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19МАТЕМАТИЧЕСКИЕ И ИНСТРУМЕНТАЛЬНЫЕ МЕТОДЫ _ЭКОНОМИКИ_
GDP Cointegration analysis of Russia and European Union countries Arshinnik D.1, Tregub I.2 (Russian Federation) Коинтеграционный анализ ВВП России и стран Европейского союза Аршинник Д. В.1, Трегуб И. В.2 (Российская Федерация)
'Аршинник Дмитрий Владимирович / Arshinnik Dmitry - студент магистратуры, международно-финансовый факультет;
2Трегуб Илона Владимировна / Tregub Ilona - доктор экономических наук, профессор, кафедра системного анализа и моделирования экономических процессов, Финансовый университет при Правительстве Российской Федерации, г. Москва
Abstract: we intend to investigate cointegration between Russian economy and European Union countries. We have taken data of gross domestic product (GDP) on quarterly basis covering period from 2003 to 20'5 for real values of indicator. We use program Eviews 9.5 Student version to perform Johansen and Granger tests for cointegration.
Аннотация: исследуется взаимовлияние экономики России и стран Европейского союза. Квартальные данные по реальному ВВП с 2003 года по 2015 проанализированы посредством тестов Йохансена и Грэнджера с помощью программы Eviews 9.5 (версия для студентов).
Keywords: Russia, European Union, cointegration, Johansen, Granger. Ключевые слова: Россия, ЕС, коинтеграция, Йохансен, Грэнджер.
The EU and Russia have a long record of cooperation on issues of bilateral and international concern. Our relationship has been seriously undermined by unilateral sanctions imposed by the European Union at the expense of economic interests of both sides for the sake of promoting dubious geopolitical schemes. Events of recent months have demonstrated that burgeoning trade and economic ties between Russia and the EU have not yet attained the level of a true strategic partnership based on the principles of equality, indivisibility of security and mutual respect for each other's interests.
Cointegration is the property of several non-stationary (integrated) time series, implying the existence of their stationary linear combination. It is an important property of many economic variables, which means that despite the occasional (slightly predictable) changes in the nature of individual economic variables, there is a long-term relationship between them, which leads to some shared, interconnected change [1, p. 115].
To test for cointegration between two or more non-stationary time series with Engle-Granger approach, it simply requires running an OLS regression, saving the residuals and then running the ADF test on the residual to determine if it is stationary. The time series are said to be cointegrated if the residual is itself stationary. In effect the non-stationary I(1) series have cancelled each other out to produce a stationary I(0) residual:
yt =A) + ut,
where y and x are non-stationary series.
According to Granger Representation Theorem, if two variables y and x are cointegrated, then the relationship between the two can be expressed as an error correction model (ECM), in which the error term from the OLS regression, lagged once, acts as the error correction term. In this case the cointegration provides evidence of a long-run relationship between the variables, whilst the ECM provides evidence of the short-run relationship [4]. A basic error correction model would appear as follows:
Ay =Zo + ZiAxt-Фы) + ъ,
where т is the error correction term coefficient, which theory suggests should be negative and whose value measures the speed of adjustment back to equilibrium following an exogenous shock. The
error correction term U^_, which can be written as: (y^_1 _ ) ,is the residual from the
cointegrating relationship.
Johansen Maximum Likelihood Procedure is a means of testing for cointegration in a multivariate context, where there is the possibility of more than one cointegrating vector being present. It follows the same principles as the Engle-Granger approach to cointegration, in so far as the order of integration of the variables are first assessed, if the variables are I(1) the Johansen Maximum Likelihood (ML) procedure can then be used to determine whether a stable long-run relationship exists between the variables [3, p. 46].
The main difference between the two test statistics is that the Trace test is a joint test where the null hypothesis is that the number of cointegrating vectors is less than or equal to r, against a general alternative that there are more than r. Whereas the maximum Eigenvalue test conducts separate tests on the individual eigenvalues, where the null hypothesis is that the number of cointegrating vectors is r, against an alternative of (r+1) [1, p. 120]. The two statistics are:
Kc (r) = _T tin (1 )
i=r+1
(r, r +1) = _T ln(1 _Mr+1)
where is the estimated value for the z'th ordered eigenvalue from the n matrix. The standard
approach to the Johansen ML procedure is to first calculate the Trace and Maximum Eigenvalue statistics, then compare these to the appropriate critical values [2].
Example of results of testing pair cointegration of Russia's and European Union countries GDP in Eviews are shown in the following tables. The level data have linear trends but the cointegrating equations have only intercepts:
Table 1. Real GDP Pairwise Granger Causality tests
Pairwise Granger Causality Tests Date: 10/16/15 Time: 12:59 Sample: 2003Q1 2015Q2 Lags: 2
Null Hypothesis: Obs F-Statistic Prob.
RUSSIA does not Granger Cause AUSTRIA AUSTRIA does not Granger Cause RUSSIA 48 40.1175 0.00237 1.E-10 0.9976
Pairwise Granger Causality Tests Date: 10/16/15 Time: 13:39 Sample: 2003Q1 2015Q2 Lags: 2
Null Hypothesis: Obs F-Statistic Prob.
RUSSIA does not Granger Cause BELGIUM BELGIUM does not Granger Cause RUSSIA 48 10.4876 0.01046 0.0002 0.9896
Forty-eight quarterly observations of real GDP are taken covering period from 2003 to 2015. Table above reveals that we cannot reject null hypothesis, that Russia does not Granger Cause for Austria and Belgium, because probability of 0.0002 is lower the critical level of 0.05.
Table 2. Real GDP Johansen System Cointegration Test
Series: CROATIA RUSSIA
Lags interval (in first differences): 1 to 1
Unrestricted Cointegration Rank Test (Trace)
Hypothesized Trace 0.05
No. of CE(s) Eigenvalue Statistic Critical Value Prob.**
None * 0.394042 29.76091 15.49471 0.0002
At most 1 * 0.112258 5.715582 3.841466 0.0168
At the critical value of 15.48 with Eigenvalue 0.39, this table reveals we cannot reject null hypothesis, that Russia does not Granger Cause for Croatia, because probability of 0.0002 is considerably lower 0,05 level. We face At most 1 cointegrating vector with eigenvalue 0.11, trace statistics 5.71 ant critical value of 3.84 with 0.05 probability. Results of this cointegration analysis will be used in further investigation of European Union and Russia dependence.
References
1. Co-Integration and Error Correction: Representation, Estimation, and Testing Robert F. Engle and C. W. J. Granger // Applied Econometrics, 2015, 39 (3), pp. 107-135.
2. Tregub I. V. Makrojekonomicheskaja model' Klejna-Goldbergera Prjamye inostrannye investicii // Jekonomika i socium. 2014. № 4-4 (13).
3. Tregub I. V. Matematicheskie modeli dinamiki jekonomicheskih sistem, monografija. - M.: Finakademija. 2009 g.
4. Tregub I. V. Investigation of the influence of unemployment on economic indicators // Research in Empirical International Trade WP# 597 November 1, 2013 C. Dougherty. Introduction to Econometrics. Oxford, University Press, 2013.
Securities as the objects of civil rights in the new edition of the civil code
of the Russian Federation Kyznetcov V. (Russian Federation) Ценные бумаги как объекты гражданских прав в новой редакции гражданского кодекса РФ Кузнецов В. В. (Российская Федерация)
Кузнецов Виктор Валерьевич /Kyznetcov Victor - магистр юриспруденции, кафедра гражданского права, Негосударственное образовательное учреждение высшего профессионального образования Санкт-Петербургская юридическая академия, г. Санкт-Петербург
Аннотация: статья посвящена некоторым новеллам в гражданско-правовом регулировании ценных бумаг как объектов гражданских прав в связи с принятием в прошлом году новой редакции Гражданского кодекса РФ.
Abstract: the article is devoted to some novels in the civil-law regulation of the securities as objects of civil rights in connection with the adoption last year of a new version of the Civil Code.
Ключевые слова: объекты гражданских прав, документарные ценные бумаги, бездокументарные ценные бумаги, обязательственные и иные права, иное имущество, корпоративные права.
Keywords: objects of civil rights, documentary securities, uncertificated securities, contracts and other rights, other property, corporate rights.
