Asymptotic and bootstrap properties of rank regressions

The paper develops the bootstrap theory and extends the asymptotic theory of rank estimators, such as the Maximum Rank Correlation Estimator (MRC) of Han (1987), Monotone Rank Estimator (MR) of Cavanagh and Sherman (1998) or Pairwise-Difference Rank Estimators (PDR) of Abrevaya (2003). It is known that under general conditions these estimators have asymptotic normal distributions, but the asymptotic variances are difficult to find. Here we prove that the quantiles and the variances of the asymptotic distributions can be consistently estimated by the nonparametric bootstrap. We investigate the accuracy of inference based on the asymptotic approximation and the bootstrap, and provide bounds on the associated error. In the case of MRC and MR, the bound is a function of the sample size of order close to n^{-1/6}. The PDR estimators belong to a special subclass of rank estimators for which the bound is vanishing with the rate close to n^{-1/2}. The theoretical findings are illustrated with Monte-Carlo experiments and a real data example.Rank Estimators, Bootstrap, M-Estimators, U-Statistics, U-Processes

Tax reform in the oil sector of Russia - a positive assessment

I analyze the system of taxes imposed on the Russian oil sector before and after the tax reform of 2002. I first establish a price parity relation explaining the gap between the world and domestic prices through export duties and alternative transportation costs. Based on it, I argue that the indirect taxes (VAT, the sales and excise taxes) do not decrease the net profits of oil producers, but are mostly shifted onto consumers. The tax burden on producers, on the other hand, consists of the export duties, resource payments, the profit tax and the property tax. I show that the tax reform had little effect on the total amount of taxes imposed on producers, but changed its structure across the types of taxes. After the reform the share of efficiently collected taxes, most importantly the extraction tax (ET), increased, explaining higher tax revenues. Finally, I estimate the extent to which the extraction tax is economically inefficient. By showing that the deadweight loss associated with ET is only a small fraction of the generated tax revenues, I argue that ET is a better choice for capturing the natural rent in the Russian oil sector than the poorly controlled profit tax. On the whole, this evidence depicts the reform of oil taxation in 2002 as a big step forward of the Russian fiscal system. This report is a shorter English version of the paper "Estimating the tax burden in the Russian oil sector under the price parity hypothesis" (Ekonomika i Matematicheskie Metody (2005), 41, 3).Russian oil sector; price parity; tax reforms in Russia

Tax reform in the oil sector of Russia - a positive assessment

I analyze the system of taxes imposed on the Russian oil sector before and after the tax reform of 2002. I first establish a price parity relation explaining the gap between the world and domestic prices through export duties and alternative transportation costs. Based on it, I argue that the indirect taxes (VAT, the sales and excise taxes) do not decrease the net profits of oil producers, but are mostly shifted onto consumers. The tax burden on producers, on the other hand, consists of the export duties, resource payments, the profit tax and the property tax. I show that the tax reform had little effect on the total amount of taxes imposed on producers, but changed its structure across the types of taxes. After the reform the share of efficiently collected taxes, most importantly the extraction tax (ET), increased, explaining higher tax revenues. Finally, I estimate the extent to which the extraction tax is economically inefficient. By showing that the deadweight loss associated with ET is only a small fraction of the generated tax revenues, I argue that ET is a better choice for capturing the natural rent in the Russian oil sector than the poorly controlled profit tax. On the whole, this evidence depicts the reform of oil taxation in 2002 as a big step forward of the Russian fiscal system. This report is a shorter English version of the paper "Estimating the tax burden in the Russian oil sector under the price parity hypothesis" (Ekonomika i Matematicheskie Metody (2005), 41, 3)

Essays on the econometric theory of rank regressions

Several semiparametric estimators recently developed in the econometrics literature are based on the rank correlation between the dependent and explanatory variables. Examples include the maximum rank correlation estimator (MRC) of Han [1987], the monotone rank estimator (MR) of Cavanagh and Sherman [1998], the pairwise-difference rank estimators (PDR) of Abrevaya [2003], and others. These estimators apply to various monotone semiparametric single-index models, such as the binary choice models, the censored regression models, the nonlinear regression models, and the transformation and duration models, among others, without imposing functional form restrictions on the unknown functions and distributions. This work provides several new results on the theory of rank-based estimators. In Chapter 2 we prove that the quantiles and the variances of their asymptotic distributions can be consistently estimated by the nonparametric bootstrap. In Chapter 3 we investigate the accuracy of inference based on the asymptotic normal and bootstrap approximations, and provide bounds on the associated error. In the case of MRC and MR, the bound is a function of the sample size of order close to n^(-1/6). The PDR estimators, however, belong to a special subclass of rank estimators for which the bound is vanishing with the rate close to n^(-1/2). In Chapter 4 we study the efficiency properties of rank estimators and propose weighted rank estimators that improve efficiency. We show that the optimally weighted MR attains the semiparametric efficiency bound in the nonlinear regression model and the binary choice model. Optimally weighted MRC has the asymptotic variance close to the semiparametric efficiency bound in single-index models under independence when the distribution of the errors is close to normal, and is consistent under practically relevant deviations from the single index assumption. Under moderate nonlinearities and nonsmoothness in the data, the efficiency gains from weighting are likely to be small for MRC in the transformation model and for MRC and MR in the binary choice model, and can be large for MRC and MR in the monotone regression model. Throughout, the theoretical results are illustrated with Monte-Carlo experiments and real data example

Tax reform in the oil sector of Russia - a positive assessment

I analyze the system of taxes imposed on the Russian oil sector before and after the tax reform of 2002. I first establish a price parity relation explaining the gap between the world and domestic prices through export duties and alternative transportation costs. Based on it, I argue that the indirect taxes (VAT, the sales and excise taxes) do not decrease the net profits of oil producers, but are mostly shifted onto consumers. The tax burden on producers, on the other hand, consists of the export duties, resource payments, the profit tax and the property tax. I show that the tax reform had little effect on the total amount of taxes imposed on producers, but changed its structure across the types of taxes. After the reform the share of efficiently collected taxes, most importantly the extraction tax (ET), increased, explaining higher tax revenues. Finally, I estimate the extent to which the extraction tax is economically inefficient. By showing that the deadweight loss associated with ET is only a small fraction of the generated tax revenues, I argue that ET is a better choice for capturing the natural rent in the Russian oil sector than the poorly controlled profit tax. On the whole, this evidence depicts the reform of oil taxation in 2002 as a big step forward of the Russian fiscal system. This report is a shorter English version of the paper "Estimating the tax burden in the Russian oil sector under the price parity hypothesis" (Ekonomika i Matematicheskie Metody (2005), 41, 3)

Essays on the econometric theory of rank regressions

Several semiparametric estimators recently developed in the econometrics literature are based on the rank correlation between the dependent and explanatory variables. Examples include the maximum rank correlation estimator (MRC) of Han [1987], the monotone rank estimator (MR) of Cavanagh and Sherman [1998], the pairwise-difference rank estimators (PDR) of Abrevaya [2003], and others. These estimators apply to various monotone semiparametric single-index models, such as the binary choice models, the censored regression models, the nonlinear regression models, and the transformation and duration models, among others, without imposing functional form restrictions on the unknown functions and distributions. This work provides several new results on the theory of rank-based estimators. In Chapter 2 we prove that the quantiles and the variances of their asymptotic distributions can be consistently estimated by the nonparametric bootstrap. In Chapter 3 we investigate the accuracy of inference based on the asymptotic normal and bootstrap approximations, and provide bounds on the associated error. In the case of MRC and MR, the bound is a function of the sample size of order close to n^(-1/6). The PDR estimators, however, belong to a special subclass of rank estimators for which the bound is vanishing with the rate close to n^(-1/2). In Chapter 4 we study the efficiency properties of rank estimators and propose weighted rank estimators that improve efficiency. We show that the optimally weighted MR attains the semiparametric efficiency bound in the nonlinear regression model and the binary choice model. Optimally weighted MRC has the asymptotic variance close to the semiparametric efficiency bound in single-index models under independence when the distribution of the errors is close to normal, and is consistent under practically relevant deviations from the single index assumption. Under moderate nonlinearities and nonsmoothness in the data, the efficiency gains from weighting are likely to be small for MRC in the transformation model and for MRC and MR in the binary choice model, and can be large for MRC and MR in the monotone regression model. Throughout, the theoretical results are illustrated with Monte-Carlo experiments and real data example

Оценка налоговой нагрузки в нефтедобыче в условиях ценового паритета между внутренним и внешним рынком

I estimate the revenues, profits and tax payments in the Russian oil sector for various counterfactual world oil prices. I base my analysis on the price parity hypothesis for the oil prices in the domestic and world markets that I verify empirically. I apply these results to analyze the effects of the tax reform in the Russian oil sector in 2002

Asymptotic and bootstrap properties of rank regressions

The paper develops the bootstrap theory and extends the asymptotic theory of rank estimators, such as the Maximum Rank Correlation Estimator (MRC) of Han (1987), Monotone Rank Estimator (MR) of Cavanagh and Sherman (1998) or Pairwise-Difference Rank Estimators (PDR) of Abrevaya (2003). It is known that under general conditions these estimators have asymptotic normal distributions, but the asymptotic variances are difficult to find. Here we prove that the quantiles and the variances of the asymptotic distributions can be consistently estimated by the nonparametric bootstrap. We investigate the accuracy of inference based on the asymptotic approximation and the bootstrap, and provide bounds on the associated error. In the case of MRC and MR, the bound is a function of the sample size of order close to n^{-1/6}. The PDR estimators belong to a special subclass of rank estimators for which the bound is vanishing with the rate close to n^{-1/2}. The theoretical findings are illustrated with Monte-Carlo experiments and a real data example

Вплив термічного фактора на склад електронно-променевих високоентропійних AlTiVCrNbMo покриттів

This paper reports results of studying the element and phase compositions of electron-beam coatings based on the high-entropy alloy AlTiVCrNbMo, depending on the deposition temperature (in the range of 300...700 °С).The high-entropy alloys were melted in an arc furnace in an atmosphere of high-purity argon. Vacuum condensates of the high-entropy alloy (AlTiVCrNbMo) with a thickness of 3–5 µm were obtained in the vacuum setup UVN-2M-1 at a working vacuum of 5·10-5 mТоrr. The alloy evaporation was performed from the water-cooled ingot mold using an electron-beam gun with a power of 5 kW. Condensation of vapors of all the elements of the alloy was performed onto copper substrates at temperatures of 300, 500, 700 °C.Based on analysis of the element composition of materials of the target made of the high-entropy six-element alloy AlTiVCrNbMo and electron-beam coatings, based on it, we established the critical parameter (specific heat of vaporization of an element) that defined a selective change in the element composition. In accordance with a characteristic change in the composition of coatings of the multi-element high-entropy alloy, 3 groups of elements were distinguished: with a specific heat of evaporation of 280...350 kJ/mol (group 1), 420…460 kJ/mol (group 2), and 590…680 kJ/mol (group 3). It was shown that the formation of a single-phase coating of the high-entropy alloy (based on BCC of the crystalline lattice) occurs at the higher deposition temperature of 500...700 °C when the coating consists of not less than 5 elements.It was established that based on the conditions for an electron-beam process of materials formation, the results obtained can be divided into two types: those determined by the condition of evaporation of the target and those determined by the conditions of coating deposition. The density of flows of elements, evaporated from the target, is determined by their specific heat of evaporation. However, the ratio of atoms in the flow, derived in this way, may not be retained in the formed coating due to the secondary evaporation of elements from the growth surface. The obtained results allow us to substantiate principles for the selection of components for achieving the optimal element and phase compositions of high-entropy alloys.На основе анализа элементного состава материалов мишени из высокоэнтропийного шестиэлементного сплава AlTiVCrNbMo и электронно-лучевых покрытий на его основе установлен критичный параметр (удельная теплота испарения элемента), определяющий селективное изменение элементного состава. Показано, что формирование однофазного покрытия высокоэнтропийного сплава происходит, когда в состав покрытия входит не менее 5 элементов. Полученные результаты позволяют обосновать принципы подбора компонент для достижения оптимальных элементного и фазового состава высокоэнтропийных сплавовНа основі аналізу елементного складу матеріалів мішені з високоентропійного шестиелементного сплаву AlTiVCrNbMo і електронно-променевих покриттів на його основі встановлено критичний параметр (питома теплота випаровування елемента), який визначає селективну зміну елементного складу. Показано, що формування однофазного покриття високоентропійного сплаву відбувається, коли до складу покриття входить не менше 5 елементів. Отримані результати дозволяють обґрунтувати принципи підбору компонент для досягнення оптимальних елементного та фазового складу високоентропійних сплаві