Absolute Convergence Research Articles

An investigation into the convergence of economic growth among Indian States and the path ahead

This study offers a comprehensive examination of economic growth and convergence in the Indian States and Union Territories (U.T.) over the period from 1991 to 2020. It investigates absolute, sigma, and conditional convergence within this diverse set of states and utilizes the augmented Solow and extended Solow models to explore conditional convergence dynamics. The empirical findings reveal several significant insights. First, there is no substantial negative correlation between the initial per capita GDP ratio and the average annual growth rate, indicating the absence of absolute convergence across the Indian States and U.T. economies during the study period. These results align with those obtained from sigma convergence analysis, reinforcing the absence of widespread convergence. However, conditional convergence is observed, as evidenced by the rate of conditional convergence (coefficient of initial GDP per capita) estimated at 0.038 among the Indian States and U.T. The presence of conditional convergence implies that while initial conditions matter, other factors, including physical and human capital, population growth, and additional variables, significantly contribute to the growth and convergence of Indian regions. The study concludes that policies aimed at promoting economic growth in the Indian States should prioritize the expansion of the labor force, investments in physical and human capital, and prudent government consumption. Furthermore, fostering an environment that encourages access to new technologies and ideas, maintaining sound macroeconomic management, and increasing investments in human capital formation are essential for sustained growth. Effective resource allocation through prudent budgetary policies and heightened investments in the health sector are recommended. Incentives to reduce fertility rates and adept monetary policy management are also identified as crucial elements for ensuring stability and sustainable growth. In summary, this research underscores the importance of adopting a holistic approach to foster economic growth and convergence in the Indian States. The suggested policy measures create a conducive environment for sustained development and prosperity in this diverse and dynamic region.

Matrix Pencil Optimal Iterative Algorithms and Restarted Versions for Linear Matrix Equation and Pseudoinverse

We derive a double-optimal iterative algorithm (DOIA) in an m-degree matrix pencil Krylov subspace to solve a rectangular linear matrix equation. Expressing the iterative solution in a matrix pencil and using two optimization techniques, we determine the expansion coefficients explicitly, by inverting an m×m positive definite matrix. The DOIA is a fast, convergent, iterative algorithm. Some properties and the estimation of residual error of the DOIA are given to prove the absolute convergence. Numerical tests demonstrate the usefulness of the double-optimal solution (DOS) and DOIA in solving square or nonsquare linear matrix equations and in inverting nonsingular square matrices. To speed up the convergence, a restarted technique with frequency m is proposed, namely, DOIA(m); it outperforms the DOIA. The pseudoinverse of a rectangular matrix can be sought using the DOIA and DOIA(m). The Moore–Penrose iterative algorithm (MPIA) and MPIA(m) based on the polynomial-type matrix pencil and the optimized hyperpower iterative algorithm OHPIA(m) are developed. They are efficient and accurate iterative methods for finding the pseudoinverse, especially the MPIA(m) and OHPIA(m).

Analysis of Economic Convergence in the European Union

Abstract The article analysis the economic convergence of member states of the European Union through ten main macroeconomic indicators. Employing a combination of statistical methodologies encompassing, such as descriptive statistics, multiple regression and ANOVA analysis, the research intends to reveal an updated outlook and also the big picture of economic convergence process within the European Union. Its results, analysing economic indicators, show the serious convergence trends between economies of EU-27 member states in general, but particularising, we can observe variations of the progress for each member state. Also, has been remarked that when the GDP per capita has increased in most of the member states, the differences have significatively decreased, these still exist. Moreover, convergence is discernible in inflation rates, unemployment rates, and trade balances. In the same way, the analysis pointed out also the differences that exist between member states, which have to be treated and separated, but together through inclusion policies, social and economic, to have as a final goal, the absolute convergence to be realised through shorter period of time than the actual trend. Premises, likewise, the realities that exist in the present can lead to a deeper and feasible convergence, even if it can offer the growing rhyme in comparing some states with others. In conclusion, the article highlights the fact that is much more than necessary that political strategies of member states individually, and also member states of the European Union to get together regarding aligning to the best economic and social level.

Dynamics of Distribution, Industry Associations and Convergence Analysis in China’s Digital Economy Development

This paper measures the scale of digital industrialization and industrial digitalisation in 30 provinces in China from 2002 to 2017 based on the input-output table, and analyses the evolution dynamics, industrial association characteristics and their convergence using Kernel density estimation, Dagum Gini coefficient, and economic convergence model. The results of the study show that there is a regional imbalance in the development of China’s digital economy with the coast being lower than the inland; the difference in the distribution of dynamics within the four major economic regions is gradually expanding, with the most obvious in the central and western regions; the characteristics of the digital industrialization correlation show the evolution path of “energy industry → service industry → manufacturing industry → agriculture”; there is a convergence in all aspects of the digital economy in the country, and the economic convergence model is applied to each economic region. There is σ — convergence in all aspects of the digital economy in the country as a whole, and the results of σ — convergence in each economic region are somewhat different; β — absolute convergence exists in the country as a whole and in each economic region, and only the central and northeastern parts of the country have insignificant results in conditional β convergence. The overall rate of convergence is characterized by “East > West > Central > Northeast”.

An iterative method for robust solutions to nonlinear Volterra integral equations: Stability, convergence, and practical applications

<p>The paper introduces an iterative method for solving nonlinear Volterra integral equations and analyzes its convergence, stability, and application through examples. It expresses the general nonlinear Volterra integral equation as a series and decomposes the nonlinear operator to derive a recursive formula for the proposed iterative method. The method ensures absolute and uniform convergence, with stability analysis conducted to ensure bounded errors in the presence of perturbations. Convergence analysis utilizes the Lipschitz condition, demonstrating the uniform convergence of the solution series. Illustrative examples, including power nonlinearity and trigonometric functions, validate the stability and convergence of the method. Through graphical representations, convergence analyses for specific integral equations demonstrate the method’s effectiveness and applicability in solving diverse nonlinear integral equations. Overall, the paper contributes a robust iterative method with insights into its stability and convergence properties, supported by practical examples.</p>

Convergence of Health Expenditure and Health Outcomes in Central Europe and the Baltic Region

ABSTRACT This research work examines the convergence of health expenditure in Central Europe and the Baltic region. The study reveals the absolute convergence in per capita health expenditures, indicating similar health outcomes for all eleven countries of the region. However, there is a divergence in health expenditure and outcomes across the eleven countries. Notably, public health expenditure diverges in Denmark, Estonia, Finland, and Norway, while, private health expenditure converges in Poland, Russia, and Sweden. Despite an overall convergence in life expectancy at birth across the countries, mortality rates due to non-communicable diseases only converge in Estonia.

Convergence in Financial Development and Growth

We evaluate the cross-country convergence of financial development and its relationship with GDP growth. Financial inclusion variables have been widely converged across countries, and the catch-up effect of countries with poor financial coverage mainly drives the convergence. In contrast, financial development measures — including domestic credit, liability, mutual fund size, and stock market capitalization — have diverged since 1985 despite the absolute convergence in GDP and financial inclusion. The GDP growth rates strongly correlate with the change in financial development but not the improvement in financial inclusion.

Spatiotemporal Pattern and Spatial Convergence of Land Use Carbon Emission Efficiency in the Pan-Pearl River Delta: Based on the Difference in Land Use Carbon Budget

Research on land use carbon emission efficiency (LUCEE) in the Pan-Pearl River Delta (PPRD) can aid in formulating regional differentiated carbon reduction strategies. In this work, the inversion of carbon emissions using night-time light (NTL) data and the modified Carnegie Ames Stanford Approach (CASA) model were used to measure the net carbon emissions from land use (NCELU). On this basis, the SBM-undesirable model was used to assess the LUCEE. Additionally, the exploratory spatial data analysis (ESDA), Dagum Gini coefficient, and spatial convergence model were further introduced to analyze the spatial correlation, regional differences, and convergence trend of the LUCEE. Findings indicate that: (1) The NCELU showed an increasing fluctuation. During the period of 2006–2020, the NCELU increased from −168.58 million tons to −724.65 million tons. (2) The LUCEE exhibited a three-phase fluctuating downward trend of “decrease–rise–decrease”. The LUCEE first decreased from 0.612 in 2006 to 0.544 in 2008, then gradually increased to 0.632 in 2016, and finally decreased to 0.488 in 2020. Spatially, the LUCEE manifested a distribution characteristic of “high in the north and south, low in the middle”, with distinct spatial clustering features. (3) The overall Gini coefficient in the study period increased from 0.1819 to 0.2461. The primary contributor to the overall difference over the entire sample period was hypervariable density. (4) The PPRD and its various subregions displayed significant features of absolute and conditional β convergence. The speed of regional convergence from fastest to slowest was central > west > east, with the absolute convergence speeds of 0.0505, 0.0360, and 0.0212, respectively. Finally, policy recommendations are proposed to achieve regional carbon neutrality for the PPRD.

Advancing Green TFP Calculation: A Novel Spatiotemporal Econometric Solow Residual Method and Its Application to China’s Urban Industrial Sectors

The Solow residual method, traditionally pivotal for calculating total factor productivity (TFP), is typically not applied to green TFP calculations due to its exclusion of undesired outputs. Diverging from traditional approaches and other frontier methodologies such as Data Envelopment Analysis (DEA) and Stochastic Frontier Analysis (SFA), this paper integrates undesired outputs and three types of spatial spillover effects into the conventional Solow framework, thereby creating a new spatiotemporal econometric Solow residual method (STE-SRM). Utilizing this novel method, the study computes the industrial green TFPs for 280 Chinese cities from 2003 to 2019, recalculates these TFPs using DEA-SBM and Bayesian SFA for the same cities and periods, and assesses the accuracy of the STE-SRM-derived TFPs through comparative analysis. Additionally, the paper explores the statistical properties of China’s urban industrial green TFPs as derived from the STE-SRM, employing Dagum’s Gini coefficient and spatial convergence analyses. The findings first indicate that by incorporating undesired outputs and spatial spillover into the Solow residual method, green TFPs are computable in alignment with the traditional Solow logic, although the allocation of per capita inputs and undesired outputs hinges on selecting the optimal empirical production function. Second, China’s urban industrial green TFPs, calculated using the STE-SRM with the spatial Durbin model with mixed effects as the optimal model, show that cities like Huangshan, Fangchenggang, and Sanya have notably higher TFPs, whereas Jincheng, Datong, and Taiyuan display lower TFPs. Third, comparisons of China’s urban industrial green TFP calculations reveal that those derived from the STE-SRM demonstrate broader but more concentrated results, while Bayesian SFA results are narrower and less concentrated, and DEA-SBM findings sit between these extremes. Fourth, the study highlights significant spatial heterogeneity in China’s urban industrial green TFPs across different regions—eastern, central, western, and northeast China—with evident sigma convergence across the urban landscape, though absolute beta convergence is significant only in a limited subset of cities and time periods.

Development and validation of a nomogram for predicting poor operative visibility during FESS in Chinese adult patients with CRS.

The purpose of this study is to develop and evaluate a nomogram that is capable of predicting poor operative visibility during functional endoscopic sinus surgery. To identify potential risk factors, patients with chronic rhinosinusitis who underwent functional endoscopic sinus surgery (FESS) between January 2019 and December 2022 were selected from our hospital's electronic medical record system. Data on general patient information, clinical manifestations, clotting-related test indices, Lund-Machay score of sinuses CT scanning, Lund-kennedy score of nasal endoscopies, anesthesia methods, intraoperative blood pressure and heart rate, and Boezaart bleeding score were collected. Minimum absolute convergence and selection operator (LASSO) regression, as well as multivariate logistic regression, were used to determine the risk factors. A nomogram was developed in order to predict poor operating visibility during FESS, and its performance was evaluated utilizing both the training and verification datasets via various measures including receiver operating characteristic (ROC) curve analysis, area under the curve (AUC), Hosmer-Lemeshow goodness-of-fit test, calibration curve, and decision curve analysis. Of the 369 patients who met the inclusion criteria, 88 of them exhibited POV during FESS. By deploying LASSO and multivariate logistic regression analyses, six risk factors were identified and used to construct a nomogram for predicting POV during FESS. These factors include prothrombin time (PT), prothrombin activity (PTA), Lund-Mackay score (LMS), Lund-Kennedy score (LKS), anesthetic method, and intraoperative hypertension. The AUC of the training set was found to be 0.820 while that of the verification set was 0.852. The Hosmer-Lemeshow goodness-of-fit test and calibration curve analysis revealed good consistency between predicted and actual probabilities. Also, the decision curve demonstrated that the nomogram had a high degree of clinical usefulness and net benefit. The constructed nomogram has a strong ability to predict the poor intraoperative field in patients with chronic rhinosinusitis, which can help preoperative judgment of high-risk patients and provide evidence for perioperative management and preoperative plan formulation.

Absolute Convergence of Output per Worker in Manufacturing and the Economy as a Whole

En este artículo revisitamos la evidencia empírica de la hipótesis de la convergencia absoluta en el crecimiento entre países en 1950-2019, poniendo el foco en el producto por trabajador. También ponemos a prueba la hipótesis de Rodrik (2013) de convergencia absoluta en el producto por trabajador en la industria manufacturera utilizando una base nueva construida por los autores, que por primera vez lo mide en dólares de igual de poder compra, para así poder investigar su relación con la convergencia en el producto por trabajador en la economía en su conjunto en 1970-2018. Encontramos evidencia robusta de convergencia absoluta en el producto por trabajador de la economía en su conjunto a partir del año 2000 y rechazamos sistemáticamente la hipótesis de Rodrik de convergencia absoluta en la industria manufacturera sin convergencia en la economía en su conjunto.

A new approach for measuring poverty or social exclusion reduction in European NUTS 2 regions

This paper examines the problem of poverty or social exclusion reduction for NUTS 2 regions in the European Union over the years 2005–2015. To do so, we extend the concept of absolute poverty convergence to conditional poverty β-convergence and use a quantile regression approach to provide a broader assessment of the heterogeneous relationships between poverty and some economic factors. We consider spatial dependence between neighbouring regions using appropriate spatial econometric specification. We focus on regional performance in tackling poverty or social exclusion using a novel indicator based on the efficiency theory and examine potential heterogeneity in regions’ ability to fight poverty. These differences are analysed in detail considering instabilities in the relationship between regional performances and a relevant asset for policy effectiveness as the quality of institutions. Our findings can help policy makers to better understand factors behind poverty reductions and develop more responsive policies at different institutional levels.

MIXED PROBLEM FOR A NONLINEAR IMPULSIVE DIFFERENTIAL EQUATION OF PARABOLIC TYPE

In this paper, we consider a nonlinear impulsive parabolic type partial differential equation with nonlinear impulsive conditions. Dirichlet type boundary value conditions with respect to spatial variable is used, and eigenvalues and eigenfunctions of the spectral problem are founded. The Fourier method of the separation of variables is applied. A countable system of nonlinear functional equations is obtained with respect to the Fourier coefficients of the unknown function. A theorem on a unique solvability of the countable system of nonlinear functional equations is proved by the method of successive approximations. A criteria of uniqueness and existence of a solution for the nonlinear impulsive mixed problem is obtained. A solution of the mixed problem is derived in the form of the Fourier series. The absolute and uniform convergence of the Fourier series is proved.

Convergence of shadow economy across U.S. states

ABSTRACT Using a novel shadow economy measure constructed from a two-sector dynamic deterministic general equilibrium model, this paper provides the first piece of evidence on the convergence dynamics of the shadow economy at the U.S. state level over the period 1999–2019. The result of the panel club convergence test demonstrates the absence of absolute convergence but also identifies the presence of six club memberships without an apparent regional conglomeration. Further analysis based on the ordered logit regression uncovers that factors such as gross state product, the share of higher education, government size, the share of union participation, capital tax rate, institutional quality, and unemployment rate significantly influence the club membership of the shadow economy. Understanding these findings is imperative for developing policies to curtail the spread of shadow economies across the states in the U.S.

An Analysis of Sequence and Series

This article provides a comprehensive exploration of sequences and series, fundamental concepts in mathematics with wide-ranging applications. Starting with an introduction to sequences, including arithmetic and geometric sequences, the discussion extends to finite sequences and n-tuple sequences. Arithmetic and geometric series are explored, with formulas for their sums. The article delves into the properties of sequences and series, discussing convergence, divergence, and absolute convergence. Various types of sequences, such as bounded and monotonic sequences, are defined, and the Cauchy Criterion is introduced as a criterion for the existence of the limit of a sequence. Elementary facts about series, including absolute convergence and the number e as the sum of a series, are covered. Additionally, the concept of sequences of functions is introduced. The article concludes by emphasizing the significance of sequences and series in fields like higher mathematics, art, science, technology, and finance, showcasing their crucial role in decision-making, financial analysis, and risk assessment across diverse disciplines.

Poverty convergence clubs

AbstractGlobal eradication of extreme poverty requires absolute convergence of poverty rates worldwide towards zero. Empirical analysis of poverty data for 100 emerging and developing countries over four decades reveals that such a goal is likely to remain elusive. Rather than absolute convergence, we find club convergence: countries' long‐run poverty rates cluster into several distinct clubs, whose number depends on the specific poverty dimension considered. Only the lowest‐poverty club exhibits poverty rates approaching zero by the end of the sample. In contrast, the highest‐poverty club, which accounts for nearly half the world's poor, evokes a poverty trap: its average poverty barely budged over the entire period examined. Overall, income—its initial level and, especially, its growth rate—matters more than inequality for shaping countries' club membership, particularly for the highest‐poverty club. Nevertheless, inequality plays a substantive role for membership in the intermediate‐poverty clubs, which achieved the greatest poverty reduction.

Measures of Relative and Absolute Convergence and Pro‐poor Growth with an Illustration based on China (2010–2018)

Measures of Relative and Absolute Convergence and Pro‐poor Growth with an Illustration based on China (2010–2018)

ANALISIS POTENSI KONVERGENSI EKONOMI NEGARA ANGGOTA ASEAN-10 TAHUN 2015-2021 DAN FAKTOR-FAKTOR YANG MEMPENGARUHINYA

In 2015 is the year of the acceleration of the establishment of the ASEAN Economic Community (AEC), therefore it is necessary to analyze the economy of each member country based on factors that affect the convergence process. This study aims to analyze the level of convergence of economic growth among ASEAN-10 member countries in 2015-2021. The data used is secondary data obtained from the world bank website. The analytical methods used in this study are sigma convergence and beta convergence. The calculation of sigma convergence uses mathematical analysis of the coefficient of variation of GDP per capita of ASEAN-10 member countries. While the calculation of beta convergence uses panel data regression analysis with a fixed effect model approach. The results showed that there was no sigma convergence among ASEAN-10 member countries, indicating that there was no decrease in inequality among member countries. The results of the analysis on beta convergence show that there is absolute and conditional beta convergence at a rate of 7,5% and 3,1%. It was found that the Foreign Direct Investment and Total Labor Force variables did not have a significant effect, while the Trade Openness variable had a significant effect.

Research on structural modulus inversion method of asphalt pavement based on BP neural networ

The current inversion methods based on pattern recognition method, database search method, genetic algorithm and other inversion methods are difficult to solve the absolute convergence problem of structural modulus inversion for asphalt pavements with more than three layers, while the deep learning models and methods widely used in the scenarios of image recognition, speech recognition, etc. as well as the ways to implement them have been increasingly improved, and they can be applied to solve the problem of structural modulus inversion for asphalt pavements. This study aims to solve the modulus inversion problem of multi-layer asphalt pavement structures, obtaining enough theoretical bending basin data of asphalt pavement structures as training samples through mechanical theory and programming calculations, and using the BP neural network model to train the prediction model of structural layer modulus inversion. The test results show that the BP neural network inverse asphalt pavement structural modulus model established in this paper can not only get the prediction results quickly and effectively, but also the prediction results have high accuracy, which provides an effective way for solving the modulus inversion problem of asphalt pavement structure with more than three layers by using the BP neural network to solve the pain point and bottleneck problems in the industry.

Bayesian physical–statistical retrieval of snow water equivalent and snow depth from X- and Ku-band synthetic aperture radar – demonstration using airborne SnowSAr in SnowEx'17

Abstract. A physical–statistical framework to estimate snow water equivalent (SWE) and snow depth from synthetic aperture radar (SAR) measurements is presented and applied to four SnowSAR flight-line data sets collected during the SnowEx'2017 field campaign in Grand Mesa, Colorado, USA. The physical (radar) model is used to describe the relationship between snowpack conditions and volume backscatter. The statistical model is a Bayesian inference model that seeks to estimate the joint probability distribution of volume backscatter measurements, snow density and snow depth, and physical model parameters. Prior distributions are derived from multilayer snow hydrology predictions driven by downscaled numerical weather prediction (NWP) forecasts. To reduce the signal-to-noise ratio, SnowSAR measurements at 1 m resolution were upscaled by simple averaging to 30 and 90 m resolution. To reduce the number of physical parameters, the multilayer snowpack is transformed for Bayesian inference into an equivalent one- or two-layer snowpack with the same snow mass and volume backscatter. Successful retrievals meeting NASEM (2018) science requirements are defined by absolute convergence backscatter errors ≤1.2 dB and local SnowSAR incidence angles between 30 and 45∘ for X- and Ku-band VV-pol backscatter measurements and were achieved for 75 % to 87 % of all grassland pixels with SWE up to 0.7 m and snow depth up to 2 m. SWE retrievals compare well with snow pit observations, showing strong skill in deep snow with average absolute SWE residuals of 5 %–7 % (15 %–18 %) for the two-layer (one-layer) retrieval algorithm. Furthermore, the spatial distributions of snow depth retrievals vis-à-vis lidar estimates have Bhattacharya coefficients above 94 % (90 %) for homogeneous grassland pixels at 30 m (90 m resolution), and values up to 76 % in mixed forest and grassland areas, indicating that the retrievals closely capture snowpack spatial variability. Because NWP forecasts are available everywhere, the proposed approach could be applied to SWE and snow depth retrievals from a dedicated global snow mission.