Economic Development of
Visegrad Countries:
Macroeconomic DSGE Models
WORKING PAPER č. 19/2007
Jiří Polanský ­ Osvald Vašíček
August 2007
Working Papers of the Research Centre for Competitiveness of Czech
Economy are issued with support of MŠMT project Research Centre
1M0524.
ISSN 1801-4496
Head: prof. Ing. Antonín Slaný, CSc., Lipová 41a, 602 00 Brno, email:
slany@econ.muni.cz, tel.: +420 549491111
ECONOMIC DEVELOPMENT OF
VISEGRAD COUNTRIES:
MACROECONOMIC DSGE MODELS
Abstract:
The Working Paper deals with estimations of cash-in-advance dynamic
stochastic general equilibrium model for the Visegrad countries and the
Euro area. The CIA approach stresses the medium-of-exchange
function of money. Money is directly used to purchase consumption
goods. This model framework is used for estimations on the quarterly
time series. The estimation is realized by Bayesian technique. More
concretely, we used the Metropolis-Hastings algorithm to Markov
Chain Monte Carlo. The values of estimated parameters for all
countries are analyzed. The behavior which is represented by impulse
response functions is discussed.
Abstrakt:
Studie se zabývá odhady cash-in-advance dynamického
stochastického modelu všeobecné rovnováhy pro visegrádské země
a Euro zónu. CIA přístup zdůrazňuje funkci peněz jako směnného
prostředku. Peníze jsou přímo použity na nákup spotřebního zboží.
Tento modelový rámec je použit k estimaci na čtvrtletních časových
řadách. Odhady jsou provedeny pomocí bayesovské techniky.
Konkrétně jde o Monte Carlo Metropolis-Hastings algoritmus. Hodnoty
odhadnutých parametrů pro všechny země jsou analyzovány. Chování,
které je představováno funkcemi impulsních odezev, je diskutováno.
Reviewer:
Mgr. Jan Vlček, PhD.
TABLE OF CONTENTS
Table of Contents .........................................................................4
1. Introduction..........................................................................5
2. Ways to Introduce Money in Macro Models .......................7
3. Cash-in-Advance Approach.................................................8
4. The CIA Model ....................................................................9
4.1. Exogenous Disturbances ............................................10
4.2. The Representative Household...................................10
4.3. The Firm.....................................................................11
4.4. The Financial Intermediary........................................12
5. Solving the Model..............................................................14
5.1. Model Equilibrium.....................................................14
5.2. Optimality Conditions................................................15
5.3. The Numerical Solution .............................................16
6. The Empirical Analysis......................................................18
6.1. The Estimation Technique .........................................18
6.2. Data and Priors...........................................................19
7. Estimation Results..............................................................21
7.1. Posterior Parameter Estimates....................................21
7.2. Impulse Response Analysis........................................26
Conclusion..................................................................................30
References..................................................................................31
Appendix 1: The Data ................................................................33
5
1. INTRODUCTION
The interest in structural macroeconomic modeling issues has been
rising rapidly since 1970s. There are many factors which underlie this
dynamic development. The advancement of computer science has
enabled estimations or simulations of linear as well as nonlinear
macroeconomic models with "complicated" interdependent relations.
The gradual abandonment of Keynesian1
macroeconomics after the
Lucas Critique in the late 1970s contributed to the increased interest in
macroeconomic modeling in order to find suitable models for the
macroeconomic analysis etc. Today, the structural dynamic stochastic
general equilibrium (DSGE) macroeconomic models are the most used
tools for the macroeconomic analysis, business cycle analysis or
monetary policy evaluation.2
These models are judged according their
ability to replicate realistic patterns of co-movement among key
macroeconomic variables and impulse responses to structural shocks
as the total factor productivity shock or the unexpected change in the
growth rate of money supply.
The neoclassical growth models are the backbone of modern business
cycle theory. In fact, real business cycle theory (RBC) is simply a
Ramsey neoclassical growth model with stochastic technology shocks.
A typical RBC model posits real side shocks as the sources of
business cycles, and these shocks are propagated over time as they
interact with production technologies and houses preferences. But the
standard neoclassical growth model represents the non-monetary
economy. Critics may argue that the absence of monetary factors is an
important weakness of RBC models. If we want to study real and
monetary sectors simultaneously, we must incorporate the monetary
sector into the model framework. Within this model framework, we are
studying the economy in the long run. Thus, the prices and wages are
flexible. In order to incorporate monetary sector, the role for money
must be specified so that the agents will wish to hold positive quantities
of money. In this paper, we use the cash-in-advance approach where
the medium-of-exchange role of money is stressed. Money is used to
purchase consumption goods.
The objective of this Working Paper is to present results of the
estimations of monetary CIA DSGE model on time series of Visegrad
countries and the Euro area. The estimation is realized by Bayesian
technique. We used the Metropolis-Hastings algorithm to Markov
Chain Monte Carlo (MCMC). The analysis of estimation results, for
example estimated values of model parameters, can help us to know
1
Today, the term "New Keynesian" is widely used in many papers. It is
adopted from some papers, such as from Clarida, Gertler and Galí (1999).
Nonetheless, a more convenient term should be "New Neoclassical Synthesis".
2
The brief history of structural macroeconomic models can be found in
Polanský (2006).
6
more about long-run development of these countries. Moreover, the
estimation results might be used for future estimations and analyses of
more sophisticated models that contain nominal rigidities, exchange
rates, adjustment costs etc.
This paper is structured as follows: section 2 briefly describes ways
that can be used to introduce money in macro models. It clears up the
MIU approach, shopping-time models and the CIA approach. The third
section of the paper demonstrates the CIA approach in detail. The
fourth section describes the CIA framework which is used for the
estimations. Section 5 presents the solution of the model. Next part
deals with estimations for the Czech Republic. It clears out the data of
the model, the Bayesian technique for the estimation, the choice of
priors for the estimation and the estimation results. The estimated
values of the model and impulse responses are discussed. Section 6
then presents estimation results for other Visegrad countries and the
Euro area. The final part concludes the paper.
7
2. WAYS TO INTRODUCE MONEY IN
MACRO MODELS
There are three general approaches to incorporating the monetary
sector into the general equilibrium (GE) models. The first one is the
money-in-the-utility (MIU) approach. It claims that real money balances
directly enter the agents' utility functions. In this case, the household
solves optimization problem where the utility function has the form


=0
)/,(max
t
ttt
t
PMCu ,
where  the discount factor, u is the utility function with some
characteristics, C denotes the real consumption and PM / denotes
real money balances. One motivation for having real money balances in
the utility function is that having cash may save time in transactions. In
other words, time for shopping is a decreasing function of real money
balances. Disadvantage of this approach is that it simply assumes the
problem of positive value for money away. The postulating that money
yields direct utility guarantees that money will be valued.3
The second approach which lies between MIU approach and cash-inadvance
models (which are the macroeconomic framework within this
paper) deals with the shopping time.4
In these models, time and money
are used to produce transaction services that are required to purchase
consumption goods. Higher levels of money holdings reduce the time
needed for shopping, thereby increasing the individual agenťs leisure.
When the total time is normalized to equal 1, the utility function of the
representative household becomes


=
--
0
)1,(
t
s
ttt
t
llCu ,
where l denotes time spent in market employment and
s
l denotes time
spent in shopping, which is an increasing function of consumption and
a decreasing function of real money holdings. Subsequently, we can
rewrite the utility as a function of consumption, labour supply and
money holdings.
On the other hand, we often think of money as yielding utility indirectly.
The third approach, the cash-in-advance theory, stresses the medium
of exchange function of money. Money is held in order to facilitate
transactions. This approach will be demonstrated in the next parts of
this paper.
3
See Walsh (2003) for more details.
4
Some authors do not classify shopping-time models into a separate category.
8
3. CASH-IN-ADVANCE APPROACH
The cash-in-advance approach to macroeconomic modeling stresses
the medium-of-exchange function of money. Money is used to
purchase consumption goods. In these models, households face at
least two constraints ­ besides the standard budget constraint it is a
cash-in-advance constraint.
The exact form of the CIA constraint depends on the two model
properties. The first feature of the CIA constraint is determined by the
types of purchases that are subjected to the CIA constraint. We may
restrict purchasing of all consumption and investment goods,
consumption goods only, some subset of consumption goods etc. The
second characteristic is model timing, more concretely opening time of
goods and credit markets.5
If the asset market opens first and then the
goods market opens, agents are able to allocate their portfolio between
cash and other assets at the start of the period, after observing any
current shocks but prior to purchasing goods. This implies that if there
is a positive opportunity cost of holding money and the asset market
opens first, agents will only hold an amount of money that is just
sufficient to finance their desired level of consumption. Whenever the
nominal interest rate is positive, the opportunity cost of holding money
is positive as well. In other words, no one would accumulate more cash
than strictly needed for consumption purposes since there are better
investment opportunities. The result is that the CIA constraint will
always hold with equality.6
The example of simply CIA constrained
economy where the credit market open first is
tttt bMCP - -1 ,
where b denotes nominal bonds.
The second possibility is that the goods market opens first. In this
case, the agents have only the cash carried over from the previous
period for their spending available. This implies that the cash balances
must be chosen before agents know how much spending they will wish
to undertake. In nominal terms, the most simplified CIA constraint with
this timing schedule has the form
1- ttt MCP .
5
See the timing of the model in the beginning of the next section.
6
This conclusion is true for the certainty case. See Walsh (2003) for more
details.
9
4. THE CIA MODEL
This section presents the monetary business cycle dynamic stochastic
general equilibrium (DSGE) model.7
The model economy consists of a
representative household, a firm, and a financial intermediary. The
financial intermediary and the representative firm are owned by
households. The firm owns the capital stock, but hires labour services
from the household.
As was noted, the model timing is very important in cash-in-advance
approach. Within this model, the representative household inherits the
entire stock of money of the economy at the beginning of periodt .
Then the representative household observes current shocks in the
economy. In other words, the portfolio decisions completely reflect
current shocks. Because the model contains monetary sector as well
as the non-monetary one, there are two shocks. The first one is the
technology shock; the second one reflects current period surprise
change in money growth. Both shocks are modeled as exogenous.
After the observation, the household determines the amount of
deposits at the financial intermediary. These deposits earn interest and
are denoted by tD . The financial intermediary receives these deposits
from the representative household and in addition, it receives a
monetary injection from the central bank. The financial intermediary
lends these funds to the representative firm.
The representative firm hires labour services from the households.
After the firm produces its output, it uses money borrowed from the
financial intermediary to pay wages to the household. Thus, the
householďs cash balances are
tttt HWDM +- ,
where W denotes the nominal hourly wage and the H denotes hours
worked. This specification of the model timing implies that all
consumption purchases must be paid for with the accumulated cash
balance.8
The firm pays dividends from its net cash inflow to the
household. Moreover, the household receives its deposits back at the
financial intermediary and dividends from the net cash inflow of the
bank.
7
This model is often called as standard CIA model in the sense that date t
exogenous disturbances occur before date t decisions are made. Naturally,
this model serves as the initial model for many extensions. See Schorfheide
(2000), Nason and Cogley (1994), Walsh (2003) and citations therein for more
details about this model.
8
The CIA constraint deals with all consumption goods. The household is not
restricted within its purchases.
10
4.1. Exogenous Disturbances
The model economy is perturbated by exogenous shocks. As was
noted earlier, the CIA model contains real and nominal sectors, so we
need to introduce at least two disturbances. The first is the technology
shock which is denoted by A . This shock evolves according to
A
ttt AA  ++= -1lnln , (1)
where ),0(~ 2
A
A
t N  .
In addition, the model includes an exogenous stochastic process for
the growth rate of the monetary injection from the central bank which
has the form
m
ttt mmm  ++-= -1
*
lnln)1(ln , (2)
where the parameter  lies between zero and one,
i.e. 10 <<  and ),0(~ 2
m
m
t N  . The unconditional mean of
monetary injection growth is denoted with
*
m . This equation can be
interpreted as a simple monetary policy rule without feedbacks, where
the monetary injection growth is defined as
ttt MMm /1+= ,
where tM denotes the stock of money base at the end of date 1-t .
The innovations
m
t capture unexpected changes of the money growth
rate due to "normal" policy. Changes in
*
m or  correspond to rare
regime shifts. Innovations to the technology and monetary injection
growth shocks are uncorrelated to all leads and lags.
4.2. The Representative Household
An infinitely lived representative household chooses consumption tC ,
hours worked tH , and non-negative deposits tD in order to maximize
the expected utility function of the form
]))1ln(ln)1(([
0
0 

=
-+-
t
tt
t
HCE  , (3)
where the parameters  and lie between zero and one,
1,0 <<  and 0E is the expectations operator conditional on
date 0 information.
11
In CIA models, households face at least two constraints. The first is the
resource constraint. It says that the income of the representative
household equals or exceeds the expenditures. Within this model,
dividend payments from the firm and the financial intermediary, labour
income, interest income on the deposits and current cash holding are
the householďs resources. The household uses these resources for
consumption purchases, making deposits at the financial intermediary
and cashing to carry into future. This constraint has the form
ttt
H
tttttttt FBDRCPHWDMM +++-+-=+ )(1 , (4)
where tD denotes current period nominal deposits tD0 , tF denotes
nominal dividends the household receives from firms, tB denotes
nominal dividends the household receives from the financial
intermediary,
H
tR is the gross nominal interest rate the household
faces in the market for deposits, tP is the price level of consumption
good, and tW denotes the nominal wage rate.
The second one is the cash in advance constraint. The cash carried
over from the previous period net of current period nominal deposits
and current labour income is available only for current consumption
purchases. The CIA constraint has the form
tttttt DMHWCP -+ . (5)
4.3. The Firm
The representative firm chooses the capital stock in the next
period 1+tK , labour demand tN , dividends tF , and loans tL in order to
maximize the expected infinite horizon of discounted stream of
dividends it pays to the household.9
Nominal dividends are discounted
by date 1+t marginal utility of consumption because the households
value a unit of nominal dividends in terms of the consumption it
enables during the next period. Thus, the firm maximizes
])/([
0
11
1
0 

=
++
+
t
ttt
t
PCFE  , (6)
where nominal dividends are valued in terms of their future
consumption. The firm faces the budget constraint which has the form
F
ttttttttt RLNWIYPLF ---+ )( , (7)
9
This objective is very similar to the objective of the financial intermediary. See
the next subsection for more details.
12
where tN denotes labour demand of the firm, tY denotes physical
output, tI denotes the physical investment, and
F
tR denotes the
interest rate at which the financial intermediary lends funds to the
firm.10
This constraint implies that the firm faces a trade-off between
capital accumulation and paying larger dividends to households. The
gross investment is defined by the standard law of motion
ttt KKI )1(1 --= + ,
where the depreciation rate lies between zero and one, 10 <<  .
Physical output is produced with the constant return to scale
production function
 =
1
)( tttt NAKY ,
where 10 <<  . Capital stock is predetermined at the beginning of
periodt . After the substitution, the equation (7) becomes
F
ttttttttttt RLNWKKNAKPLF ---+-+ +
])1()([
1
1

. (8)
The last constraint says that the firm finances its current period wage
bill by borrowing from the financial intermediary
ttt LNW  . (9)
4.4. The Financial Intermediary
The financial intermediary is owned by the household. As well as the
firm, it maximizes the expected infinite horizon of discounted dividends
which pays to the households
])/([
0
11
1
0 

=
++
+
t
ttt
t
PCBE  . (10)
Nominal dividends are again valued in terms of their future
consumption.
The financial intermediary faces three constraints - the budget
constraint, the balance sheet constraint, and a zero profit condition.
The budget constraint has the form
ttt
H
tt
F
ttt XLDRLRDB +--+= , (11)
10
As was noted, the firm owns the capital stock.
13
where tL is the nominal amount of loans the financial intermediary
makes to firms,
F
tR denotes the gross interest rate charged on those
loans, and tX denotes the monetary injection during the date t
.1 ttt MMX -= +
The balance sheet of the financial intermediary has the form
ttt DXL + . (12)
The final constraint is a zero profit condition along the equilibrium path.
Profits on loans to firms net of the monetary injection equals the
principle and interest the financial intermediary owes to households
period by period. This condition has the form
)( tt
F
tt
H
t XLRDR -= . (13)
14
5. SOLVING THE MODEL11
5.1. Model Equilibrium
The equilibrium of dynamic stochastic general equilibrium model
means that all markets are cleared simultaneously. The presented
cash in advance model contain the goods market, the labor market, the
credit market, and the money market. All markets are modeled as
perfectly competitive.
The credit market clears when the equation (12), the balance sheet of
the financial intermediary, holds with strict equality. After
rearrangement and substitution into equation (13), we get
.RRR F
t
H
t =
After substitution, this results into the equation (11), which again holds
with strict equality in equilibrium, and after some rearranging, we can
find that dividends the financial intermediary pays to households equal
.ttt XRB =
The money market is cleared when the demand for money equals the
money supply. Within this cash-in-advance model, the money demand
can be described by nominal consumption demand, because money is
held to purchase all consumption goods. Money supply equals the
current nominal balances and monetary injections. We equal the
money demand with the money supply to get the equilibrium in the
money market
.tttt XMCP += (14)
Equation (14) requires labour market equilibrium. The demand for
labour must be equated to the labour supply. This can be expressed by
the equation
.tt HN =
Moreover, credit market clearing imposed on equations (5) and (9) to
hold with strict equality.
The goods market clears when output equals consumption plus
investment
.)()1( 1
1

 +
=--+ tttttt NAKKKC (15)
Then, we need to compute decision rules for the household, firm, and
the financial intermediary. They maximize their functions with respect
to the constraints. In a more detailed analysis, the representative
11
This section is based on Nason and Cogley (1994).
15
household maximizes the utility function (3) with respect to equations
(4) and (5). The representative firm maximizes (6) with respect to
equations (7) and (9). The financial intermediary maximizes (10) with
respect to equations (11) and (12). During the derivation, we assume
that the representative household, the representative firm, and the
financial intermediary treat the equilibrium process generating 1+tA ,
1+tM , tP , tW , and tR as given.
5.2. Optimality Conditions
The model has three optimality conditions which restrict equilibrium
paths in the four markets. The optimality in the goods market defines
the trade-off that the economy faces in moving consumption across
time. Since the cash-in-advance constraint binds in equilibrium, money
has a positive finite value. This implies that in terms of marginal utility,
the intertemporal consumption trade-off is one period ahead weighed
by the purchasing power of money. The Euler equation has the form
.0)}/()]1(
)([)/({
22
1
11
1
1111
=-+
++-
++
-
++
-
++++
tt
tttttttt
PC
NAKPPCPE

 
(16)
The intratemporal condition which restricts labour market optimality
depends on the structure of the credit market. Because the firm finances
its current period wage bill by borrowing from the financial intermediary,
the structure of the credit market affects the representative firm's labour
demand. We can rewrite the equation (9) as
ttt NLW /=
in equilibrium. Then, the optimality intratemporal condition for labour
market equates labour supply, the marginal rate of substitution
between leisure and consumption, and labor demand and has a form
.0/)]1/()][1/([ =+--- ttttt NLNPC (17)
The optimality in the credit market requires that the householďs loss in
current consumption from increasing its deposits at the financial
intermediary equals the discounted expected gain in future
consumption from these deposits. The intertemporal Euler equation for
this optimality condition is12
[ ] .0)/(1)/(1 11 =- ++ tttttt PCERPC  (18)
In the equilibrium, the representative firm equates the increase in its
nominal revenue generated by an extra unit of labor to the nominal
cost of borrowing required to pay that unit of labor. The equilibrium
12
The optimality condition depends on date t information.
16
gross nominal interest rate equals the ratio of the marginal revenue
product of labor to the nominal wage rate
tttttt WNAKPR /)1( 1 
 --
-= .
5.3. The Numerical Solution
The next step we should take in order to solve the model is to count
the numerical solution of optimization problems. We detrend the model
variables. The real variables are detrended by the productivity tA , so
the detrending of real side aggregates involves
ttt Aqq /^ = , where [ ]1,,, += ttttt KICYq
The price level is detrended by tt AM / and other nominal variables
are detrended by tM . Thus, the transformed nominal variables are
,1// 1 -= + tttt MMMX
,/^
tttt MAPP =
ttt MQQ /^ = , where [ ]tttt WLDQ ,,=
After detrending, we get the equilibrium conditions (next three
equations). The first equation is the aggregate resource constraint
(equation (19)), equation (20) is the money market condition and the
last equation (21) is the credit market equilibrium condition.
[ ] [ ] ,^)(exp)1(^)(exp^^ 1
1 t
A
ttt
A
ttt KNKKC  
+--++-=+ -
+
(19)
,^^
ttt mCP = (20)
.^^1 ttt LDm =+- (21)
The numerical solution to the cash­in-advance model ties the
equilibrium conditions (equations (19)-(21)) with the detrended
versions of the optimality conditions (equations (16)-(18)). Along with
the exogenous stochastic processes for technology and monetary
injection growth shocks, this system of six nonlinear equations
determines the equilibrium distributions for the six unknowns
[ ].^,^,^,^,,^
1 tttttt PLCDNK +
17
Given these equilibrium distributions, the equilibrium distributions for
output, real wages, inflation rate, and nominal interest rate can be
found.13
13
For more details, see technical appendix in Nason ­ Cogley (1994). Note
that there is an initial minus sign missing in equation (A1).
18
6. THE EMPIRICAL ANALYSIS
6.1. The Estimation Technique14
The modeled CIA system contains rational expectations. The
Blanchard-Kahn condition holds. This means that there are the same
number of eigenvalues larger than 1 as the number of forward-looking
variables.15
This implies that a unique steady-state exists. The
estimation was realized by Bayesian technique. More concretely, we
used the Metropolis-Hastings algorithm to Markov Chain Monte Carlo
(MCMC). The model is estimated with Dynare 3 toolbox for Matlab 7.
100000 iterations and 5 blocks were used for the model.
The Markov Chain Monte Carlo is the algorithm for sampling from
probability distributions which is based on constructing a Markov chain.
The chain has the desired distribution as its stationary distribution. The
idea is that rather than computing a probability density denoted for
example )|( yp  , we would be just as happy to have a large random
sample from )|( yp  as to know the precise form of the density. If the
sample was large enough, we could approximate the form of the
probability density.
There are some characteristics of the Markov chain stochastic process
)0,( tt unfolded over time.
* The first is that it has the same set of possible values (the same
state space) as 
* It is easy to simulate
* The equilibrium or stationary distribution (which we use to draw
samples) is )|( yp  after Markov chain has been run for a very
large number of iterations to produce a sample of
,...)1,( =tt from the posterior distribution
The Metropolis-Hastings algorithm to Markov chain Monte Carlo is the
most widely used approach.16
It is based on a suggestion that given an
initial value 0 , we can construct a chain by recognizing that any
Markov chain that has found its way to a state t can be completely
characterized by the probability distribution for time 1+t . This
algorithm relies on a proposal or candidate distribution )|( tf  for
14
This subsection is based on LeSage (1999). Notation within this subsection
is different from the rest of the paper.
15
Blanchard ­ Kahn (1980).
16
Another approach is known as the Gibbs sampling.
19
time 1+t , given that we have t . A candidate point
*
 is sampled from
the proposal distribution and:
1. This point is accepted as
*
1  =+t with probability
]
)|()|(
)|()|(
,1min[),( *
**
*
tt
t
tH
fyp
fyp


 = .
2. Otherwise, tt  =+1 , that is we stay with the current value of
 .
For example, we toss a Bernoulli (fair) coin with probability H of
heads. Then we move to
*
1  =+t if we see heads, otherwise we
set tt  =+1 . It can be demonstrated that this approach to sampling
represents Markov chain with the correct equilibrium distribution
capable of producing samples from the posterior )|( yp  we are
interested in.17
6.2. Data and Priors
The model for each country is estimated on the quarterly data. All time
series are seasonably adjusted. These data are depicted in the
Appendix 1. obsgy _ is the growth coefficient of per capita real GDP
and obsgp _ is the growth coefficient of the CPI. For the estimations,
we used time series from 1996 to 2007. For the model of Czech
economy, we used data from the Czech National Bank. Other data, i.e.
data of Hungarian economy, Slovak economy, Polish economy, and
Euro Area, are taken from statistical offices of individual countries.
The priors were chosen in accordance with economic theory. They
reflect our beliefs of the likely locations of structural. However, microlevel
studies on these parameters for Visegrad states are relatively
scarce. Therefore, we considered prior values from other similar
estimates. 18
The choice of prior distributions reflects restrictions on the
parameters. Beta distribution was chosen for parameters that are
constrained on the unit interval. Inverse gamma distribution was
chosen for the standard deviations of the shocks. Normal distribution
17
LeSage (1999).
18
For more details, see for example Schorfheide (2000), Christiano and
Eichenbaum (1992) and (1995) or Nason and Cogley (1994).
20
was chosen for the rest of the parameters.19
Prior distribution for the
monetary business cycle model is summarized in Table 1.
Table 1: Prior distribution of model parameters
19
Another commonly used distribution is a gamma distribution which could be
chosen for parameters restricted to be positive.
Parameter Range Density Prior Mean SE
 [0,1] Beta 0.360 0.0200
 [0,1] Beta 0.993 0.0020
 R Gaussian 0.004 0.0015
*
m R Gaussian 1.003 0.0070
 [0,1] Beta 0.985 0.0030
 [0,1] Beta 0.602 0.0500
 [0,1] Beta 0.006 0.0030
A +
R InvGamma 0.012 inf
m +
R InvGamma 0.005 inf
21
7. ESTIMATION RESULTS
7.1. Posterior Parameter Estimates
Table 2 provides us with an overview of the estimation results. The
posterior means and the confidence intervals are simulated by the
Metropolis Hastings algorithm. The magnitudes of model parameters
are in accordance with economic theory. All parameters are statistically
significant.
The posterior means of the parameter for the capital share lie
between 0.3629 and 0.3769. These values are in accordance with
economic theory and are often used for calibrations within many
structural models. These values suggest structural similarities between
economies. The highest value is for the Euro Area. It is interesting that
this parameter is somewhat higher for economy of the United States,
where estimations suggest the value around 0.04. We expect that in
the future, this value will grow slightly to the similar value as is
estimated for the US economy.
The posterior means for the discount factor  are approximately 0.992
for Czech economy, Hungarian economy and the Euro Area and 0.993
for Polish economy and Slovak economy. These estimates imply that
the steady-state real interest rates are similar for all economies. The
value of 0.992 suggests an annualized steady-state real interest rate
slightly above 3%. The higher value of the discount parameter for
Poland and the Slovak Republic implies that the real steady state rate
of interest is slightly below 3%.20
The technology growth rate is
captured by the parameter . The values for the Czech Republic and
Hungary are relatively high in comparison to other Visegrad countries
or developed countries, such as the EU or the USA. These estimates
speak clearly in favour of these two countries which suggests that
these can be referred to as countries with dynamically developing
economies. The value for the Euro Area is a bit lower than it is
common for developed countries.21
20
The steady-state real interest rate is  /)1( -=r .
21
For example, Schorfheide (2000) estimated this value around 0.004 for
similar two monetary models on the US data.
22
Table 2: Posterior means and confidence intervals for the Visegrad
countries and Euro Area
CZ HU SK PO EU
 0.3629
(0.3297 ­
0.3955)
0.3640
(0.3304 ­
0.3991)
0.3737
(0.3410 ­
0.4088)
0.3754
(0.3413 ­
0.4067)
0.3769
(0.3443 ­
0.4100)
 0.9922
(0.9890 ­
0.9957)
0.9923
(0.9891 ­
0.9958)
0.9931
(0.9901 ­
0.9961)
0.9931
(0.9901 ­
0.9962)
0.9923
(0.9892 ­
0.9956)
 0.0063
(0.0048 ­
0.0078)
0.0074
(0.0064 ­
0.0084)
0.0045
(0.0030 ­
0.0060)
0.0025
(0.0009 ­
0.0041)
0.0022
(0.0014 ­
0.0030)
*
m 1.0053
(0.9949 ­
1.0166)
1.0052
(0.9945 ­
1.0165)
1.0038
(0.9919 ­
1.0146)
1.0037
(0.9926 ­
1.0154)
1.0045
(0.9963 ­
1.0131)
 0.9860
(0.9818 ­
0.9910)
0.9858
(0.9816 ­
0.9907)
0.9832
(0.9783 ­
0.9884)
0.9830
(0.9779 ­
0.9882)
0.9847
(0.9802 ­
0.9896)
 0.5957
(0.5158 ­
0.6818)
0.5882
(0.5039 ­
0.6684)
0.5880
(0.5076 ­
0.6715)
0.6000
(0.5132 ­
0.6754)
0.5908
(0.5065 ­
0.6683)
 0.0063
(0.0014 ­
0.0108)
0.0063
(0.0015 ­
0.0109)
0.0036
(0.0010 ­
0.0061)
0.0037
(0.0007 ­
0.0065)
0.0044
(0.0008 ­
0.0077)
A 0.0085
(0.0069 ­
0.0100)
0.0059
(0.0048 ­
0.0071)
0.0150
(0.0121 ­
0.0175)
0.0243
(0.0190 ­
0.0292)
0.0044
(0.0036 ­
0.0052)
m 0.0039
(0.0032 ­
0.0046)
0.0043
(0.0035 ­
0.0050)
0.0066
(0.0054 ­
0.0079)
0.0078
(0.0059 ­
0.0094)
0.0015
(0.0012 ­
0.0018)
This parameter  characterizes the utility preferences of households.
The estimated posterior means are about 0.59 for all countries. This
implies that the utility preferences of households are analogous. The
value is smaller than estimations for the US economy. Roughly
speaking, this means that by those households, consumption is more
appreciated. The estimated autocorrelation of money growth is
relatively high and is also similar for all countries. This can be partly
caused by the nature of the model. Because prices in the model are
flexible, a large  is needed to capture the persistence in inflation.
The parameter for capital depreciation has similar estimation results
for Czech and Hungarian economy on the one side, and for Polish and
Slovak economy on the other side. The value for the Euro Area lies
approximately between these two. Note that these estimated
parameters have relatively large confidence intervals.
23
Figures 1 to 5 plot priors and posteriors for parameters of Visegrad
economies and the Euro economy. The first two parameters are
standard errors of the exogenous shocks. They grey line represents
the prior distributions, the black line shows the posterior distributions.
The dotted green line depicts the value at the posterior mode.
Figure 1: Priors and posteriors for parameters of CZ economy
0.02 0.04 0.06
0
100
200
300
400
SE_e_a
0.005 0.01 0.015 0.02 0.025
0
500
1000
SE_e_m
0.25 0.3 0.35 0.4 0.45
0
5
10
15
20
alp
0.98 0.985 0.99 0.995 1
0
50
100
150
200
bet
0 5 10
x 10
-3
0
100
200
300
400
gam
0.98 1 1.02 1.04
0
20
40
60
mst
0.97 0.98 0.99 1
0
50
100
150
rho
0.4 0.6 0.8
0
2
4
6
8
psi
0 0.01 0.02 0.03
0
50
100
150
del
Figure 2: Priors and posteriors for parameters of HU economy
0.01 0.02 0.03
0
200
400
600
SE_e_a
0.005 0.01 0.015 0.02 0.025
0
200
400
600
800
SE_e_m
0.3 0.4 0.5
0
5
10
15
20
alp
0.98 0.985 0.99 0.995 1
0
50
100
150
200
bet
4 6 8 10
x 10
-3
0
200
400
600
gam
0.98 1 1.02 1.04
0
20
40
60
mst
0.97 0.98 0.99 1
0
50
100
150
rho
0.4 0.6 0.8
0
2
4
6
8
psi
0 0.01 0.02 0.03
0
50
100
150
del
24
Figure 3: Priors and posteriors for parameters of PO economy
0.02 0.04 0.06
0
50
100
SE_e_a
0.01 0.02 0.03
0
100
200
300
400
SE_e_m
0.3 0.4 0.5
0
5
10
15
20
alp
0.98 0.985 0.99 0.995 1
0
50
100
150
200
bet
-2 0 2 4 6 8
x 10
-3
0
100
200
300
400
gam
0.96 0.98 1 1.02 1.04
0
20
40
60
mst
0.97 0.98 0.99
0
50
100
rho
0.4 0.6 0.8
0
2
4
6
8
psi
0 10 20
x 10
-3
0
100
200
del
Figure 4: Priors and posteriors for parameters of SK economy
0.02 0.04 0.06 0.08
0
100
200
SE_e_a
0.01 0.02 0.03
0
200
400
SE_e_m
0.3 0.4 0.5
0
5
10
15
20
alp
0.98 0.985 0.99 0.995 1
0
50
100
150
200
bet
0 5 10
x 10
-3
0
100
200
300
400
gam
0.96 0.98 1 1.02 1.04
0
20
40
60
mst
0.97 0.98 0.99 1
0
50
100
rho
0.4 0.6 0.8
0
2
4
6
8
psi
0 5 10 15
x 10
-3
0
100
200
del
25
Figure 5: Priors and posteriors for parameters of Euro economy
0.02 0.04 0.06
0
200
400
600
800
SE_e_a
0.01 0.02 0.03
0
1000
2000
SE_e_m
0.3 0.4 0.5
0
5
10
15
20
alp
0.98 0.985 0.99 0.995 1
0
50
100
150
200
bet
0 2 4
x 10
-3
0
200
400
600
800
gam
0.98 1 1.02
0
20
40
60
80
mst
0.97 0.98 0.99 1
0
50
100
rho
0.4 0.6 0.8
0
2
4
6
8
psi
0 0.01 0.02
0
50
100
150
200
del
26
7.2. Impulse Response Analysis
This subsection presents impulse response functions of the modeled
economy and describes some features of the models. We depict only
impulse responses of the Czech model and explain the behavior of the
modeled economy. Impulse responses of other models are analogous.
The next figures show impulse response functions for the modeled
economy. Figures 6 and 7 depict impulse response functions to the
positive technology shock. Figures 8 and 9 depict impulse response
functions to the positive monetary shock. obsgy _ and obsgp _ are
observable model variables which are shown in Appendix 1. Note that
in order to depict the behavior of the variable after the shock, the data
are in growth coefficients. For example, Figure 7 shows that the real
GDP is increasing after the positive technology shock. Other impulse
responses are shown as deviations from the steady-state and are
depicted in decimal notation. We can see from these impulse
responses that movements of macroeconomic variables to the steady
states are very gradual after the shock. Some variables return to the
steady state several decades. Moreover, be careful of the scales of
these figures. Some deviations are very small.
The reaction of economy to the technology shock is analogous to that
published in the real business cycle literature. From the first panel of
figure 8, the real GDP is rising. The second panel shows that the price
level is counter-cyclical which is consistent with the RBC theory. This is
in accordance with stylized facts as published by Cooley and Hansen
(1995). They mention the confusion that may result from many
textbooks in macroeconomics: "which would probably lead one to
suspect that the consensus view is that prices are procyclical".22
As
was noted, the movements of macroeconomic variables to steady
states are very gradual. The exception is the trajectory of the real rate
of return which returns very quickly and then oscillates around its
steady-state value. We simulated the behavior for more periods and
recognized that the amplitude is diminishing in time. Note that the
scale is very small in this case.
When analyzing behavior of an economy after the monetary shock, it is
important to mention some features of the model economy. The model
does not generate a liquidity effect. If money growth displays positive
persistence, then unanticipated shocks to the growth rate of money
drive interest rates up, not down as is predicted by the liquidity effect.
This is due to the fact that in these models, money shocks affect
interest rates exclusively through an anticipated inflation effect.23
22
Cooley and Hansen (1995), page 182.
23
Possible way of introduction the liquidity effect into the model framework is
discussed in Christiano and Eichenbaum (1992, 1995). There must be rigidity
in the part of money that is allocated in consumption goods. Within this
27
After the money growth shock, the representative household can
adjust its deposits contemporaneously. The nominal interest rate is
approximately equal to the real rate of interest plus the expected
inflation. The agents observe the shock to the growth rate of money
and they recognize that it will cause higher inflation. The expected
inflation rate will increase. This will lead to an increase of the nominal
interest rate and a slight decrease of the output. This can be seen from
figure 10. Hence, the model predicts sudden increase in the price level
which results in the inflation in the first period.
Higher interest rate causes an increase in investment spending and a
decline in the consumption. The reason is that the rise of interest rate
can be viewed as a tax on the consumption goods but on the other
side, a subsidy on the investment (credit) goods. The hours worked
fall. Because the worked time decreased and the stock of capital is
unchanged, current output falls as well. So the positive monetary
shock drives the interest rate up and unemployment, consumption, and
output down.
Figure 6: Impulse response functions to the CZ technology shock
10 20 30
0
1
2
3
4
x 10
-3 P
10 20 30
-8
-6
-4
-2
0
x 10
-3 c
10 20 30
-5
0
5
10
x 10
-3 e
10 20 30
0
1
2
3
x 10
-3 W
10 20 30
-2
0
2
4
x 10
-5 R
10 20 30
-0.4
-0.3
-0.2
-0.1
0
k
10 20 30
0
1
2
3
x 10
-3 d
10 20 30
0
2
4
6
8
x 10
-4 n
10 20 30
0
1
2
3
x 10
-3 l
framework, a positive monetary shock increases the total percentage of the
money supply available to financial intermediaries because households do not
spend newly acquired money on consumption goods. Financial intermediaries
lend all cash at their disposal to firms. For firms to do so voluntarily, interest
rate must fall. But if the growth rate of money displays positive persistence, the
expected inflation effect of a change in the growth rate of money exerts
countervailing pressure on interest rates.
28
Figure 7: Impulse response functions to the CZ technology shock
5 10 15 20 25 30
0
1
2
3
4
5
6
7
x 10
-3 gy_obs
5 10 15 20 25 30
-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0
x 10
-3 gp_obs
5 10 15 20 25 30
-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0
x 10
-3 y
5 10 15 20 25 30
0
0.002
0.004
0.006
0.008
0.01
dA
Figure 8: Impulse response functions to the CZ monetary shock
10 20 30
0
1
2
3
4
x 10
-3 m
10 20 30
0
2
4
6
x 10
-3 P
10 20 30
-3
-2
-1
0
x 10
-3 c
10 20 30
0
2
4
6
8
x 10
-3 W
10 20 30
0
1
2
3
4
x 10
-3 R
10 20 30
0
1
2
x 10
-4 k
10 20 30
-4
-3
-2
-1
0
x 10
-3 d
10 20 30
-8
-6
-4
-2
0
x 10
-4 n
10 20 30
0
1
2
3
4
x 10
-4 l
29
Figure 9: Impulse response functions to the CZ monetary shock
5 10 15 20 25 30
-15
-10
-5
0
5
x 10
-4 gy_obs
5 10 15 20 25 30
0
2
4
6
x 10
-3 gp_obs
5 10 15 20 25 30
-3
-2
-1
0
x 10
-3 y
30
CONCLUSION
This paper presented estimations of monetary CIA model for the
Visegrad countries and the Euro Area. In order to incorporate
monetary sector into the model, money is incorporated into the longrun
neoclassical DSGE framework through the cash-in-advance
constraint. This approach stresses the function of money as that of a
medium of exchange. The model is estimated on the seasonally
adjusted quarterly time series of the Visegrad countries and the Euro
Area. The comparison of final values is made on the basis of estimated
parameters. The estimation was realized by Bayesian technique. More
concretely, we used the Metropolis-Hastings algorithm to Markov
Chain Monte Carlo.
The analysis of estimated parameters and the behavior of the model
economies can help us to know more about long-run development of
these countries. Estimated parameters for Visegrad countries are
similar, which results in analogous impulse response functions. If we
study the parameter values in more detail, we can divide the Visegrad
countries into two groups. The first group consists of Hungary and the
Czech Republic and the second is made up by Poland and the Slovak
Republic. The former group (CZ and HU) has better characteristics
than the latter. This is obvious from the parameter for the technology
growth rate. The estimated values speak clearly in favour of these two
countries as dynamically developing.
Moreover, the estimation results might be used for future estimations
and analyses of more sophisticated models that contain nominal
rigidities, exchange rates, adjustment costs etc. These models may
complete the analysis and will be the object of our future research.
31
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33
APPENDIX 1: THE DATA
Figure 10: Czech data
1996 1998 2000 2002 2004 2006
1
1.005
1.01
1.015
1.02
1.025
1.03
gy_obs
1996 1998 2000 2002 2004 2006
1
1.005
1.01
1.015
1.02
1.025
1.03
gp_obs
Figure 11: Hungarian data
1996 1998 2000 2002 2004 2006
1
1.005
1.01
1.015
gy_obs
1996 1998 2000 2002 2004 2006
1
1.01
1.02
1.03
1.04
1.05
gp_obs
34
Figure 12: Slovak data
1996 1998 2000 2002 2004 2006
0.98
0.99
1
1.01
1.02
1.03
gy_obs
1996 1998 2000 2002 2004 2006
1
1.01
1.02
1.03
1.04
1.05
gp_obs
Figure 13: Polish data
1996 1998 2000 2002 2004 2006
0.98
1
1.02
1.04
1.06
gy_obs
1996 1998 2000 2002 2004 2006
1
1.01
1.02
1.03
1.04
gp_obs
35
Figure 14: Data of the Euro Area
1996 1998 2000 2002 2004 2006
0.998
1
1.002
1.004
1.006
1.008
gy_obs
1996 1998 2000 2002 2004 2006
1
1.002
1.004
1.006
1.008
gp_obs
36
V roce 2005 vyšlo:
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Petr Chmelík: Vliv institucí přímé demokracie na hospodářskou politiku
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Osvald Vašíček and Karel Musil: The Czech Economy with Inflation
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práva?
WP č. 2/2006
Pavel Breinek: Vybrané institucionální aspekty ekonomické výkonnosti
WP č. 3/2006
Jindřich Marval: Daňová kvóta v ČR
WP č. 4/2006
Zdeněk Tomeš ­ Daniel Němec: Demografický vývoj ČR 1990­2005
WP č. 5/2006
Michal Beneš: Konkurenceschopnost a konkurenční výhoda
WP č. 6/2006
Veronika Bachanová: Regulace a deregulace v ČR v období 1990-
2005
WP č. 7/2006
Petr Musil: Tendence na českém trhu práce v období transformace
WP č. 8/2006
Zuzana Hrdličková: Vliv sociální politiky na konkurenceschopnost
české ekonomiky
WP č. 9/2006
Pavlína Balcarová ­ Michal Beneš: Metodologie měření a hodnocení
makroekonomické konkurenceschopnosti
WP č. 10/2006
Miroslav Hloušek: Czech Business Cycle Stylized Facts
WP č. 11/2006
Jitka Doležalová: Vliv politiky na konkurenceschopnost České
republiky
WP č. 12/2006
Martin Chromec: Dlouhodobé efekty monetární politiky: může ČNB
ovlivnit ekonomický růst?
WP č. 13/2006
Tomáš Paleta: Strukturální změny české ekonomiky ve světle
privatizace a podpory malého a středního podnikání
WP č. 14/2006
Tomáš Otáhal: Vývoj korupce v ČR v období transformace
WP č. 15/2006
Jan Jonáš: Ekonomická svoboda a konkurenční schopnost české
ekonomiky
38
WP č. 16/2006
Michal Tvrdoň: Regulace trhu práce v ČR
WP č. 17/2006
Martina Vašendová: Pohyb kapitálu v průběhu transformace a jeho vliv
na konkurenceschopnost české ekonomiky
WP č. 18/2006
Ondřej Moravec: Hospodářská soutěž a její vliv na
konkurenceschopnost české ekonomiky
WP č. 19/2006
Milan Viturka ­ Viktorie Klímová: Globálně orientované hodnocení
konkurenční pozice krajů České republiky
WP č. 20/2006
Monika Jandová: Vývoj komoditních, teritoriálních a institucionálních
aspektů zahraničního obchodu ČR
WP č. 21/2006
Vladimír Žítek ­ Josef Kunc ­ Petr Tonev: Vybrané indikátory
regionální konkurenceschopnosti a jejich vývoj
WP č. 22/2006
Aleš Franc: Hlavní tendence ve vývoji pracovních migrací v České
republice
WP č. 23/2006
Osvald Vašíček ­ Karel Musil: Behavior of the Czech Economy: New
Open Economy Macroeconomics DSGE Model
WP č. 24/2006
Jaroslav Rektořík: Zapojení vysokých škol do přípravy a realizace
strategických dokumentů regionů ­ podmínka rozvoje inovačních
aktivit
WP č. 25/2006
Ladislav Šiška: Analýza finanční úspěšnosti tuzemských podniků
WP č. 26/2006
Daniel Němec: Demografický vývoj SR 1990­2005
39
V roce 2007 vyšlo:
WP č. 1/2007
Naďa Voráčová: Maďarská fiskální politika a hospodářský růst
WP č. 2/2007
Martin Chromec: Monetární politika a její dopad na konkurenceschopnost
Slovenské republiky
WP č. 3/2007
Martina Vašendová: Pohyb zahraničního kapitálu v průběhu
transformace a jeho vliv na konkurenční schopnost slovenské
ekonomiky
WP č. 4/2007
Jitka Doležalová: Vliv politiky na konkurenceschopnost Slovenské
republiky
WP č. 5/2007
Daniel Němec: Komparace demografického vývoje Maďarska a Polska
v období transformace
WP č. 6/2007
Veronika Bachanová: Regulace a deregulace v Maďarsku v období
1990­2006
WP č. 7/2007
Martina Vašendová: Pohyb zahraničního kapitálu v průběhu
transformace a jeho vliv na konkurenční schopnost polské ekonomiky
WP č. 8/2007
Tomáš Otáhal: Vývoj korupce v SR v období transformace
WP č. 9/2007
Jitka Doležalová: Rozvoj demokracie v Polsku a jeho vliv na výkonnost
hospodářství
WP č. 10/2007
Monika Jandová: Zahraniční obchod Slovenské republiky 1993­2006
WP č. 11/2007
Milan Viturka: Inovační profily regionů
WP č. 12/2007
Veronika Bachanová: Regulace a deregulace v Polsku a ve Slovenské
republikce v období 1990­2006
WP č. 13/2007
Jitka Doležalová: Demokracie a její vliv na výkonnost maďarského
hospodářství
WP č. 14/2007
Tomáš Paleta: Strukturální politika Slovenské republiky 1990­2005
40
WP č. 15/2007
Naďa Voráčová: Hospodářský růst na Slovensku a v Polsku: jaký vliv
měla fiskální politika?
WP č. 16/2007
Monika Jandová: Komparace zahraničního obchodu Maďarska a
Polska (1990-2006)
WP č. 17/2007
Miroslav Hloušek: Growth Accounting for Visegrad States: Dual
Approach
WP č. 18/2007
Jaromír Tonner ­ Osvald Vašíček: Odhad časově proměnných
parametrů v modelech české ekonomiky
WP č. 19/2007
Jiří Polanský ­ Osvald Vašíček: Economic Development of
Visegrad Countries: Macroeconomic DSGE Models