Time-varying Factor Model Research Articles

Distinguishing Time-Varying Factor Models

Time-varying factor models have been widely used to model changing relationships among economic and financial variables. The existing literature usually specifies the time-varying factor loadings as deterministic functions of time or unit root processes. This article proposes two consistent tests to distinguish between these two specifications based on a randomization approach. By setting the null hypothesis as either specification, we show that the proposed test statistics follow an asymptotic Chi-squared distribution under the respective null hypotheses and diverge to infinity in probability under the respective alternatives. Simulation studies reveal that both test statistics perform reasonably well in finite samples. We apply the proposed tests to the U.S. macroeconomic and global macroeconomic and financial datasets. The results suggest that the time-varying factor loadings as deterministic functions of time should be adopted for these two applications.

Avoiding jumps in the rotation matrix of time-varying factor models

Time-varying factor models have gained much popularity in recent years. However, the newly developed local estimator is susceptible to a time-varying rotation matrix that may exhibit jumps. This letter proposes a simple method to avoid the jumps. We show by simulations that the proposed procedure can effectively eliminate jumps in the rotation matrix, leading to a substantially lower mean-square forecasting error.

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.

The pricing of unexpected volatility in the currency market

Many recent papers have investigated the role played by volatility in determining the cross-section of currency returns. This paper employs two time-varying factor models: a threshold model and a Markov-switching model to price the excess returns from the currency carry trade. We show that the importance of volatility depends on whether the currency markets are unexpectedly volatile. Volatility innovations during relatively tranquil periods are largely unrewarded in the market, whereas during the unexpected volatile period, this risk has a substantial impact on currency returns. The empirical results show that the two time-varying factor models fit the data better and generate a smaller pricing error than the linear model, while the Markov-switching model outperforms the threshold factor models not only by generating lower pricing errors but also distinguishes two regimes endogenously and without any predetermined state variables.

Robust high-dimensional alpha test for conditional time-varying factor models

This paper considers the problem of testing the presence of alpha in high-dimensional conditional time-varying factor model. We proposed a spatial-sign-based test procedure which is robust and efficient for heavy-tailed distributions. We established the theoretical properties of the proposed test statistic under some mild conditions. Simulation studies and a real data example also show the superior of our test procedure to the existing methods.

Global financial cycles since 1880

We analyse global aggregate and segment-specific cycles across credit, house prices, equity prices, and interest rates in 17 economies over 130 years using a time-varying dynamic factor model. We show that global financial cycles have gained relevance over time. For equity prices, they now constitute the main driver of fluctuations in most countries. Global cycles in credit and housing have become more pronounced and protracted since the 1980s, and their relevance has increased for a sub-group of financially open and developed economies. Panel regressions show that a country’s susceptibility to global financial cycles tends to increase with financial openness and financial integration, the extent of mortgage-related lending, and the efficiency of stock markets. Understanding changes in global co-movement over time and its heterogeneous role across countries matters for the design of financial stabilization policies.

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.

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.

Identification of Time-Varying Factor Models

The emergence of large datasets with long time spans has cast doubt on the assumption of constant loadings in conventional factor models. Being a potential solution, the time-varying factor model (TVFM) has attracted enormous interest in the literature. However, TVFM also suffers from the well-known problem of nonidentifiability. This article considers the situations under which both the factors and factor loadings can be estimated without rotations asymptotically. Asymptotic distributions of the proposed estimators are derived. Theoretical findings are supported by simulations. Finally, we evaluate the forecasting performance of the estimated factors subject to different identification restrictions using an extensive dataset of the U.S. macroeconomic variables. Substantial differences are found among the choices of identification restrictions.

Analytical algorithm for time-varying friction force and torque of pitting helical gear

Friction excitation is an important factor affecting gear vibration and noise. This paper analyzes the variation law of sliding friction during helical gear meshing, and the calculation algorithm of friction force and torque of helical gear is derived. The effects of working parameters on the friction force and torque are analyzed based on the time-varying friction factor model. The calculation method of the friction force and friction torque of pitting helical gear is given by establishing the quadrilateral pitting model on the tooth surface of the helical gear. The influence of pitting parameters on the friction force and torque is analyzed, which can provide the research basis for the dynamic response analysis of pitting gear.

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.

Measuring dynamic pandemic-related policy effects: A time-varying parameter multi-level dynamic factor model approach

This study evaluates the dynamic impact of various policies adopted by U.S. states, including social distancing, financial assistance, and vaccination policies. We propose a time-varying parameter multilevel dynamic factor model (TVP-MDFM) to improve the model’s accuracy for evaluating the dynamic policy effect. The estimation is based on the Bayesian shrinkage method jointly with the Markov chain Monte Carlo (MCMC) algorithm that combines model selection and parameter estimation into the same iterative sampling process. The advantages and reliability of the TVP-MDFM are explored using simulation studies and robustness tests. The main empirical results highlight that the direct causal effect of the social distancing policy is more significant than the indirect effect mediated through human behavior. We also find income heterogeneity in financial assistance policies. Moreover, we provide evidence that banning vaccination certification by legislation is a stronger driver of the new case rate than executive orders during the Omicron dominance.

Can financial factors affect corporate debt leverage convergence?

This study examines the individual and macro financial factors affecting Chinese corporations' debt leverage convergence. Based on the nonlinear time-varying factor model, this study tests the convergence of the debt leverage of Chinese A-share non-financial listed companies from 1998 to 2017, and obtains two company groups, big club and non-big club. Further study tests the influence of financial factors on Chinese corporations' debt leverage convergence. Internal funds (total return on assets, free cash flow, cash holding, cash dividend payment) and monetary policy are taken as the agent variables of individual and macro financial factors, respectively. The results show that companies lacking internal funds are more likely to converge to big club than those that have sufficient internal funds, and the debt leverage convergence of companies in big club is significantly affected by monetary policy compared with those in non-big club. This study shows that the impact of China's monetary policy on the trend of corporate debt leverage is heterogeneous. Structural adjustments must be made to its current monetary policy to maintain reasonable corporate leverage and control debt risks.

Club Convergence in R&D Expenditure across European Regions

The increasing disparities between European regions constitute a great challenge for sustainable development and require identification of the factors responsible for this process. Given the substantive role of R&D in shaping innovativeness and economic development, understanding its dynamics and spatial patterns can provide new insights into regional growth prospects. Although prior studies have investigated the patterns of innovation convergence, apparently none has attempted to test the convergence club hypothesis in R&D expenditure in the European regional scope. Therefore, the present study aims to fill this gap. The paper aims at examining the convergence path of R&D expenditure across European regions and at identifying the factors conditioning club membership. Data were retrieved from Eurostat’s regional database and Regional Innovation Scoreboard datasets over 2008–2018. Employing a nonlinear time-varying factor model, we reveal that R&D expenditure in the examined regions follows the pattern of club convergence. The results of our research allow to identify five convergence clubs characterised by distinct disparities in the R&D expenditures. We also demonstrate that the emergence of the identified convergence clubs might be attributable to the initial differences in human capital, external knowledge embedded in patents and technological structures across regions as measured by employment in medium-high and high-tech manufacturing and knowledge-intensive services. These results provide policy implications in terms of the formulation and implementation of more tailored innovation policies, based on smart development and specialisation strategies. The presence of business R&D convergence clubs requires shifting EU policy actions towards a more sustainable model promoting both the advantages of the strongest regions and the development opportunities in less-developed ones.