Annotation of the results obtained in 2020
It is well-known that modern economic and financial markets are affected by crises and many of their key variables, including financial returns, exhibit large fluctuations, volatility clusters, and nonlinear dependence. The key variables in the markets, such as asset prices and natural resources prices, exhibit large downfalls that lead to considerable losses for market participants and also states and governments. One of the main approaches to modeling variables and indicators that are characterized by large fluctuations and downfalls is that based on applications of heavy-tailed distributions. For variables with such distributions, the likelihoods of crises occurrence are much greater than under normality assumptions. According to empirical results reported in the literature (e.g., those that are discussed in the monographs by R. Ibragimov and A. Prokhorov, Ibragimov, M., Ibragimov, R. and Walden, J. (2015), "Heavy-Tailed Distributions and Robustness in Economics and Finance", Lecture Notes in Statistics 214, Springer; R. Ibragimov and A. Prokhorov (2017), "Heavy Tails and Copulas: Topics in Dependence Modelling in Economics and Finance", World Scientific; и I. Pinelis, V. H. de la Peña, R. Ibragimov, A. Osekowski and I. Shevtsova (2017), "Inequalities and Extremal Problems in Probability and Statistics", Academic Press) and those obtained during the work on the project, heavy-tailed distributions provide good models for many key financial and economic variables, including financial returns, foreign exchange rates, prices on natural resources, insurance risks, income and wealth distributions, and a number of others. Another important characteristic of financial and economic indicators and markets is their mutual interdependence. Unfortunately, as is demonstrated, for instance, by quick propagation of the 2008 global crisis from the US to other markets and countries, financial and economic markets exhibit financial contagion: large losses on them are often observed simultaneously. In addition, as is well-known, many financial time series such as financial returns and foreign exchange rates exhibit volatility clustering and nonlinear dependence. Standard assumptions of independence cannot be used in modeling financial and economic markets and their key indicators. The research in the framework of the project demonstrates that under deviations from such standard assumptions as normal distributions and homogeneity, the conclusions of many important models in economics and finance, including the analysis of diversification optimality may reverse and be replaced by the opposite ones. For instance, diversification of a portfolio of stocks or risks becomes suboptimal in the case of risks and financial returns that have extremely heavy-tailed distributions. At the same time, an important conclusion is that the properties of a number of key economic and financial models obtained under normality assumptions also continue to hold for heavy-tailed distributions that are often encountered in practice. An important direction of research on the project concentrates on the study of (non-)robustness of key models in economics and finance to assumptions of dependence, in addition to heavy-tailedness. It is based on applications of fields of active research in statistics and probability theory given by the theory of copulas - functions that capture all dependence properties of random variables under study - and the theory of heavy-tailed distributions. The results obtained in research on the project show that many properties of a number of fundamental models in economics and finance continue to hold under many classes of dependence that are observed in practice. At the same time, several conclusions of these models may be reversed and become the opposite ones. Important results that are obtained in research on the project are given by determination of exact conditions - the degrees of dependence and heterogeneity of economic and financial variables and data - under which the standard conclusions of the models are robust and continue to hold. The above problems of potential non-robustness of key economic and financial models to assumptions of heavy-tailedness and dependence emphasize the importance of applications of statistical methods whose conclusions remain valid under such assumptions. That is, it is important to use statistical approaches that are applicable under data that exhibits, as is often the case in practice, heterogeneity, and correlation and thus do not satisfy the standard assumptions of independence and identical distributions. An important part of the research on the project consists in the development of a wide range of simple to use robust statistical methods and their applications in the analysis of modern economic and financial markets. Working in the above directions in the reporting period, the project participants have continued the research on the analysis of fundamental models in economics and finance to the assumptions of heavy-tailedness and dependence in their key variables and indicators. In particular, the grant participants have completed the research on complete characterization of optimal bundling strategies for a multiproduct monopolist under heavy-tailedness and potential dependence in consumers' valuations and preferences. The results obtained in the course of research show that the form of the above optimal bundling strategies is determined by the degree of heavy-tailedness and the dependence structure of consumers' preferences and valuations as well as by the degree of complementarity and substitutability in the goods provided. The results and conclusions from the study appear to be relevant for modelling of bundling strategies observed in real-world economic and financial markets. Over the course of reseach on methodology of robust statistical and econometric analysis, the project participants have made contributed to the following areas: The development of new and improved methods of robust statistical and econometric analysis of (non-)efficiency of economic and financial markets. In the course of research in this direction, the project participants have proposed and developed new and improved measures of nonlinear dependence, volatility clustering and (non-) efficiency in financial markets. They have further developed new methods for robust estimation and inference on the above measures using the new and improved approaches to robust statistical and econometric analysis developed over the course of work on the project. The development of new methods for robust statistical analysis and forecasting of the dynamics of financial and economic markets on the base of widely ysed predictive regression models for financial returns and other key economic and financial indicators. In the course of research in this direction, the project participants have proposed and devloped new classes of robust methods for statistical analysis and hypothesis testing for unknown parameters of predictive regression models under the problems of heterogeneity, dependence, potential non-stationarity and heavy-tailedness in regressor variables and regression errors. The development of new and improved methods for robust estimation and statistical inference on dependence structures on the base of copulas - functions that complete characterize the dependence properties between several variables of interest such as key economic or financial indicators. Over the course of research in the reporting period, the project participants have proposed new and improved approaches to approximation and estimation of copula densities using triangulation methods and nonparametric maximum likelihood estimates for coefficients of spline approximations to the copulas considered. The obtained results show that the proposed classes of estimates for copula dependence structures can be obtained using the standard convex optimization methods. The project participants have completed the research on applications of the proposed estimation approaches for copula dependence structures in a number of important problems in economics and econometrics, including the inference on dependence in inheritance models, characterization of copula structures for modelling dependence between the price indices and interest rates in the well-known Gibson paradox in macroeconomics, as well as tests of independence between key economic and financial indicators. Adaptation and applications of new and improved statistical inference methods developed over the course of work on the project in the problems of robust estimation and comparison of income and wealth inequality measures. The project partcipants have proposed new robust inference methods using of t-statistics calculated using group estimates of parameters of interest (income, wealth or well-being inequality indices) for robust statistical analysis and comparisons of inequality measures under the problems of dependence, heterogeneity and heavy-tailedness in observations. The development of new and improved methods for robust statistical and econometric analysis of potentially correlated, dependent and hetogeneous time series and datasets of economic and financial observations with missing data. In the reporting period, the project participants have obtained a wide range of empirical applications of robust inference methods dealt with in the project in the analysis of the key financial and economic indicators in Russia, emerging markets and the economies in the West. The results obtained in this direction provide robust estimates for predictive and forecasting regressions as well as for the degree of heavy-tailedness and the likelihood of crises and large downfalls in financial returns in Russia and many emerging markets and their comparisons with countries of the West. The grant participants have also completed the robust statistical and econometric analysis of predictive and forecasting regressions for returns and prices on cryptocurrency markets. They have further mostly finished the robust analysis of pricing models in the art market using statistically and econometrically justified machine learning methods and the new robust inference approaches developed over the course of the project. The project participants have mostly completed the research on robust estimation and comparisons of the degree of the degree of heavy-tailedness and comparisons of income inequality measures in Russian regions on the base of new and improved approaches to robust inference under the problems of heterogeneity, potential dependence and heavy-tailedness in observations. The grant participants have also completed the robust statistical and econometric analysis of structural changes in the dynamics of key indicators and time series in the World's financial and economic markets, including financial returns and prices in them, due to the beginning of the COVID-19 pandemic. They have also completed the robust statistical analysis of the dynamics and heavy-tailedness properties in key variables that characterize the pandemic's development. The robust statistical analysis of the main indicators and time series in financial and economic markets in Russia, emerging economies, and countries of the West, including their financial returns and income distributions, conducted by the project participants points to pronounced heavy-tailedness, heterogeneity and dependence in these variables. These conclusions imply inapplicability of widely used statistical and econometric methods in the analysis of the above indicators and time series. They further emphasize the importance of the use of robust statistical and econometric methods, including the robust inference approaches developed in the research on the project, in the analysis of modern financial and economic markets. In the reporting period, the project participants have continued their work on the incorporation of the robust inference methods developed over the course of the project into Matlab, Python, Stata and R packages and packages for other widely used computer programs. They have also continued their work on applications of the developed software packages in the analysis of large databases on financial and economic markets, including markets in Russia, emerging markets, economies of the West and cryptocurrency markets. They have also worked on further development of the internet resources of the project and the database on key economic and financial variables in markets in Russia, emerging markets, the economies of the West and cryptocurrency markets that was used in the empirical research on the project as well as the database on financial and economic crises that affected the Russian and post-Soviet economies. The results of the reseach on the development and applications of robust econometric and statistical methods conducted by the project participants have been included in undergraduate and graduate (MSc and Ph.D.) courses they are teaching at universities in Russia and abroad. They were also suggested to students as possible research topics for their course projects, MSc and Ph.D. dissertations or their parts. Over the reporting period, the project participants have conducted active and productive organizational work on the creation and the development of the Center for econometrics and business-analystics (CEBA) at Saint-Petersburg University. In this direction, they have achieved active collaboration with and involvement of students and young colleagues at Higher School of Management, the Department of Economics, the Department of Mathematics and Mechanics and the Department of Applied Mathematics and the Management Processes at the university in the research in project's area. In the framework of the organizational work on the creation and the development of the CEBA, the project particpants have also organized the first in Russia regular weekly online seminar in econometrics and business analytics (http://ceba.lab.tilda.ws/seminars, https://sites.google.com/site/artembprokhorov/seminars/ceba-talks). The seminar's activities have included research presentations by leading experts and researchers in the fields of econometrics, economics and finance in Russia and abroad. The research results obtained in the reporting period have been presented in project participants' papers that are published, received Revise and resubmit editorial decisions or submitted for possible publication in leading journals in finance, economics, econometrics and statistics such as the Oxford Bulletin of Economics and Statistics, the Journal of Business and Economic Statistics; the Journal of Productivity Analysis and the Journal of Empirical Finance. The project participants were actively involved in organization and presentation of their research at leading conferences, simposia and seminars in Russia and abroad, such as the World Congress of the Econometric Society-2020, the 13th International Conference on Computational and Financial Econometrics, CFE-2019, the Joint Meeting of the VII International Conference on Modern Econometric Tools and Applications - META2020 and the 2nd HSE Workshop on Applied Econometrics, the International Symposium on Forecasting, the 7th International GSOM Emerging Markets Conference 2020: New Reality During and After COVID-19, the Granger Centre Seminar, Nottingham School of Economics; the seminar on Stochastic Analysis and its Application at the Laboratory of Stochastic Analysis and its Applications, Higher School of Economics; the seminars of the Center for Econometrics and Business Analytics, St. Petersburg State University, organized over the course of the project's development, and other seminars in Russia, the UK, Australia and other countries.

 

Publications

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Annotation of the results obtained in 2019
In the reporting period, the project participants have conducted the research in the main directions planned for 2018. In particular, they have conducted research in the following directions: 1. The development of new approaches to robust statistical and econometric analysis and forecasting using predictive regressions. The developed methods were used for robust econometric analysis of economic and financial markets in Russia, emerging economies and the West. 2. The development of new approaches to robust tests of parametric copula models of high dimensions. including so-called vina copula models of dependence. 3. Development of new approaches to the analysis of volatility clusters and (non-)efficiency of economic and financial markets using robust inference approaches developed over the course of work on the project. 4. Development of new results on robust econometric and statistical analysis of predictive regressions and their applications. 5. The development and applications of improved robust approaches to statistical and econometric inference under the problems of correlation, heterogeneity, outliers, and heavy-tailedness in observations; 6.The development and applications of improved robust approaches to statistical and econometric inference under the problems of correlation, heterogeneity, outliers, and heavy-tailedness in observations; 7. Econometric analysis of different economic and financial markets, including those in Russia, emerging economies and the West, using the proposed robust inference approaches. It is well-known that modern economic and financial markets are affected by crises and many of their key variables, including financial returns, exhibit large fluctuations, volatility clusters, and nonlinear dependence. The key variables in the markets, such as asset prices and natural resources prices, exhibit large downfalls that lead to considerable losses for market participants and also states and governments. One of the main approaches to modeling variables and indicators that are characterized by large fluctuations and downfalls is that based on applications of heavy-tailed distributions. For variables with such distributions, the likelihoods of crises occurrence are much greater than under normality assumptions. According to empirical results reported in the literature (e.g., those that are discussed in the monographs by R. Ibragimov and A. Prokhorov, Ibragimov, M., Ibragimov, R. and Walden, J. (2015), "Heavy-Tailed Distributions and Robustness in Economics and Finance", Lecture Notes in Statistics 214, Springer; R. Ibragimov and A. Prokhorov (2017), "Heavy Tails and Copulas: Topics in Dependence Modelling in Economics and Finance", World Scientific; и I. Pinelis, V. H. de la Peña, R. Ibragimov, A. Osekowski and I. Shevtsova (2017), "Inequalities and Extremal Problems in Probability and Statistics", Academic Press) and those obtained during the work on the project, heavy-tailed distributions provide good models for many key financial and economic variables, including financial returns, foreign exchange rates, prices on natural resources, insurance risks, income and wealth distributions, and a number of others. Another important characteristic of financial and economic indicators and markets is their mutual interdependence. Unfortunately, as is demonstrated, for instance, by quick propagation of the 2008 global crisis from the US to other markets and countries, financial and economic markets exhibit financial contagion: large losses on them are often observed simultaneously. In addition, as is well-known, many financial time series such as financial returns and foreign exchange rates exhibit volatility clustering and nonlinear dependence. Standard assumptions of independence cannot be used in modeling financial and economic markets and their key indicators. The research in the framework of the project demonstrates that under deviations from such standard assumptions as normal distributions and homogeneity, the conclusions of many important models in economics and finance, including the analysis of diversification optimality may reverse and be replaced by the opposite ones. For instance, diversification of a portfolio of stocks or risks becomes suboptimal in the case of risks and financial returns that have extremely heavy-tailed distributions. At the same time, an important conclusion is that the properties of a number of key economic and financial models obtained under normality assumptions also continue to hold for heavy-tailed distributions that are often encountered in practice. An important direction of research on the project concentrates on the study of (non-)robustness of key models in economics and finance to assumptions of dependence, in addition to heavy-tailedness. It is based on applications of fields of active research in statistics and probability theory given by the theory of copulas - functions that capture all dependence properties of random variables under study - and the theory of heavy-tailed distributions. The results obtained in research on the project show that many properties of a number of fundamental models in economics and finance continue to hold under many classes of dependence that are observed in practice. At the same time, several conclusions of these models may be reversed and become the opposite ones. Important results that are obtained in research on the project are given by determination of exact conditions - the degrees of dependence and heterogeneity of economic and financial variables and data - under which the standard conclusions of the models are robust and continue to hold. The above problems of potential non-robustness of key economic and financial models to assumptions of heavy-tailedness and dependence emphasize the importance of applications of statistical methods whose conclusions remain valid under such assumptions. That is, it is important to use statistical approaches that are applicable under data that exhibits, as is often the case in practice, heterogeneity, and correlation and thus do not satisfy the standard assumptions of independence and identical distributions. An important part of the research on the project consists in the development of a wide range of simple to use robust statistical methods and their applications in the analysis of modern economic and financial markets. Working in the above research directions, in the reporting period, the project participants have completed a detailed analysis of the effects of asymmetry, dependence and heavy-tailedness in risks' distributions on the structure of financial and insurance markets and its robustness. The results obtained in these directions explain the presence and optimality of monoline and multiline insurance companies and structures in different real-world markets, including insurance markets for losses due to crises and natural disasters. They have important conclusions for regulation and functioning of financial and insurance markets depending on the properties of asymmetry, heavy-tailedness, and correlation in their key variables. In the reporting period, the project participants have also completed a detailed theoretical analysis of the effects of income distribution and inequality and their structural changes on market demand models. The obtained results provide characterizations of changes in income distribution and inequality and tax policy measures on models of market demand and equilibrium. The results emphasize the importance of econometrically justified and robust estimates for income inequality and distribution for the analysis of key economic models and the effects of economic policy measures. The project participants' contributions to the methodology of robust statistical and econometric inference include The development of new robust methods for the construction of confidence intervals for the dates of structural changes in (cointegrating) regression models with nonstationary regressors. The developed tests and confidence intervals have more accurate coverage rate as compared to widely used existing approaches. The developed approaches to robust inference have been applied for construction of confidence intervals for the dates of structural changes in cointegrating regressions that describe the dependence between time series in economic and financial markets in Russia, including the real GDP, consumption and investment, and oil prices. The constructed confidence intervals point out to structural breaks in regression models for the time series considered due to the beginning of the 2008-2009 crisis; new robust tests for nonstationarity based on computer bootstrap. The developed bootstrap tests for nonstationarity based on maximum likelihood ratios have better properties as compared to widely used traditional asymptotic and computer tests; a detailed analysis of the robustness of regression analysis in the case of matched samples, a widely used approach to the analysis of samples with missing data. The obtained results demonstrate inconsistency of the standard regression estimates for the above samples. The project participants have developed new semiparametric estimates with bias correction and have analyzed their asymptotic properties. The computer-based numerical results confirm good properties of the proposed robust inference approaches in finite samples and point out to their wide applicability; new approaches to and results on robust modeling, inference, and testing of copula models of dependence and joint distributions of risks and time series. The project participants have obtained several theoretical and numerical results that indicate the importance of the use of robust statistical methods in the analysis of dependence and long memory properties of copula-based time series models and the study of financial and economic markets affected by nonlinear dependence, heterogeneity, crises and financial contagion. The project participants have developed new approaches to robust testing and inference in copula models that have significant advantages over widely used inference methods, especially in the case of high dimensional - so-called vine copula - dependence models. They have also proposed new methods for robust estimation of dynamic joint distributions of returns and prices on many assets under nonlinear dependence, volatility clusters, heavy-tailedness and the effects of crises; In the reporting period, the project participants have obtained a wide range of empirical applications of robust inference methods dealt with in the project in the analysis of the key financial and economic indicators in Russia, emerging markets and the economies in the West. The results obtained in this direction provide robust estimates for the degree of heavy-tailedness and the likelihood of crises and large downfalls in financial returns in Russia and many emerging markets and their comparisons with countries of the West. The results obtained in the reporting period also provide robust estimates for the degree of heavy-tailedness and the implied income inequality measures in Russia. The robust analysis of the dynamic of financial returns in emerging markets points out to their more pronounced heavy-tailedness as compared to developed economies, and to structural breaks in heavy-tailedness degree due to the beginning of the 2008 crisis. At the same time, the degree of heavy-tailedness in income distribution in Russia is found to be similar to that in the economies of the West. The robust statistical analysis of the main indicators and time series in financial and economic markets in Russia, emerging economies and countries of the West, including their financial returns and income distributions, conducted by the project participants points out to pronounced heavy-tailedness, heterogeneity and dependence in these variables. These conclusions imply inapplicability of widely used statistical and econometric methods in the analysis of the above indicators and time series. They further emphasize the importance of the use of robust statistical and econometric methods, including the robust inference approaches developed in the research on the project, in the analysis of modern financial and economic markets. In the reporting period, the project participants have continued their work on the development of Matlab, Python, Stata and R packages and packages for other widely used computer programs designed for robust econometric and statistical analysis and forecasting of economic and financial variables. They have also continued their work on the deveploment of the database on financial and economic crises that affected the Russian and post-Soviet economies and key economic and financial variables in these markets. The results of the reseach on the development and applications of robust ecoometric and statistical methods conducted by the project participants have been included in undegraduate and graduate (MSc and Ph.D.) courses they are teaching at universities in Russia and abroad. The research results obtained in the reporting period have been published in project participants' papers in leading journals in economics, finance, econometrics, statistics and probality theory in the first quartile – Q1 - according to their impact factor, such as the Review of Finance (one of four top journals in finance with highest ranking, percentile: 91, impact factor: 2.023, one of 50 research journals used in the Financial Times' ranking of Business schools and their MBA programs), Journal of Econometrics (the main, top journal in econometrics, impact factor: 1.632), Econometric Reviews (one of the main, top journals in econometrics, impact factor: 1.218), Oxford Bulletin of Economics and Statistics (leading journal in Econometrics and Statistics, impact factor: 1.512), Emerging Markets Review (leading journal in economics and econometrics, impact factor: 1.871), Economic Theory (leading journal in economics), Journal of Empirical Finance (leading journal in applied econometrics and finance), Probability Surveys (leading journal in probability theory and statistics) and others. The project participants were actively involved in organization and presentation of their research at leading conferences, simposia and seminars in Russia and abroad, such as International Conference on Computational and Financial Econometrics (CFE 2019, London, December 2019), the Fifth International Symposium in Computational Economics and Finance (ISCEF-2019, Paris, April 2019), International Conference on Econometrics and Statistics (EcoSta 2019, Taiwan, June 2019), and seminars at universities in Russia, the United Kingdom, Australia, the United States and Europe.

 

Publications

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