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The authors derive a risk lower bound in estimating the threshold parameter without knowing whether the threshold regression model is continuous or not. The bound goes to zero as the sample size n grows only at the cube-root rate. Motivated by this finding, the authors develop a continuity test for the threshold regression model and a bootstrap to compute its p-values. The validity of the bootstrap is established, and its finite-sample property is explored through Monte Carlo simulations.

The purpose of this study is to examine the nonlinear relationship between financial constraints and the chief executive officer (CEO) stock options compensation and to analyze whether the impact of financial constraints on the CEO stock options compensation changes at certain level of financial constraints or not.

This study is based on a sample of 90 French firms for the period extending from 2008 to 2019. To deal with the non-linearity, the authors use a panel threshold method.

Using different measures of financial constraints [KZ index (Baker et al., 2003), SA index (Hadlock and Pierce, 2010) and FCP index (Schauer et al., 2019)], the results reveal that the impact of the financial constraints (SA index and FCP index) is positive below the threshold value and it becomes negative above.

The non-linearity between financial constraints and CEO stock options shows that the level of financial constraints can be a major determinant of the CEO compensation structure. More specifically, this study sheds light on the key role played by the level of financial constraints and how this latter influence management decisions.

This paper is the first to the best of the authors' knowledge to examine the nonlinear relationship between financial constraints and the CEO stock options compensation using a panel threshold model.

This research investigates the threshold effects of the interplay between finance, development and carbon emissions across 97 countries, including 50 low-income and 47 high-income countries, during the period from 1991 to 2019.

Employing various econometric modeling techniques such as dynamic linear regression, dynamic panel threshold regression and in/out of sample splitting, this study analyzes the data obtained from the World Bank's world development indicators.

The results indicate that low-income countries require a minimum financial development threshold of 0.354 to effectively reduce carbon emissions. Conversely, high-income countries require a higher financial development threshold of 0.662 to mitigate finance-induced carbon emissions. These findings validate the presence of a finance-led Environmental Kuznet Curve (EKC). Furthermore, the study highlights those high-income countries exhibit greater environmental concern compared to their low-income counterparts. Additionally, a minimum GDP per capita of US$ 10,067 is necessary to facilitate economic development and subsequently reduce carbon emissions. Once GDP per capita surpasses this threshold, a rise in economic development by a certain percentage could lead to a 0.96% reduction in carbon emissions across all income levels.

This study provides a novel contribution by estimating practical financial and economic thresholds essential for reducing carbon emissions within countries at varying levels of development.

Driven by the development of the global digital economy, knowledge management in industrial enterprises offers more possibilities for green innovation. Based on the perspective of external knowledge sources, this study aims to construct a panel regression model to explore the relationship between digital economy and industrial green innovation efficiency.

Panel data from 30 regions in China from 2011 to 2020 were selected as research samples. All data are obtained from national and provincial statistical yearbooks. Coupling coordination degree analysis, entropy method, panel regression analysis, robustness test and threshold effect test by Stata 16.0 were used to test the hypotheses.

The empirical results demonstrate the hypotheses and reveal the following findings: the digital economy is positively related to industrial green innovation efficiency and external knowledge sources, and external knowledge sources mediate the relationship between them. Moreover, based on the threshold test results, the digital economy has a double-threshold effect on industrial green innovation efficiency.

Based on the perspective of external knowledge sources, the proposed mediating mechanism between the digital economy and industrial green innovation efficiency has not been established previously, further enriching the research on the antecedents and outcomes of external knowledge sources. Moreover, this study estimated the direct influence mechanism and double-threshold effect of the digital economy on industrial green innovation efficiency from theoretical and empirical analysis, thus responding to the call of scholars and adding to existing research on how the digital economy affects the green transformation of industrial enterprises.

This study aims to examine the potential threshold effect in the association between corporate social responsibility (CSR) performance and social reputation.

This study includes an international and cross-sector sample covering 41 countries, nine sectors and 45,395 firm-year observations. It applies a parabolic relationship, rather than linear regressions, between CSR engagement and social reputation via CSR awarding. This implies that CSR performance should increase until a certain point to gain a social reputation but then should decrease after reaching that threshold point considering limited financial resources.

The findings of country-industry-year fixed-effects logistic regressions confirm the threshold effect with an inverted U-shaped relationship between CSR and CSR awarding. More specifically, firms increase their environmental and social engagement until a certain point, and then they reduce it after reaching a social reputation. This finding is confirmed by three dimensions of the environmental pillar (i.e. resource use, emissions and eco-innovation) as well as four dimensions of the social pillar (i.e. workforce, human rights, community and product responsibility). The findings are robust to alternative samples, alternative methodology and endogeneity concerns.

The findings of this study have implications for firms about the better allocation of available funds between CSR and operations. The findings could be particularly useful for CSR teams/committees of the firms who formulate CSR policies and how to mobilize firm resources for better social enhancement via environmental and social reputation.

This study examines deeper the nature of the association between CSR engagement and social reputation and considers the possibility of an inverted U-shaped relationship between them. The determination of a threshold effect suggests that CSR engagement increases social reputation, but once it reaches a certain point, social reputation will decrease owing to financial resource constraints.

The authors employ the vessels that comprise the dry bulk segment of the maritime industry and examine how market sentiment affects the herding behavior of shipping investors in a real asset market.

The authors employ a threshold regression model to examine how changes in market sentiment can affect herding behavior in oceanic dry bulk shipping.

The results show that the behavioral aspect of investing, measured through intentional and unintentional herding, contrary to the results for financial markets, is affected by sentiment on the buy side (newbuildings) but not on the sell side (scrapping). Furthermore, the authors provide evidence that when market sentiment is negative, investors tend to follow market leaders (intentional herding), while, when sentiment is positive, unintentional herding leads to common investment practices among shipping investors.

The results have significant implications both for academics and for practitioners since they reflect a clear distinction of the pattern of investment decisions for real assets, compared to financial assets.

While some countries have used debt to drive economic growth, the asymmetric effect on sub-Saharan African (SSA) countries has received little attention in the empirical literature. This paper therefore examines the asymmetric effect of external debts on economic growth.

The panel nonlinear autoregressive distributed lag (NARDL) approach was employed in the study for 29 sub-Saharan African countries from 1990 to 2021. The cross-sectional dependence test was used to determine the presence of cross-sectional dependence, while the second-generation panel unit root tests was used to examine the unit-root properties.

The empirical results show that external debt has an asymmetric effect on economic growth in both the short and long run. In the long run, a positive shock in external debts of 1% triggers an upturn in economic growth by 0.216% while a negative shock triggers 0.354% decline in economic growth. This implies that the negative shock of external debts has a much stronger impact on economic growth than the positive shock. In the short run, a positive shock in external debts by 1% triggers a decline in economic growth by 0.641%, while a negative shock of 1% triggers a fall in economic growth of 0.170%.

The paper used the NARDL model to examine the asymmetric impact of external debt on the economic growth of SSA countries, which has not been extensively studied. It is recommended that governments in the selected countries in sub-Saharan Africa should drive economic growth by promoting domestic revenue mobilization since external debts impede economic growth.

The purpose of this paper is to investigate sustainable green economy in sub-Saharan African (SSA) countries over the period 1990–2019 using a quantile regression approach, considering the nexus between urbanization, economic growth, renewable energy, trade and carbon dioxide (CO₂) emissions.

The study used a dynamic panel quantile regression to investigate the conditional distribution of CO₂ emissions along the turn-points of urbanization, economic growth, renewable energy, trade and the regressors via quadratic modeling specifications.

The main findings are established as follows. There is strong evidence of the Kuznets curve in the nexus between urbanization, economic growth, renewable energy, trade and CO₂ emissions, respectively. Second, urbanization thresholds that should not be exceeded for sustainability to reduce CO₂ emissions are 0.21%, and 2.70% for the 20th and 75th quantiles of the CO₂ emissions distribution. Third, growth thresholds of 3.64%, 3.84%, 4.01%, 4.36% and 5.87% across the quantiles of the CO₂ emissions distribution. Fourth, energy thresholds of 3.64%, 3.61%, 3.70%, 4.02% and 4.34% across the quantiles of the CO₂ emissions distribution. Fifth, trade thresholds of 3.37% and 4.47% for the 20th and median quantiles of the CO₂ emissions distribution, respectively.

The empirical shreds of evidence offer policy implications in such that building sustainable development and environment requires maintaining the critical mass, not beyond those insightful thresholds to achieving sustainable development and environmentally friendly SSA countries.

Sustainable cities and communities in an era of economic recovery path COVID-19 mitigate greenhouse gas. The policy relevance is of particular concern to the sustainable development goals.

The study is novel considering the extant literature by providing policymakers with avoidable thresholds for policy formulations and implementations in the nexus between urbanization, economic growth, renewable energy and trade openness.

Most empirical papers on threshold effects between debt and growth focus on developed countries or a mix of developing and developed economies, often using public debt. Evidence for developing economies is inconclusive, as is the analysis of other threshold effects such as those probably caused by the level of relative development or the repayment capacity. The objective of this study was to examine threshold effects for developing economies, including external and total debt, and identify them in the debt-growth relation considering three determinants: debt itself, initial real Gross Domestic Product (GDP) per capita and debt to exports ratio.

We used a panel threshold regression model (PTRM) and a dynamic panel threshold model (DPTM) for a sample of 47 developing countries from 1970 to 2019.

We found (1) no evidence of threshold effects applying total debt as a threshold variable; (2) one critical value for external debt of 42.32% (using PTRM) and 67.11% (using DPTM), above which this factor is detrimental to growth; (3) two turning points for initial GDP as a threshold variable, where total and external debt positively affects growth at a very low initial GDP, it becomes nonsignificant between critical values, and it negatively influences growth above the second threshold; (4) one critical value for external debt to exports using PTRM and DPTM, below which external debt positively affects growth and negatively above it.

The outcome suggests that only poorer economies can leverage credits. The level of the threshold for the debt to exports ratio is higher than that found in previous literature, implying that the external restriction could be less relevant in recent periods. However, the threshold for the external debt-to-GDP ratio is lower compared to previous evidence.

Most emerging economies have made conscious efforts through policy initiatives to attract foreign direct investment (FDI). However, a significant obstacle to FDI inflow has been the prevalence of corruption in the host country. This study, therefore, aims to examine whether there is an optimum corruption value that results in threshold effects of corruption on FDI.

To achieve this objective, this study used Hansen’s (1999) panel threshold regression (PTR) model by using a panel data of 30 sub-Saharan African (SSA) countries from 2000 to 2021.

This study finds that the nexus between corruption and FDI has a single threshold effect, with a 5.37% optimum corruption threshold value. At this threshold value, corruption affects FDI negatively. Any corruption value that is below the threshold value also elicits a negative corruption–FDI relationship. Despite having a negative relationship when the corruption value is above the optimum corruption threshold, it is not statistically significant.

The implication of the results is that it is deleterious to use corrupt practices to draw FDI to SSA nations.

To the best of the authors’ knowledge, this study is one of the first in the corruption–FDI nexus literature to use Hansen’s PTR model to estimate an optimal corruption threshold. The authors recommend that policymakers in the selected SSA countries reconsider the use of corruption to attract FDI because there is an optimal corruption threshold that could impact FDI in the host country.