > 5) was a distinctive characteristic of the estimation of Model 3, in line with what has been observed for the results of Model 2.

**Figure 3.** Residual plots for Model 3 with Actual Budget Balance as the dependent variable.


**Table 4.** Regression coefficients of Model 3 (see Table 1 and Section 2 for the model description).

#### *3.4. Outcomes of Model 4*

To cope with the weak multi-collinearity observed in Model 3, the variables IMPO and EXPO were replaced with their difference, named BAGS, in Model 4. The residual plots in Figure 4 indicate that the basic assumptions were not violated with this specification. The proportion of explained variance remained satisfactory (adjusted-R2 = 0.73). ABB-1 and BAGS are significant at α = 0.01, ELE is significant at α = 0.05, TYGR is marginally significant at α = 0.05, and ABB-2 is marginally significant at α = 0.1 (Table 5). Low VIF values indicate no evidence of multicollinearity.

**Figure 4.** Residual plots for Model 4 with Actual Budget Balance as the dependent variable.



#### *3.5. Outcomes of Model 5*

Unemployment rate (UNR) was introduced as an additional predictor in Model 5. The proportion of explained variance was satisfactory (adjusted-R2 = 0.75). Plots of residuals (Figure 5) indicate no violation of the basic econometric assumptions for Model 5. ABB-1 is significant at α = 0.01, ELE, ABB-2, TYGR, BAGS, are all significant at α = 0.05, and UNR is significant at α = 0.1. Low VIF values indicate no evidence of multicollinearity (Table 6).

**Figure 5.** Residual plots for Model 5 with Actual Budget Balance as the dependent variable.

**Table 6.** Regression coefficients of Model 5 (see Table 1 and Section 2 for the model description).


In order to investigate possible differences in the mean growth rate (%) of total (real) GDP between the two ELE groups (i.e., election and non-election years), the null hypothesis H0: μ<sup>1</sup> − μ<sup>2</sup> = 0 was tested against the alternative H1: μ<sup>1</sup> − μ<sup>2</sup> = 0, where μ<sup>1</sup> = E(DTYGR1|ELE = 0) and μ<sup>2</sup> = E(DTYGR1|ELE = 1). H0 is rejected at α = 0.05, and the differences in the means of GDP growth are significant. The results of our analysis were presented in Table 7 and Figure 6.

**Figure 6.** Interval Plot (95% Confidence Interval around the mean) of changes over time in the growth rate (%) of total (real) Gross Domestic Product (DTYGR1) against election year (1) or non-election year (0); pooled standard deviation (3.20) was used to calculate the intervals.


**Table 7.** Descriptive statistics of the growth rate (%) of total (real) Gross Domestic Product (DTYGR1) by election year.
