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This survey of the literature on the convergence of carbon dioxide (CO₂) emissions informs researchers on areas for future research by summarizing the countries examined, the types of convergence tested and the methodological approaches undertaken.

This survey examines peer-reviewed empirical studies of CO₂ emissions convergence with respect to country coverage and alternative approaches to test for various types of convergence.

For large multicountry studies, the support for convergence is quite limited. However, studies focused exclusively on a subset of countries defined by income classification, geographic region or institutional structure reveal the finding of convergence is more prevalent. Studies at the subnational level have primarily been in the cases of the US and China with the exception of two studies across industry sectors in Portugal and Sweden.

This study focuses exclusively on peer-reviewed published studies.

This study is relevant to the design of mitigation strategies to reduce CO₂ emissions and the assumption of convergence underlying climate change models.

As a major component of greenhouse gas emissions, CO₂ emissions is of global importance in its impact on the environment and climate change.

This study provides the most recent and comprehensive survey of the empirical literature on the convergence of CO₂ emissions.

In this study, we aim to test the stochastic convergence of per capita clean energy use in 30 OECD (Organization for Economic Co-operation and Development) countries for the period of 1965–2017.

This study employed both linear and nonlinear panel unit root tests, and unlike other studies, this study allowed fractional values in addition to integer values for frequencies in the Fourier functions. Integer values of frequency indicate temporary breaks, while fractional values show permanent breaks.

The results of the linear panel unit root test indicate that clean energy use does not converge to group average for almost all OECD countries. However, the results of nonlinear panel unit root tests provide evidence that the stochastic convergence hypothesis of clean energy consumption cannot be rejected for most countries. This study does not find any evidence for stochastic convergence of clean energy use in Australia, Canada, Denmark, Ireland, Norway or Sweden. Therefore, the policies regarding clean energy are mandatory in these countries due to their effectiveness. This study also reveals that there are permanent structural breaks in the convergence process of clean energy consumption in approximately half of OECD countries.

This study considers temporary and permanent smooth structural shifts in addition to nonlinearity when testing the stationarity of clean energy consumption in a country i relative to the group average. This new method eliminates deficiencies of the previous panel data techniques. Thus, it provides more reliable results compared to existing literature.

The purpose of this paper is to use quarterly time series data from Canada and the Canadian provinces to determine if the unemployment rates in the Canadian provinces are converging to the national rate of unemployment.

First, the authors check for existence of stochastic convergence using recent unit root statistics, see Perron and Rodríguez (2003) and Rodríguez (2007). Second, the authors verify existence of convergence using methods proposed by Volgelsang (1998) and Bai and Perron (1998, 2003). All these methods allows for structural break(s) in the data.

Results from different unit root tests, without and with structural breaks, confirm that stochastic convergence exists in all provinces. The other results show strong evidence that deterministic convergence exists and the unemployment rates of the Canadian provinces are converging to the unemployment rate of Canada. This conclusion is stronger when multiple breaks are allowed in the trend function using the approach of Bai and Perron (1998, 2003).

Since the authors have verified the existence of stochastic convergence, any intervention in the labor markets of the Canadian provinces to control the provincial unemployment rate would have a temporary effect and these policies will not have a permanent influence on the unemployment rates. However, existence of β-convergence in the Canadian provinces shows that general policies toward lowering the national unemployment rate would decrease the provincial unemployment rates as well.

To the best of the knowledge, the paper attempts to study the unemployment rate convergence in the Canadian provinces using the above-mentioned approaches. These approaches allow the authors to take into consideration the possibility of structural breaks in order to get results that are more accurate.

The policy of globalization for India was a mix bag contributing benefits and losses. Increased foreign trade, foreign exchange reserves, market expansion was contrasted with fall in domestic industries, unemployment and increase in inequality. The present study analyzes the presence of convergence or divergence of incomes of the states in India using the concepts of Sigma convergence, Beta convergence, and stochastic convergence for the post-reform period of 1993–1994 to 2014–2015. The study tests for absolute β – convergence by using trend line analysis; regression of CAGR (Compound Annual Growth Rate) as a function of the Average PCSDP (Per Capita State Domestic Product) of initial three years of the observed period and regression of point-to-point growth rate of per capita income to the growth rate of initial three years. A negative relationship shall imply the presence of convergence. Further the study uses panel unit root test and relevant dynamic processes to test for conditional β and stochastic convergences. It reveals the evidence of divergence in income across the states.

This paper investigates income convergence using different convergence concepts and methodologies for 72 countries over the period between 1960 and 2010.

This study applies beta (β), sigma (s), stochastic and club convergence approaches. For β-convergence analysis, it derives the cross-country growth regressions of the Solow growth model under the basic and augmented Cobb–Douglass (CD) production functions and estimates them using cross-section and panel data estimators. While it employs both the widely used coefficient of variation and recently developed weak s-convergence approaches for s-convergence, it applies three different unit root tests for stochastic convergence. To test club convergence, it estimates the log-t regression.

The results reveal that (1) there exists conditional β-convergence, meaning that poorer countries grow faster than richer countries; (2) income per worker is not (weakly) s-converging, and cross-sectional variation does not tend to fall over the years; (3) stochastic convergence is not found and (4) countries in the sample do not converge to the unique equilibrium, and there exist five distinctive convergence clubs.

The results clearly show that heavily relying on one of the convergence techniques might lead researchers to obtain misleading results regarding the existence of convergence. Therefore, to draw reliable inferences, the results should be checked using different convergence concepts and methodologies.

Contrary to the previous literature, which is generally restricted to testing the existence of absolute and conditional β-convergence between countries, to the best of the author’s knowledge, this is the first study to consider and compare all originally and recently developed fundamental concepts of convergence altogether. Besides, it uses the Penn World Table (PWT) 9.1 and extends the period to 2010. From this point of view, this study is believed to provide the most up-to-date empirical evidence.

To generalize the traditional 2nd order stochastic perturbation technique for input random variables and fields and to demonstrate for flow problems.

The methodology is based on an n‐th order expansion (perturbation) for input random parameters and state functions around their expected value to recover probabilistic moments of the response. A finite element formulation permits stochastic simulations on irregular meshes for practical applications.

The methodology permits approximation of expected values and covariances of quantities such as the fluid pressure and flow velocity using both symbolic and discrete FEM computations. It is applied to inviscid irrotational flow, Poiseulle flow and viscous Couette flow with randomly perturbed boundary conditions, channel height and fluid viscosity to illustrate the scheme.

The focus of the present work is on the basic concepts as a foundation for extension to engineering applications. The formulation for the viscous incompressible problem can be implemented by extending a 3D viscous primitive variable finite element code as outlined in the paper. For the case where the physical parameters are temperature dependent this will necessitate solution of highly non‐linear stochastic differential equations.

Techniques presented here provide an efficient approach for numerical analyses of heat transfer and fluid flow problems, where input design parameters and/or physical quantities may have small random fluctuations. Such an analysis provides a basis for stochastic computational reliability analysis.

The mathematical formulation and computational implementation of the generalized perturbation‐based stochastic finite element method (SFEM) is the main contribution of the paper.

We investigate the convergence of Chinese real GDP per capita at regional and provincial levels, looking separately at the sub‐periods before and after major economic reforms and paying attention to the possibility of structural breaks induced by the ‘Great Leap Forward’. At the regional level we reject convergence pre‐ and post‐reform. At the provincial level we find evidence of a common regional trend for the Eastern region and again for the Central region, but not for the Western region. We conclude that, contrary to the policy objectives of the Chinese government, the regions of China have not shared a common development path.

The purpose of this paper is to investigate convergence or divergence trends at global scale.

The paper questions the methodology and findings of the conventional convergence literature using linear OLS models. It introduces polynomial (quadratic) weighted least square (WLS) regression analysis to explore whether a number of economic performance indicators follow a non‐linear pattern of change.

The results indicate the formation of two groups in the world: a convergence one, including countries with low to medium‐high development levels, and a divergence one including countries with medium‐high to very high development levels.

Data availability after 1990 (for the composite indicators).

The findings shed light on important issues, such as the decrease of economic disparities between countries, the prospects for global economic convergence, and the development of a more equal world. Apart from obvious policy implication such findings are also of theoretical significance, providing a basis to check (indirectly) the validity of alternative growth theories.

This is the first paper (to the authors' knowledge) that explores world convergence/divergence employing quadratic WLS regression analysis with a number of economic indicators. WLS regressions enable the removal of the impact of country size on results, whereas non‐linear modelling allows the possibility of multiple equilibria and different development trajectories to be taken into account. Finally, the employment of various economic‐performance indicators (simple and composite) works as a cross‐check of validity for the results provided.

This study aims to investigate the stationarity and convergence of CO₂ emissions series in MENA countries. The stationarity and unit root properties of per capita carbon dioxide (CO₂) emissions series are explored by an increasing amount of studies, which use different methodologies. Examining the time series properties of energy and environmental series is crucial for both researchers and the policymakers, given the close link between energy, environment and the real economy. In fact, if energy exhibits the presence of a unit root, this suggests that this series does not revert to its equilibrium level after being hit by a shock.

The contribution of this work is twofold. First, to the author’s knowledge, a very little attention has been paid to the topics of stationarity and convergence of CO₂ emissions in the case of Middle East and North Africa (MENA) member states, especially in a panel context. Convergence analyses of CO₂ emissions for MENA countries can improve the knowledge of energy and environmental scenario of the area, giving some ideas for appropriate future policies. Second, this is the first study that jointly analyzed time series and panel data properties of emissions series for these countries.

The author finds that relative per capita CO₂ emissions in the 19 MENA countries are a mixture of I(0) and I(1) processes and there is a weak evidence to support the stationarity of CO₂ emissions. After having verified the presence of cross-sectional dependence in the series, the panel unit root tests in presence of cross-section dependence show strong evidence in favor of non-stationarity. In addition, after performing tests for ß-convergence, it is also found that per capita CO₂ emissions are converging on average in 11 out of 19 sample’s countries, while s-convergence analysis reveals that the variance of per capita CO₂ emissions decreased over time, which is an indication of convergence.

Important policy implications emerge from the empirical results. Sustainable environmental and energy policies rely heavily on the CO₂ series’ properties. In this regard, determining whether shocks to CO₂ emissions are permanent or transitory is important for setting feasible goals for sustainable environmental policies. Given that per capita CO₂ emissions are essentially associated with a quality of life, the issues of their reduction have been the leading agenda in energy and environmental management over the past two decades.