3.2.2. Selection and Justification of Econometric Models
The choice of panel data models is central to our analysis, which examines the economic and environmental dynamics of twenty African countries over a twenty-two-year period. Given the structure of our data, with time periods (T) outnumbering units (N), the use of panel cointegration techniques emerges as a methodologically sound choice, adept at navigating the complexities of the extensive time series data inherent in our study.
Within the spectrum of econometric models suitable for panel data analysis, we have a number of options, each designed to shed light on different aspects of our research questions. Static models, including fixed effects (FE) and random effects (RE), are particularly effective in dealing with unobserved heterogeneity, allowing the unique characteristics of each country to be considered. Conversely, when our focus shifts to the dynamic interplay of variables over time, models such as Vector Autoregression (VAR) and Vector Error Correction Model (VECM) become indispensable for their ability to elucidate the temporal dependencies and paths to equilibrium within the data.
To further enhance our econometric toolkit, the Generalized Method of Moments (GMM) stands out for its ability to deal with potential specification errors or endogeneity through its innovative use of data moments for parameter estimation. In the context of cointegrated series, both Dynamic Ordinary Least Squares (DOLS) and Fully Modified Ordinary Least Squares (FMOLS) offer refined estimates of long-run relationships, while the Canonical Cointegration Regression (CCR) model provides adjustments for endogeneity and serial correlation, ensuring robust long-run analysis.
For analysis that requires a nuanced understanding of both group-level homogeneities and individual-specific dynamics, the Pooled Mean Group (PMG), Mean Group (MG), and Dynamic Fixed Effect (DFE) estimators offer versatile approaches. These methods are adept at balancing the need for individual specificity with overarching trends across the dataset. In addition, the Driscoll and Kraay model’s resistance to cross-sectional dependence and its ability to provide consistent standard error estimates make it a valuable addition to ensure analytical robustness.
However, the Autoregressive Distributed Lag (ARDL) model, as formulated by Pesaran et al. (2001), is chosen primarily for its ability to accommodate variables of mixed integration orders, thus facilitating a comprehensive examination of both the short-run dynamics and the long-run relationships among the variables under study. The applicability of this model to our relatively small sample size and its compatibility with the PMG, MG, and DFE methodologies underscore its utility in providing a nuanced examination of the economic and environmental interfaces within our dataset. Through the judicious application of these econometric models, our study seeks to uncover the intricate relationships between environmental taxes, productive capacities, and environmental quality in the context of African economies, paving the way for informed policy interventions and sustainable development strategies. The ARDL model, which is central to the analysis of the interactions in our study, is described as follows:
In this equation, is the dependent variable for each country at time , is the individual-specific intercept, and and are the coefficients on the lagged dependent variable and the explanatory variable , respectively. Here, and denote the number of lags for and each , encapsulating the depth of historical influence on current observations, while embodies the error term.
Extending the conceptual foundation laid out in equation (2), our customized ARDL model refines and specifies the variables directly relevant to our investigative lens, as delineated within our theoretical framework. The refined model equation is thus expressed as follows:
In equation (4), the intercept captures the country-specific constants that affect per capita GHG emissions. The coefficients, though , quantify the impact of our economic and demographic variables, and are log-transformed to stabilize the variance and improve model interpretability. Specifically, is tasked with capturing the quadratic relationship indicative of the EKC hypothesis. The inclusion of lagged terms, and , is crucial for incorporating the influence of past emissions and ancillary variables on current environmental outcomes, thereby embedding the temporal dynamics integral to our analysis. The error term, , adheres to the assumption of a normal distribution and accounts for the unexplained variability in emissions across countries and time periods.
Recognizing the substantial utility of the ARDL model in our analysis, as described in equation (3), leads us to consider its limitations in the context of first-generation econometric techniques. Originally groundbreaking, the conventional panel ARDL framework assumes cross-sectional independence across units, an assumption that may not hold in the face of global economic dynamics and common external shocks that may affect multiple countries simultaneously. This oversight risks introducing bias by neglecting cross-sectional dependencies, which are increasingly recognized as crucial for robust econometric analysis.
To overcome these obstacles, second-generation econometric models offer refined methodologies that account for cross-sectional dependencies. Coakley et al. (2006) critically assess the ability of Pesaran et al.’s (1999) MG estimator to account for cross-sectional interdependencies, prompting the emergence of methodologies capable of effectively modeling these interrelationships. Pesaran (2006) introduces an augmented ARDL framework that incorporates a cross-sectional mean of observable variables to adequately represent unit correlations.
This methodological enhancement, refined by Chudik and Pesaran (2015) and Everaert and De Groote (2016), introduces the Common Correlated Effects (CCE) approach, based on the assumption that integrating cross-sectional means into model estimations provides a consistent approximation of common factors. This advance allows for two different adaptations of the panel-adjusted ARDL model: the Cross-Section Augmented Distributed Lag (CS-DL) for longitudinal analyses and the Cross-Section Augmented Autoregressive Distributed Lag (CS-ARDL) model for comprehensive short- and long-term studies. Our analysis gravitates toward the CS-ARDL model, as proposed by Chudik et al. (2016), for its nuanced ability to incorporate an optimal lag structure while ensuring robust estimates amidst cross-sectional dependencies.
Consequently, the CS-ARDL model selected for our empirical investigation enhances the traditional ARDL model by incorporating cross-sectional averages of all variables, thereby accounting for common factors that collectively affect the panel. The augmented model is expressed as follows:
Here, and denote the cross-sectional averages of the dependent and independent variables, respectively, for each lag and , thereby mitigating the influence of common trends across the panel. The coefficient associated with the time fixed effects and the term denoting the individual fixed effects encapsulate the unique characteristics of each country, while describes the error term specific to the time observations for each unit. This methodological progression underscores our commitment to addressing the multifaceted dynamics of environmental sustainability in the African context by accounting for both the individual peculiarities of the countries studied and the overarching trends that affect them collectively.
To further refine our econometric analysis, the incorporation of the Dynamic Common Correlated Effects Mean Group Estimator (DCCEMG) and Augmented Mean Group (AMG) models offers advanced perspectives on dealing with unobserved common factors in panel data. The DCCEMG model, introduced by Chudik and Pesaran (2015), embodies a sophisticated approach by assimilating lags of cross-sectional means. This inclusion allows for a comprehensive treatment of cross-sectional dependencies and slope heterogeneity, and accounts for potential structural breaks within the dataset. The model is written as follows:
In this model, represents the individual fixed effect identifying unique attributes of each unit, while and correspond to the coefficients on the lags of the dependent and explanatory variables, respectively. The terms and adjust for lagged cross-sectional averages, effectively controlling for the influence of unobserved common factors. denotes the individual-specific fixed effects, and is the idiosyncratic error term.
In parallel, the Augmented Mean Group (AMG) model conceptualized by Eberhardt and Teal (2010) introduces a common dynamic effect
. This effect quantifies the overarching impact of unobserved common factors on the entire panel, thereby enriching the analysis with the ability to account for the dynamic interplay of global economic trends and structural changes. The AMG model is written as:
Where is the individual fixed effect, and are the coefficients on the lags of the dependent and explanatory variables, is the common dynamic effect that captures the average influence of unobserved factors, and is the cross-sectional average used to model the common effects. We leave as the idiosyncratic error term.
Adapting the methodologies embodied in the CS-ARDL, DCCEMG, and AMG models to our empirical analysis allows for a nuanced understanding of the interplay between environmental taxes, productive capacities, and environmental quality across twenty African countries. These adapted models, which are precisely tailored to the variables of our study, provide a multifaceted approach to accounting for the cross-sectional dependencies and heterogeneities inherent in our panel data.
The CS-ARDL model refines the traditional ARDL approach by incorporating cross-sectional averages of all variables, thereby controlling for unobserved common factors that potentially affect all countries in the panel. This adjustment is expressed as:
where
is the natural log of per capita GHG emissions for country
at time
,
captures individual fixed effects,
and
are coefficients of the lagged dependent and explanatory variables respectively, adjusted for cross-sectional averages, and
is the error term.
The DCCEMG model further controls for cross-sectional dependencies and slope heterogeneity by including lags of cross-sectional averages. Its formulation is:
Here and are coefficients for the lags of the dependent and explanatory variables, respectively, and account for the lagged cross-sectional average effects, and is the individual fixed effect.
The AMG model introduces a common dynamic effect,
, which reflects the average impact of unobserved common factors on all units in the panel:
where
represents the contemporaneous effect of common factors, providing a unique perspective on the interconnectedness of economies and structural variation within panel data.
Incorporating these advanced econometric models into our analysis enhances our ability to navigate the complex dynamics at play, ensuring a robust examination of the effects of environmental policies and productive capacities on environmental quality. Through these advanced econometric strategies, our study delves into the multifaceted relationships between economic development, environmental protection, and sustainability goals in the African context. This comprehensive approach, detailed through equations and variable descriptions, strengthens the empirical foundation of our research and provides insights into policy formulation and the pursuit of sustainable development across the continent.