Corresponding author: Aizhan Bolatbayeva ( aizhan.bolatbayeva@nu.edu.kz ) © 2020 Nonprofit partnership “Voprosy Ekonomiki”.
This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BYNCND 4.0), which permits to copy and distribute the article for noncommercial purposes, provided that the article is not altered or modified and the original author and source are credited.
Citation:
Bolatbayeva A, Tolepbergen A, Abilov N (2020) A macroeconometric model for Russia. Russian Journal of Economics 6(2): 114143. https://doi.org/10.32609/j.ruje.6.47009

The paper outlines a structural macroeconometric model for the economy of Russia. The aim of the research is to analyze how the domestic economy functions, generate forecasts for important macroeconomic indicators and evaluate the responses of main endogenous variables to various shocks. The model is estimated based on quarterly data starting from 2001 to 2019. The majority of the equations are specified in error correction form due to the nonstationarity of variables. Stochastic simulation is used to solve the model for expost and exante analysis. We compare forecasts of the model with forecasts generated by the VAR model. The results indicate that the present model outperforms the VAR model in terms of forecasting GDP growth, inflation rate and unemployment rate. We also evaluate the responses of main macroeconomic variables to VAT rate and world trade shocks via stochastic simulation. Finally, we generate exante forecasts for the Russian economy under the baseline assumptions.
macroeconometric model, Cowles Commission approach, structural macroeconomic model, macroeconomic model for Russia, forecasting
In pursuit of accurate macroeconomic forecasting and effective policy analysis, structural macroeconomic models have advanced significantly with the use of more sophisticated computational techniques. The literature contains a variety of structural macroeconometric models for different countries. The common objective of these works is to construct a model which can explain fluctuations in major macroeconomic variables and be used for the purpose of policy analysis. This paper presents a structural macroeconometric model for the economy of Russia. The model has been constructed for the following essential objectives. First, the model gives better insight into the structural relationships between different macroeconomic variables underpinning the Russian economy. Second, it allows to determine the economic implications of policy changes. Investigating the responses of endogenous variables to various shocks is an additional advantage of a structural macroeconometric model. Third, the model can generate forecasts for main macroeconomic indicators.
Most equations are estimated in errorcorrection form based on quarterly data starting from 2001 to 2019. Other equations are estimated using Tobit regression and the ARIMA model via the maximum likelihood estimation (MLE) technique. The estimated equations are in line with economic theory and satisfy standard statistical properties by the robustness checks on the residuals. The model is solved for expost and exante analysis using a stochastic simulation technique. To demonstrate the properties of the model for using it as a tool for exogenous shock analysis, we conduct two additional simulation exercises. First, we investigate the responses of endogenous variables to an increase in the value added tax (VAT) rate by two percentage points. This issue stands at the top of the agenda at the time of writing this paper since the VAT rate has been raised from 18% to 20% starting from January 1, 2019. Second, we analyze the effect of a negative world trade shock on the Russian economy. In particular, we assume a contraction of the world trade by 5% and show associated changes in real GDP growth, inflation rate, unemployment rate and other relevant macroeconomic variables. Assessing the impact of a world trade shock is relevant because the Russian economy has mostly been dependent on exports of oil and other raw materials. In addition, the macroeconometric model is a useful tool for generating exante forecasts with various assumptions on exogenous variables, and the stochastic simulation technique allows us to construct confidence bands around median forecasts.
The structure of the paper is as follows. Section 2 presents a review of relevant research on macroeconometric modeling and also discusses various versions of macroeconometric models for Russia. In Section 3, we present the data description in detail and discuss the main barriers encountered in the data structuring process. Section 4 presents the main characteristics and structure of the model, including the specification of the equations. The expost simulation of the model is discussed in Section 5. Section 6 presents the results of the model under VAT rate and world trade shocks. Section 7 outlines exante forecasts generated for some endogenous variables, and Section 8 provides concluding remarks.
One of the models that the Federal Reserve Board used for forecasting and macroeconomic analysis of fiscal and monetary policies was the FRB/US model. A detailed description of the model and its equations is presented in
There also exists literature on macroeconometric modeling for emerging countries including the Russian economy.
Structural macroeconometric models have been also developed by various Russian scientific organizations and government agencies. The Central Economics and Mathematics Institute of the Russian Academy of Sciences (CEMI RAS) constructed a structural econometric model for the Russian economy. The model is built as a system of six simultaneous equations based on quarterly data starting from the fourth quarter of 1994. Short term forecasts can be generated for several endogenous variables. One can independently formulate scenarios and obtain forecasts for this model on the official website of CEMI RAS.^{1} The Institute of Economic Forecasting of the Russian Academy of Sciences (IEF RAS) built a quarterly macroeconomic model known as the QUMMIR model for the Russian economy. Approximately 460 variables and 200 regression equations are used in the model. Short and mediumterm forecasts can be generated online within the framework of various scenarios.^{2}IEF RAS publishes quarterly forecasts of macroeconomic indicators for Russia based on the QUMMIR model.
The section describes the data used in the model in detail. The model is estimated based on quarterly data without seasonal adjustments. The data spans the period from 2001 to 2019 (76 observations) for the majority of variables. The primary source of national accounts and labor market data is the Federal State Statistics Service of the Russian Federation (hereinafter — the Federal State Statistics Service). The government revenues and expenditures data are retrieved from the database of the Federal Treasury of the Russian Federation. Other data is gathered from the Bank of Russia, Bloomberg and the International Monetary Fund databases.
A number of adjustments have been made to the raw data from the national accounts. The Federal State Statistics Service publishes quarterly data on expenditure components of GDP, and on the domestic output calculated by the production side.^{3} In theory, GDP figures calculated by the expenditure and production sides must be equal, but in practice, they do not coincide and the difference is usually attributed to a statistical discrepancy. Some adjustments have also been made to GDP and its expenditure components at constant prices. During the period between 2001 and 2019, the Federal State Statistics Service changed the base year for the calculation of GDP and expenditure components of GDP at constant prices four times. In this model, the base period is taken to be the first quarter of 2010. The equations below explain the way GDP and expenditure components have been calculated at 2010 prices:^{4}
where i refers to GDP and expenditure components of GDP; D_{i,t} is the price deflator; k refers to the base years of 2003, 2008, 2011 and 2016 from the national accounts; A_{i,t} is the adjusted price ratio; P_{i,t} is the price variable; Q_{i,t} is the quantity variable. Equation 2 demonstrates the way price deflators calculated in Equation (1) are used to find the price ratios. Equation 3 converts nominal values of GDP and expenditure components of GDP to 2010 prices. As a result, we find GDP and expenditure components of GDP at 2010 prices and refer to them as being the real GDP and real expenditure components of GDP.
Data on capital stock is not available for Russia. The Perpetual Inventory Method (PIM) is used to obtain a suitable capital stock variable. This approach is based on the idea that today’s stock of capital is composed of gross investment in the current period added to the capital stock from the previous period less depreciation. Equation (4) demonstrates the way the capital stock is derived based on the PIM:
where K_{t} is the capital stock at time t; I_{t} is the gross fixed capital formation in the current period; δ is the depreciation rate in the current period. The application of the PIM approach requires the initial value of the capital stock. Data from the Penn World Table is used to estimate the value of the capital stock in 2001. The capitaloutput ratio of 2.55 is deduced using the capital stock and the real GDP values from the Penn World Table. Then we use the depreciation rates from the Penn World Table to calculate the capital stock over the sample via the PIM. Since the data on depreciation rates is only available until 2014, we further assume a constant depreciation rate of 4.3% per annum from 2015 onwards.
Since the data on total population and population of working age are available in annual frequency, we convert them into quarterly frequency by assuming an exponential growth within a given year. That is, total population and workingage population grow at a constant rate each quarter in a given year to make the annual growth rate compatible with the actual observed growth rate.
We start the modelbuilding by analyzing the properties of variables (see Appendix A) in order to specify regression equations for estimation purposes. Unit root tests are used to check the stationarity of variables. Commonly applied statistical tests such as Augmented Dickey–Fuller (ADF), Phillips–Perron (PP) and Kwiatkowski–Phillips–Schmidt–Shin (KPSS) are used to determine whether a given series has a unit root or not. The test results show that most variables are nonstationary in levels and stationary in yearoveryear measures (YoY).^{5}
Most of the variables are integrated of order one (I(1)) processes and have a cointegrating relation with a set of other variables. First, we specify longrun equations in logarithmic levels and estimate them via OLS to extract residuals. Second, the residuals are tested for unit root via ADF, PP and KPSS tests. If the tests confirm the stationarity of residuals, then the nonstationary endogenous variables have a cointegrating relation with the set of nonstationary righthand side variables. Hence, the cointegration relation is included into the regression equation as the longrun relationship between the variables. Appendix E presents the results of the tests for cointegration. They indicate that there indeed exists cointegration between dependent and independent variables in many equations. As a result, most regression equations are specified in error correction form with the inclusion of a long run relation. Other equations have been specified in levels due to the stationary nature of dependent variables. The residual diagnostics have been conducted for all equations, the results of which are presented in Appendix D.
We also use YoY measures of variables as a form of differencing in regression equations. In this way, we address the seasonality present in the data. In addition, dummy variables have been added into most equations to address the problems of structural breaks and shifts. The model uses a backwardlooking approach in forming expectations through the inclusion of lagged dependent variables in the equations. Thus, the model possesses the property of adaptive expectations.
The model is composed of the following blocks: supply side, goods market, labor market, financial market, central bank policy rule, prices, and the government sector. The supply block consists of equations for potential output, labor supply, longrun total factor productivity (TFP) and natural unemployment rate. Potential output is determined by the Cobb–Douglas production function which is assumed to exhibit constant returns to scale.
where A_{t} stands for TFP and B is any normalizing constant. The shares of capital and labor are fixed at 0.4 and 0.6, respectively. The potential output is calculated using the capital stock, natural level of employment and TFP. We use the nonaccelerating inflation rate of unemployment (NAIRU) and the labor force to calculate the natural employment. Therefore, we find the NAIRU by applying the Hodrick–Prescott (HP) filter to the actual unemployment rate. The Solow residual from the estimated production function is also detrended via the HP filter to extract the trend of TFP. Finally, we specify and estimate regression equations for NAIRU, trend TFP and labor force to endogenize these variables in the model. The labor force depends on its own lag and real wages, and both variables enter the regression with a positive sign. NAIRU and trend TFP equations are specified in ARIMA form. The resulting equations for potential output, labor supply, trend TFP and NAIRU form the supply side of the model.
1) Cobb–Douglas production function equation:
2) Potential output equation:
3) Labor force equation:
4) NAIRU trend equation:
5) Trend TFP equation:
The demand side of the model consists of five real expenditures components of GDP with each being modeled separately: private consumption, private investment, oil exports, nonoil exports, and imports. Government consumption is treated as an exogenous variable in the model. According to the Keynesian consumption function, household consumption is a function of current disposable income. In addition, the permanent income hypothesis implies that economic agents make their consumption decisions taking into account discounted future wealth (see Friedman, 1957). As a result, we use an error correction term which is the longrun relationship between private consumption and disposable income. In addition, the household interest rate is used as a proxy for the wealth effect via discounting factor. The negative sign of the latter implies that the higher interest rate leads to lower wealth, which in turn results in decline in private consumption. We use the nominal interest rate in the equation due to Fair (2018), who establishes that the nominal interest rate provides a better empirical fit than the real interest rate in determining consumption. The equation is also explained by a lagged consumption variable that represents habit formation. The significant positive sign of the coefficient implies persistence in consumption behavior.
6) Private consumption equation:
Private investment in the model depends on the lagged value of itself, demand for domestic goods and services, and longterm interest rate. The lagged value of the dependent variable represents investment adjustment costs which enter the righthand side of the equation with a positive sign as well as the demand for domestic goods variable. The positive response of the latter can be explained by the fact that firms tend to add more capacity when the demand for their goods rises. The interest rate has a significant negative impact on investment since firms tend to cut on investment when the opportunity cost of capital rises.
7) Investment equation:
The link between the country’s economy and the rest of the world is established via the equations for oil exports, nonoil exports, and imports. Due to the important role of crude oil exports in determining domestic economic conditions in Russia, we disaggregate it into oil and nonoil exports. Moreover, the disaggregation allows for estimation of the equations for these variables based on different sets of explanatory variables. The oil exports depend on the lagged dependent variable, world trade index and oil price where the world trade index is a proxy for the amount of international trade. All these variables have a positive impact on oil exports as expected.
8) Oil exports equation:
The nonoil exports equation is determined by the lagged value of itself, the world trade index and the real exchange rate. The latter affects nonoil exports in line with the mainstream view whereas the world trade has a positive influence on the dependent variable as expected. Both explanatory variables have statistically significant coefficients.
9) Nonoil exports equation:
Imports of goods and services also form an important part of international linkage of the Russian economy with the rest of the world. The lagged value of imports is added into the imports equation to allow for smooth adjustment. The equation is estimated in error correction form, in which the cointegrating relation exists between imports, domestic output, and real exchange rate. The estimated coefficients of domestic output and real exchange rate are positive and statistically significant in line with economic theory.
10) Imports equation:
The labor market of the economy is based on a theoretical framework of the bargaining model, in which firms and unions negotiate over wages and employment. Thus, we estimate equations for average nominal wage and labor demand. The average nominal wage is influenced by the lagged value of itself, labor productivity, unemployment rate and inflation rate. The positive and significant coefficient of the lagged dependent variable implies the existence of persistence. Unemployment rate has a negative impact on average nominal wage, whereas the labor productivity affects it positively. The cointegrating relation has been imposed in the estimated equation between the average nominal wage and price level, the restriction being one to one movement of the nominal wage with the price level in the long run.
11) INominal wage equation:
The other part of the labor market, the employment equation, is estimated in the form of Tobit regression. We define the dependent variable as the ratio of employment to labor force. Hence, the MLE technique is exploited to estimate the regression model with the censored dependent variable with censoring being at 0 and 0.99. The dependent variable is determined by the lagged value of itself, growth in production and real wage. All coefficients have expected signs and are statistically significant.
12) Employment equation:
Aggregate price levels are also included into the model by specifying and estimating regression equations for them. The annual rate of inflation has been modeled as depending on lagged inflation, output growth and nominal exchange rate. We assume adaptive expectations in the model which explains the reason the lagged inflation appears on the righthand side of the equation. The nominal exchange rate is included as a regressor since imported goods are a substantial part of the consumer basket in Russia. The GDP deflator equation is defined in terms of lagged dependent variable, local CPI and consumer price level in the US. The price level in the US affects the GDP deflator in Russia due to the managed floating exchange rate regime against US dollar that prevailed in Russia until 2014. We also construct equations for other price deflators, including private consumption deflator, government consumption deflator, exports and imports deflators.
13) CPI equation:
14) GDP deflator equation:
15) Private consumption deflator equation:
16) Government consumption deflator equation:
17) Export deflator equation:
18) Import deflator equation:
Financial markets of the model consist of equations for real exchange rate, mediumterm government bond yield and household saving rate. On the foreign exchange market, the real effective exchange rate (REER) is explained by changes in the domestic price level (inflation rate), nominal exchange rates and policy interest rate differential. In this case, a rise of the real exchange rate means a real appreciation of the domestic currency. Since the REER index is determined as the weighted average of bilateral exchange rates of Russian ruble against other major currencies, we include nominal exchange rates of euro and US dollar against the ruble as explanatory variables on the righthand side. The equation for the mediumterm government bond yield represents the bonds market. The equation is specified in levels due to the stationary nature of the dependent variable. The mediumterm government bond yield depends on its own lagged value and the central bank policy rate. Similarly, the household saving rate equation is determined in levels and consists of the lagged dependent variable and the central bank policy rate.
19) Real exchange rate equation:
20) Mediumterm government bond yield equation:
21) Household saving rate equation:
The central bank policy rate equation has been included in the model as a relevant monetary policy instrument. The Bank of Russia has been conducting monetary policy under the inflation targeting regime since the end of 2014. The inflation rate enters the equation as its deviation from the target level, which is currently set at 4%. Data on inflation targets for the period 2001–2013 was taken from “Guidelines for the Single State Monetary Policy” annually published by the Bank of Russia. Since the equation is constructed in the spirit of Taylor rule, we also include output gap on the righthand side. Due to the export dependent nature of the economy, the real effective exchange rate has been added on the righthand side as an important indicator in determining the conduct of monetary policy.
22) Central bank policy rate equation:
The model also contains regression equations for relevant government revenue components such as personal income taxes, corporate income taxes, VAT, excises, and other taxes. All equations on the government side of the model are estimated in error correction form. The personal income tax equation is estimated as depending on the lagged value of itself and nominal wages paid to employees. Revenues from corporate income taxes are explained by the nominal GDP multiplied by the corporate income tax rate. Value added tax revenues are associated with total consumption expenditures multiplied by the VAT rate. Excise tax revenues are determined by the lagged dependent variable in the short run and the cointegrating relation with private consumption of households in the long run. Finally, other tax revenues are determined by the nominal GDP in the economy.
23) Personal income taxes equation:
24) Corporate income taxes equation:
25) VAT equation:
26) Excise tax equation:
27) Other tax equation:
We have estimated all the relevant equations, and then identities are introduced to complete the model. The identities of the model are given in Appendix B.
Once the model specification has been completed, the model is solved for expost and exante simulation. Stochastic simulation is used to provide a measure of uncertainty in the results. In comparison with a deterministic solution where error terms are set to their expected value, which is zero, stochastic simulation requires the error terms to be drawn randomly from the estimated residuals (see
The ability of the model to repeat the dynamics of actual endogenous variables is assessed based on expost simulation for the period 2004–2019. Fig. F1 to Fig. F6 in Appendix F show the median values of the expost simulation for the following macroeconomic variables: real GDP growth, potential output growth, inflation rate, unemployment rate, real wage growth and real exchange rate. Solid lines show actual observations and dashed lines represent median values of baseline stochastic simulations. The simulation exercise reveals reasonable accuracy of the model in tracking the actual dynamics of the relevant endogenous variables.
The expost simulation of the model is evaluated by forecast evaluation measures. In particular, we compare expost forecasts obtained by the structural macroeconometric model with expost forecasts generated by the VAR(2) model. We resort to commonly used forecast evaluation measures such as mean absolute percentage error (MAPE), Theil’s inequality coefficient U2, root mean squared error (RMSE) and mean absolute error (MAE) to compare the performance of the two models. Table
Variable  Macroeconometric model  VAR(2) model  
MAPE  Real GDP growth  52.949  137.339 
Unemployment rate  5.596  34.699  
Inflation rate  28.591  59.754  
Theil’s U2  Real GDP growth  0.155  0.821 
Unemployment rate  0.684  0.428  
Inflation rate  0.598  1.338  
RMSE  Real GDP growth  0.013  0.014 
Unemployment rate  0.003  0.021  
Inflation rate  0.020  0.034  
MAE  Real GDP growth  0.010  0.012 
Unemployment rate  0.003  0.015  
Inflation rate  0.016  0.030 
An additional advantage of the present model is its ability to evaluate the impact of various shocks on the economy. In this section, we present the results of two additional simulation exercises which are carried out to analyze the responses of main economic indicators to various shocks. First, the impact of an increase in the VAT rate is investigated. Second, the effect of a contraction in the world trade by 5% is considered. The influences of these shocks on GDP growth and inflation rate of the Russian economy are presented in Appendix F Figs F7–F10. Notably, the figures show the difference between the endogenous variables under the baseline and alternative scenarios.
In 2018, the Russian government introduced amendments to the tax code with the key change being an increase in the VAT rate from 18% to 20%. Therefore, we find it reasonable to analyze the effect of the fiscal policy on important macroeconomic indicators. The increase in the VAT rate translates into the slowdown in real disposable income, which in turn affects private consumption of households in a negative manner. Hence, the GDP growth of the Russian economy falls under the alternative scenario. The maximum deviation from the baseline scenario is 0.11 percentage points. According to the model simulation under the alternative scenario, the impact of the VAT rate shock on inflation seems to be insignificant, even though the effect persists for five years as shown in Appendix F Fig. F8. Based on these results, the model indicates that the VAT rate increase in January 2019 will not create a significant upward inflation pressure in the economy.
The world trade shock produces an intense and persistent effect on economic growth since the Russian economy is heavily dependent on commodity exports. Real GDP quickly returns to its baseline level (see Appendix F Fig. F9). The most significant deviation from the baseline was found in oil exports (see Appendix F Fig. F11). The variable falls by 1.6 percentage points in the year when the shock arises followed by an immediate increase in the next year. In comparison, nonoil exports show a lower deviation from the baseline and the effect of the shock disappears rapidly as illustrated in Appendix F Fig. F12. The response of inflation to the shock appears to be more persistent, but the maximum deviation from the baseline is only 0.15 percentage points.
Since the model performance is reasonably good in expost simulation we use it for exante forecasting in this section. Assumptions on the future paths of exogenous variables are made within the model, including the assumptions on oil prices, nominal exchange rates, foreign price levels, US federal funds rate, population growth and world trade.
Table
Exante forecasts under the scenario of oil price 30 dollars per barrel (%).
Real GDP growth  Potential output growth  Inflation rate  Unemployment rate  
2020  –0.5  2.0  3.2  5.0 
2021  2.9  1.9  4.5  4.8 
2022  2.1  1.6  5.0  4.7 
2023  1.6  1.2  4.9  4.5 
According to exante simulation results, the real GDP is expected to decline by 0.5% in 2020. The Russian economy will likely face the negative growth due to the contraction in world trade and declining oil prices caused by the pandemic of coronavirus. We assume that the world trade contracts by 11% in 2020 and recovers with an increase of 8.4% in 2021 based on the World economic outlook projections prepared by the International Monetary Fund (IMF, 2020). The inflation rate is forecast to remain below its target level in 2020, while the unemployment rate is anticipated to rise to 5%. The economic situation is expected to improve in the following periods. The real GDP growth reaches 2.9% in 2021 and stays positive until the end of the forecast horizon. The potential output growth and the unemployment rate are forecast to slow down by 2023, while the inflation rate is rising.
Fig. F13 to Fig. F16 in Appendix F present fan charts for exante forecasts of real GDP growth, potential output growth, inflation rate and unemployment rate under the scenario of oil price 30 dollars per barrel. The fan charts illustrate a range of possible outcomes with corresponding confidence bands. The grey bands reflect uncertainty over the evolution of the abovementioned variables in the future. The lightest band reflects the 95% confidence interval, while the darkest band — 60%. The median forecast is shown by the solid line for the forecast horizon.
The paper builds the structural macroeconometric model for the Russian economy. The model is composed of the following blocks: supply side, goods market, labor market, financial market, central bank policy rule, prices, and the government sector. The majority of the equations are estimated in errorcorrection form based on quarterly data spanning from 2001 to 2019. Thus, the equations capture the short run dynamics and longrun relationships between the variables. Stochastic simulation is used for both expost and exante simulation. The method provides a measure of uncertainty in the results by drawing the error terms randomly from estimated residuals.
The performance of the model in expost simulation for 2004–2019 reveals good accuracy in tracking the actual dynamics of relevant endogenous variables. The expost simulation of the model is also assessed by the forecast evaluation measures. In particular, expost forecasts obtained for the structural macroeconometric model are compared with forecasts generated by the VAR model for GDP growth, inflation rate and unemployment rate. The results indicate that the structural macroeconometric model gives a better fit for all variables than the VAR model does. In order to illustrate the impact of various shocks on main macroeconomic variables in the model, we investigate the way the economy reacts to the increase in the VAT rate from 18% to 20%, and the drop in the world trade index by 5%. The responses of the endogenous variables to the shocks are in line with the mainstream view in the literature. The model is also used to generate exante forecasts from 2020 to 2023 for important macroeconomic indicators. The results indicate that the real GDP is expected to drop by 0.5% in 2020 due to a decline in economic activity caused by the pandemic. Overall, the model demonstrates good performance in repeating the actual behavior of endogenous macroeconomic variables and conducting exogenous shock analysis.
Variables  Definitions  Units of measurement  Source 

Endogenous  
Capsr  Capital stock, real  Billion RUB10 ^{a)}  Own 
Cdef  Private consumption deflator  Index  Own 
Cn  Private consumption, nominal  Billion RUB  STAT ^{b)} 
Cr  Private consumption, real  Billion RUB10  Own 
Cpi  Consumer price index, 2010 = 100  Index  STAT 
Demandr  Final demand, real  Billion RUB10  Own 
Emp  Number of employees  Million  STAT 
Excises  Excises revenues  Billion RUB10  FT ^{c)} 
Exoilr  Exports of oil, real  Billion RUB10  Own 
Exotherr  Exports of other, real  Billion RUB10  Own 
Expdef  Exports deflator  Index  Own 
Gdef  Government consumption deflator  Index  Own 
Gdpdef  GDP deflator  Index  Own 
Gdpn  GDP by expenditure, nominal  Billion RUB  STAT 
Gdpr  GDP by expenditure, real  Billion RUB10  Own 
Gr  Government consumption, real  Billion RUB10  Own 
Hp_nairu  NAIRU  Percentage  Own 
Hp_tfp  TFP  Level  Own 
Impdef  Imports deflator  Index  Own 
Impr  Imports of goods and services, real  Billion RUB10  Own 
Incomen  Disposable income of private households, nominal  Billion RUB10  Own 
Incomer  Disposable income of private households, real  Billion RUB10  Own 
Inctaxcorp  Corporate income tax revenues  Billion RUB10  FT 
Inctaxpers  Personal income tax revenues  Billion RUB10  FT 
Infl  Inflation rate  Percentage  Own 
Invr  Gross fixed capital formation, real  Billion RUB10  Own 
Lforce  Labor force  Million  STAT 
Midgovb  Midterm government bond rate  Percentage  CBRF ^{d)} 
Cbpr  Policy interest rate of the Central Bank  Percentage  CBRF 
Othertax  Other tax revenues  Billion RUB  FT 
Prod  Labor productivity  1000 RUB10 per employee  Own 
Reer  Real effective exchange rate index  Index  CBRF 
Unemp  Unemployment  Million  STAT 
Unemprate  Unemployment rate  Percentage  Own 
VAT  VAT revenues  Billion RUB  FT 
Wageav  Average gross wage per employee, nominal  RUB  STAT 
Wageavr  Average gross wage per employee, real  RUB10  Own 
Ygap  Output gap  Billion RUB10  Own 
Ypot  Potential output  Billion RUB10  Own 
Exogenous  
Cpic  CPI in China  Index  Bloomberg 
Uscpi  CPI in the USA  Index  Bloomberg 
Depr  Capital stock depreciation rate  Percentage  Own 
Fedr  Federal funds rate  Percentage  Bloomberg 
Gn  Government consumption  Billion RUB  STAT 
Corprate  Corporate income tax rate  Percentage  Own 
Inventr  Change in inventory, real  Billion RUB10  Own 
Inflt  Target inflation rate  Percentage  CBRF 
Rubeur  Nominal exchange rate RUB/EUR  RUB  CBRF 
Rubusd  Nominal exchange rate RUB/USD  RUB  CBRF 
Oilpusd  Oil price, Brent  USD/Barrel  Bloomberg 
Wapop  Working age population, 15 to 72 years  Thousands  STAT 
Socpol  Social policy  Billion RUB  FT 
Vatrate  VAT rate  Percentage  FT 
Wtrade  World trade index, 2010=100  Index  Bloomberg 
Variable (level)  ADF (c)  ADF (c,t)  PP (c)  KPSS 
Capsr  –0.751  –2.168  0.697  1.188+++ 
Cbpr  –2.573  –2.481  –2.572  0.785+++ 
Cdef  0.339  –2.318  0.488  1.180+++ 
Cn  0.199  –2.949  1.242  1.187+++ 
Cpi  0.632  –2.241  0.801  1.178+++ 
Cpic  0.455  –4.157^{***}  1.019  1.186+++ 
Cr  –1.800  –2.384  –1.480  1.068+++ 
Demandr  –2.094  –1.774  –2.730^{*}  1.014+++ 
Emp  –1.668  –2.359  –2.348  1.084+++ 
Excises  –0.492  –3.535^{**}  –0.994  1.072+++ 
Exoilr  –2.687^{*}  –2.830  –2.616^{*}  0.662++ 
Exotherr  –1.171  –2.520  –2.040  1.134+++ 
Expdef  –0.592  –3.688^{**}  –0.317  1.165+++ 
Fedr  –2.736^{*}  –3.432^{*}  –2.218  0.330 
Gdef  0.505  –3.287^{*}  1.385  1.188+++ 
Gdpdef  0.287  –2.974  0.420  1.184+++ 
Gdpn  0.592  –2.903  1.054  1.186+++ 
Gdpr  –2.255  –1.802  –3.102^{**}  1.071+++ 
Gn  0.944  –2.885  1.853  1.188+++ 
Gr  –2.001  –2.525  –2.201  0.97+++ 
Hsr  –4.078^{***}  –3.959^{**}  –3.782^{***}  0.524++ 
Impdef  –0.130  –2.114  –0.148  1.055+++ 
Impr  –1.969  –2.070  –2.238  0.82+++ 
Incomen  –0.410  –2.346  0.269  1.207+++ 
Incomer  –2.209  –1.580  –2.085  1.086+++ 
Inctaxcorp  –0.278  –4.322^{***}  –1.188  1.029+++ 
Inctaxpers  0.862  –2.737  –0.172  1.19+++ 
Infl  –2.276  –3.354^{*}  –2.283  0.692++ 
Inflt  –1.446  –2.117  – 1.443  0.844+++ 
Inventr  –2.264  –3.967^{**}  –7.326^{***}  1.037+++ 
Invr  –2.052  –1.989  –6.810^{***}  1.225+++ 
Lforce  –2.529  –1.103  –2.533  0.959+++ 
Midgovb  –2.959^{**}  –2.877  –3.013^{**}  0.127 
Oilpusd  –2.291  –2.193  –2.207  0.415+ 
Othertax  2.457  0.566  2.698  1.128+++ 
Prod  –2.433  –1.980  –3.642^{***}  1.048+++ 
Reer  –2.129  –1.895  –2.099  0.396+ 
Rubeur  –0.728  –2.156  –0.728  1.019+++ 
Rubusd  –0.351  –1.725  –0.372  0.861+++ 
Socpol  –0.043  –6.928^{***}  –0.13  1.185+++ 
Tcn  0.372  –3.026  1.603  1.188+++ 
Unemp  –1.623  –4.398^{***}  –2.129  0.97+++ 
Unemprate  –1.506  –4.466^{***}  –1.986  1.016+++ 
Uscpi  –0.462  –2.180  –0.460  1.179+++ 
Util  –3.295^{**}  –3.305^{*}  –11.364^{***}  0.194 
Vat  –1.171  –4.435^{***}  –1.171  1.129+++ 
Vatrate  –1.782  –1.062  –1.840  0.368+ 
Wageav  1.740  –1.500  1.971  1.19+++ 
Wageavr  –1.253  –2.483  –1.376  1.09+++ 
Wtrade  –1.522  –3.569^{**}  –1.012  1.119+++ 
Ygap  –3.295^{**}  –3.305^{*}  –11.364^{***}  0.194 
Ypot  –2.258  –2.926  –5.362^{***}  1.098+++ 
Variable (YoY)  ADF (c)  ADF (c,t)  PP (c)  PP(c,t) 
Capsr  –2.460  –2.238  –1.943  –1.533 
Cbpr  –2.961^{**}  –2.978  –3.615^{***}  –3.872^{**} 
Cdef  –2.996^{**}  –3.007  –3.219^{**}  –3.259^{*} 
Cn  –2.514  –2.542  –2.675^{*}  –2.736 
Cpi  –2.917^{**}  –2.873  –2.552  –2.528 
Cpic  –2.256  –2.232  –3.124^{**}  –3.170^{*} 
Cr  –2.099  –3.478^{**}  –2.523  –2.741 
Demandr  –4.062^{***}  –4.310^{***}  –2.861^{*}  –3.002 
Emp  –3.035^{**}  –3.987^{**}  –3.253^{**}  –3.384^{*} 
Excises  –1.438  –0.930  –5.174^{***}  –5.130^{***} 
Exoilr  –3.567^{***}  –3.769^{**}  –3.567^{***}  –3.769^{**} 
Exotherr  –3.06^{**}  –3.073  –6.898^{***}  –6.949^{***} 
Expdef  –5.156^{***}  –5.103^{***}  –3.535^{***}  –3.457^{*} 
Fedr  –2.961^{**}  –2.810  –2.788^{*}  –2.645 
Gdef  –2.434  –2.515  –2.759^{*}  –2.924 
Gdpdef  –3.609^{***}  –3.557^{**}  –3.018^{**}  –2.919 
Gdpn  –3.931^{***}  –4.002^{**}  –2.962^{**}  –2.945 
Gdpr  –3.673^{***}  –4.032^{**}  –2.747^{*}  –2.589 
Gn  –2.357  –2.635  –2.357  –2.635 
Gr  –1.846  –1.718  –2.804^{*}  –2.866 
Hsr  –3.672^{***}  –3.593^{**}  –3.641^{***}  –3.540^{**} 
Impdef  –3.024^{**}  –3.010  –3.281^{**}  –3.294^{*} 
Impr  –3.775^{***}  –3.857^{**}  –2.918^{**}  –2.965 
Incomen  –3.816^{***}  –3.768^{**}  –3.862^{***}  –3.810^{**} 
Incomer  –3.496^{**}  –3.899^{**}  –3.475^{**}  –3.937^{**} 
Inctaxcorp  –4.805^{***}  –4.799^{***}  –4.865^{***}  –4.862^{***} 
Inctaxpers  –3.308^{**}  –3.613^{**}  –3.242^{**}  –3.596^{**} 
Infl  –2.925^{**}  –2.915  –3.386^{**}  –3.366^{*} 
Inflt  –3.085^{**}  –3.188^{**}  –3.227^{**}  –3.257^{**} 
Inventr  –3.566^{***}  –3.525^{**}  –3.786^{***}  –3.750^{**} 
Invr  –3.274^{**}  –3.460^{*}  –3.340^{**}  –3.54^{**} 
Lforce  –3.26^{**}  –3.995^{**}  –3.363^{**}  –3.995^{**} 
Midgovb  –3.126^{**}  –3.110  –3.455^{**}  –3.436^{*} 
Oilpusd  –4.52^{***}  –4.596^{***}  –3.843^{***}  –3.893^{**} 
Othertax  –2.757^{*}  –3.755^{**}  –2.702^{*}  –3.775^{**} 
Prod  –3.575^{***}  –3.974^{**}  –2.902^{*}  –3.162 
Reer  –4.356^{***}  –4.731^{***}  –3.568^{***}  –3.601^{**} 
Rubeur  –3.064^{**}  –3.003  –3.331^{**}  –3.280^{*} 
Rubusd  –2.560  –2.564  –3.015^{**}  –3.050 
Socpol  –5.966^{***}  –5.905^{***}  –6.562^{***}  –6.506^{***} 
Tcn  –2.386  –2.458  –2.564  –2.677 
Unemp  –4.147^{***}  –4.134^{***}  –3.38^{**}  –3.362^{*} 
Unemprate  –4.198^{***}  –4.171^{***}  –3.414^{**}  –3.380^{*} 
Uscpi  –2.326  –2.359  –3.945^{***}  –3.955^{**} 
Util  –4.543^{***}  –4.505^{***}  –2.862^{*}  –2.831 
Vat  –2.884^{*}  –2.925  –2.968^{**}  –2.975 
Vatrate  –1.836  –2.630  –2.194  –2.883 
Wageav  –1.764  –3.646^{**}  –2.100  –2.899 
Wageavr  –2.789^{*}  –2.768  –2.566  –2.580 
Wtrade  –5.944^{***}  –5.987^{***}  –3.116^{**}  –3.185^{*} 
Ygap  –4.543^{***}  –4.505^{***}  –2.862^{*}  –2.831 
Ypot  –1.136  –0.938  –1.206  –1.290 
Equation  JB  LM  BPG  ARCH 
Average nominal wage equation  0.673  0.118  6.31  0.081 
Central bank policy rate equation  40.102^{***}  0.426  92.439^{***}  0.163 
Consumption deflator equation  56.773^{***}  6.511^{**}  20.566^{***}  0.389 
Corporate income taxes equation  0.004  3.957  1.073  1.165 
CPI equation  13.932^{***}  10.212^{***}  3.297  0.025 
Employment equation  0.479  –  –  – 
Excise tax equation  4.259  4.706^{*}  13.541^{**}  1.553 
Export deflator equation  1.677  2.698  2.793  1.294 
GDP deflator equation  1.013  4.295  4.386  0.016 
Government spending deflator equation  1.349  0.137  9.896^{*}  0.006 
Household saving rate equation  55.132^{***}  1.905  19.568^{***}  0.068 
Imports deflator equation  0.290  4.447  0.316  3.366^{*} 
Imports equation  5.560^{*}  0.247  12.156^{*}  0.295 
Investment equation  0.173  1.851  3.351  1.865 
Labor force equation  0.580  –  –  – 
NAIRU equation  28.172^{***}  7.656^{**}  29.695^{***}  0.178 
Medium–term government bond yield equation  22.636^{***}  –  –  – 
Non–oil exports equation  0.321  7.497^{**}  4.229  0.504 
Oil exports equation  1.135  0.175  14.302^{**}  0.809 
Other tax equation  99.664^{***}  1.153  15.343^{***}  0.208 
Personal income tax equation  9.510^{***}  0.567  8.073^{*}  0.372 
Private consumption equation  0.743  3.752  9.799  1.697 
Real exchange rate equation  5.803^{*}  8.596^{**}  12.216^{**}  4.285^{**} 
Real GDP equation  4.224  –  –  – 
TFP trend equation  19.266^{***}  –  –  – 
VAT equation  13.781^{***}  7.523^{**}  1.508  0.361 
Unit root tests of residuals from longrun equation (test for cointegration).
Equation  ADF  PP  KPSS 
Average nominal wage equation  –2.904^{*}  –3.942^{***}  0.261 
Consumption deflator equation  –2.976^{**}  –2.946^{**}  0.161 
Corporate income taxes equation  –2.424  –4.495^{***}  0.149 
Excise tax equation  –1.703  –2.219  0.281 
Export deflator equation  –4.791^{***}  –4.927^{***}  0.045 
Government spending deflator equation  –2.496  –3.560^{***}  0.227 
Imports equation  –3.671^{***}  –6.626^{***}  0.057 
Non–oil exports equation  –3.443^{**}  –8.622^{***}  0.101 
Oil exports equation  –2.155  –4.825^{***}  0.406+ 
Other taxes equation  –4.964^{***}  –4.964^{***}  0.182 
Personal income taxes equation  –1.767  –8.409^{***}  0.408+ 
Private consumption equation  –6.795^{***}  –6.798^{***}  0.177 
VAT equation  –5.305^{***}  –5.305^{***}  0.055 
Real effective exchange rate (the weighted average of the ruble against the basket of all currencies).