Publications
77 results found
Embrechts P, 2015, Implications of Heavy-Tailedness, HEAVY-TAILED DISTRIBUTIONS AND ROBUSTNESS IN ECONOMICS AND FINANCE, Publisher: SPRINGER, Pages: 11-81, ISBN: 978-3-319-16876-0
Embrechts P, 2015, Inference and Empirical Examples, HEAVY-TAILED DISTRIBUTIONS AND ROBUSTNESS IN ECONOMICS AND FINANCE, Publisher: SPRINGER, Pages: 83-109, ISBN: 978-3-319-16876-0
Ibragimov M, Ibragimov R, Walden J, 2015, Heavy-tailed distributions and robustness in economics and finance, Publisher: Springer, ISBN: 978-3-319-16877-7
This book focuses on general frameworks for modeling heavy-tailed distributions in economics, finance, econometrics, statistics, risk management and insurance. A central theme is that of (non-)robustness, i.e., the fact that the presence of heavy tails can either reinforce or reverse the implications of a number of models in these fields, depending on the degree of heavy-tailed ness. These results motivate the development and applications of robust inference approaches under heavy tails, heterogeneity and dependence in observations. Several recently developed robust inference approaches are discussed and illustrated, together with applications.
Ibragimov MY, Ibragimov RM, Sinnikova YM, et al., 2014, About the progressive tax system of labor remuneration in Russia, Asian Social Science, Vol: 10, Pages: 28-35, ISSN: 1911-2017
This paper presents the results of research aimed at improvement of the taxation of wages in Russia. It analyses the problem of determining the progressive income tax scale as being a more socially equitable than the current flat rate in Russia with 13% tax rate on income. Proposed tax scale of tax rates exempts the poor citizens from income tax, shifting the tax burden from the poor to the rich. In accordance with the principle of redistribution that leads to a reduction in income inequality in Russia.
Ibragimov R, 2014, On the robustness of location estimators in models of firm growth under heavy-tailedness, Journal of Econometrics, Vol: 181, Pages: 25-33, ISSN: 0304-4076
Focusing on the model of demand-driven innovation and spatial competition over time in Jovanovic and Rob (1987), we study the effects of the robustness of estimators employed by firms to make inferences about their markets on the firms’ growth patterns. We show that if consumers’ signals in the model are moderately heavy-tailed and the firms use the sample mean of the signals to estimate the ideal product, then the firms’ output levels exhibit positive persistence. In such a setting, large firms have an advantage over their smaller counterparts. These properties are reversed for signals with extremely heavy-tailed distributions. In such a case, the model implies anti-persistence in output levels, together with a surprising pattern of oscillations in firm sizes, with smaller firms being likely to become larger ones next period, and vice versa. We further show that the implications of the model under moderate heavy-tailedness continue to hold under the only assumption of symmetry of consumers’ signals if the firms use a more robust estimator of the ideal product, the sample median.
Valitov S, Ibragimov M, Ibragimov R, 2014, Elasticity analysis of unemployed people quantity in relation to gross domestic product of Russia, World Applied Sciences Journal, Vol: 30, Pages: 1357-1364, ISSN: 1818-4952
The article estimates parameters of interrelation between accession rate of unemployed people quantity and gross domestic product volume in Russia on the grounds of quarterly data for 1995-2013. For estimation of model parameters the authors use the method of instrumental variable. Analysis of mutual influence of unemployed people quantity and gross domestic product increase is performed on the grounds of elasticity notion. © IDOSI Publications, 2014.
Ibragimov M, Ibragimov R, Kattuman P, 2013, Emerging markets and heavy tails, Journal of Banking and Finance, Vol: 37, Pages: 2546-2559, ISSN: 1872-6372
Emerging countries are held to be subject to more frequent and more pronounced external and internal shocks than their developed counter-parts. This suggests that key variables pertaining to their markets, including their exchange rates, will be marked by greater likelihood of extreme observations and large fluctuations. We focus on the hypothesis that compared to developed country exchange rates, emerging country exchange rates will be more pronouncedly heavy-tailed. We find support for the hypothesis using recently proposed robust tail index estimation methods which, in particular, perform well under heavy-tailed dependent GARCH processes that are often used for modeling exchange rates. According to the estimation results reported in the paper, variances may be infinite for several emerging country exchange rates. Tail index values ζ = p ∈ (2.6, 2.8) appear to be at the dividing boundary between the two sets of countries: while the moments of order p ∈ (2.6, 2.8) are finite for most of the developed country exchange rates, they may be (or are) infinite for most of the emerging country exchange rates. We also study the impact of the on-going financial and economic crisis, and find that heavy-tailedness properties of most exchange rates did not change significantly with the onset of the crisis. At the same time, some foreign exchange markets have experienced structural changes in their heavy-tailedness properties during the crisis.
Ibragimov R, Walden J, 2011, Value at risk under dependence and heavy-tailedness: Models with common shocks, Annals of Finance, Vol: 7, Pages: 285-318, ISSN: 1614-2446
This paper presents an analysis of diversification and portfolio value at risk for heavy-tailed dependent risks in models with multiple common shocks. We show that, in the framework of value at risk comparisons, diversification is optimal for moderately heavy-tailed dependent risks with common shocks and finite first moments, provided that the model is balanced, i.e., that all the risks are available for portfolio formation. However, diversification is inferior in balanced extremely heavy-tailed risk models with common factors. Finally, in several unbalanced dependent models, diversification is optimal, even though there is extreme heavy-tailedness in common shocks or in idiosyncratic parts of the risks. Analogues of the obtained results further hold for efficiency comparisons of linear estimators in random effects models with dependent and heavy-tailed observations.
Ibragimov R, Jaffee D, Walden J, 2011, Diversification disasters, JOURNAL OF FINANCIAL ECONOMICS, Vol: 99, Pages: 333-348, ISSN: 0304-405X
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- Citations: 114
Gabaix X, Ibragimov R, 2011, Rank-1/2: A simple way to improve the OLS estimation of tail exponents, Journal of Business and Economic Statistics, Vol: 29, Pages: 24-39, ISSN: 0735-0015
Despite the availability of more sophisticated methods, a popular way to estimate a Pareto exponent is still to run an OLS regression: log(Rank) = a − b log(Size), and take b as an estimate of the Pareto exponent. The reason for this popularity is arguably the simplicity and robustness of this method. Unfortunately, this procedure is strongly biased in small samples. We provide a simple practical remedy for this bias, and propose that, if one wants to use an OLS regression, one should use the Rank −1 / 2, and run log(Rank − 1 / 2) = a − b log(Size). The shift of 1 / 2 is optimal, and reduces the bias to a leading order. The standard error on the Pareto exponent ζ is not the OLS standard error, but is asymptotically (2 / n)1 / 2ζ. Numerical results demonstrate the advantage of the proposed approach over the standard OLS estimation procedures and indicate that it performs well under dependent heavy-tailed processes exhibiting deviations from power laws. The estimation procedures considered are illustrated using an empirical application to Zipf’s law for the United States city size distribution.
Ibragimov R, Walden J, 2010, Optimal Bundling Strategies Under Heavy-Tailed Valuations, MANAGEMENT SCIENCE, Vol: 56, Pages: 1963-1976, ISSN: 0025-1909
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- Citations: 24
Ibragimov R, Mueller UK, 2010, t-Statistic based correlation and heterogeneity robust inference, Journal of Business and Economic Statistics, Vol: 28, Pages: 453-468, ISSN: 0735-0015
We develop a general approach to robust inference about a scalar parameter of interest when the data is potentially heterogeneous and correlated in a largely unknown way. The key ingredient is the following result of Bakirov and Székely (2005) concerning the small sample properties of the standard t-test: For a significance level of 5% or lower, the t-test remains conservative for underlying observations that are independent and Gaussian with heterogenous variances. One might thus conduct robust large sample inference as follows: partition the data into q≥2 groups, estimate the model for each group, and conduct a standard t-test with the resulting q parameter estimators of interest. This results in valid and in some sense efficient inference when the groups are chosen in a way that ensures the parameter estimators to be asymptotically independent, unbiased and Gaussian of possibly different variances. We provide examples of how to apply this approach to time series, panel, clustered and spatially correlated data.
Ibragimov R, Jaffee D, Walden J, 2010, Pricing and Capital Allocation for Multiline Insurance Firms, JOURNAL OF RISK AND INSURANCE, Vol: 77, Pages: 551-578, ISSN: 0022-4367
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- Citations: 19
Ibragimov R, 2010, On functions not preserving majorization pre-ordering and their applications, UZBEK MATHEMATICAL JOURNAL, Pages: 64-71
Ibragimov M, Ibragimov R, Karimov J, 2010, Uzbekistan population forecast, Bulletin of Tashkent University of Information Technologies
Ibragimov M, Ibragimov R, Sirajiddinov N, 2010, MODELING AND FORECASTING INCOME TAX REVENUE: THE CASE OF UZBEKISTAN, ECONOMIC FORECASTING, Editors: Molnar, Publisher: NOVA SCIENCE PUBLISHERS, INC, Pages: 213-227, ISBN: 978-1-60741-068-3
Choros B, Ibragimov R, Permiakova E, 2010, Copula estimation, WORKSHOP ON COPULA THEORY AND ITS APPLICATIONS, Editors: Durante, Haerdle, Jaworski, Rychlik, Publisher: Springer, Pages: 77-92
Ibragimov M, Ibragimov R, 2010, Measurement of economic progress, INTERNATIONAL ENCYCLOPEDIA OF STATISTICAL SCIENCE, Publisher: Springer
Ibragimov M, Ibragimov R, Sirajiddinov N, 2009, Modeling and forecasting income tax revenue: The case of Uzbekistan, Income Distribution: Inequalities, Impacts and Incentives, Pages: 187-199, ISBN: 9781606922026
Income tax revenue crucially depends on the wage distribution across and within the industries. However, many transition economies present a challenge for a sound econometric analysis due to data unavailability. The paper presents an approach to modeling and forecasting income tax revenues in an economy under missing data on individual wages within the industries. We consider the situations where only the aggregate industry-level data and sample observations for a few industries are available. Using the example of the Uzbek economy in 1995-2005, we show how the econometric analysis of wage distributions and the implied tax revenues can be conducted in such settings. One of the main conclusions of the paper is that the distributions of wages and the implied tax revenues in the economy are well approximated by Gamma distributions with semi-heavy tails that decay slower than those of Gaussian variables. © 2009 Nova Science Publishers, Inc. All rights reserved.
Ibragimov R, 2009, Copula-based characterizations for higher order Markov processes, ECONOMETRIC THEORY, Vol: 25, Pages: 819-846, ISSN: 0266-4666
Ibragimov R, Jaffee D, Walden J, 2009, Nondiversification traps in catastrophe insurance markets, Review of Financial Studies, Vol: 22, Pages: 959-993, ISSN: 0893-9454
We develop a model for markets for catastrophic risk. The model explains why insurance providers may choose not to offer insurance for catastrophic risks and not to participate in reinsurance markets, even though there is a large enough market capacity to reach full risk sharing through diversification in a reinsurance market. This is a “nondiversification trap.” We show that nondiversification traps may arise when risk distributions have heavy left tails and insurance providers have limited liability. When they are present, there may be a coordination role for a centralized agency to ensure that risk sharing takes place.
Anoshkina V, Davidova Z, Ibragimov M, et al., 2009, Labor market equilibrium and income tax rates: The case of Uzbekistan, Tax Policy and Practice (Moscow, Russia)
Ibragimov R, 2009, Portfolio diversification and value at risk under thick-tailedness, Quantitative Finance, Vol: 9, Pages: 565-580, ISSN: 1469-7688
This paper focuses on the study of portfolio diversification and value at risk analysis under heavy-tailedness. We use a notion of diversification based on majorization theory that will be explained in the text. The paper shows that the stylized fact that portfolio diversification is preferable is reversed for extremely heavy-tailed risks or returns. However, the stylized facts on diversification are robust to heavy-tailedness of risks or returns as long as their distributions are moderately heavy-tailed. Extensions of the results to the case of dependence, including convolutions of α-symmetric distributions and models with common shocks are provided.
Ibragimov R, 2009, Heavy-tailed densities, THE NEW PALGRAVE DICTIONARY OF ECONOMICS ONLINE, Editors: Durlauf, Blume, Publisher: Palgrave Macmillan
Ibragimov R, 2008, Heavy-tailedness and threshold sex determination, STATISTICS & PROBABILITY LETTERS, Vol: 78, Pages: 2804-2810, ISSN: 0167-7152
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- Citations: 3
Ibragimov R, 2008, A tale of two tails: peakedness properties in inheritance models of evolutionary theory, JOURNAL OF EVOLUTIONARY ECONOMICS, Vol: 18, Pages: 597-613, ISSN: 0936-9937
Ibragimov R, Phillips PCB, 2008, Regression asymptotics using martingale convergence methods, ECONOMETRIC THEORY, Vol: 28, Pages: 1-60
Ibragimov R, Walden J, 2008, Portfolio diversification under local and moderate deviations from power laws, Insurance: Mathematics and Economics, Vol: 42, Pages: 594-599, ISSN: 0167-6687
This paper analyzes portfolio diversification for nonlinear transformations of heavy-tailed risks. It is shown that diversification of a portfolio of convex functions of heavy-tailed risks increases the portfolio’s riskiness if expectations of these risks are infinite. In contrast, for concave functions of heavy-tailed risks with finite expectations, the stylized fact that diversification is preferable continues to hold. The framework of transformations of heavy-tailed risks includes many models with Pareto-type distributions that exhibit local or moderate deviations from power tails in the form of additional slowly varying or exponential factors. The class of distributions under study is therefore extended beyond the stable class.
Ibragimov M, Ibragimov R, 2008, Optimal constants in the Rosenthal inequality for random variables with zero odd moments, Statistics and Probability Letters, Vol: 78, Pages: 186-189, ISSN: 0167-7152
We obtain estimates for the best constant in the Rosenthal inequality for independent random variables with zero first odd moments, . The estimates are sharp in the extremal cases and , that is, in the cases of random variables with zero mean and random variables with zero first odd moments.
Ibragimov M, Ibragimov R, 2007, Market demand elasticity and income inequality, ECONOMIC THEORY, Vol: 32, Pages: 579-587, ISSN: 0938-2259
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- Citations: 6
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