Macroeconomic Relationships for Russian Economic Regions

This paper deals with macroeconomic relationships for Russian economic regions. An economic region is the main item of the regional statistics of the Russian Federation. Nowadays there are near 90 of regions and according to classification these can be industrial, agroor subsidized regions A study is based upon the disaggregated macromodel for the Russian economic region. Then classification of the Russian regions by types of economic activity is made. Finally, we construct macroeconomic relationships for Russian economic regions specific by their type of economic activity This paper can be considered as the first attempt to create the model of the Russian regional level.

VAR model are not often selected as methodology for creation of applied macroeconomic models. "A curse of dimensionality" is the main idea which limits the application of VAR models to the analysis of the Russian economy.
Therefore at the macro level the third approach to applied macroeconomic modeling (Cowles commission) is more often used. Below we dwell upon the basic principles of structural macroeconomic model of Russian regions.

Methodology
In the early 1990s, after the liberalization of prices and foreign trade, three macro-sectors of economic activity emerged in Russia's real production sphere. Different in terms of competition for domestic and foreign markets these sectors usually include: Export-Oriented Sector (EOS); Domestic-Oriented Sector (DOS), Natural Monopolies (NM).
So, for the proposed model the following system of assumptions is accepted: three-sector structure of the production sector; the different price's priorities in the EOS, DOS, NM; exogeneity of prices. Further, the model assumes that the products of each sector are parametricized by: p -price level (base index), Y -real production output, Incaggregated income level, D -total subsidies, investment into a sector. In addition, the following symbols in the model are used:  -the direct cost ratio,  -the average nominal wage,  -the world (export) price, Ex , Im -real exports and imports, respectively,  -the rate of inflation,  -elasticity of the output with respect to the labor, e -exchange rate dollar/rouble.   However, excessive credit resources rates e  , d  will lead, on the contrary, to an increase in the number of bankruptcies of real sector enterprises and to a decrease in the output of EOS and DOS sectors.
With a small share of exports of the DOS sector output d Y will also be small in comparison with e Y , and when predicting the dynamics of aggregate output, it is possible to be limited in dynamics prediction by indicator e Y .
However, when the d Y increases its role, the model becomes a system of two difference equations describing the dynamics of e Y and e Y indicators.

Classification of the Russian regions by types of economic activity
Classification of Russian regions by types of economic activity was done to achieve more accurate calibration of the equations of the model. A fairly simple heuristic algorithm of clustering is proposed in this report. The basic idea is: at the input of the algorithm is the GRP (gross regional product) structure vector with the normalized (by aggregate Russian values) components, the number of clusters in general is equivalent to the number of economic activity types (see [12]). We refer a region to a particular cluster by the maximum value of the ratio of the output of the corresponding type of economic activity of the region to the aggregate Russian output of the corresponding type of economic activity.

Macroeconomic relationships for the Russian economic regions
As a result, classification of the Russian regions into truly subsidized, agricultural, and industrially developed regions is proposed in the report. Then we constructed macroeconomic relationships for each type of a region. In particular, for truly subsidized regions of Russia the following relationship holds 01 log log where t GRP -gross regional product (deflated for base index), t SUBSIDIES -volume of subsidies to the region, t  -residuals which assumed to be stationary. For Republic of Dagestan, from the sample 2001-2016 (yearly data) the following econometric coefficients were obtained: 0   -28.075 ***(0.931), 1   1.831*** (0.055) (the error level 1%). In the above constructed system we used correction of the nominal value of SUBSIDIES for the basis price index on the consumer market of the region. After that we used the test of Dickey-Fuller ( [13]), [14]) for testing stationarity (non-stationarity) of time series. This test tells us that all initial variables have the order (1) I . This result gives us reasons for searching cointegration relationship. Residuals in the constructed relationship are stationary (test of Davidson-MacKinnon [15]). So, the constructed macroeconometric relationship is of true cointegration type. 2 R  0.98. The analogous results were obtained for other types of regions.

Conclusions
The development of macro-model of the Russian economic region is considered in the article. The core idea (methodology and equations) of the approach is illustrated with the disaggregated macroeconomic model of Russia. The main conclusions of the analytical model are statistically tested with real data and generally confirmed at the regional level.
Classification of Russian regions by types of economic activity was done to achieve more accurate calibration of the equations of the model. It was essential to distinguish between many regions steadily (truly) subsidized, for which the influence of macro-factors could be overwhelmed by regularly received subsidies. The analysis of regions in terms of subsidies revealed the stability of the group of subsidized regions over time, as well as the stability of the form of the empirical curve of the distribution of regions by the index value -the ratio of accumulated subsidies of the region to the accumulated GRP.
The practical importance of the results follows from the basic idea to construct macroeconomic relationships of the Russian macroeconomic regions and to make the first attempt to create the macroeconomic model of the Russian regional level.