Download Macroeconomic Analysis and Parametric Control Based on

Macroeconomic Analysis and Parametric
Control Based on Computable General
Equilibrium Model of the Regional Economic
Union
Abdykappar Ashimov, Yuriy Borovskiy,
Nikolay Borovskiy, and Bahyt Sultanov
Kazakh National Technical University named after K. Satpayev,
22 Satpayev St., 050013, Almaty City, Kazakhstan
[email protected], {yuborovskiy,nborowski86}@gmail.com,
sultanov [email protected]
http://www.kazntu.kz/en
Abstract. The paper describes a proposed mathematical model of the
regional economic union. The model relates to a class of computable
general equilibrium models (CGE models). There are given results of
parametric identification and verification of the model. There are also
described setting and solving of parametric control problems on evaluation of economic policy tools at the level of single countries and the
economic union based on a verified model. It has been shown that the
problem solution for estimating optimal values of the tools at the level
of the regional economic union is rational than one at the level of single
countries.
Keywords: Computable general equilibrium model, Multiregional economic modeling, Model verification, Parametric control.
1
Introduction
Since 2010 there has been functioning the Customs Union (CU) of three countries (the Republic of Kazakhstan, the Russian Federation, and the Republic
of Belarus), and since 2012 the Common Economic Space (CES) which unites
the mentioned countries. Based on it, there is expected creation of the Eurasian
Economic Union by 2015.
Implementation of this objective requires at first comprehensive vision of
middle-term prospects of the interaction between countries-members of the Customs Union and the Common Economic Space and adequate tool for macroeconomic analysis and recommendations-making for optimal economic policy which
considers potential effects of different external and internal factors.
There are not set any problems for estimating optimal values of economic
policy tools in existing dynamic stochastic general equilibrium models [1], [2], [3]
proposed for the description of the regional economic unions and in computable
J. Światek
et al. (eds.), Advances in Systems Science,
Advances in Intelligent Systems and Computing 240,
c Springer International Publishing Switzerland 2014
DOI: 10.1007/978-3-319-01857-7_44, 453
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A. Ashimov et al.
general equilibrium models proposed for the description of effects of global and
regional economic policies on ecology [4], [5], [6].
This paper is about estimation of optimal values of economic policy tools at
the level of the regional economic union taking for example the Customs Union
and the Common Economic Space of three countries (Kazakhstan, Russia, and
Belarus). The mentioned estimation is made based on the CGE models and the
theory of parametric control of macroeconomic systems.
Application of the proposed CGE model differs from existing results by the
following:
– values of all its exogenous and endogenous variables economic indicators for
the identification period reproduce corresponding statistical meanings, the
models structure does not change in the forecasting period compared to one
in the identification period;
– calculation of equilibrium values of endogenous variables in the nonlinear
model is made without model linearization;
– the model describes the government sector, which incorporates an expanded
interpretation of monetary and fiscal policies;
– the model describes investments into fixed assets by producers, the government, the rest of the union’s countries, and the rest of the world.
2
CGE Model for the Customs Union and the Common
Economic Space
The Constructed Customs Union CGE model describes a behavior and interaction of stated below economic agents of the three mentioned countries in the
framework of the CU agreements as with each other, so with the rest of the
world. A model of the Common Economic Space (hereinafter Model) is a CGE
model of the CU with additional conditions of harmonization of macroeconomic
policy in terms of three inequalities, which impose on the values of endogenous
variables of the CU’s model from 2012. Economic agents of the Model and their
main functions are stated below (hereinafter i = 1,2,3 – serial number of the CU
Country, i = 1 appropriates to Kazakhstan, i =2 – Russia, i =3 – Belarus).
Agent – Aggregate Producers (AP) of the Country i: Produce intermediate, consumer, investment products for domestic consumption, and also export
products for other Countries and for the rest of the world; Consume (domestic
and imported) intermediate and investment products, and also labor; Pay taxes
to Government; Define demands for loans and deposits of legal entities.
Agent – Households of the Country i: Offer labor for AP of the Country
i: Consume domestic and imported consumer products; Pay taxes and compulsory pension contributions to Government and receive from it subsidies; Define
demands for loans and deposits of individuals.
Agent – Government of the Country i: Forms government income and government spending of the Country i; Defines government demand for domestic
Macroeconomic Analysis and Parametric Control Based on CGE Model
455
and imported Consumer products; Subsidizes Households and AP transfers of
the Country i; Forms National fund income and National fund spending. Governments of three Countries distribute jointly collected customs duties on import
among Countries.
Agent – Banks of the Country i: Define refinancing interest rate, money
holding, interest rates for deposits and loans in the Country i; Meet demands
for loans and deposits of AP and households of the Country i.
Agent – the Rest of the World: Define prices for export and import products
to (from) the rest of the world for each Country i; fully meet demands for export
and import products of Countries.
Markets of the Model are to define the prices, at which obtains corresponding
equalities of demands and supplies of products (including VAT) and of labor.
The Model has three markets of domestic intermediate products of each Country;
three markets of domestic consumer products of each Country; three markets
of domestic investment products of each Country; three labor markets of each
Country; six markets of export (import) products for each pair of Countries;
General view of the Model is presented by the following system [7], [8].
1. Subsystem of difference equations, linking values of variables x1 (t) (outputs,
fixed assets of agents-producers, account balances of agents in banks and
others for the three above mentioned countries) for two successive years:
x1 (t + 1) = f1 (x1 (t), x2 (t), x3 (t), u(t), a(t)) , x1 (0) = x1,0 .
(1)
Here t = 0, 1, . . . , (n − 1) – serial number of year, discrete time; x(t) =
(x1 (t), x2 (t), x3 (t)) ∈ Rm – vector of all endogenous variables of system,
describing statuses of economies in the three countries of economic union;
xi (t) ∈ Xi (t) ⊂ Rmi , i = 1, 2, 3 .
(2)
Here m1 + m2 + m3 = m; x2 (t) – demand and supply values of agents in all
markets and others; x3 (t) – different types of market prices; u(t) ∈ U (t) ⊂ Rq
– vector function of controllable parameters. Coordinate values of this vector correspond to different government economic policy tools of mentioned
three countries, for example, as different tax rates, refinancing interest rates,
money holdings, etc.; a(t) ∈ A ⊂ Rs – vector function of uncontrollable parameters (factors). Coordinate values of this vector describe different depending on time external and internal social and economic factors of union’s countries: prices for different kind of export and import productions, labor quantity, production function parameters, etc.; X1 (t), X2 (t), X3 (t), U (t) – compact sets with non-empty interiors; Xi ∈ ∪nt=1 Xi (t), i = 1, 2, 3; X ∈ ∪3i=1 Xi ;
m1
U ∈ ∪n−1
– continuous
t=0 U (t); A – open connected set; f1 : X × U × A → R
mapping.
2. Subsystem of algebraic equations, describing behavior and interaction of
agents in different markets during chosen year, these equations assume expressing variables x2 (t) via rest endogenous variables for chosen exogenous
functions u(t) and a(t):
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x2 (t) = f2 (x1 (t), x3 (t), u(t), a(t)) ,
(3)
f2 : X1 × X3 × U × A → Rm2 – continuous mapping.
3. Subsystem of recurrence relations for iterative solution of market prices’
equilibrium values in all markets of the Model:
x3 (t)[Q + 1] = f3 (x2 (t)[Q], x3 (t)[Q], u(t), a(t), L) .
(4)
Here Q = 0, 1, . . . – serial number of iteration; L – set of positive numbers
(adjustable iteration constants; economic system faster obtains its equilibrium as their values decrease, however the risk of price shifting to the negative
side increases simultaneously; f3 : X2 × X3 × U × A × (0, +∞)m3 → Rm3 –
continuous mapping (joint with f2 ) is contracting at fixed t, x1 (t) ∈ X1 (t)
and some fixed L. In this mapping case the mappings f2 , f3 have the only
fixed point, to which leads the iterative process (3), (4).
CGE model (1), (3), (4) at fixed values of exogenous functions u(t) and a(t)
for each moment t defines values of endogenous variables x(t), appropriate to
demand and supply equilibrium prices in all markets of the Model.
3
Parametric Identification and Verification of the Model
Parametric identification (calibration) of the Model has been performed in three
stages.
On the first stage, the parameters of multiplicative production functions which
determine the values of gross outputs by the aggregate producers of all CU
Countries depending on factors of production (fixed assets, labor, intermediate
products, and imported oil) were evaluated.
On the second stage, the values of exogenous functions u(t), a(t) of the Model
for the historical period (2000–2011) were taken based on observed statistical
data of the Countries and the rest of the world.
On the third stage, the values of correcting coefficients from the Model’s
corresponding equations for the period 2000–2011 were determined based on
observed statistical data for exogenous and endogenous variables of the Model.
The evaluated model accurately reproduces the statistical data of 362 endogenous variables of the Model for the period 2000–2011. Basic calculation of the
Model for the period 2000–2018 is made by forecasting exogenous functions and
coefficients of the Model for 2012–2018.
Verification of the evaluated Model has been made through estimation of
stability indicators, retroforecast and estimation of sensitivity coefficients.
The stability indicator of the Model is a diameter of ball’s (with the one
percent radius and the center at the point of some exogenous parameters of the
Model) image in relative values for (set by the Model) mapping from exogenous variables onto endogenous ones. Here, as exogenous parameters were taken
various types of external prices, output shares and expense shares of all three
countries’ AP, and others for 2000. As output parameters, there were taken GDP
Macroeconomic Analysis and Parametric Control Based on CGE Model
457
and CPI of the CU countries for the chosen year. All obtained stability indicators’ results do not exceed 9.93, which characterizes the stability of the Model
when estimated till 2018 as sufficiently high (see the Table 1).
Table 1. Stability indicators of the Model
Year
2000 2001 2002 2003 2004 2005 2006 2007 2008 2009
Indicator 0.96 1.54 2.11 2.54 1.69 3.31 4.01 4.46 5.25 5.34
Year
2010 2011 2012 2013 2014 2015 2016 2017 2018
Indicator 5.85 6.58 7.52 6.94 7.98 8.08 8.66 9.19 9.93
The verification of the Model with retroforecast is made as following.
– With observed data for 2000–2010, there was created a version of the Model.
– Corresponding values of all endogenous macroeconomic indicators of the
Model were calculated based on extrapolation of exogenous variables of the
Model version for 2011–2012.
– The relative root-mean-square deviation of all calculated values for 2011–
2012 from corresponding observed values was about 2.9 percent.
The verification of the Model was also made through estimation of sensitivity
(elasticity) coefficients for values of endogenous variables of the Model by its
exogenous parameters to verify the compliance of signs of obtained estimates
with main tenets of the macroeconomic theory. The following Table 2 shows
estimation of sensitivity coefficients for two variables of Kazakhstan – GDP and
Consumer price level (CPL) calculated on the basis of the Model.
The verification results of the Model by three approaches show the Models
acceptable adequacy.
4
Macroeconomic Analysis of Causal Factors of the 2009
Recession Based on the Model
One of the directions of macroeconomic analysis based on the Model aimed to
determine reasons of macroeconomic events which were related to basic macroeconomic indicators of the Countries changing during the crisis period in 2009.
In the framework of solving this problem, there was evaluated the sensitivity
of impact of the following parameters (external and internal exogenous factors
including government policy tools for 2008–2009) for assigning GDP variables
(Y gi ) and the consumer price index (Pi ) for 2009:
1. prices on the Countries export products into the rest of the world (P exi );
2. prices on various products imported to the Countries from the rest of the
world (P cIi , P zIi , P nIi );
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Table 2. Sensitivity coefficients
Parameter
GDP
(2008)
(2009) (2009)
Price of non-oil export products
0.23
1.24
Price of imported consumer products from the rest of the world
-0.06
-0.94
Price of imported intermediate products from the rest of the world 0.00
CPL
-0.89
Price of imported investment products from the rest of the world
-0.06
-0.62
Technological coefficient of gross output
1.03
0.64
Intermediate products’ share in output
0.03
0.02
Consumer products’ share in output
0.00
0.07
Investment products’ share in output
0.00
-0.01
Export products’ share in output
0.02
0.01
Consumption share of AP intermediate products
0.00
0.04
Consumption share of AP investment products
-0.01
-0.01
Share government spending in the state budget
0.21
0.41
Effective rate of CIT (corporate income tax)
-0.37
0.29
Refinancing rate shock
-0.18
-0.40
Money holding shock
0.07
0.12
Oil price
0.26
1.26
3. technological coefficients of the gross output production functions of the
Countries (Yi );
4. the share of AP production of various products in the Countries (Ezi , Eci ,
Eni , Eexi );
5. the share of AP consumption of various products in the Countries (Ozi ,
Oni );
6. the share of government consumption in government spending of the Countries (Gi );
7. effective rates of corporate income tax of the Countires (Ti );
8. refinancing rates of the Countries (Refi );
9. money holdings of the Countries (DBi );
10. oil price (P oil).
Analysis of calculated elasticity coefficients (Table 2) shows that the impact of
output shares (Eci , Eni , Eexi ) and consumption shares (Ozi , Oni ) on studied
macroeconomic indicators is little enough.
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Further, by using counterfactual scenario analysis the impact degree of indicated above parameters on variables Y gi and Pi fluctuations was evaluated in
accordance with the following algorithm.
1. Ten scenarios are calculated in which one j-parameter of the given list (except Eci , Eni , Eexi , Ozi , Oni ) remains in 2008 and 2009 at the level of one
in 2007, and the rest of indicators from the list are statistical. Corresponding increments of the variables Y gi and Pi compared to baseline values are
obtained: ΔY gij and ΔPij .
2. The scenario in which all mentioned ten parameters in 2008 and 2009 remain
at the level of those in 2007 is calculated. Corresponding increments of the
variables Y gi and Pi compared to baseline values are ΔY gi and ΔPi .
3. Relationships of ΔY gij /ΔY gi and ΔPij /ΔPi (in %) are calculated. These
relationships characterize the impact degree of corresponding factors on the
increments of indicators.
It is worth to note that if the values of mentioned parameters for 2008–2009
remained at the level of those in 2007 the real GDP of Kazakhstan for 2009
would have been higher than the observed one by 11.8%, and CPI by 3.7%.
The results of mentioned impact degrees for Kazakhstan are presented in the
Table 3.
Table 3. Impact degrees of parameters fluctuations on increments of the variables in
2009 (in %)
Parameter
Variable P ex1 P cI1 P zI1 P nI1 Y1
G1
T1 Ref1 DB1 P oil Others Total
Y g1
-62.0 1.2
0.8
1.2
-64.0 61.2 5.5 30.1
36.1 -88.5 -18.0
-100
P1
-53.7 3.2
2.4
2.1
-6.5
10.0 -70.7 -16.6
-100
19.8 0.7 11.0
Analysis of the Table 3 shows that state policy measures in 2008–2009 were
correct but not optimal (as the following results of parametric control indicate).
5
Parametric Control Problems of the Regional Economic
Union Based on the Model
Next group of experiments on parametric control problems solving [7] was made
during evaluation of counterfactual optimal values of budgetary and fiscal policy
tools of the CU Countries for 2007–2011 in case of absence and presence of coordination such policies. Here are four such Problem P ri (i = 0, 1, 2, 3) informal
definitions, where the values of uncontrollable exogenous variables of the Model
correspond with basic (retrospective) prognosis of these variables.
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P ri Parametric Control Problems Setting. On the basis of the Model,
to find the values of tax rates and shares of government spendings in budgets
for 2007–2011 for each Problem P ri , which provide maximum of criterion Ki ,
(i = 0, 1, 2, 3) at corresponding restrictions for controllable parameters and some
endogenous variables to meet the conditions of debt stability and competitiveness
of the CU Countries. Here i = 1, 2, 3 – serial number of the CU Country, criterion
Ki – average real GDP of the Country i for 2013–2017, only government policy
tools of the Country i are used. In the Problem P r0 criterion K0 is average
real total GDP of three CU Countries for 2013–2017, and applying government
policy tools consist of corresponding tools of three CU Countries.
Increments of the mentioned criteria Ki (in percent relative to basic variant),
corresponding with computational solutions for Problems P ri are illustrated in
the Table 4, and the CU GDP diagrams are on the Fig. 1. An analysis of the Table
4 indicates that in the framework of Problems P ri (i = 0, 1, 2, 3) an approach
of parametric control on the level of all Union Countries provides effect for each
Union Country not less (for two Countries larger) than parametric control on
the level of single Country.
Table 4. Four parametric control problems solutions results
Increment of criterion (in %)
Problem K1
K2
K3
K0
P r1
4.05
0.64
0.14
0.58
P r2
0.78
3.68
1.75
2.36
P r3
0.25
0.43
3.83
0.32
P r0
4.07
3.68
4.06
3.77
To make recommendations on optimal state policy of the CU countries the
following parametric control problem has been solved for 2014–2018.
Setting the Problem 2. Based on the Model, to determine values of economic
tools (effective rate of CIT, share of government consumption in government
spending) at the level of each CU country for 2014–2018 which allow the maximum of Kr criterion at corresponding limits of the coordination Indicators of
macroeconomic policies and of the values of these economic tools.
Here: Kr = a1 × K1 − a2 × K2 + a3 × K3 − a4 × K4 − a5 × K5;
K1 – Normalized average (for 5 years) value of the CUs GDP per capita, in
USD;
Macroeconomic Analysis and Parametric Control Based on CGE Model
461
Fig. 1. CU GDP in bn USD, in prices of 2000
K2 – Normalized average (for 5 years) value of the government debt in the
CU countries, in million USD;
K3 – Normalized average (for 5 years) value of export from the CU countries,
in million USD;
K4 – Normalized average (for 5 years) value of import into the CU countries,
in million USD;
K5 – Normalized criterion which characterizes the convergence of the CU
countries by rates of GDP, CPI and the ratio of the government budget deficit
to GDP;
aj (j = 1, . . . , 5) – weight coefficients, in the example aj ≡ 1.
The following Tables 5 and 6 illustrate the results of Problem 2 solving by
numerical procedure of the Nelder-Mead algorithm. Here, Kji are components
of the criterion Kj (j = 1, . . . , 4), pertaining to the Country i (i = 1, 2, 3).
Table 5. Kj criteria changes relative to basic variant (in %)
Criterion K1
Change
K2
K3
K4
K5
+3.71 -3.87 +6.61 -3.22 -2.88
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Table 6. Kij criteria changes relative to basic variant (in %)
Criterion
Country
K1i
K2i
K3i
K4i
Kazakhstan (i = 1) +3.78 -3.71 +6.63 -3.36
Russia (i = 2)
+3.65 -3.84 +6.57 -3.20
Belarus (i = 3)
+3.71 -4.21 +6.40 -3.69
Analysis of the Tables 5 and 6 shows high potentials of the parametric control
approach for making recommendations on coordinated optimal state economic
policies of the regional economic Union’s Countries.
6
Conclusion
1. A computable general equilibrium model for the regional economic union
has been proposed taking for example the Customs Union.
2. Effectiveness of parametric control theorys application for estimation of optimal values of economic policy tools has been shown.
3. Preference for solution of the estimation problems of values of economic tools
at the level of the regional economic union rather than at the level of single
countries of the union has been illustrated.
4. Obtained results could be used for solving practical problems in economic
policies of regional economic unions.
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