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The analysis of convergence behavior with respect to emissions and measures of environmental quality can be categorized into four types of tests: absolute and conditional β-convergence, σ-convergence, club convergence, and stochastic convergence. In the context of emissions, absolute β-convergence occurs when countries with high initial levels of emissions have a lower emission growth rate than countries with low initial levels of emissions. Conditional β-convergence allows for possible differences among countries through the inclusion of exogenous variables to capture country-specific effects. Given that absolute and conditional β-convergence do not account for the dynamics of the growth process, which can potentially lead to dynamic panel data bias, σ-convergence evaluates the dynamics and intradistributional aspects of emissions to determine whether the cross-section variance of emissions decreases over time. The more recent club convergence approach tests the decline in the cross-sectional variation in emissions among countries over time and whether heterogeneous time-varying idiosyncratic components converge over time after controlling for a common growth component in emissions among countries. In essence, the club convergence approach evaluates both conditional σ- and β-convergence within a panel framework. Finally, stochastic convergence examines the time series behavior of a country’s emissions relative to another country or group of countries. Using univariate or panel unit root/stationarity tests, stochastic convergence is present if relative emissions, defined as the log of emissions for a particular country relative to another country or group of countries, is trend-stationary. The majority of the empirical literature analyzes carbon dioxide emissions and varies in terms of both the convergence tests deployed and the results. While the results supportive of emissions convergence for large global country coverage are limited, empirical studies that focus on country groupings defined by income classification, geographic region, or institutional structure (i.e., EU, OECD, etc.) are more likely to provide support for emissions convergence. The vast majority of studies have relied on tests of stochastic convergence with tests of σ-convergence and the distributional dynamics of emissions less so. With respect to tests of stochastic convergence, an alternative testing procedure accounts for structural breaks and cross-correlations simultaneously is presented. Using data for OECD countries, the results based on the inclusion of both structural breaks and cross-correlations through a factor structure provides less support for stochastic convergence when compared to unit root tests with the inclusion of just structural breaks. Future studies should increase focus on other air pollutants to include greenhouse gas emissions and their components, not to mention expanding the range of geographical regions analyzed and more robust analysis of the various types of convergence tests to render a more comprehensive view of convergence behavior. The examination of convergence through the use of eco-efficiency indicators that capture both the environmental and economic effects of production may be more fruitful in contributing to the debate on mitigation strategies and allocation mechanisms.


Jennifer L. Castle and David F. Hendry

Shared features of economic and climate time series imply that tools for empirically modeling nonstationary economic outcomes are also appropriate for studying many aspects of observational climate-change data. Greenhouse gas emissions, such as carbon dioxide, nitrous oxide, and methane, are a major cause of climate change as they cumulate in the atmosphere and reradiate the sun’s energy. As these emissions are currently mainly due to economic activity, economic and climate time series have commonalities, including considerable inertia, stochastic trends, and distributional shifts, and hence the same econometric modeling approaches can be applied to analyze both phenomena. Moreover, both disciplines lack complete knowledge of their respective data-generating processes (DGPs), so model search retaining viable theory but allowing for shifting distributions is important. Reliable modeling of both climate and economic-related time series requires finding an unknown DGP (or close approximation thereto) to represent multivariate evolving processes subject to abrupt shifts. Consequently, to ensure that DGP is nested within a much larger set of candidate determinants, model formulations to search over should comprise all potentially relevant variables, their dynamics, indicators for perturbing outliers, shifts, trend breaks, and nonlinear functions, while retaining well-established theoretical insights. Econometric modeling of climate-change data requires a sufficiently general model selection approach to handle all these aspects. Machine learning with multipath block searches commencing from very general specifications, usually with more candidate explanatory variables than observations, to discover well-specified and undominated models of the nonstationary processes under analysis, offers a rigorous route to analyzing such complex data. To do so requires applying appropriate indicator saturation estimators (ISEs), a class that includes impulse indicators for outliers, step indicators for location shifts, multiplicative indicators for parameter changes, and trend indicators for trend breaks. All ISEs entail more candidate variables than observations, often by a large margin when implementing combinations, yet can detect the impacts of shifts and policy interventions to avoid nonconstant parameters in models, as well as improve forecasts. To characterize nonstationary observational data, one must handle all substantively relevant features jointly: A failure to do so leads to nonconstant and mis-specified models and hence incorrect theory evaluation and policy analyses.