Nonlinear Factor Model Research Articles

Health outcome convergence and the roles of public health financing and governance in Africa.

Progress in health outcomes across Africa has been uneven, marked by significant disparities among countries, which not only challenges the global health security but impede progress towards achieving the United Nations' Sustainable Development Goals 3 and 10 (SDG 3 and SDG 10) and Universal Health Coverage (UHC). This paper examines the progress of African countries in reducing intra-country health outcome disparities between 2000 and 2019. In other words, the paper investigates the convergence hypothesis in health outcome using a panel data from 40 African countries. Data were sourced from the World Development Indicators, the World Governance Indicators, and the World Health Organization database. Employing a non-linear dynamic factor model, the study focused on three health outcomes: infant mortality rate, under-5 mortality rate, and life expectancy at birth. The findings indicate that while the hypothesis of convergence is not supported for the selected countries, evidence of convergence clubs is observed for the three health outcome variables. The paper further examine the factors contributing to club formation by using the marginal effects of the ordered logit regression model. The findings indicate that the overall impact of the control variables aligns with existing research. Moreover, governance quality and domestic government health expenditure emerge as significant determinants influencing the probability of membership in specific clubs for the child mortality rate models. In the life expectancy model, governance quality significantly drives club formation. The results suggest that there is a need for common health policies for the different convergence clubs, while country-specific policies should be implemented for the divergent countries. For instance, policies and strategies promoting health prioritization in national budget allocation and reallocation should be encouraged within each final club. Efforts to promote good governance policies by emphasizing anti-corruption measures and government effectiveness should also be encouraged. Moreover, there is a need to implement regional monitoring mechanisms to ensure progress in meeting health commitments, while prioritizing urbanization plans in countries with poorer health outcomes to enhance sanitation access.

Improving the explainability of autoencoder factors for commodities through forecast-based Shapley values

Autoencoders are dimension reduction models in the field of machine learning which can be thought of as a neural network counterpart of principal components analysis (PCA). Due to their flexibility and good performance, autoencoders have been recently used for estimating nonlinear factor models in finance. The main weakness of autoencoders is that the results are less explainable than those obtained with the PCA. In this paper, we propose the adoption of the Shapley value to improve the explainability of autoencoders in the context of nonlinear factor models. In particular, we measure the relevance of nonlinear latent factors using a forecast-based Shapley value approach that measures each latent factor’s contributions in determining the out-of-sample accuracy in factor-augmented models. Considering the interesting empirical instance of the commodity market, we identify the most relevant latent factors for each commodity based on their out-of-sample forecasting ability.

Using moderated nonlinear factor models to adjust for differential item functioning in the Student-Teacher Relationship Scale from kindergarten to Grade 6

Prior research has demonstrated that children form developmentally salient relationships with teachers and that these relationships are uniquely predictive of subsequent functioning both in and outside of school. However, prior work estimating trajectories and predictors of teacher-student relationship quality has failed to test and adjust for bias in questionnaire items. The present study used longitudinal data from the NICHD Study of Early Child Care and Youth Development (SECCYD; N = 1140) to test and adjust for measurement bias in the Student-Teacher Relationship Scale (STRS; Pianta, 2001) across grades (K–6) and sociodemographic characteristics (i.e., birth sex, race/ethnicity, family income-to-needs ratio, and maternal education) to generate less biased estimates of trajectories of teacher-student relationship quality. Results identified differential item functioning for three of seven STRS items assessing conflict and three of eight STRS items assessing closeness, with items functioning differentially across child grade, birth sex, race/ethnicity, and maternal education level. Comparisons of growth models using non-adjusted and adjusted STRS scores highlight substantive differences between scoring approaches, such that the effects of race/ethnicity, maternal education, and maternal sensitivity on teacher-student relationship quality were masked prior to adjusting for item bias. These findings demonstrate the importance of testing and correcting for item bias in questionnaire-based assessments of teacher-student relationship quality to ensure valid conclusions.

Real‐time weakness of the global economy

SummaryWe propose an empirical framework to measure the real‐time weakness of the global economy. This framework relies on nonlinear factor models to identify recessionary and expansionary episodes, fitted to several macroeconomic variables, for the largest advanced and emerging economies. The country‐specific inferences are then combined to construct both a Global Weakness Index and a Global Intensity Index. As new economic data become available from different regions, this information is continually updated to provide high‐frequency, real‐time insights into (i) the strength of the global economy, (ii) the economic regions supporting this strength, (iii) country‐specific and global risk assessments, and (iv) the intensity of recessionary and expansionary episodes.

Spatial and temporal convergence of provincial coal mine safety accidents and production and their influencing factors: Data from 23 coal-producing provinces in China (2005–2021)

As a high-risk industry, coal mine safety accidents can create significant loss of life and property to the nation and its people. In this work, a nonlinear time-varying factor model was adopted to investigate the spatial and temporal variation rule of coal mine safety accidents and coal production in 23 provinces of China from 2005 to 2021. The driving factors of coal mine safety accidents in 2005, 2010, 2015 and 2020 were analyzed using the geographical detector method. We further obtained the explanatory power of the primary factors and the change process of interaction. The findings showed that there are convergence clubs for both the number of coal mine safety accidents and coal production in the Chinese provinces. However, the geographical distribution of the convergence clubs varied. The geographical detector results indicated that coal mine safety accidents are affect by a combination of factors. The explanatory power of each factor for coal mine safety accidents changed over time. Notably, the explanatory power of coal production for coal mine safety accidents decreased. Industry structure, salary, security inputs, coal consumption and gross domestic product (GDP) played a significant role. The lever of impact of each factor on coal mine safety accidents was enhanced after interaction. The relationship between the factors entailed nonlinear enhanced interaction. The research findings not only contribute to a greater understanding of the macroscopic patterns of accident occurrence but also increase the awareness of the government and enterprises regarding the driving factors of coal mine safety accidents. Furthermore, such research holds crucial significance for precise prevention and control of coal mine safety accidents.

Physician density: will we ever close the gap?

ObjectivePhysician density is a crucial element of a well-functioning health system. Previous research has investigated factors affecting country-level physician supply. To date, however, no evidence has been provided about the patterns of convergence in physician density among countries. This paper thus tested club convergence in physician density in 204 countries worldwide from 1990 to 2019. A nonlinear time-varying factor model was adopted to identify potential clubs, wherein groups of countries tend to converge towards the same level of physician density. Our primary purpose was to document the potential long-lasting disparity in future global physician distribution.ResultsDespite physician density increasing in all regions globally from 1990 to 2019, we found no evidence in favor of the hypothesis of global convergence. Conversely, the clustering algorithm successfully identified three main patterns (i.e., three final clubs). With few exceptions, the results indicated an uneven physician distribution between the majority of North and Sub-Saharan African countries (where physician density would remain well below the estimated threshold of at least 70% of the Universal Health Coverage Services Index) and the rest of the world. These findings support the WHO's global strategy to reverse the chronic under-investment in human resources for health.

Health outcome convergence in Africa: the roles of immunization and public health spending

BackgroundReducing health outcomes disparities in Africa is a major concern for policymakers. Inter-country disparities in Africa is well documented. However, little is known about the accurate trajectory of these disparities over time. Thus, this paper investigates the convergence hypothesis in health outcomes in 40 African countries using data from the World Development Indicators. The study used panel data from 2000 to 2019.MethodThe study employs a nonlinear time-varying factor model to test the convergence hypothesis on infant mortality rate, under-five mortality, and life expectancy at birth. Then, we use the marginal effects of the ordered logit regression model to investigate the factors that explain club memberships.ResultsThe findings showed the absence of overall convergence for the three variables of interest. However, we identified the presence of convergence clubs. Moreover, we observed substantial gaps between the estimated clubs. The marginal effect results reveal that real GDP per capita, population structure, urbanization, trade, access to basic sanitation, and external health expenditure are essential to club formation. In addition, DTP immunization and the general government health expenditure as a percentage of the general government expenditure (our Abuja Declaration instrument) also play a significant role in explaining the club membership.ConclusionThe findings suggest that policymakers should develop and implement targeted club-specific health policies. Furthermore, interventions to promote increased immunization, particularly among children, should be encouraged. Governments should also make substantial efforts to increase the share of their national budget allocated to the health sector by at least 15 percent.

Financial and Macroeconomic Data Through the Lens of a Nonlinear Dynamic Factor Model

Through the lens of a nonlinear dynamic factor model, we study the role of exogenous shocks and internal propagation forces in driving the fluctuations of macroeconomic and financial data. The proposed model 1) allows for nonlinear dynamics in the state and measurement equations; 2) can generate asymmetric, state-dependent, and size-dependent responses of observables to shocks; and 3) can produce time-varying volatility and asymmetric tail risks in predictive distributions. We find evidence in favor of nonlinear dynamics in two important U.S. applications. The first uses interest rate data to extract a factor allowing for an effective lower bound and nonlinear dynamics. Our estimated factor coheres well with the historical narrative of monetary policy. We find that allowing for an effective lower bound constraint is crucial. The second recovers a credit cycle. The nonlinear component of the factor boosts credit growth in boom times while hinders its recovery post-crisis. Shocks in a credit crunch period are more amplified and persist for longer compared with shocks during a credit boom.

Health expenditure convergence and the roles of trade and governance in Africa

This study investigates the convergence hypothesis in health expenditures in 40 African countries over the 2000–2019 period. The new non-linear dynamic factor model is used on panel data extracted from the World Development Indicator and the World Governance Indicator. We consider two categories of health expenditures: the domestic general government health expenditure as a percentage of government expenditure and the domestic general government health expenditure per capita. The results show the absence of full panel convergence for the two indicators used. However, there is evidence of convergence clubs. The overall marginal effect of the control variables is consistent with the existing literature. The results further show a strong influence of trade in attaining convergence among the clubs for both models. However, governance quality only affects the probability of converging in a club for the general government health expenditure as a percentage of government expenditure model. The findings suggest that policies on promoting health expenditure convergence should pursue initiatives that encourage trade. Efforts should also be targeted to improve the quality of governance.

The Convergence in Greenhouse Gas Emissions Across G-7 Countries

Environmental degradation, such as climate crisis, global warming, etc., is one of the crucial issues for countries. Studies in the literature analyze the convergence in environmental degradation regarding the environmental convergence hypothesis using different indicators such as carbon dioxide emissions, ecological footprint, etc. to identify the differences in environmental quality across countries. This study tests the environmental convergence hypothesis for G-7 countries over the period 1997-2018. To do so, we use greenhouse gas emissions per capita as an indicator of environmental degradation and apply non-linear dynamic factor model developed by Phillips and Sul (2007). According to the results, countries do not converge to a single equilibrium point. However, Phillips and Sul (2007) convergence methodology allows us to identify possible convergence clubs. The club clustering algorithm identifies three convergence clubs, each converging to a different steady-state. Club 1, which converges to higher greenhouse gas emissions per capita level, includes Canada and United States, whereas Club 2 includes Germany and Japan, and Club 3 includes France, Italy, and the United Kingdom. The results confirm that the that the environmental convergence hypothesis does not hold for G-7 countries.

On the Club Convergence in China’s Provincial Coal Consumptions: Evidence from a Nonlinear Time-Varying Factor Model

Coal has been the fundamental energy source supporting China’s energy supply and consumption. This paper examines convergence clubs for per capita coal consumption among 30 provinces of China between 1997 and 2019 by means of a nonlinear time-varying factor model. Meanwhile, the ordered probit model is further used to identify the causes affecting convergence. The results of analyses of data strongly support the existence of convergence clubs, indicating that there are four convergence clubs and one divergence group at the interprovincial level. Among the factors that potentially influence provincial coal consumption, the GDP-per capital, industrial structure, intensity of environment regulations and carbon emissions are positively related to per capita coal consumption, while investment in fixed assets, degree of openness to the outside world and technological progress are negatively related to per capita coal consumption. Increases in GDP-per capital, industrial structure, intensity of environment regulations and carbon emissions enhance the odds of belonging to a high coal consumption intensity club. Increases in investment in fixed assets, degree of openness to the outside world and technological progress reduce the odds of belonging to a high coal consumptions intensity club. These findings help policy makers to set coal production and consumption targets for different regions and reduce the differences in coal consumption across regions.

Which (Nonlinear) Factor Models?

Which (Nonlinear) Factor Models?

Operational management efficiency and club convergence of Chinese state-owned toll road companies: A three-stage SBM-DEA model

Based on the panel data of 33 Chinese state-owned toll road companies (CSTCs) from 2013 to 2019, this study evaluates companies' operational management efficiency using a three-stage SBM-DEA model that can purge the effects of environmental factors and statistical noise. On this basis, a nonlinear time-varying factor model is then used to conduct a club convergence analysis of the operational management efficiency of CSTCs. The results show that the mean value of the operational management efficiency of CSTCs is 0.938, and the operational management efficiency is underestimated to varying degrees if environmental factors and statistical noise are not considered. The operational management efficiency of CSTCs shows spatial imbalance and temporal stability. The club convergence test indicates that there are three potential club clusters for the operational management efficiency of CSTCs, and it presents a “blockchain” clustering distribution. The findings of this study extend the research scope of managerial efficiency and have practical significance for helping CSTCs achieve high-quality and more efficient development.

Testing for Convergence Innovation and Club Clustering in Selected Economies 1995-2017

Innovation convergence is a deterministic process resulting from the change in micro and macro innovation determinants. It is characterized by firms' search for innovative opportunities in other economic sectors and in their development from mining through heavy industry to material processing sector, discovering new technologies that connect individual products to a more integrated global system, diversifying, ensuring technical scope growth, and start-ups contributing to new managerial leadership. The aim of this study is to contribute to our knowledge of convergence innovation by providing empirical evidence on it. To this purpose, we use a nonlinear time-varying factor model to test for convergence innovation and countries' club clustering. For the sample of 29 countries from 1995 to 2017, we identify two significant convergence clubs and one divergent group (Cyprus, Czech Republic, and The Netherlands). The empirical evidence indicates that innovation singularity could appear as a significant barrier and limiting factors for firms' and countries' growth in the future. Design and new product development trends in these countries follow a different decoupling path from the rest of the sample. Policymakers and practitioners should carefully evaluate innovation determinants and constraints (decoupling drivers) in setting up innovation policies on a micro and macro level.

Statistical Measurements and Club Effects of High-Quality Development in Chinese Manufacturing

Advanced manufacturing is the pillar for building a modern economic system. We measured the level of high-quality development of manufacturing (HQDM) in China, and found that it has gone through the three stages of expansion, cultivation, and promotion. Spatially, it is characterized as "high in the east, low in the west" and "fast in the west, slow in the east", and presents non-equilibrium characteristics. To overcome the subjective bias introduced by artificially set clubs, we utilize a data-driven nonlinear time-varying factor model for clustering into four convergent clubs, where provinces with higher intensity of environmental regulation and environmental preference tend to move closer to the clubs with a higher level of HQDM. We reveal the convergence patterns and regional differences in HQDM, which provides a new perspective for determining the trends of high-quality manufacturing development, thus allowing for policy recommendations targeted at narrowing the manufacturing development gap.

Research on club convergence effect and its influencing factors of per capita energy consumption: Evidence from the data of 243 prefecture-level cities in China

Energy consumption plays an important role in supporting economic growth. As the largest developing country in China, the uncoordinated energy consumption among regions has seriously affected economic growth and the realization of energy strategic goals. Based on the data of per capita energy consumption of 243 prefecture-level cities in China from 2005 to 2019, the nonlinear time-varying factor model and its clustering algorithm are adopted to test the club convergence effect of urban per capita energy consumption, and the Ordered Probit model is further used to reveal their influence factors. The research shows that there are 4 convergent clubs and 1 divergent club in 243 prefecture-level cities in China, and it is determined that initial energy endowment, the level of urban industrialization structure, the level of opening to the outside world and per capita GDP are the influencing factors on the convergence of per capita energy consumption. The research conclusions can provide a basis and reference for realizing the transformation of energy consumption between regions, and then promoting the coordinated development of regions.

Study on the Spatial Convergence Club and Growth Momentum of China’s Regional Economies

The purpose of this paper is to clarify the convergence pattern of China’s regional economies, explore the driving force of their coordinated development, and provide policy suggestions for coordinated and high-quality development. We used nighttime light data from 1992 to 2020 and combined an exploratory spatial data analytical method and a log-t test of a nonlinear time-varying factor model to identify the spatial convergence clubs of regional economic growth and the economic growth drivers of different clubs based on a spatial econometric model. We found that the eastern region is strong while the development of the central, western, and northeastern regions follows China’s long-term trend. Three high-level economic clubs (Shanghai, Jiangsu, and Zhejiang belong to Club 1; Shandong, Hebei, Anhui, Henan, and Liaoning belong to Club 2; Hainan, Fujian, and Guangdong belong to Club 3) have formed in the eastern coastal and central regions, while a low-level one (Inner Mongolia, Hubei, Chongqing, Qinghai, Guizhou, Sichuan, Guangxi, Yunnan, Xizang, Shaanxi, Gansu, Hunan, Ningxia, Xinjiang, Jiangxi, Heilongjiang, and Jilin) has formed in the central, western, and northeastern regions. Beijing, Tianjin, and Shanxi are not convergent. The coordinated development of these regions requires improving the levels of economic growth in the western and northeastern regions to give full play to the role of the Yangtze River Delta as a growth pole and its economic radiation capacity. An analysis of the influence mechanism and spatial spillover effects shows that industrial development and market vitality are the most important driving forces for economic growth. For the low-level club, service industry development, human capital, and resource consumption are also key factors for achieving sustained and stable economic growth.

Testing Club Convergence in Female Smoking Prevalence.

In this paper, we applied the concept of convergence to examine the evolution of smoking prevalence among women in 191 countries worldwide from 1990 to 2019. First, the non-linear time-varying factor model proposed by Phillips and Sul was adopted to identify potential clusters (clubs), wherein groups of countries converge to similar female smoking rates. Second, an ordered logit regression model was used to assess the impact of cigarette affordability on the probability of falling within a given cluster. The hypothesis of global convergence was rejected. However, the clustering algorithm successfully identified five and nine clubs, within countries with increasing and decreasing smoking prevalence, respectively. A higher relative income-price ratio (i.e., lower cigarette affordability) increased the likelihood of belonging to a club of countries with a low prevalence of female tobacco smoking.

Join the club! Dynamics of global ESG indices convergence

We investigate the convergence behaviour of 18 ESG stock market indices from a global perspective. We rely on the convergence tests and clustering procedures by Phillips and Sul (2007, 2009) which are based on a time-varying nonlinear panel factor model. In particular, we find a structural break in May 2019. Prior to the break, we identify Brazil and China as co-diverging units and find some heterogeneity in relative convergence clusters for the remaining countries. After the break, we do not find only relative, but also level convergence amongst all considered countries in one single club. The structural break and its timing can be linked to significantly increased global investor attention for ESG.

Schooling Ain’t Learning in Europe: A Club Convergence Perspective

Convergence in human capital is a key precondition to achieve income convergence in the European Union; however, so far research on this topic has nearly been absent. Our paper contributes to the literature by investigating the human capital convergence dynamics within the EU over the period 1990–2016 using a nonlinear dynamic factor model. While we find evidence of absolute convergence with respect to the average years of schooling, we identify four convergence clubs with respect to learning outcomes, and the divergence across those four clubs is increasing over time. A subsequent analysis of the determinants of the learning clubs reveals that institutional and learning spillovers are decisive for whether an EU Member State is on a high or low human capital trajectory.