Modeling of Wages and Prices Behavior: System Dynamic Approach
VALERIY KOZYTSKYY
Department of Mathematical Economics, Econometrics, Financial and Insurance Mathematics
Ivan Franko National University of Lviv
1, Universytetska Str., Lviv, 79000
UKRAINE
NELYA PABYRIVSKA
Department of Mathematics
Lviv Polytechnic National University
5 Mytropolyta Andreia Str., Lviv, 79007
UKRAINE
GALYNA BEREGOVA
Department of Computational Mathematics and Programming
Lviv Polytechnic National University
5 Mytropolyta Andreia Str., Lviv, 79007
UKRAINE
Abstract: - The economies of almost every country in the whole word have been suffered from coronavirus
pandemic consequences. The damage was especially hard for labor markets. The large magnitude of demand and
production shocks that was caused by COVID-19 significantly disturbed the dynamics of output, wages and
prices. The research problem addressed in this paper focuses on dynamic properties of wages and prices behavior
influenced by shocks with different magnitudes and types. We apply a system dynamic approach to conduct the
simulations of economic variables and investigate the possibility of their convergence to some stable path. We
examine the impact of demand and production shocks on the output and prices as well as on wage and inflation
behavior. It is proved that values of models parameters are crucial for existing of new steady state and
convergence of economic variables. The paper determines the bifurcation points that separate different modes of
transition period in moving towards or away from equilibrium. The research includes the investigation of the
impact of economy’s original state and emphasizes the importance of initial point of the system for the next its
dynamics after shock. The research results derived in the paper serves as a useful learning tool to develop a
discussion of the policy design issues related to reduction of negative impact of severe and unanticipated
disturbance like COVID-19.
Key-Words: - System Dynamics, Simulation Model, Wage, Price, Convergence, Equilibrium, Shocks
Received: July 18, 2021. Revised: November 22, 2021. Accepted: December 22, 2021. Published: January 9, 2022.
1 Introduction
Nowadays the economies of almost every country in
the whole word have been suffered from coronavirus
pandemic consequences [1], [2]. The labor markets
have been damaged especially hard [3]. In response
to shocks, unemployment jumps sharply [4], the
economic activity and production capability are
extremely unstable [5]. Shopping preferences of
consumers change not even in the structure of the
consumer’s good and services basket but also in the
consumers’ way of making shopping. Some part of
enterprises were pushed into bankruptcy, the huge
pool of labor force faced with a significant wage
reducing or even became unpaid for an extended
period of time, future appeared to be highly
unpredictable and uncertain. The large magnitude of
demand and production shocks that has been
observed recently significantly disturbed the
dynamics of output, prices and wages, hurt industrial
enterprise [6], provoked unemployment [7],
negatively affect the international trade [8] and
interfered the socio-economic regional development
[9]. Negative market disturbances have considerable
and asymmetric impact not only on short-term
dynamic behavior of labor force participation,
unemployment, wages and inflation but can cause
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Valeriy Kozytskyy,
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long-term negative impact with substantive nonlinear
effect [10]. It is unpredictable if economic variables
will reach a new steady state with balancing growth
paths after shock as well as when they will achieve
stabilization [11].
2 Literature Review
Danzer and Grundke (2020) examined the impact of
labor demand shock caused by export prices on
wages of workers. They revealed that shocks created
incentives for agricultural sector to increase labor-
intensive production and emphasized that the
competitive structures in local labor markets had
important impact on wage evaluation in developing
countries [12]. Bazhenova, Oliskevych and
Lukianenko (2020) used a modern nonlinear
econometric approach extended by regime switching
technics to investigate the unemployment rate and
labor force fluctuations in Eastern European
countries. They proved the asymmetric and nonlinear
impact of market shocks on their dynamics [13].
Lee, Yang, Kim and Kim (2018) studied the
change in the supply and their impact on changes in
prices. They focused on agricultural distribution
network in Korea and developed a dynamic model
describing the production fluctuation and the
consumer’s reaction on changes in product input and
output flows through the adjustment of prices [14].
Other scientists found out that the evaluation of
magnitudes and frequency of negative and positive
economic shocks on labor market indicators is
important factor of its economic [15].
In order to examine the dynamic of economic
variables and their response on market shocks
scientists estimated different types of econometric
vector autoregressive models as well as used machine
learning instruments. They developed models based
on supervised and unsupervised learning [16], fuzzy
logic approaches [17], predictive analytics and
applications [18].
Zhu, Liao and Chen (2021) built a time-varying
parametric VAR model with random fluctuations to
examine the response of nonferrous metals industry
in China on the uncertainty of the time-varying oil
prices and economic policy [19]. Perez (2020)
examine the effect of unexpected increase in the real
wage in formal and informal sectors. Based on
combined unconditional quantile regressive models
with a differences-in-differences structure,
researcher suggested the reasons of wage exposure to
the shocks and emphasized the importance of wages
close to the minimum wage changes in Colombia
[20].
Oduyemi and Owoeye (2020) investigated the
dynamics of oil prices and showed that in oil
exporting countries the reliance of government
finance on oil revenue put in risk the income stability
and had an impact on development of human capital
[21]. Kaminskyi, Nehrey and Komar (2020)
developed a complex approach to analyze risks of
investment in Exchange Trade Funds of agriculture.
They applied general portfolio ideas extended by
different conceptual taking into account specific
characteristics of agricultural investments and
estimation of shocks in probability [22].
The researches also estimated the long-run
equilibrium relationships between economic
variables in combination with their short-term
dynamic fluctuating behavior. It was proved the
existence of adjustments forces that influenced fuel
consumption to converge to the stable trajectories
[23]. Bielinskyi et al. (2021) proved the inadequacy
of the quantitative approach for pricing processes
evaluation and received the evidences for instability
of the price dynamics on the energy market that can
produce severe shocks and crashes [24].
3 Methodology
The research paper focuses on the dynamic of prices
and output fluctuations in response to market shocks
that disturb the economic activity. Our purpose is to
analyze output and price adjustments and to create
model that describes their behavior in transitory
period and steady state. Suppose, Y – the total output
of firms; y – the total output of firms that correspond
to the flexible-price or natural level of output; L –
labor force; l – labor force surplus; p – price level; w–
wage; π – inflation. Suppose the production function,
Y = F(L), is a twice differentiable and invertible
function and L = F-1(Y) = f(Y), f´(Y)>0. The
equilibrium price level, pe, is described as a marginal
wage cost and is determined by f(Y). Therefore, pe =
f´(Y). The equilibrium aggregate demand, G[pe, f(Ye)]
that depends on equilibrium price level and labor is
equal to supply Ye, so output gap y, labor force
surplus l and inflation π are zero.
In the short term, we observe price and output
fluctuations with adjustments
p´ = μ ( G(p, f(Y)) – Y), μ > 0, (1)
Y´ = λ ( p – f´(Y) ), λ > 0. (2)
Then the model extend by equations
f´(Y) = α0 + α1 Y + α2 Y2 + εY, (3)
G(p, f(Y)) = β0+ β1p+ β2p2+ β3p3+ γ1Y+ γ2Y2 + εp , (4)
where εY, εp are assumed to be independent white-
noise processes.
Next, we denote gw – the short-run deviation
between the long run desired real wage and actual
real wage; gπ – deviation of actual inflation and
natural long run expected inflation. For simulation of
real wage and inflation behavior, we use a system
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dynamics model that is described by system of first-
order differential equations
gw´ = π, (5)
gπ´ = η gπ – gw – η gw 2 gπ (6)
and can be represented by a second-order equation
gw´´ – η (1 – gw 2) gw´ + gw = 0. (7)
We take various initial points of system and
discover how the dynamics of wage and inflation
depends on value of parameter δ. It is important to
establish the set of δ where the variables reach the
equilibrium and to investigate if the equilibrium is
stable.
3 Results and Discussion
The initial points of system (1) – (4) variables and
value of models’ parameters that evaluated
sensitiveness have important impact on simulation
results and dynamics of system.
The change in parameter λ that determine the level
of output sensitivity have significant impact on
behavior of output and price during the business
cycles (Fig. 1, 2). Strong sensitivity of output
production to the deviation between price and
marginal wage cost leads to more visible oscillation
in short term whereas in the long term the output
capability stabilizes. The level of new stable state
depends on magnitude of shock. In case of a strong
negative shock, the output drops significantly and
does not return to the original level. The price
dynamics shows decreasing behavior that
corresponds to recession of market activity.
Figure 1: The output dynamics for different level of
production capability adjustment after shock
Figure 2: The price dynamics for different level of
production capability adjustment after shock
In case of a strong negative shock (Fig. 3, orange
points set), the output drops significantly and does
not return to the original level. The price dynamics
shows decreasing behavior that corresponds to
recession of whole market activity. Eventually the
economics reach the new stable position with lower
output and lower price index.
Figure 3: Convergence of output and price level for
different level of production capability adjustment
after shock
The simulation of model for different
combination of both sentitivity coefficients are
shown in Fig. 4, 5, 6. We take both adjustments
coefficients less that 1 so they characterize weak
response of variables to both demand and supply
discrepancies. However, the dynamics reveals to be
quite different even for small changes in parameters
of model. The adjustemnt is not quick, the respose to
shocks are rather cautious. The market needs some
time to adjust to new market condition even for small
value of price and output sensitivities.
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Figure 4: The impact of change in demand and
production adjustment coefficients combination on
output dynamics
Figure 5: The impact of change in demand and
production adjustment coefficients combination on
price dynamics
Figure 6: The impact of change in demand and
production adjustment coefficients combination on
convergence pattern
For model (5)–(6) variables, the transition period
varies depending on starting market conditions.
In case when δ is less than –2, the wage gap and
inflation eventually stabilize and reach the equilibria
(Fig. 7).
Figure 7: The dynamics of wage and inflation from
different initial points for δ = –3
When δ belong to the interval (–2; 0) (–2 < δ <0) the
equilibrium point is still steady (Table 1).
Table 1: The simulation results for wage and
inflation gaps in cases of stable focus
Value of
parameter
Time
Inflation gap
Initial value
gpi0 = 0.3
δ = –1.5
1
0.6641
2
-0.0667
3
-0.2062
4
-0.1374
5
-0.0548
6
-0.0097
7
0.0050
8
0.0059
9
0.0032
10
0.0011
11
0.0001
12
-0.0002
13
-0.0002
14
-0.0001
15
0.0000
However, the dynamics of variables as well as the
shape of phase diagram are very distinguish (Fig. 8)
from the first case when δ is less than –2.
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Figure 8: The stable focus convercence (δ = –1.5) of
wage and inflation to equilibrium from different
initial points
If δ equals zero the behavior of the system variables
changes dramatically and follows a circle (Table 2).
Table 2: The simulation results for wage and
inflation gaps in cases of circle
Value of
parameter
Time
Inflation gap
Wage gap
Initial value
gpi0 = –0.5
gw0 = 0.5
δ = –1
1
-0.0412
0.3440
2
0.1584
0.0650
3
0.1397
-0.0779
4
0.0500
-0.0851
5
-0.0129
-0.0373
6
-0.0286
0.0024
7
-0.0176
0.0157
8
-0.0032
0.0114
9
0.0040
0.0031
10
0.0043
-0.0018
11
0.0019
-0.0026
12
-0.0001
-0.0013
13
-0.0008
-0.0001
14
-0.0006
0.0004
15
-0.0002
0.0004
If δ becomes a positive value the fixed point is no
longer stable (Fig. 9) and the phase diagram is no
longer a circle (Fig, 10).
Figure 9: The inflation gap behavior moving away
from equilibrium poit for different value of δ in case
of unstable focus
Figure 10: Pathes of wages and prices moving away
from equilibrium, unstable focus behavior
4 Conclusion
The impact of shocks produced by the COVID-19 is
difficult to predict. It is even hard to establish with
reasonable accuracy whether economies will
converge to some new stable states like there were
before the start of the pandemic or they will move in
some other uncertain directions. The research
provided in the paper shows that next behavior of
output, wages, prices and inflation after the shock
very depends on the initial state of economics that
was inherent for the particular country before shock.
The parameters of economies’ functioning,
sensitivity of wages and prices to demand and output
capability changes have even more determining
effect. It was revealed the existence of two types of
bifurcations that created dynamics about a stable path
or around unstable point. The different magnitudes of
cycles suddenly appeared as an outcome of changes
in model’s parameters. The economic systems could
exhibit multiple equilibria and jump from one to
another stable equilibrium if market susceptibility
varied. The research results derived in the paper
serves as a useful learning tool to develop a
discussion of the policy design issues related to
reduction of negative impact of severe and
unanticipated disturbance like coronavirus pandemic.
References:
[1] Mahmud, Appel, Donghong Ding and Md.
Morshadul Hasan, "Corporate Social
Responsibility: Business Responses to
Coronavirus (COVID-19) Pandemic," SAGE
Open, Vol. 11(1), 2021, 21582440209.
[2] Hryhoruk, Pavlo, Nila Khrushch, Svitlana
Grygoruk, Kateryna Gorbatiuk and Liudmyla
Prystupa, "Assessing the impact of covid-19
pandemic on the regions’ socio-economic
development: The case of Ukraine," European
Journal of Sustainable Development,
Vol. 10(1), 2021, pp. 63–80.
WSEAS TRANSACTIONS on COMPUTERS
DOI: 10.37394/23205.2022.21.6
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[3] Pantelimon, Florin-Valeriu, Bogdan-Stefan
Posedaru, Elena-Aura Grigorescu and Dimitrie-
Daniel Placinta, "Labor Market Trends During
The COVID-19 Pandemic," Informatica
Economica, Academy of Economic Studies -
Bucharest, Romania, Vol. 25(2), 2021, pp. 50–
63.
[4] Oliskevych, Marianna and Iryna Lukianenko,
"European unemployment nonlinear dynamics
over the business cycles: Markov switching
approach," Global Business and Economics
Review, Inderscience Publishers, Vol. 22, Issue
4, 2020, pp. 375–401.
[5] Guryanova, Lidiya, Olena Bolotova,
Vitalii Gvozdytskyi and Olena Sergienko,
"Long-term financial sustainability: An
evaluation methodology with threats
considerations," Rivista di Studi sulla
Sostenibilita, Vol. 2020(1), 2020, pp. 47–69.
[6] Matviychuk, Andriy, Oleksandr Novoseletskyy,
Serhii Vashchaiev, Halyna Velykoivanenko and
Igor Zubenko, "Fractal analysis of the economic
sustainability of industrial enterprise," in CEUR
Workshop Proceedings, 2422, 2019, pp. 455–
466.
[7] Lukianenko, Iryna and Marianna Oliskevych,
"Evidence of Asymmetries and Nonlinearity of
Unemployment and Labour Force Participation
Rate in Ukraine," Prague Economic Papers,
Vol. 26, Issue 5, 2017, pp. 578–601.
[8] Hayakawa, Kazunobu and Hiroshi Mukunoki,
"The impact of COVID-19 on international
trade: Evidence from the first shock," Journal of
the Japanese and International Economies,
Elsevier, Vol. 60(C), 2021, Article 101135.
[9] Hryhoruk, Pavlo, Nila Khrushch and
Svitlana Grygoruk, "Using multidimensional
scaling for assessment economic development
of regions," International Journal of Industrial
Engineering and Production Research, Vol.
31(4), 2020, pp. 597–607.
[10] Oliskevych, Marianna and Iryna Lukianenko,
"Labor Force Participation in Eastern European
Countries: Nonlinear Modeling," Journal of
Economic Studies, Emerald Publishing, Vol. 46,
No. 6, 2019, pp. 1258–1279.
[11] Skrypnyk, Andriy and Maryna Nehrey, "The
formation of the deposit portfolio in
macroeconomic instability," in CEUR
Workshop Proceedings, 1356, 2015, pp. 225–
235.
[12] Danzer, Alexander and Robert Grundke,
"Export price shocks and rural labor markets:
The role of labor market distortions," Journal of
Development Economics, Elsevier, Vol. 145(C),
2020.
[13] Bazhenova, Olena, Marianna Oliskevych and
Iryna Lukianenko, "Regime Switching
Modeling of Unemployment Rate in Eastern
Europe," Journal of Economics, Institute of
Economic Research of Slovak Academy of
Sciences, Vol. 68, Issue 4, 2020, pp. 380–408.
[14] Lee, Daekyung, Seong-Gyu Yang, Kibum Kim
and Beom Jun Kim, "Product flow and price
change in an agricultural distribution
network," Physica A: Statistical Mechanics and
its Applications, Elsevier, Vol. 490(C), 2018,
pp. 70-76.
[15] Оliskevych, Marianna and Viktor Tokarchuk,
"Dynamic modelling of nonlinearities in the
behavior of labor market indicators in Ukraine
and Poland," Economic Annals – XXI, Vol. 169,
Issue 1-2, 2018, pp. 35–39.
[16] Babenko, Vitalina, Andriy Panchyshyn, Larysa
Zomchak, Maryna Nehrey, Zoriana Artym-
Drohomyretska and Taras Lahotskyi, "Classical
Machine Learning Methods in Economics,"
WSEAS Transactions on Business and
Economics, vol. 18, Art. #22, 2021, pp. 209–
217.
[17] Matviychuk, Andriy, "Fuzzy logic approach to
identification and forecasting of financial time
series using Elliott wave theory," Fuzzy
Economic Review, Vol. 11(2), 2006, pp. 51–68,
2006.
[18] Guryanova, Lidiya, Roman Yatsenko,
Nadija Dubrovina and Vitalina Babenko,
"Machine learning methods and models,
predictive analytics and applications," in CEUR
Workshop Proceedings, 2649, 2020, pp. 1–5.
[19] Zhu, Xuehong, Jianhui Liao and Ying Chen,
"Time-varying effects of oil price shocks and
economic policy uncertainty on the nonferrous
metals industry: From the perspective of
industrial security," Energy Economics,
Elsevier, Vol. 97(C), 2021, Article 105192.
[20] Pérez, Jorge Pérez, "The minimum wage in
formal and informal sectors: Evidence from an
inflation shock," World Development, Elsevier,
vol. 133(C), 2020.
[21] Oduyemi, Gabriel and Taiwo Owoeye, "Oil
Price Fluctuation and Health Outcomes in an Oil
Exporting Country: Evidence from
Nigeria," International Journal of Energy
Economics and Policy, Econjournals, vol. 10(4),
2020, pp. 212–220.
[22] Kaminskyi, Andrii, Maryna Nehrey and
Mariana Komar, "Complex Risk Analysis of
Investing in Agriculture ETFs," International
WSEAS TRANSACTIONS on COMPUTERS
DOI: 10.37394/23205.2022.21.6
Valeriy Kozytskyy,
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Journal of Industrial Engineering & Production
Research, vol. 31 (4), 2020, pp. 579–586.
[23] Оliskevych, Marianna, Galyna Beregova and
Viktor Tokarchuk, "Fuel Consumption in
Ukraine: Evidence from Vector Error
Correction Model," International Journal of
Energy Economics and Policy, Vol. 8(5), 2019,
pp. 58–63.
[24] Bielinskyi, A., I. Khvostina, A. Mamanazarov,
A. Matviychuk, S. Semerikov, O. Serdyuk, V.
Solovieva and V. Soloviev, "Predictors of oil
shocks, Econophysical approach in
environmental science," in IOP Conference
Series: Earth and Environmental
Science, Vol. 628(1), 2021, 012019.
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