A macroeconometric model for Russia
expand article infoAizhan Bolatbayeva, Alisher Tolepbergen, Nurdaulet Abilov
‡ NAC Analytica, Nur-Sultan, Kazakhstan
Open Access


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 non-stationarity of variables. Stochastic simulation is used to solve the model for expost and ex-ante 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 ex-ante forecasts for the Russian economy under the baseline assumptions.


macroeconometric model, Cowles Commission approach, structural macroeconomic model, macroeconomic model for Russia, forecasting

JEL classification: B22, E17, E27.

1. Introduction

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 error-correction 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 ex-post and ex-ante 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 ex-ante 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 ex-post 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 ex-ante forecasts generated for some endogenous variables, and Section 8 provides concluding remarks.

2. Literature review

Tinbergen (1939) was one of the first economists to construct a fully-specified macroeconometric model. His textbook, Business Cycles in the United States, 1919–1932, describes a 48 equations model of the US economy that explains business cycles. The model uses macroeconomic concepts to explain accurately cyclical fluctuations for testing the theories of business cycles and evaluating public policies. The model consists of four blocks: demand for goods and services, supply or price equations for food and services, demand and supply in the money and capital markets, and income formation. The majority of equations are linear in parameters with regression coefficients treated as constant over time. He also studies the model under various scenarios, namely in the presence of stock market boom and hoarding. The last part of his study tests the effects of different policies on the business cycles and briefly discusses the validity of some business cycle theories from the point of view of statistical analysis.

Fair (1984) gives a detailed discussion of macroeconometric model building for the US economy. His methodology allows to determine which model best approximates the structure of the economy. He also emphasizes four primary sources of forecast uncertainty in the model: error terms, coefficient estimates, exogenous variable forecasts and possible misspecification of the model. The model consists of 30 stochastic equations that are estimated via either two-stage least squares (TSLS) or ordinary least squares (OLS). Statistical tests on regression coefficients show that they have expected signs and are significant in line with economic theory. The estimation results of the US model show that the choice of estimator does not make a significant difference. Fair (1984) also analyzes two versions of the US model with the first model containing rational expectations only in the bond market and the other accounting for rational expectations both in the bond and stock markets. He first modifies the US model to be consistent with rational expectations assumption, then examines the sensitivity of the policy properties of the model to this assumption in the bond and stock markets.

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 Brayton and Tinsley (1996). The FRB/US is a large-scale structural macroeconometric model of the US economy, which contains around 50 stochastic equations and 250 identities. The model consists of four types of equations: arbitrage equilibria, equilibrium planning, dynamic adjustment, and forecasting. They also discuss different approaches to introducing expectations in the model. One approach is VAR expectations which assumes only limited knowledge about the joint dynamics of the variables. The second approach is full-model expectations that implies expectations to be consistent with the forecasts of the model.

Dreger and Marcellino (2007) build an aggregate macroeconometric model for the Euro economy useful for both forecasting and policy analysis. They use instrumental variables (IV) estimation technique to avoid inconsistent estimates of coefficients which occur due to the presence of endogenous right-hand side variables. One-step forecasts of endogenous variables from static simulations are used as instruments in IV estimation. Thus, the problem of endogeneity is handled appropriately, and estimates of coefficients are consistent. In comparison to the previous version, where Dreger (2003) relies on the two-step procedure suggested by Engle and Granger (1987), this paper employs one step-procedure suggested by Stock and Watson (1993). The paper also compares the forecasting performance of the model to ARIMA and VAR models. For most variables prediction errors of the structural model are smaller than errors of alternative models. Several scenario analyses are simulated within the model, namely, a temporary slowdown in the GDP growth of the US economy, an interest rate shock and sudden currency appreciation.

There also exists literature on macroeconometric modeling for emerging countries including the Russian economy. Abilov et al. (2019) and Weyerstrass et al. (2018) construct macroeconometric models for Kazakhstan and Slovenia respectively. They assess the forecasting performance of the model and generate ex-ante and ex-post forecasts. Aivazian et al. (2017) present a two-part methodology for constructing a disaggregated macroeconomic model of the Russian economy for the period 1990–2010. They conclude that the Russian economy can be theoretically described based on a structural disaggregated model, which in turn can be used for macroeconometric modeling. Benedictow et al. (2010) gives a good treatment of a macroeconometric model of the Russian economy, aimed at evaluating the impact of changes in the oil price and economic policy variables. Two alternative scenarios with different oil prices are discussed in the paper. Although the results show substantial output growth in the absence of an increase in the oil price, simulation exercises reveal that the Russian economy is sensitive to large oil price fluctuations. Demeshev and Malakhovskaya (2015) discuss the forecasting performance of Bayesian vector autoregressions (BVARs) based on the Russian economy data. In particular, they compare the forecast accuracy of BVAR with other VARs and random walk with drift models for important macroeconomic variables. The authors find that for many variables BVARs are superior to the other models in terms of forecasting performance. Nevertheless, in some cases, a small-dimensional BVAR shows better forecasting results than its high-dimensional counterpart does. Modern factor models have also become a useful tool in policy analysis and real-time forecasting. Borzykh (2016) uses the combination of factor models and time-varying parameter VAR to assess the effectiveness of bank lending channel of monetary policy in Russia. Porshakov et al. (2015) exploit nowcasting techniques based on factor models to generate short-term forecasts in real time based on mixed frequency data on 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 medium-term forecasts can be generated online within the framework of various scenarios.2IEF RAS publishes quarterly forecasts of macroeconomic indicators for Russia based on the QUMMIR model.

3. Data description

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; Di,t is the price deflator; k refers to the base years of 2003, 2008, 2011 and 2016 from the national accounts; Ai,t is the adjusted price ratio; Pi,t is the price variable; Qi,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 Kt is the capital stock at time t; It 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 capital-output 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 working-age 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.

4. The model

We start the model-building 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 non-stationary in levels and stationary in year-over-year 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 long-run 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 non-stationary endogenous variables have a cointegrating relation with the set of non-stationary right-hand side variables. Hence, the cointegration relation is included into the regression equation as the long-run 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 backward-looking 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, long-run 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 At 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 non-accelerating 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, non-oil 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 long-run 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 long-term interest rate. The lagged value of the dependent variable represents investment adjustment costs which enter the right-hand 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, non-oil 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 non-oil 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 non-oil exports equation is determined by the lagged value of itself, the world trade index and the real exchange rate. The latter affects non-oil 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) Non-oil 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 right-hand 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, medium-term 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 right-hand side. The equation for the medium-term government bond yield represents the bonds market. The equation is specified in levels due to the stationary nature of the dependent variable. The medium-term 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) Medium-term 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 right-hand side. Due to the export dependent nature of the economy, the real effective exchange rate has been added on the right-hand 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.

5. Simulation

Once the model specification has been completed, the model is solved for ex-post and ex-ante 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 Fair, 2018). Drawing errors in this way is known as bootstrapping. Thus, the model simulation was run 1,000 times to obtain confidence intervals for all endogenous variables over the simulation horizon.

The ability of the model to repeat the dynamics of actual endogenous variables is assessed based on ex-post simulation for the period 2004–2019. Fig. F1 to Fig. F6 in Appendix F show the median values of the ex-post 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 ex-post simulation of the model is evaluated by forecast evaluation measures. In particular, we compare ex-post forecasts obtained by the structural macroeconometric model with ex-post 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 1 presents the forecast evaluation measures for some chosen macroeconomic variables. The results indicate that the structural macroeconometric model gives a better fit for GDP growth, inflation rate and unemployment rate.

Table 1

Forecast evaluation measures.

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

6. Shock analysis

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, non-oil 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.

7. Ex-ante forecasts and scenarios

Since the model performance is reasonably good in ex-post simulation we use it for ex-ante 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 2 presents ex-ante forecasts for key macroeconomic variables, including real GDP growth, potential output growth, inflation rate, and unemployment rate. The results are the median values obtained from stochastic simulation. The forecast horizon covers the period from 2020 to 2023 under the scenario of oil prices remaining at 30 dollars per barrel from the second quarter of 2020.

Table 2

Ex-ante 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 ex-ante 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 ex-ante 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 above-mentioned 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.

8. Conclusion

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 error-correction form based on quarterly data spanning from 2001 to 2019. Thus, the equations capture the short run dynamics and long-run relationships between the variables. Stochastic simulation is used for both ex-post and ex-ante 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 ex-post simulation for 2004–2019 reveals good accuracy in tracking the actual dynamics of relevant endogenous variables. The ex-post simulation of the model is also assessed by the forecast evaluation measures. In particular, ex-post 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 ex-ante 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.


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3 Expenditure components of GDP: private consumption, private investment, government consumption, exports and imports.
4 For simplicity, we refer to the first quarter of 2010 prices simply as 2010 prices.
5 The unit root test results are presented in Appendix C.

Appendix A

Table A1

List of variables.

Variables Definitions Units of measurement Source
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
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

Appendix B

Appendix C

Table C1

Unit root test results of variables in levels.

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+++
Table C2

Unit root test results of variables in year over year measure.

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

Appendix D

Table D1

Normality, heteroskedasticity and autocorrelation tests.

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

Appendix E

Table E1

Unit root tests of residuals from long-run 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

Appendix F

Fig. F1.

Real GDP growth rate (%).

Fig. F2.

Potential output growth (%).

Fig. F3.

Inflation rate (%).

Fig. F4.

Unemployment rate (%).

Fig. F5.

Real wage growth rate (%).

Fig. F6.

Real effective exchange rate (the weighted average of the ruble against the basket of all currencies).

Fig. F7.

Real GDP growth response to the VAT rate shock.

Fig. F8.

Inflation rate response to the VAT rate shock.

Fig. F9.

Real GDP growth response to the world trade shock.

Fig. F10.

Inflation rate response to the world trade shock.

Fig. F11.

Oil exports response to the world trade shock.

Fig. F12.

Non-oil exports response to the world trade shock.

Fig. F13.

Real GDP growth rate forecast (%).

Fig. F14.

Potential output growth forecast (%).

Fig. F15.

Inflation rate forecast (%).

Fig. F16.

Unemployment rate forecast (%).