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This study examines whether OECD countries have converged over time in terms of export diversification. Focusing on the period 1995–2023, the study employs a new Fourier function-enhanced panel unit root test that takes into account gradual changes instead of sudden breaks. The findings show that more than half of OECD countries have not converged in terms of export diversification. Export diversification plays an important role in achieving economic growth and development as well as long-term sustainability goals. In this context, the study provides critical data for policymakers in support of sustainable development goals. The results point to the need to reassess the economic and environmental impacts of export diversification policies in OECD countries.

Our study investigates the relationship between technology innovation and human development in technologically advanced countries using data from quarterly observations from the last decade of the twentieth century to the first two decades of the twenty-first century. This objective of this study is to implement Quantile-on-Quantile regression (QQ) technique that as formulated by Sim and Zhou (J Bank Finance 55:1–8, 2015) and the renowned Granger-causality in quantiles as proposed by Troster (Econom Rev 37(8):850–866, 2018) examine the basic relationship between the given quantiles of technology innovation and their effects on the quantiles of human development. Therefore, the outcomes of this study explain the overall interdependence of technology innovation and affect the overall human development index. It is enumerated that the empirical results indicate that a significant positive relationship exists between technology innovation and human development in all selected technologically advanced countries, predominantly in both low and high tails. Moreover, the outcomes of Granger causality quantiles indicate a bi-directional fundamental relationship between these two variables in the dataset of all countries. The outcomes of the observations are extended to the recent findings on these two variables’ nexus and imply a differential impact on the technologically advanced countries. This causality guides us to offer some specific policy recommendations to each group of countries.

In the aftermath of the COVID-19 pandemic crisis, government debt has surged to unprecedented levels in most countries, including those of North Africa. In this study, we investigate the issue of public debt sustainability in four North African countries (Algeria, Libya, Morocco, and Tunisia). The Generalized Supremum Augmented Dickey–Fuller (GSADF) results show that Algeria, Libya, Morocco, and Tunisia have experienced periods of explosive public debt during the studied period. The identified episodes of explosive debt behavior can be seen as periods of unsustainable fiscal policy. Moreover, the Quantile Auto-Regressive (QAR) unit root results point to strong debt sustainability at the lower quantiles for the selected countries, while at the middle and upper quantiles, public debt exhibits an unsustainable dynamic. This finding, therefore, points to weak sustainability of debt and fiscal policies in Algeria, Morocco, Libya, and Tunisia. This paper provides further evidence that fiscal policies have become more unsustainable than sustainable in recent years in these countries. Consequently, fiscal policymakers in MENA countries should not overlook the unsustainability of public debt and its various effects when developing any strategy aimed at stimulating the economy through ever larger debt levels.

We develop inference methods about long-run comovement of two time series. The parameters of interest are defined in terms of population second moments of low-frequency transformations (\"low-pass\" filtered versions) of the data. We numerically determine confidence sets that control coverage over a wide range of potential bivariate persistence patterns, which include arbitrary linear combinations of I(0), I(1), near unit roots, and fractionally integrated processes. In an application to U.S. economic data, we quantify the long-run covariability of a variety of series, such as those giving rise to balanced growth, nominal exchange rates and relative nominal prices, the unemployment rate and inflation, money growth and inflation, earnings and stock prices, etc.

This study examines the stationarity properties of fossil fuel energy consumption in BRICS countries - Brazil, Russia, India, China, and South Africa - utilizing panel stationarity tests alongside the Zivot-Andrews unit root test. Conducted with annual data spanning from 1995 to 2023, the analysis first assesses cross-sectional dependence and investigates the interdependencies of energy consumption shocks across the nations. Following this, second-generation unit root tests are implemented based on the initial findings. The panel unit test results indicate that while oil and coal consumption exhibit stationary characteristics, natural gas consumption does not. Further country-specific analyses reveal the presence of structural breaks in fossil fuel consumption patterns. The findings suggest that the dynamics of energy consumption in BRICS countries are significantly influenced by economic transformations and policy shifts. This study highlights the necessity of accounting for structural breaks when assessing long-term trends in energy consumption and offers crucial insights for policymakers tasked with formulating sustainable energy policies.

Pesaran, Shin, and Smith (2001) (PSS) proposed a bounds procedure for testing for the existence of long run cointegrating relationships between a unit root dependent variable ( $y_{t}$ ) and a set of weakly exogenous regressors $\\boldsymbol{x}_{t}$ when the analyst does not know whether the independent variables are stationary, unit root, or mutually cointegrated processes. This procedure recognizes the analyst’s uncertainty over the nature of the regressors but not the dependent variable. When the analyst is uncertain whether $y_{t}$ is a stationary or unit root process, the test statistics proposed by PSS are uninformative for inference on the existence of a long run relationship (LRR) between $y_{t}$ and $\\boldsymbol{x}_{t}$ . We propose the long run multiplier (LRM) test statistic as a means of testing for LRRs without knowing whether the series are stationary or unit roots. Using stochastic simulations, we demonstrate the behavior of the test statistic given uncertainty about the univariate dynamics of both $y_{t}$ and $\\boldsymbol{x}_{t}$ , illustrate the bounds of the test statistic, and generate small sample and approximate asymptotic critical values for the upper and lower bounds for a range of sample sizes and model specifications. We demonstrate the utility of the bounds framework for testing for LRRs in models of public policy mood and presidential success.

New methods are developed for identifying, estimating, and performing inference with nonstationary time series that have autoregressive roots near unity. The approach subsumes unit-root (UR), local unit-root (LUR), mildly integrated (MI), and mildly explosive (ME) specifications in the new model formulation. It is shown how a new parameterization involving a localizing rate sequence that characterizes departures from unity can be consistently estimated in all cases. Simple pivotal limit distributions that enable valid inference about the form and degree of nonstationarity apply for MI and ME specifications and new limit theory holds in UR and LUR cases. Normalizing and variance stabilizing properties of the new parameterization are explored. Simulations are reported that reveal some of the advantages of this alternative formulation of nonstationary time series. A housing market application of the methods is conducted that distinguishes the differing forms of house price behavior in Australian state capital cities over the past decade.

We propose a double frequency fourier Dickey–Fuller (DF) unit root test. The asymptotic theory of the newly proposed test is first presented in this study. We conduct a series of simulations which suggest the proposed test statistic has correct size performance and gains more power when breaks are located at the beginning and end of the sample and in smooth type. In empirical analysis, we utilize the new test to examine the unit root hypothesis of relative commodity prices measured by Harvey et al. (Rev Econ Stat 92(2):367–377, 2010). The empirical results show that more relative commodity prices are stationary around a deterministic trend generated from double frequency Fourier function.

This study investigates whether post-Soviet countries are caught in the middle-income trap, using the Robertson and Ye (2013) approach. A comprehensive set of unit root tests was employed, including traditional tests (ADF), nonlinear tests (KSS, Kruse, Sollis), and advanced Fourier-based tests (FKPSS, FF-ADF, FADF, FKSS, FKruse, FSollis) to analyze the data spanning from 1990 to 2023. The results revealed a significant heterogeneity in convergence patterns across the countries. It can be concluded that Moldova, Kyrgyzstan, Tajikistan, Armenia, Azerbaijan, Belarus, and Georgia exhibited stationarity in most tests, indicating that these countries are in the middle-income trap. In contrast, Kazakhstan, Uzbekistan, Turkmenistan, Russia, and Ukraine displayed non-stationary results, suggesting that they are not in the trap and are converging toward higher income levels. In addition, the radar chart, coefficient of variation, and three different Multi-Criteria Decision Analysis techniques (Equal Weight Score, Discrimination Weighted Score, and Entropy Weighted Score) were used for robustness check. The results of these tests appear to be consistent with the outcomes of the unit root tests.

As the third-largest SO2 emitter in the world, China is facing mounting domestic and external pressure to tackle the increasingly serious SO2 pollution. Figuring out the convergence and persistence of sulfur dioxide (SO2) emissions matters much for environmental policymakers in China. This study mainly utilizes the Fourier quantile unit root test to survey the convergence of the SO2 emissions per capita in 74 cities of China during the period of December 2014 to June 2019, by conducting five traditional unit root tests and a quantile root unit test as a comparative analysis. The empirical results indicate that the SO2 emissions per capita in 72 out of 74 cities in China are convergent in the sample period. The results also suggest that the unit root behavior of the SO2 emissions per capita in these cities is asymmetrically persistent at different quantiles. For the cities with the convergent SO2 emissions, the government should consider the asymmetric mean-reverting pattern of SO2 emissions when implementing environmental protection policies at different stages. For Hefei and Nanjing, the local governments need to enact stricter environmental protection policies to control the emission of sulfur dioxide.