4.1. Descriptive Statistics
Table 1 reports the descriptive statistics for seven variables based on 80 observations. The dependent variable, Δln GDP per capita (the growth rate), shows an average value of 0.014 (1.4% per year) with a standard deviation of 0.039. The carbon tax variable records a mean of 40.350 USD/tCO
2e and a large standard deviation of 38.176, indicating substantial cross-country variation. Inflation shows considerable volatility with a mean of 9.766% and a standard deviation of 28.721, reflecting extreme inflationary episodes in certain observations.
Table 2 reports the Variance Inflation Factors (VIF). All values range from 1.10 to 2.26, with a mean VIF of 1.67, well below the critical threshold of 10. There is no evidence of problematic multicollinearity.
Table 3 presents an approximate AR(1) residual-correlation check (ρ = −0.093,
p = 0.265) together with the Durbin–Watson statistic (2.06), both consistent with no material serial correlation. Note: the classical Wooldridge test is designed for a levels fixed-effects model and does not directly apply once the dependent variable is itself first- differenced (see
Section 3.3); clustered standard errors provide additional protection against residual within-country correlation.
Table 4 presents the Breusch–Pagan test for heteroskedasticity. The significant result (chi2 = 22.653,
p = 0.0009) leads to rejection of homoskedasticity. Accordingly, all regression estimates are computed using clustered robust standard errors.
Table 5 reports the model selection test results, based on the Model 2 specification (six regressors), which nests Model 1 and Model 3 and provides the most conservative test of country-specific effects. The F-test (F(15,58) = 7.614,
p < 0.0001) indicates significant country-specific effects, rejecting pooled OLS. The Hausman test (chi2(6) = 98.253,
p < 0.0001, with six degrees of freedom now correctly matching Model 2’s six regressors) rejects the null that the random effects estimator is consistent. Consequently, the fixed effects model is adopted as the preferred specification.
Because the panel spans only 16 countries and six years, conventional cluster-robust inference may be imprecise.
Table 5’s clustered standard errors are additionally computed with a small-sample correction (G/(G − 1) × (N − 1)/(N − K)); this widens standard errors only marginally and does not alter significance patterns in
Table 6. A Pesaran cross-sectional dependence (CD) test on the Model 2 residuals indicates significant cross-sectional dependence (CD = 2.39,
p = 0.017), consistent with correlated global or regional shocks (e.g., energy-price movements) affecting multiple sample countries simultaneously; country-clustered standard errors address within-country serial correlation but not this cross-sectional component, so results should be interpreted with this additional caveat in mind. With only 16 cross-sectional units, the Wooldridge test for serial correlation also has limited power, reinforcing reliance on the AR(1) and Durbin-Watson diagnostics already reported in
Table 3.
To aid economic interpretation,
Table 6 coefficients are re-expressed using economically meaningful changes. In the preferred Model 2, a USD 10 increase in the carbon tax rate is associated with a 1.21-percentage-point reduction in annual GDP-per capita growth, and a one-standard-deviation increase in the carbon tax rate (USD 38.18) is associated with a 4.62-percentage-point reduction. A one-standard-deviation increase in investment (4.55 percentage points of GDP) is associated with a 37.94-percentage-point increase in growth, and a one-standard-deviation increase in inflation (28.72 percentage points) with a 0.80-percentage-point reduction. These magnitudes, rather than the raw per-unit coefficients, should be used when discussing the practical size of each effect, since the raw carbon tax coefficient (−0.00121) is easy to misread as negligible when in fact a realistic policy-relevant tax increase corresponds to a non-trivial growth effect.
The investment figure has been re-checked, and the arithmetic is correct (Model 2 investment coefficient of 0.08331 multiplied by the 4.55-percentage-point standard deviation of investment/GDP), but the resulting 37.94-percentage-point magnitude is implausibly large as an estimate of the marginal effect of capital formation on growth and should not be read as a structural capital-output elasticity. Two features of the estimation likely inflate it. First, with only 16 countries observed over five years (80 observations) and country fixed effects absorbing all cross-country level differences, the coefficient is identified solely from short-run within-country co-movement between investment and growth; in a panel this short, that co-movement is dominated by the shared 2020–2021 COVID-19 contraction and 2021–2022 rebound, when investment and growth fell and recovered together for reasons (the pandemic shock itself) that are not causally attributable to investment. Second, gross capital formation may proxy for broader concurrent improvements, such as economic confidence or policy stabilisation, that independently raise growth, so the coefficient likely captures a combination of the investment effect and these correlated factors rather than investment alone.
Accordingly, this magnitude is reported for internal comparability with the other re-expressed coefficients in this section, and it is treated as a reduced-form association rather than a causal capital-output elasticity; this qualification is now noted explicitly here and in the Discussion and Limitations.
4.4. Discussion
The empirical results provide meaningful insights when interpreted through the lenses of Pigovian Tax Theory and Endogenous Growth Theory. The negative coefficient of carbon taxation across all three models, now statistically significant at the 5% level in every specification, suggests that increases in carbon pricing impose adjustment costs on production and output.
Pigou (
1920) argues that corrective taxation internalises external environmental costs by increasing private production costs to reflect social damages, consistent with findings by
Goulder et al. (
2019) and
Shi et al. (
2023).
A further limitation is that the fixed-effects specification does not fully resolve potential endogeneity between the carbon tax rate and economic development. Wealthier, institutionally stronger economies may be more willing and able to introduce and sustain higher carbon tax rates, which could bias the estimated coefficient if unobserved, time-varying drivers of both tax policy and growth are not fully captured by country fixed effects. As a robustness check, Model 2 was re-estimated using the one-year-lagged carbon tax rate in place of the contemporaneous rate; the coefficient weakens to −0.00147 and loses statistical significance (p = 0.126), while the other coefficients remain broadly stable. This is a genuine and important finding: it is consistent with—though does not prove—the endogeneity concern, and it appropriately tempers a strictly causal interpretation of H1. Future research with a longer panel could apply instrumental-variable or dynamic GMM approaches to address this concern more directly.
The results should not be interpreted as evidence against carbon taxation as a growth-supporting instrument in the long term. According to
Romer (
1990), sustained economic expansion depends on innovation, knowledge spillovers and capital accumulation. Carbon pricing policies can stimulate innovation by raising the relative cost of carbon-intensive production (
Febrianti & Karlinah, 2025;
Liu et al., 2022). The estimated short-term coefficient, though larger than initially reported, may still capture transitional restructuring rather than a permanent growth penalty—a distinction this six-year panel is not designed to test directly.
Investment shows a robust positive relationship with GDP-per capita growth across all models, strongly supporting H3 and the predictions of endogenous growth models (
Barro, 1991;
Romer, 1990). Inflation exhibits a consistently negative and statistically significant effect, confirming H4 (
Banna et al., 2023;
Bruno & Easterly, 1998).
Energy intensity enters with a POSITIVE and statistically significant sign in both Models (2) and (3), contrary to H2’s hypothesised negative relationship. This reversal coincides with the removal of year fixed effects (necessitated by the collinearity issue described in
Section 3.1): with country fixed effects only, the coefficient partly reflects the fact that energy intensity in this sample declines steadily over time for every country while growth rates fluctuate year to year, so the within-country co-movement no longer isolates a clean energy-intensity effect in the way a two-way fixed-effects model would. This result should be treated with caution and revisited once year effects can be reintroduced with genuinely country-varying energy-intensity data; it does not overturn the theoretical expectation in H2 so much as highlight a data-structure limitation of the current sample.
The political stability coefficient is negative and statistically significant at the 10% level in Model 2 only (and not significant in Model 3), which appears to contradict H5. Within the fixed effects framework, the estimated coefficient captures within-country variation over time rather than cross-sectional differences. The sample is considerably more geographically diverse than a Nordic/European characterisation suggests—it spans Europe, the Americas, Asia, and Africa (Argentina, Canada, Chile, Denmark, Finland, France, Ireland, Japan, Mexico, Norway, Portugal, Singapore, South Africa, Sweden, Switzerland, and the United Kingdom)—so any explanation of the within-country decline in political stability scores should be framed at the level of the full sample rather than attributed mainly to Nordic or Northern European geopolitical developments. This within-country temporal variation may produce a negative coefficient despite political stability being positively associated with growth in the cross-sectional dimension (
Aisen & Veiga, 2013).
The COVID dummy variable is POSITIVE and highly statistically significant (H6 not supported, sign reversed), which—now that year fixed effects are no longer separately included (
Section 3.1)—most plausibly reflects the growth-rate series capturing a post-pandemic rebound in 2021 relative to the 2020 contraction and subsequent years, rather than a common downturn effect. This differs from the original account, which attributed the COVID dummy’s null result to year fixed effects absorbing the shock; that explanation no longer applies once year FE are removed, and the sign reversal itself is a substantive finding that should be discussed rather than treated as a nuisance parameter (
Rathnayake, 2022).