Adv Syst Sci Appl 2022; 03:124–134
Published online at https://ijassa.ipu.ru.

The Model of the Production Side of the Russian Economy: the
Updated Version

Nikolay Pilnik, Stanislav Radionov*,

Financial Research Institute of the Ministry of Finance of the Russian Federation, Moscow, Russia

Abstract: In this paper we propose the new version of the model of the production side of the
Russian economy presented in [25]. We add several new features such as more general production
function, more tractable human capital variable and the method of COVID-19 pandemic shock
description. The new version of the model is capable of reproducing the wide set of main Russian
macroeconomic indicators with sufficiently high accuracy even during the COVID-19 pandemic.

Keywords: dynamic optimization, complementary slackness conditions, production of GDP

1. INTRODUCTION AND LITERATURE REVIEW

In [25] we presented the model of production side of the economy, which represents the
aggregate description of all economic agents who produce the added value. This aggregated
agent, which can be called Producer, constitutes the important part of economy and, together
with Consumer, Government etc., forms the basic structure of general equilibrium description
of the economy. The model presented in [25] is based on the solution of the optimization
problem of the agent who maximizes his discounted profit flow under technologic,
demographic and financial constraints in the spirit of the standard microeconomic description
of the firm. The model, however, contains a wider set of economic instruments available to
Producer – it is connected not only to labor and capital markets, but also to the banking
system via loans in both national and foreign currencies. Several heuristic methods such
as relaxation of complementary slackness conditions are used to derive the model which is
capable of reproducing the Russian macroeconomic variables with sufficiently high precision.

In this paper we add several new features to the model. First, we use more general constant
elasticity of substitution (CES) production function instead of Cobb-Douglas production
function. CES production function was introduced in [4] and is widely used both in theoretic
and applied works dedicated to the description of the production side of economy both on
macro- and microeconomic levels (see [20], [21], [9], [14], [10], [22], [2], [7], [5] and the
special issue of Journal of Macroeconomics in June 2008 for examples and discussion).
The modelling of gross domestic product using the production functions of different kinds
(see for example [11], [12], [15], [18]) can be mentioned separately due to the closeness
of these works to ours. The Cobb-Douglas production function, which is a special case of
CES, is used more commonly than CES due to its analytic tractability. In particular, Cobb-
Douglas production functions are ubiquitous in DSGE models (see for example [28], [29],
[8]). However, one of the properties of the Cobb-Douglas production function is that it implies
the constant shares of labor and capital contributions to production, which is not confirmed
on the Russian macroeconomic data. Hence we decided to switch to more sophisticated CES
production function.

∗Corresponding author: saradionov@edu.hse.ru



THE MODEL OF THE PRODUCTION SIDE OF THE RUSSIAN ECONOMY: THE UPDATED VERSION 125

Second, in the new version of the model we use the human development index calculated
by the United Nations (see [27]) as a measure of human capital. This index is calculated
based on such indicators as gross national income per capita, literacy rate, education level.
Note that these indicators are essentially out of control of the production side of economy, so
this variable is considered as exogenous in the model.

Third, we introduce the mechanism which exogenously restricts the ability to hire the
labor force. It us used to explain the dynamics of employment during the COVID-19
pandemic. It is worth mentioning that the impact of COVID-19 pandemic and the related
government measures stimulated the great volume of research. Notable examples include
[13], [3], [19], [1], [6], [16] among many others. In our model we use the COVID-19
stringency index introduced in [17], which is a numeric indicator of strictness of COVID-
related measures, as a factor which puts a pressure on employment rate.

In the rest of the paper we describe the new version of the model and analyze its ability
to reproduce the Russian macroeconomic variables.

2. THE MODEL: STATEMENT

As in [25], we consider the model of the whole sector of the economy, which generates the
added value, as a single agent. We formulate the optimization problem, solve it and then,
using several heuristics, we reduce the solution to the dynamic model.

As in [25], the investments are divided into two parts: investments in the maintenance of
fixed assets Ju(t) and investments in building up fixed assets Jm(t).

The formation of production capital (fixed assets) M(t) is described by the following
relations:

d

dt
M (t) = Jm (t)− δam (t)M (t) , (2.1)

0 ≤ Jm (t) . (2.2)

where δam (t) is the coefficient of depreciation rate, which is assumed to be constant and
equal to 0.00275. The equation (2.1) allows to calculate the series Jm (t) based on statistics
on the level of fixed assets and depreciation. The balance of investments

J (t) = Jm (t) + Ju (t) , (2.3)

where J (t) is the overall level of investment (gross fixed capital formation), allows to
calculate the investments in the maintenance of fixed assets Ju (t). The balance can also
be written in nominal terms

pJ (t) = pm (t) Jm (t) + pu (t) Ju (t) , (2.4)

where pJ (t) is the overall level of investments (gross fixed capital formation) in the current
prices, pm (t) and pu (t) are the deflators of the corresponding elements of investments. In
this version of the model, however, we assume them being equal.

We introduce the human capital per capita denoted by H(t). As was noted in the
introduction, in this version of the model we consider it as an exogenous variable.

Next, we introduce the total amount of payments made by the Producer to its employees,
which is called wage and mixed income in the system of national accounts. We denote this
variables by W (t).

As was noted in the introduction, we assume that the production function of the agent we
consider has a constant elasticity of substitution. Namely, we assume the following structure
of the production function:

Copyright © 2022 ASSA. Adv Syst Sci Appl (2022)



126 N. PILNIK, S. RADIONOV

Y (t) = A
(
α (uM (t)M (t))θ + (1− α) (uH (t)H (t)Rmax (t))

θ
) 1

θ
, (2.5)

where uM (t) and uH (t) are the utilization rates, respectively, of fixed assets and human
capital. We define these indicators in the following non-linear way:

uM (t) =

(
Ju (t)

M (t)

)b

, uH (t) =

(
R (t)

Rmax (t)

)a

. (2.6)

We substitute (2.6) into (2.5) and also substitute A with several normalization coefficients in
order to avoid the dimensionality problem. As a result, the production function takes the form

Y (t)

Y0
=

[
α

(
Ju(t)

J0

)bρ(
M(t)

M0

)(1−b)ρ

+ (1− α)

(
H(t)

H0

)ρ(
R(t)

R0

)bρ(
Rmax(t)

Rmax0

)(1−b)ρ
] 1

ρ

.

(2.7)
The volume of production 0 ≤ Y (t) and the volume of products sold 0 ≤ Yp (t) may vary,
which leads to the introduction of stock 0 ≤ Z (t) in the model. Its change can be calculated
as

d

dt
Z (t) = Y (t)− Yp (t) . (2.8)

Denote the loans attracted by the Producer in national currency (rubles) by L (t). The
average terms for which loans are attracted will be denoted by (βl (t))

−1. The variable βl (t)
is the inverse duration and interpreted as the average frequency of the loans return. Then the
dynamics of ruble loans is defined by the equation

d

dt
L (t) = K (t)− βl (t)L (t) , (2.9)

where 0 ≤ K (t) is the flow of newly attracted loans and rL (t) is the effective interest rate on
loans.

Producer also attracts loans in foreign currency, which are nominated in dollars in the
Russian statistical data. We denote the corresponding value by vL (t). The dynamics of
foreign currency loans is described by the equation similar to (2.9):

d

dt
vL (t) = vK (t)− βvl (t) vL (t) . (2.10)

Here βvl (t) is the reverse durations of currency loans, newly attracted foreign currency loans
are denoted by 0 ≤ vK (t) and the effective interest rate on foreign currency loans is denoted
by rvl (t).

The taxes Producer pays can be aggregared into four groups: value added tax, labor
taxes, property taxes and income taxes. The rates of these aggregated taxes are denoted
by τy (t), τr (t), τtm (t), τpr (t) correspondingly. For servicing operations related to loans
and investments, the producer uses current account N (t). In this version of the model it
is assumed that its volumes are proportional to ruble and foreign currency loans and fixed
assets. These proportions are defined by the coefficients νl, νvl, νm:

N (t) ≥ νlL (t) + νvlwvl (t) vL (t) + νmpm (t)M (t) , (2.11)

where wvl (t) denotes the exchange rate.

Copyright © 2022 ASSA. Adv Syst Sci Appl (2022)



THE MODEL OF THE PRODUCTION SIDE OF THE RUSSIAN ECONOMY: THE UPDATED VERSION 127

Other expenses of the Producer are denoted by OC o (t) and are considered as the
exogenous variable. We also denote the profit after taxation by Pr (t). The financial balance
of the Producer can be written as

d

dt
N (t) = K (t)− βl (t)L (t)− rl (t)L (t)− (1 + τpr (t)) Pr (t)+

wvl (t) (vK (t)− βvl (t) vL (t)− rvl (t) vL (t))−OC o (t)

+ (1− τy (t)) py (t)Yp (t)− pj (t) Ju (t)− pm (t) Jm (t)−
τtm (t) ptm (t)M (t)− (1 + τr (t))wr (t)R (t) .

(2.12)

The above relationships represent the limitations imposed on the Producer’s ability to
choose the values of its planned variables (controls):

Ju (t) , Jm (t) , K (t) , L (t) ,M (t) , N (t) ,Pr (t) ,

R (t) ,Yp (t) , Z (t) , vK (t) , vL (t) , Y (t) .
(2.13)

According to the principle of rational expectations, when planning its control variables, the
producer can rely on an accurate forecast of information variables:

H (t) ,OC o (t) , Rmax (t) , βl (t) , βvl (t) , δah (t) , δam (t) , pj (t) , pm (t) , ptm (t) ,

py (t) , rl (t) , rvl (t) , τh (t) , τpr (t) , τr (t) , τtm (t) , τy (t) , wh (t) , wr (t) , wvl (t) .

As in [25], the goal of the producer in the model is to maximize the total discounted utility
from the profit after taxation. We assume that the discount rate in the utility function is equal
to the GDP deflator: ∫ T

t0

e−∆ t

1− η

(
Pr (t)

py (t)

)1−η

dt. (2.14)

The problem is supplemented with terminal condition, which can be interpreted as a
growth condition for some linear combination of the phase variables:

Ω (t0 ) γ ≤ Ω (T ) , (2.15)
where Ω (t) = aL (t)L (t) + aM (t)M (t) + aN (t)N (t) + aZ (t)Z (t) + avL (t) vL (t).
This is the analogue of no Ponzi condition written in terms of the Producer’s own capital
which is a difference between its assets and liabilities.

As in [25], we derive the solution of the maximization problem of the function (2.14)
under constraints (2.1) – (2.12) and the terminal condition (2.15) with respect to the variables
(2.13) using the Lagrange method. We obtain the system of sufficient optimality conditions,
which can be divided into several groups: equations for primal variables, differential
equations for dual variables, complementary slackness conditions and the terminal condition.
This system is then tranformed to the more tractable form using the method described in
detail in [26].

First, we transform it to the discrete time by replacing derivatives with increments
(backward increments are used for direct variables and forward increments are used for
dual variables). Second, some direct variables are replaced by their values in the previous
period. Third, differential equations for the dual variables are replaced by expressions of
corresponding separatrices. Forth, the complementary slackness conditions are replaced by
their more regular approximations (the procedure is called the relaxation of complementary
slackness conditions). After all these transformations, we proceed to the dynamic system
which can also be presented by several groups of expressions.

Copyright © 2022 ASSA. Adv Syst Sci Appl (2022)



128 N. PILNIK, S. RADIONOV

The first group consists of several expressions defining growth rates of different
exogenous variables (in different forms) and two more auxiliary variables:

gpm (t) =
pm (t)− pm (t− 1)

pm (t− 1)
, gwh (t) =

wh (t)− wh (t− 1)

wh (t− 1)
,

gpy (t) =
py (t)− py (t− 1)

py (t− 1)
, gtaupr (t) =

τpr (t)− τpr (t− 1)

τpr (t− 1) + 1
,

gtauh (t) =
τh (t)− τh (t− 1)

1 + τh (t− 1)
, grmax (t) =

Rmax (t)−Rmax (t− 1)

Rmax (t− 1)
,

gttauy (t) = −τy (t)− τy (t− 1)

−τy (t− 1) + 1
,

RR(t) =

(
H(t− 1)

H0

) θ
−bθ+1

(
Y (t)

Y 0

)− θ
−bθ+1

(
Rmax(t)

Rmax0

) (1−b)θ
−bθ+1

×

×
(
bY (t) py(t) (1− α) (1− τy(t))

wr(t)R0 (1 + τr(t))

) bθ
−bθ+1

,

RR2(t) = −pj(t) Ju(t)− (1 + τr(t))wr(t)R(t)−OCo(t)+

+ Y (t) (1− τy(t)) py(t)− Pr(t) (τpr(t) + 1) .

The second group consists of expressions defining “real” variables such as GDP and its
components included in the model, fixed capital stock and the number of employed.

Real GDP in the model is defined as

(
Y (t)

Y 0

) (1−b)θ
−bθ+1

= α

(
M(t− 1)

M0

) (1−b)θ
−bθ+1

(
αbpy(t) (1− τy(t))

pj(t) J0

) bθ
−bθ+1

+

+ (1− α)

(
Rmax(t)

Rmax0

) (1−b)θ
−bθ+1

(
H(t− 1)

H0

) θ
−bθ+1

(
bpy(t) (1− α) (1− τy(t))

wr(t)R0 (1 + τr(t))

) bθ
−bθ+1

.

The number of employed R (t) and the level of investments in the maintenance of fixed
assets Ju (t) are adjusted at this stage to better take into account the particularities of Russian
macroeconomic dynamics during the recent years. The expression which defines the number
of employed persons derived as first order optimality condition is denoted by R∗(t). It is
adjusted to better take into account the situation of partial employment. This leads to the
following expressions:

R∗(t) =

(
H(t− 1)

H0

) θ
−bθ+1

(
Rmax(t)

Rmax0

) (1−b)θ
−bθ+1

R0

(
Y (t)

Y 0

)− θ
−bθ+1

×

×
(
bY (t) py(t) (1− α) (1− τy(t))

wr(t)R0 (1 + τr(t))

) 1
−bθ+1

,

R (t) = arRmax (t) + brR
∗ (t) ,

Similarly, the expression which defines the investments in the maintenance of fixed assets
obtained from first order optimization conditions is denoted by Ju∗(t). It is adjusted to
take into account the exogenous constraint related to the measures introduced to limit the

Copyright © 2022 ASSA. Adv Syst Sci Appl (2022)



THE MODEL OF THE PRODUCTION SIDE OF THE RUSSIAN ECONOMY: THE UPDATED VERSION 129

COVID-19 spread. As was mentioned in the introduction, we use the COVID-19 stringency
index denoted by covid(t) to measure the strictness of the introduced measures. The resulting
expressions are the following:

Ju∗(t) =

(
Y (t)

Y 0

)− θ
−bθ+1

(
M(t− 1)

M0

) (1−b)θ
−bθ+1

J0

(
αbY (t) py(t) (1− τy(t))

pj(t) J0

) 1
−bθ+1

,

Ju (t) = min{M(t− 1) (mm (1− covid(t)))
1
b , Ju∗(t)}.

The profit of producer Pr(t), investments in building up fixed assets Jm(t) and the change
of stocks Z(t) are defined by the following relations:

Pr(t) =

(
−∆− gtaupr(t) + ρ(t)

η
+

(
−1

η
+ 1

)
gpy(t)

)
Pr(t− 1) + Pr(t− 1) ,

Jm(t) = b2

(
δam(t) +

−δam(t)− τtm(t) + gpm(t)− RR(t)α(−1+b)(τy(t)−1)Y (t)py(t)

M(t−1)pm(t)

δam(t)num+ 1

)
M(t− 1)−

b2gpm(t)M(t− 1)− a2 ((δam(t)num+ 1) ρ(t) + δam(t) + τtm(t)− gpm(t))M(t− 1)+

+
RR(t)α (−1 + b) (τy(t)− 1)Y (t) py(t)

pm(t)
+

cc2RR2(t)

pm(t)
,

Z(t) = Z(t− 1) + (b5 − a5 (−gpy(t)− gttauy(t) + ρ(t)))Z(t− 1) +
cc5RR2(t)

py(t) (1− τy(t))
.

The expression defining the stock of the fixed capital M(t) is also adjusted – we introduce
its smoothed version denoted by Msm(t). This smoothed variable is compared with the
statistical values of M(t).

M (t) = Jm (t)− δam (t)M (t− 1) +M (t− 1) ,

Msm(t) = κMsm(t− 1) + (1− κ)M(t).

The last group are the equations defining financial variables, both stocks and flows.

vK(t) = b3

(
βvl(t)−

rvl(t) + gwvl(t)

βvl(t)nuvl − 1
− gwvl(t)

)
vL(t− 1)−

a3 ((βvl(t)nuvl − 1) ρ(t) + rvl(t) + gwvl(t)) vL(t− 1)− cc3RR2(t)

wvl(t)
,

K(t) =

(
b4

(
− rl(t)

η(t)nul − 1
+ η(t)

)
− a4 ((η(t)nul − 1) ρ(t) + rl(t))

)
L(t− 1)+

+ (−1 + cc1 + cc2 + cc3 + cc5)RR2(t),

N (t) = νlL (t− 1) + νvlwvl (t) vL (t− 1) + νmpm (t)M (t− 1) ,

L (t) = K (t)− βl (t)L (t− 1) + L (t− 1) ,

vL (t) = vK (t)− βvl (t) vL (t− 1) + vL (t− 1) .

Copyright © 2022 ASSA. Adv Syst Sci Appl (2022)



130 N. PILNIK, S. RADIONOV

3. THE MODEL: IDENTIFICATION AND RESULTS

The presented version of the model is identified on the Russian macroeconomic data from
2005q1 to 2021q4. The sources of the data are essentially the same as in [25] – Rosstat data
is used for GDP and its components, capital stock etc., Bank of Russia data is used for the
variables related to the interactions with the banking sector, and The Federal Treasury data is
used for the taxation data. The seasonality identification procedure described in [23] is applied
where necessary. The new data sources include the COVID-19 stringency database [17] and
the human capital development database [27]. The first dataset is available on a daily basis,
and we use the quarterly average value. The second dataset is available on a yearly basis, and
we extrapolate the given values for the quarters.

We identify the parameters of the model in two ways. The first one is the standard dynamic
system approach used in [25]. We calculate the growth rates of eight variables (Y , R, M , L,
vL, N , Pr, W ) to the corresponding quarter of the previous year. The function of errors is
the sum of squares of the discrepancies between the statistics and the model data with some
weights. We put the weight 25 for the GDP as the most important variable and 1 for all other
variables. Using the command lsqnonlin of the MATLAB Optimization package, we find the
set of model parameters which minimizes this function of errors. The accuracy of data fit is
shown on the plots below. As we can see, the model performs rather well even during the
COVID-19 pandemic.

(a) GDP (b) Number of employed

(c) Fixed assets (d) Ruble loans

Copyright © 2022 ASSA. Adv Syst Sci Appl (2022)



THE MODEL OF THE PRODUCTION SIDE OF THE RUSSIAN ECONOMY: THE UPDATED VERSION 131

(e) Foreign currency loans (f) Current accounts

(g) Profit (h) Wages

Mean average percentage errors of forecasts are shown in the table 3.1.

Table 3.1. Mean absolute percent errors of the model variables, dynamic system

Y R M L vL N Pr W
1.77 1.01 8.38 8.91 8.82 12.45 5.13 1.13

The second method of the parameters identification we apply is based on the idea of
multistep forecasting proposed in [24]. In this framework the parameters of the model are
identified in such a way that the error of forecasts for a given length of forecasting is
minimized. We consider the forecasts up to 6 quarters ahead and again using the command
lsqnonlin of the MATLAB Optimization package find a set of parameters which minimizes
the sum of squares of forecast errors. As for the previous case, we minimize the total error of
growth rates of the modelled variables compared to their values 4 quarters ago. Mean absolute
percentage errors of the forecasts for a given variable and a given number of quarters ahead
is presented in the table 3.2. For the comparison, we also present mean absolute percentage
errors of the simple autoregressive AR(1) models. As we can see, for the variables vL, Pr, W
the model performs better than AR(1) for the whole period, for R, L, N the model performs
better or about the same for long-term forecasts, for M the model and AR(1) perform about
the same, and for Y the model performs worse than AR(1).

Copyright © 2022 ASSA. Adv Syst Sci Appl (2022)



132 N. PILNIK, S. RADIONOV

Table 3.2. Mean absolute percent errors of the model variables, multistep forecasting

1 2 3 4 5 6
Y model 3.58 3.41 3.30 3.31 3.21 3.09
Y AR(1) 1.12 1.58 1.80 2.17 2.29 2.35
R model 0.89 0.87 0.89 0.87 0.83 0.78
R AR(1) 0.48 0.65 0.72 0.85 0.83 0.91
M model 0.08 0.16 0.23 0.31 0.37 0.42
M AR(1) 0.08 0.16 0.23 0.30 0.35 0.40
L model 2.66 3.57 4.49 5.21 5.50 5.63
L AR(1) 2.12 3.35 4.25 5.11 5.71 6.29
vL model 3.06 3.72 3.90 4.05 3.81 4.72
vL AR(1) 3.43 4.74 6.21 7.27 8.20 8.78
N model 10.48 10.18 10.06 10.10 9.80 9.97
N AR(1) 4.30 6.57 8.48 10.24 10.17 9.82
Pr model 3.21 3.99 4.71 5.86 5.63 5.45
Pr AR(1) 4.43 5.81 6.42 7.88 8.39 9.08
W model 1.03 0.99 1.00 0.98 0.93 0.87
W AR(1) 1.36 1.77 2.32 3.00 3.25 3.74

4. CONCLUSION

We propose the new version of the model of the production side of the Russian
economy. Introduction of several new features such as more complex production function
and the exogenous COVID-19-related restrictions allowed to reproduce the wide set of
macroeconomic variables with rather high accuracy even during the COVID-19 pandemic.
One of the possible future directions of research is the introduction of sanctions-related
restrictions the Russian economy currently faces into the model.

ACKNOWLEDGEMENTS

This work is supported by the Russian Science Foundation under grant 21-18-00482.

REFERENCES

[1] D. Acemoglu, V. Chernozhukov, I. Werning, and M. D. Whinston. Optimal targeted
lockdowns in a multigroup sir model. American Economic Review: Insights, 3(4):487–
502, 2021.

[2] D. Acemoglu, S. Johnson, J. Robinson, and Y. Thaicharoen. Institutional causes,
macroeconomic symptoms: Volatility, crises and growth. Journal of monetary
economics, 50(1):49–123, 2003.

[3] F. Alvarez, D. Argente, and F. Lippi. A simple planning problem for covid-19 lock-
down, testing, and tracing. American Economic Review: Insights, 3(3):367–82, 2021.

[4] K. J. Arrow, H. B. Chenery, B. S. Minhas, and R. M. Solow. Capital-labor substitution
and economic efficiency. The review of Economics and Statistics, pages 225–250, 1961.

Copyright © 2022 ASSA. Adv Syst Sci Appl (2022)



THE MODEL OF THE PRODUCTION SIDE OF THE RUSSIAN ECONOMY: THE UPDATED VERSION 133

[5] D. Backus, E. Henriksen, and K. Storesletten. Taxes and the global allocation of capital.
Journal of Monetary Economics, 55(1):48–61, 2008.

[6] S. R. Baker, R. A. Farrokhnia, S. Meyer, M. Pagel, and C. Yannelis. Income, liquidity,
and the consumption response to the 2020 economic stimulus payments. Technical
report, National Bureau of Economic Research, 2020.

[7] R. S. Chirinko. Corporate taxation, capital formation, and the substitution elasticity
between labor and capital. National Tax Journal, 55(2):339–355, 2002.

[8] L. J. Christiano, M. Eichenbaum, and C. L. Evans. Nominal rigidities and the dynamic
effects of a shock to monetary policy. Journal of political Economy, 113(1):1–45, 2005.

[9] R. M. Coen. Tax policy and investment behavior: Comment. The American Economic
Review, 59(3):370–379, 1969.

[10] P. J. Dhrymes and P. Zarembka. Elasticities of substitution for two-digit manufacturing
industries: A correction. The Review of Economics and Statistics, pages 115–117, 1970.

[11] B. Dunaev. Calculating gross domestic product as a function of labor and capital.
Cybernetics and Systems Analysis, 40(1):86–96, 2004.

[12] D. Ecfin. The production function approach to calculating potential growth and output
gaps estimates for eu member states and the us. 2006.

[13] M. S. Eichenbaum, S. Rebelo, and M. Trabandt. The macroeconomics of epidemics.
The Review of Financial Studies, 34(11):5149–5187, 2021.

[14] R. Eisner and M. I. Nadiri. Investment behavior and neo-classical theory. The review of
economics and statistics, pages 369–382, 1968.

[15] N. P. Epstein and C. Macchiarelli. Estimating Poland’s Potential Output: a Production
Function Approach. Number 10-15. International Monetary Fund, 2010.

[16] J. Granja, C. Makridis, C. Yannelis, and E. Zwick. Did the paycheck protection program
hit the target? Journal of Financial Economics, 145(3):725–761, 2022.

[17] T. Hale, N. Angrist, R. Goldszmidt, B. Kira, A. Petherick, T. Phillips, S. Webster,
E. Cameron-Blake, L. Hallas, S. Majumdar, et al. A global panel database of pandemic
policies (oxford covid-19 government response tracker). Nature human behaviour,
5(4):529–538, 2021.

[18] T. Kawamoto, T. Ozaki, N. Kato, K. Maehashi, et al. Methodology for estimating output
gap and potential growth rate: An update. 2017.

[19] D. Krueger, H. Uhlig, and T. Xie. Macroeconomic dynamics and reallocation in an
epidemic: evaluating the ‘swedish solution’. Economic Policy, 2020.

[20] R. E. Lucas Jr and L. A. Rapping. Real wages, employment, and inflation. Journal of
political economy, 77(5):721–754, 1969.

[21] G. Maddala. Productivity and technological change in the bituminous coal industry,
1919-54. Journal of Political Economy, 73(4):352–365, 1965.

[22] G. S. Olley and A. Pakes. The dynamics of productivity in the telecommunications
equipment industry. Econometrica: Journal of the Econometric Society, pages 1263–
1297, 1996.

Copyright © 2022 ASSA. Adv Syst Sci Appl (2022)



134 N. PILNIK, S. RADIONOV

[23] N. Pilnik, I. Pospelov, and I. Stankevich. Ob ispolzovanii fiktivnikh peremennikh dlya
resheniya problemy sezonnosti v modelyah obshego ravnovesiya (on the use of dummy
variables for the solution of the seasonality problem in the general equilibrium models).
HSE Economic Journal, 19(2):249–270, 2015.

[24] N. Pilnik and S. Radionov. O novykh podkhodah k identifikacii blokov modeley
obshego ravnovesiya [on the new approaches to the identification of the blocks of
general equilibrium models]. MIPT Proceedings, 9(3):151–160, 2017.

[25] N. Pilnik and S. Radionov. The model of the production side of the russian economy.
Advances in Systems Science and Applications, 21(3):63–74, 2021.

[26] N. Pilnik, S. Radionov, and A. Yazikov. The model of the russian banking system with
indicators nominated in rubles and in foreign currency. In Y. Evtushenko, M. Jaćimović,
M. Khachay, Y. Kochetov, V. Malkova, and M. Posypkin, editors, Optimization and
Applications, pages 427–438, Cham, 2019. Springer International Publishing.

[27] U. U. N. D. Programme). Human development report 2020. UNDP (United Nations
Development Programme), 2020.

[28] F. Smets and R. Wouters. An estimated dynamic stochastic general equilibrium model
of the euro area. Journal of the European economic association, 1(5):1123–1175, 2003.

[29] F. Smets and R. Wouters. Shocks and frictions in us business cycles: A bayesian dsge
approach. American economic review, 97(3):586–606, 2007.

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	Introduction and Literature Review
	The model: statement
	The model: Identification and results
	Conclusion