Journal Description
Econometrics
Econometrics
is an international, peer-reviewed, open access journal on econometric modeling and forecasting, as well as new advances in econometrics theory, and is published quarterly online by MDPI.
- Open Access— free for readers, with article processing charges (APC) paid by authors or their institutions.
- High Visibility: indexed within Scopus, ESCI (Web of Science), EconLit, EconBiz, RePEc, and other databases.
- Rapid Publication: manuscripts are peer-reviewed and a first decision is provided to authors approximately 33.4 days after submission; acceptance to publication is undertaken in 7.8 days (median values for papers published in this journal in the first half of 2026).
- Recognition of Reviewers: reviewers who provide timely, thorough peer-review reports receive vouchers entitling them to a discount on the APC of their next publication in any MDPI journal, in appreciation of the work done.
- Journal Cluster of Economics, Finance and Risk Systems: Commodities, Econometrics, Economies, FinTech, Forecasting, Games, International Journal of Financial Studies, Journal of Risk and Financial Management, Platforms and Risks.
Impact Factor:
1.4 (2025);
5-Year Impact Factor:
1.5 (2025)
Latest Articles
Do Stablecoin Deviations Matter? A Bubble Crash–GARCH Approach to Risk Forecasting and Contagion with Traditional Cryptocurrencies
Econometrics 2026, 14(3), 42; https://doi.org/10.3390/econometrics14030042 - 13 Aug 2026
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Although stablecoins occupy a segment of digital-asset markets in which price stability is central by design, their temporary departures from reference values may reveal important information about latent risk and market stress. In this paper, we examine whether bubble and crash signals extracted
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Although stablecoins occupy a segment of digital-asset markets in which price stability is central by design, their temporary departures from reference values may reveal important information about latent risk and market stress. In this paper, we examine whether bubble and crash signals extracted from traditional cryptocurrencies and stablecoins improve volatility, Value-at-Risk, and Expected Shortfall forecasting and, in connection with these forecasting gains, contribute to the assessment of cross-asset contagions. The analysis applies the Bubble Crash–GARCH models, in which extreme price phases are identified through the Phillips, Shi, and Yu real-time monitoring procedure and incorporated into the conditional mean of returns through event-based dummy variables. For stablecoins, extreme episodes are not inferred from price dynamics in isolation but from deviations between the observed price and the asset-specific reference value. The empirical investigation focuses on Bitcoin, Ethereum, Tether’s USD-pegged (USDT), and Tether Gold and evaluates asset-specific bubble–crash effects and bidirectional contagion channels between traditional cryptocurrencies and stablecoins, using Bitcoin and Tether as the leading representatives of the two market segments. The findings indicate that accounting for bubble and crash episodes leads to more accurate volatility forecasts than standard GARCH benchmarks. For Value-at-Risk and Expected Shortfall, the bubble–crash specifications can improve tail risk forecasting at several tail probability levels through more accurate coverage, lower quantile loss, and stronger ESR backtesting performance. The results also reveal different degrees of price exuberance across the two asset categories: while extreme price dynamics are more evident among traditional cryptocurrencies, deviations from fundamentals are rare for stablecoins. Among stablecoins, USDT exhibits limited but detectable exuberance, whereas Tether Gold does not display extreme price episodes. However, when such deviations occur, as in the case of USDT, they generate significant contagion effects on major cryptocurrencies. Notably, extreme episodes originating in USDT have a stronger impacts on Bitcoin and Ethereum than the reverse spillovers from traditional cryptocurrencies to USDT. Overall, the evidence suggests that stablecoins are not merely passive instruments within the digital-asset ecosystem. Even temporary deviations from their reference values contain valuable information for risk forecasting and contagion monitoring.
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Open AccessArticle
Digital Adoption and Digital Maturity in Ecuadorian SMEs: A Cross-Sectional Econometric Analysis of the 2021 National Digital Skills Survey
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Ely Borja Salinas, Carlos Freire-Cadme, Washington Guevara Piedra and Washington Guevara Macias
Econometrics 2026, 14(3), 41; https://doi.org/10.3390/econometrics14030041 - 7 Aug 2026
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The post-pandemic acceleration of digital tools has reshaped how small and medium-sized enterprises (SMEs) in Latin America compete, yet the resulting maturity gains remain poorly understood in individual emerging-market economies. Ecuador exemplifies this gap: SMEs account for over ninety per cent of the
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The post-pandemic acceleration of digital tools has reshaped how small and medium-sized enterprises (SMEs) in Latin America compete, yet the resulting maturity gains remain poorly understood in individual emerging-market economies. Ecuador exemplifies this gap: SMEs account for over ninety per cent of the formal business register but appear in few econometric studies, most based on convenience samples. This study asks how strongly digital adoption is associated with the digital maturity of Ecuadorian SMEs and which tools best predict e-commerce engagement. The analysis draws on the National Digital Skills Survey (ENHD, Encuesta Nacional de Habilidades Digitales), administered by Ecuador’s Ministry of Telecommunications (MINTEL), covering 847 SMEs in 2021. A ten-indicator Digital Adoption Index (DAI) is related to the ENHD maturity score through least squares regression with robust standard errors, and a binary logit model with multicollinearity diagnostics identifies the tools that predict e-commerce adoption. The DAI explains over half of the variance in digital maturity, robust to firm-size and sector controls. Website presence exerts the largest marginal effect on e-commerce adoption, followed by cloud services. Top adopters score twice as high as non-adopters, consistent with cumulative advantage. Policy implications include subsidised digital-foundations bundles for laggard micro-enterprises.
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(This article belongs to the Special Issue Advancements in Macroeconometric Modeling and Time Series Analysis)
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An Econometric Analysis of Alcohol Consumption and Its Relationship to Social, Gender, and Economic Factors
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David Kerr, Alex Russell, Katherine Taken Smith and Lawrence Murphy Smith
Econometrics 2026, 14(3), 40; https://doi.org/10.3390/econometrics14030040 - 6 Aug 2026
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Alcohol consumption is associated with significant social and economic challenges for nations worldwide, including alcohol-related healthcare costs and alcohol-related crime. According to the U.S. Center for Disease Control (CDC), even moderate drinking correlates with greater health risks compared with not drinking at all.
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Alcohol consumption is associated with significant social and economic challenges for nations worldwide, including alcohol-related healthcare costs and alcohol-related crime. According to the U.S. Center for Disease Control (CDC), even moderate drinking correlates with greater health risks compared with not drinking at all. These health risks include physical harm to a person’s heart, brain, liver, and other organs; impaired social functioning; reduced work performance; and increased incidence of alcohol-related violence and injury (e.g., physical and sexual assault and drunk driving-related injuries and death). Although personal health and social problems are correlated with alcohol consumption across genders, women experience disproportionately worse problems associated with alcohol-related crime and family disruption. At the societal level, alcohol use coincides with substantial negative economic problems, including increased healthcare costs, often covered by the government; reduced worker productivity; and higher criminal justice system costs. This paper applies an econometric analysis to evaluate the association between alcohol consumption and key social and economic factors and suggests actions that business firms, government entities, universities, and other organizations can take to reduce alcohol-related harm, such as encouraging sobriety in the workplace, offering alcohol-related counseling services, and not establishing associations with nor accepting payments of any kind from alcohol beverage companies. The findings have implications for business managers, government leaders, policy-makers, and others.
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Open AccessArticle
Debt, Industry Structure, and Market Valuation: Sector-Specific Evidence from India’s IT and Automobile Firms
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Priyanka Goyal and Ash Narayan Sah
Econometrics 2026, 14(3), 39; https://doi.org/10.3390/econometrics14030039 - 15 Jul 2026
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The relationship between capital structure and firm market valuation remains a central yet unresolved question in corporate finance, with outcomes shaped critically by industry-specific asset structures and financing environments. This study investigates how capital structure influences market valuations across two structurally divergent sectors
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The relationship between capital structure and firm market valuation remains a central yet unresolved question in corporate finance, with outcomes shaped critically by industry-specific asset structures and financing environments. This study investigates how capital structure influences market valuations across two structurally divergent sectors in India, the asset-light information technology (IT) industry and the asset-intensive automobile industry, using balanced panel data for 14 firms in each sector over 2005–2024. Fixed effect and random effect panel regression models are employed to isolate the direct effect of leverage on earnings per share (EPS), with model selection determined by the Hausman specification test. Complementing these estimations, the Graphical Lasso is applied to recover a sparse conditional dependence network among key financial variables, an approach particularly suited to this research question, as capital structure, profitability, tangibility, and growth are jointly determined, rendering pairwise correlations insufficient for identifying genuine financial linkages. The findings establish that debt exerts a positive and statistically significant effect on market valuations in both sectors, but through distinct economic channels: moderate leverage amplifies profitable growth signals in IT firms, while tax shield benefits drive valuation in automobile firms, constrained by asset tangibility and debt-servicing thresholds. These results support trade-off theory in the automobile sector and pecking order logic in the IT sector, underscoring that sector-specific financing strategies yield superior valuation outcomes compared to universally applied capital structure prescriptions.
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On Walter’s Model and Cash-Flow-Based Payout Ratio
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C. N. V. Krishnan and Yue Lang
Econometrics 2026, 14(3), 38; https://doi.org/10.3390/econometrics14030038 - 14 Jul 2026
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We examine whether Walter’s model holds in that firms with greater growth opportunities would pay out less, using operating cash-flow-based payout measures that include only dividends, only repurchases or both. Two groups of explanatory variables are considered. The first group consists of firm
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We examine whether Walter’s model holds in that firms with greater growth opportunities would pay out less, using operating cash-flow-based payout measures that include only dividends, only repurchases or both. Two groups of explanatory variables are considered. The first group consists of firm characteristics (including contemporaneous and lagged P/E ratios to control for dividend growth model prediction), and the second group comprises macroeconomic indicators reflecting economic conditions. Across Fixed effects (within) estimator with clustered standard errors, Random Forest, Lasso and Ridge methodologies, the cash-flow-based payout ratios consistently and significantly show contemporaneous association with growth opportunities, providing some support for Walter’s model.
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Exploring the Dynamics of ZAR/USD Exchange RateVolatility Using the fGARCH and First-Order Beta-Skew-T-EGARCH Models
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Dzulani Mashavhela, Thakhani Ravele and Caston Sigauke
Econometrics 2026, 14(3), 37; https://doi.org/10.3390/econometrics14030037 - 13 Jul 2026
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This study investigates and explores the volatility dynamics of the South African rand against the US dollar (ZAR/USD) using the Family GARCH (fGARCH) model and the First-Order Beta-Skew-T-Generalised Autoregressive Conditional Heteroskedasticity (Beta-Skew-T-EGARCH) model. Currency volatility across the globe, uncertainties, and instability in emerging
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This study investigates and explores the volatility dynamics of the South African rand against the US dollar (ZAR/USD) using the Family GARCH (fGARCH) model and the First-Order Beta-Skew-T-Generalised Autoregressive Conditional Heteroskedasticity (Beta-Skew-T-EGARCH) model. Currency volatility across the globe, uncertainties, and instability in emerging markets have become increasingly consequential for trade flows, investment allocation, and macroeconomic management. The ZAR/USD serves as a benchmark of South Africa’s economic wealth and vulnerability to external shocks and is one of the most valued, significant, and heavily traded pairings of emerging market currencies. Simple standard GARCH (sGARCH) is one of the most useful models for exchange rate volatility; however, the sGARCH model has some limitations: it fails to accommodate or allow the long memory effects, skewness distribution, and leverage dynamics consistently observed in emerging-market currency returns. This study addresses these limitations by using the fGARCH model, which includes the most popular GARCH models and Beta-Skew-T-EGARCH for daily ZAR/USD returns ranging from 5 January 2000 to 1 October 2024. Five innovation distributions are used for evaluation and comparison under fGARCH and sGARCH, namely generalised hyperbolic (GH), generalised error (GED), skewed Student’s t (SSTD), skewed generalised error (SGED), and Student’s t (STD), with model fitness criteria assessed using the Shibata criterion (SIC), Hannan–Quinn criterion (HQ), Bayesian information criterion (BIC), and Akaike information criterion (AIC), choosing the specification with the lowest overall penalty. It is found that the fGARCH(1,1) model fitted to return-frequency data under the SSTD achieves the lowest AIC, outperforming sGARCH. The study also includes an analysis among covariates, which are day, month, trend, oil, and platinum; the trend variable is a statistically significant predictor, with p = 0.007, showing a positive influence on ZAR/USD volatility. The Beta-Skew-T-EGARCH model with two components divides volatility into long-run and short-run components, which is found to deliver a superior fit over the one-component variant, evidenced by a lower BIC (3.068435) and a higher log-likelihood (−748.464826). The two components confirm that the model captures declining conditional volatility, whereas the one-component model sustains persistence in the evaluated estimates.
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Productivity, Crude Oil Supply Shocks and the Economy of Iran in a Dynamic Stochastic General Equilibrium Framework
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Bahram Adrangi, Maryam Amini, Saman Hatamerad and Kambiz Raffiee
Econometrics 2026, 14(3), 36; https://doi.org/10.3390/econometrics14030036 - 8 Jul 2026
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This paper investigates the responses of key macroeconomic variables—including output, consumption, investment, capital accumulation, and employment—to productivity and oil market shocks in Iran. Using quarterly data from 1975 to 2024, we estimate an RBC DSGE model and further calibrate a variant incorporating oil
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This paper investigates the responses of key macroeconomic variables—including output, consumption, investment, capital accumulation, and employment—to productivity and oil market shocks in Iran. Using quarterly data from 1975 to 2024, we estimate an RBC DSGE model and further calibrate a variant incorporating oil supply shocks. The results show that positive productivity and oil shocks generate immediate expansions in output, consumption, investment, labor hours, and wages, reflecting strong short-term multipliers and forward-looking behavior by households and firms. However, these gains are temporary, with impulse responses following a hump-shaped path and gradually declining as shocks dissipate, capital depreciation sets in, and policy or market frictions emerge. This underscores the transient nature of both productivity and oil windfalls and the need for policies that mitigate short-run volatility while fostering structural reforms and diversification. For an oil-dependent economy such as Iran, the findings highlight that while shocks can stimulate activity in the short term, sustainable long-run growth requires institutional mechanisms to channel temporary gains into lasting development.
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The Relationship Between Economic Activity and CO2 Emissions: Is There a GDP Growth Consistent with No Growth in CO2 Emissions?
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Jaime Marquez, Jiayi Ding and Soobin Lee
Econometrics 2026, 14(3), 35; https://doi.org/10.3390/econometrics14030035 - 2 Jul 2026
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This paper offers estimates of the per-capita GDP growth trajectories consistent with zero growth in per-capita CO2 emissions using Ordinary Least Squares (OLS) and Instrumental Variables (IVs). The focus is on six developed economies (Canada, Germany, Italy, Japan, Singapore, and the United
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This paper offers estimates of the per-capita GDP growth trajectories consistent with zero growth in per-capita CO2 emissions using Ordinary Least Squares (OLS) and Instrumental Variables (IVs). The focus is on six developed economies (Canada, Germany, Italy, Japan, Singapore, and the United States) and six emerging economies (China, India, Indonesia, Malaysia, Mexico, and South Korea). To this end, we postulate a model linking the growth of per-capita CO2 emissions to per-capita GDP growth and technology. Given the parameter estimates, we use the model to estimate the growth rate of per-capita GDP that is consistent with zero growth in CO2 emissions.
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Fiscal Multipliers in a Diversifying Economy: Comparing Government Consumption and Infrastructure Investment Effects on Non-Oil GDP in Saudi Arabia a Quarterly SVAR Analysis
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Abdelrahman Mohamed Mohamed Saeed
Econometrics 2026, 14(3), 34; https://doi.org/10.3390/econometrics14030034 - 2 Jul 2026
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Saudi Arabia’s Vision 2030 aims to diversify the economy away from oil by reallocating public expenditure from current consumption toward infrastructure mega-projects. This research estimates and compares the fiscal multipliers of government consumption and government investment on non-oil GDP using quarterly data from
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Saudi Arabia’s Vision 2030 aims to diversify the economy away from oil by reallocating public expenditure from current consumption toward infrastructure mega-projects. This research estimates and compares the fiscal multipliers of government consumption and government investment on non-oil GDP using quarterly data from 2010Q2 to 2026Q1. A vector error correction model with Cholesky identification is employed alongside local projections to ensure robustness. Results indicate that the investment multiplier is substantially larger and more persistent than the consumption multiplier, reaching 2.34 after twelve quarters compared to 0.58 for consumption. A structural break analysis reveals that multipliers have increased markedly since 2016, with the eight-quarter investment multiplier rising from 1.24 pre-Vision 2030 to 2.61 thereafter. Variance decomposition confirms that government investment shocks explain over 27% of non-oil output fluctuations at longer horizons, independent of oil price movements. These findings provide empirical support for the strategic emphasis on capital formation under Vision 2030 and suggest that prioritising infrastructure investment over current expenditure yields superior growth dividends in a diversifying oil economy.
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(This article belongs to the Special Issue Innovations in Bayesian Econometrics: Theory, Techniques, and Economic Analysis)
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A Dynamic Panel Threshold Approach to Decarbonization by Neutral Fiscal Policy: Application to the OECD
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Feridoon Koohi-Kamali, Willi Semmler and Samuel Owusu
Econometrics 2026, 14(3), 33; https://doi.org/10.3390/econometrics14030033 - 2 Jul 2026
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This paper addresses the output and employment impacts of a climate self-financed taxation/subsidy policy on CO2 emission reduction. We model balanced climate fiscal expenditure using a two-regime CO2-based threshold autoregressive model that separates periods of rising emissions by positive CO
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This paper addresses the output and employment impacts of a climate self-financed taxation/subsidy policy on CO2 emission reduction. We model balanced climate fiscal expenditure using a two-regime CO2-based threshold autoregressive model that separates periods of rising emissions by positive CO2 log-differences and of falling emissions by negative CO2 log-differences. Applied to data sets for 16 OECD countries over 23 years (1995–2018), we find that self-financing equal amounts of tax and subsidy over the lifespan of the data set yields a CO2-reducing regime that dominates, with significant threshold and marginal policy impacts on both output and employment. The policy impacts, as shown by the panel data variance decomposition forecast, indicate that the policy shock to total output variance outweighs other effects for up to three years, and to total employment variance for up to four years. The assessment of a two-regime/threshold model of neutral fiscal policy constitutes our contribution to the literature.
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External Debt and Economic Growth: The Role of Institutional Quality in Lower- and Upper-Middle-Income Countries
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Janaki Imbulana Arachchi, M. B. Ranathilaka, Wasantha Athukorala and Shunsuke Managi
Econometrics 2026, 14(3), 32; https://doi.org/10.3390/econometrics14030032 - 30 Jun 2026
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This study examines the moderating and threshold effects of institutional quality on the relationship between external debt and economic growth using panel data from 39 lower- and upper-middle-income countries over the period of 1996–2023. To address econometric challenges commonly found in previous studies—including
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This study examines the moderating and threshold effects of institutional quality on the relationship between external debt and economic growth using panel data from 39 lower- and upper-middle-income countries over the period of 1996–2023. To address econometric challenges commonly found in previous studies—including endogeneity, cross-sectional dependence, and slope heterogeneity—the analysis employs a dynamic common correlated effect (DCCE) estimator and a dynamic panel threshold model (DPTM). The DCCE results indicate that external debt exerts a negative and statistically significant effect on economic growth, whereas institutional quality has a positive effect. Furthermore, the interaction between external debt and institutional quality is positive and significant, suggesting that stronger institutions mitigate the adverse growth effects of external debt. The threshold analysis reveals significant institutional quality thresholds across income groups. For the full sample, the estimated threshold value of institutional quality is 2.74. Disaggregated results indicate thresholds of 1.80 for lower-middle-income countries (LMICs) and 4.33 for upper-middle-income countries (UMICs). Although external debt continues to exert a negative impact on growth in both regimes, the magnitude of this adverse effect declines once institutional quality surpasses the threshold levels. These findings highlight the critical role of institutional quality in shaping the debt–growth nexus. Strengthening governance structures—including improving transparency, rule of law, and fiscal accountability—can help mitigate the growth-reducing effects of external debt and improve countries’ capacity to manage debt sustainability in developing economies.
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Impact of Fourth Industrial Revolution (4IR) Automation on Agricultural Employment in South Africa
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Jenny Mokhaukhau and Phineas Khazamula Chauke
Econometrics 2026, 14(3), 31; https://doi.org/10.3390/econometrics14030031 - 29 Jun 2026
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The Fourth Industrial Revolution (4IR) has introduced modern, high technologies that are automated, such as precision farming, to enhance agricultural production. However, this comes at the cost of human labor being replaced by machines that are deemed efficient. This study investigated the impact
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The Fourth Industrial Revolution (4IR) has introduced modern, high technologies that are automated, such as precision farming, to enhance agricultural production. However, this comes at the cost of human labor being replaced by machines that are deemed efficient. This study investigated the impact of 4IR automation on agricultural employment in South Africa, spanning from 1990 to 2024. To analyze this, the study employed the Johansen test for cointegration and the vector error correction model to test for long-run and short-run dynamics. Stationarity was achieved, and the Johansen test confirmed cointegration. The vector error correction model results revealed that both long-run and short-run relationships between 4IR automation and agricultural employment exist, indicating that human labor is particularly at risk of being replaced by automation, such as advanced agricultural machinery. The results imply that, although automation improved agricultural productivity, it caused an increase in agricultural unemployment within South Africa. Therefore, to balance the advancement of technology and agricultural employment, the study recommends skills improvement and government intervention for enhancing human labor within the agricultural sector.
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Nonlinear Trading-Performance Patterns Among Novice Participants in an Incentivized Trading Simulation
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Alain Finet, Kevin Kristoforidis and Julie Laznicka
Econometrics 2026, 14(2), 30; https://doi.org/10.3390/econometrics14020030 - 22 Jun 2026
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This article analyses trading-performance patterns in a stock market simulation conducted with 134 second-year students at the University of Mons (Belgium) on 11 December 2025. Participants had a virtual capital of 100,000 euros and were free to trade CAC 40 securities without any
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This article analyses trading-performance patterns in a stock market simulation conducted with 134 second-year students at the University of Mons (Belgium) on 11 December 2025. Participants had a virtual capital of 100,000 euros and were free to trade CAC 40 securities without any restrictions on the number or volume of transactions. An academic incentive scheme, combining a participation bonus and bonuses for the three best portfolios, created a tournament-style environment with continuous ranking feedback. This feature is considered as part of the experimental context rather than as a separately identified causal mechanism. We estimate a quadratic model linking performance to activity, measured by the number of mean-centered transactions to reduce the collinearity between the first-degree term and its square, and control exposure via the average percentage of cash in the portfolio, portfolio variability (measured as the standard deviation of portfolio value) and the average trade size. Breusch–Pagan and White tests indicate heteroscedasticity, justifying a robust inference. The results highlight a convex relationship between activity and performance: the marginal association is initially negative but becomes positive above a model-implied upper-tail level corresponding to approximately 46 transactions. This value should not be interpreted as a behavioral level or as a trading rule. The percentage of cash in the portfolio and the average trade size are negatively associated with performance, while the portfolio variability does not show a statistically significant association with performance. Overall, the results indicate heterogeneous trading patterns rather than a single activity–performance profile.
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Open AccessArticle
General Data Protection Regulation (GDPR) and Cross-Border M&A by Chinese E-Commerce Firms
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Aining Sun and IKM Mokhtarul Wadud
Econometrics 2026, 14(2), 29; https://doi.org/10.3390/econometrics14020029 - 22 Jun 2026
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The General Data Protection Regulation (GDPR), adopted by the European Union in 2018, aims to enhance consumer trust and market efficiency by strengthening data protection. The concurrent stringent compliance requirements raise operational costs and could reshape competition by favoring larger firms with greater
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The General Data Protection Regulation (GDPR), adopted by the European Union in 2018, aims to enhance consumer trust and market efficiency by strengthening data protection. The concurrent stringent compliance requirements raise operational costs and could reshape competition by favoring larger firms with greater regulatory capacity. While the GDPR reduces data-related risks and promotes global digital trade through its extraterritorial reach, the potential advantage to larger firms could incentivize strategic responses such as mergers and acquisitions (M&A) to consolidate market power. Given the rapid expansion of Chinese digital firms in e-commerce, social media, and cloud services across the EU, this study examines how the GDPR has affected their cross-border M&A activities between 2014 and 2021. Based on difference-in-difference analysis, the study finds that the GDPR did not have a statistically significant impact on the number or value of mergers and acquisitions by Chinese digital firms in the EU in the short term. This suggests that firms may enhance their institutional adaptability by strengthening their compliance capabilities. However, institutional and cultural differences pose long-term entry barriers for the firms. The study contributes by highlighting how firms adjust internationalization strategies under stringent regulatory regimes, offering policy-relevant insights for governments and regulatory authorities.
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Threshold-Dependent Dominance in Tail Risk Approximation
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Terence D. Agbeyegbe
Econometrics 2026, 14(2), 28; https://doi.org/10.3390/econometrics14020028 - 17 Jun 2026
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Regulatory risk measurement under Basel III’s Fundamental Review of the Trading Book places Expected Shortfall (ES) at the center of market risk capital, yet the fourth-order Edgeworth expansion, still widely used for Value-at-Risk (VaR) and ES calculations, can produce negative densities in the
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Regulatory risk measurement under Basel III’s Fundamental Review of the Trading Book places Expected Shortfall (ES) at the center of market risk capital, yet the fourth-order Edgeworth expansion, still widely used for Value-at-Risk (VaR) and ES calculations, can produce negative densities in the tail regions where these measures concentrate, while saddlepoint approximations preserve positivity but face their own limits in heavy-tailed and sub-Gaussian settings. Whether either method delivers reliable tail estimates in the rare-disaster regimes documented in the empirical consumption-disaster literature therefore remains an open question. We address it by comparing the two approximations across 648 rare-disaster parameter combinations and five additional distributional families (Student-t, Hansen skewed-t, generalised error distribution (GED), two-sided jump mixture, and generalised hyperbolic), and by deriving a closed-form characterisation of the Edgeworth validity envelope. We establish three core findings. First, the validity envelope is bounded above by a sharp kurtosis ceiling at and laterally by a non-monotone skewness boundary peaking at at ; of the rare-disaster grid falls outside it. Second, accuracy is threshold-dependent: Edgeworth dominates at moderate quantiles, saddlepoint at extreme quantiles, with negative-density regions inflating Edgeworth ES error from inside the envelope to outside it. Third, these results reconcile only when point probability, density validity, and integrated-tail accuracy are treated as distinct accuracy criteria. The findings have direct implications for ES-based regulatory capital in heavy-tailed regimes and motivate a regime-conditional rather than universal approximation choice.
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A Natural Copula
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Peter B. Lerner
Econometrics 2026, 14(2), 27; https://doi.org/10.3390/econometrics14020027 - 16 Jun 2026
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Copulas are widely used in financial economics, as well as in other areas of applied mathematics. Yet, there is much arbitrariness in their choice. The author proposes a “natural copula” concept that minimizes the Wasserstein distance between distributions in a space in which
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Copulas are widely used in financial economics, as well as in other areas of applied mathematics. Yet, there is much arbitrariness in their choice. The author proposes a “natural copula” concept that minimizes the Wasserstein distance between distributions in a space in which both distributions are embedded. Transport properties and hydrodynamic interpretation are discussed with two examples of distributions of financial significance. In 2D, a natural copula can be parsimoniously estimated by linear programming methods. A discussion of the construction of multivariate copulas follows. Finally, the quality of the multivariate copula approximation is investigated using the Kolmogorov–Arnold neural network (KAN).
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India’s Macroeconomic Response to Global Shocks: Evidence from Oil Prices, Financial Crisis and COVID-19
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Nikhil Bhardwaj, Ivana Miklošević and Nalinee Chauhan
Econometrics 2026, 14(2), 26; https://doi.org/10.3390/econometrics14020026 - 12 Jun 2026
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In past decades, the macroeconomic stability of India has been tested repeatedly by major global disruptions, including oil price shocks, the 2008 global financial crisis and the COVID-19 pandemic. Analysing how macroeconomic variables respond to these shocks is essential for evaluating external vulnerability
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In past decades, the macroeconomic stability of India has been tested repeatedly by major global disruptions, including oil price shocks, the 2008 global financial crisis and the COVID-19 pandemic. Analysing how macroeconomic variables respond to these shocks is essential for evaluating external vulnerability and policy resilience in emerging economies. Our study provides a comprehensive empirical investigation of the dynamic responses of wholesale price inflation, industrial output, oil prices and exchange rates in India by employing monthly data from January 1993 to December 2024. To examine long-run equilibrium relationships along with short-run adjustment dynamics, the present study employs co-integration analysis within a Vector Error Correction Model (VECM) framework. Further, we applied impulse response functions and forecast error variance decomposition to track volatility spillover mechanisms. Quantile regression and ARCH–GARCH models were further estimated to account for distributional heterogeneity and time-varying volatility. The findings of our study suggested stable long-run linkages among the selected variables, where oil price shocks emerged as a key external source of macroeconomic fluctuations. Short-run dynamics suggested that shocks in oil prices are transmitted primarily through inflation and exchange rate channels and then affect industrial output. Distributional estimates revealed the effects were stronger during stress periods, indicating tail risks that were not captured by the mean-based models. Lastly, volatility analysis confirmed persistent clustering, especially during phases of crisis. Overall, the findings suggest that India’s macroeconomic system remains externally sensitive, with adjustment mechanisms that operate gradually but come under strain during global disruptions. These results underscore the importance of energy risk management and crisis-responsive macroeconomic stabilisation policies.
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Modeling the Dynamic Relationship Between Stock Market Performance and Key Macroeconomic Indicators in Saudi Arabia: An ARDL-ECM Approach
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Mohamed Sharif Bashir and Sharif Mohd
Econometrics 2026, 14(2), 25; https://doi.org/10.3390/econometrics14020025 - 16 May 2026
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This study investigates the short-term and long-term impacts of gross domestic product (GDP), inflation, foreign capital flows, trade balance and interest rate on stock market performance in Saudi Arabia for the period 1990–2023. The autoregressive distributed lag (ARDL) approach and error correction model
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This study investigates the short-term and long-term impacts of gross domestic product (GDP), inflation, foreign capital flows, trade balance and interest rate on stock market performance in Saudi Arabia for the period 1990–2023. The autoregressive distributed lag (ARDL) approach and error correction model (ECM) are employed to empirically examine the short-run and long-run relationships. The ARDL-ECM technique is effective for analyzing cointegration and assessing adjustment processes. Additionally, impulse response function (IRF) analysis based on the vector autoregression (VAR) model, estimated using these macroeconomic indicators, is applied in this paper. This study provides novel insights and addresses emerging gaps in the literature concerning Saudi Arabia as a developing economy. The long-term relationship in the bounds test results confirms its existence. In the long run, inflation and interest rate exert a statistically significant negative effect on stock market performance, while the trade balance has a significant positive impact. GDP and foreign capital inflows do not exhibit statistically significant long-run effects. Short-run dynamics indicate persistence in stock market performance along with significant effects from inflation and interest rate changes, while GDP and foreign capital inflows remain statistically insignificant in the long-run scenario. Forecast error variance decomposition (FEVD) results show that approximately 68.5% of the variation in market performance is explained by its own shocks, followed by foreign capital flows (16.3%) and inflation (8.4%). While foreign capital flow does not exhibit statistical significance in the ARDL long-run estimates, its contribution in variance decomposition highlights its role as an important source of external shocks. These findings are relevant to various stakeholders, including investors and policymakers. Additionally, policy emphasis should be placed on controlling inflation and maintaining stable interest rates while improving trade balance conditions. Although foreign capital flow does not show a direct long-run effect, its role in influencing market variability suggests the need for a stable and well-regulated investment environment.
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Open AccessArticle
Measuring the Return to Online Advertising: Estimation and Inference of Endogenous Treatment Effects
by
Shakeeb Khan, Denis Nekipelov and Justin Rao
Econometrics 2026, 14(2), 24; https://doi.org/10.3390/econometrics14020024 - 12 May 2026
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In this paper we aim to conduct inference on the “lift” effect generated by an online advertisement display: specifically we want to analyze if the presence of the brand ad among the advertisements on the page increases the overall number of consumer clicks
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In this paper we aim to conduct inference on the “lift” effect generated by an online advertisement display: specifically we want to analyze if the presence of the brand ad among the advertisements on the page increases the overall number of consumer clicks on that page. A distinctive feature of online advertising is that the ad displays are highly targeted—the advertising platform evaluates the (unconditional) probability of each consumer clicking on a given ad, which leads to a higher probability of displaying the ads that have a higher a priori estimated probability of click. As a result, inferring thecausal effect of the ad display on the page clicks by a given consumer from typical observational data is difficult. To address this we propose a multi-step estimator that focuses on the tails of the consumer distribution to estimate the true causal effect of an ad display. This “identification at infinity” approach alleviates the need for independent experimental randomization but results in nonstandard asymptotic theory, motivating our novel inference method. To validate our results, we use a set of large-scale randomized controlled experiments that Microsoft has run on its advertising platform. Our dataset has a large number of observations and a large number of variables and we employ LASSO to perform variable selection. Providing a basis for comparison with our estimates, we use a study conducted by Microsoft with approximately 9.3 million search sessions focusing on consumer click behavior across search result pages of a major search engine. Randomized experiments indicate that displaying a brand advertisement increases the probability of visiting the advertiser’s website by about 2.27 percentage points relative to a baseline visit rate of roughly 78 percent. Our non-experimental estimates exhibit broadly similar patterns to those obtained from randomized controlled trials, suggesting that the proposed observational estimator can recover qualitatively comparable treatment effects in large-scale advertising data.
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Open AccessArticle
Internationalization and Financing Decisions of Chinese Enterprises: Evidence from Hong Kong Listings
by
Pujie Lin and Tsz Leung Yip
Econometrics 2026, 14(2), 23; https://doi.org/10.3390/econometrics14020023 - 7 May 2026
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This study explores the impact of internationalization on the financing decisions and finance costs of Chinese enterprises listed in Hong Kong, extending the pecking order theory to an international context. Utilizing data from 785 companies from 2010 to 2020, the research investigates how
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This study explores the impact of internationalization on the financing decisions and finance costs of Chinese enterprises listed in Hong Kong, extending the pecking order theory to an international context. Utilizing data from 785 companies from 2010 to 2020, the research investigates how the degree of internationalization influences corporate finance strategies, with a focus on the mediating role of the pecking order and the moderating effects of international business factors. The findings reveal that while broader internationalization increases finance costs, deeper internationalization reduces them. Legal distance is found to negatively moderate this relationship, whereas the structure of the financial system positively influences it. The results suggest that multinational enterprises with extensive overseas resource allocation demonstrate greater flexibility in financing decisions, particularly in foreign markets characterized by strong investor protection and efficient direct finance mechanisms. Managers should be cautious about pursuing wide geographic expansion without adequate operating depth because a broad but shallow international presence may increase financing frictions. By contrast, deeper resource commitment abroad can strengthen financing flexibility and improve access to lower-cost funds, especially when institutional conditions in the financing market are favorable.
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