Introduction
The research of parameter estimation in DSGE models with rational expectations is the
core of contemporary macroeconomics. Dynamic systems are viewed as a laboratory
where economic theories can be confronted with real data, and where researchers
can find recommendations for policy makers (see Fernández-Villaverde and RubioRamírez,
2007). Institutions where DSGE models are used for monetary policy analysis
include the Federal Reserve System in the USA (Erceg, Guerrieri and Gust, 2005),
the European Central Bank (Christoffel, Coenen and Warne, 2007), the central bank
of Canada (Murchison and Rennison, 2006), the central bank of Sweden (Adolfson
et al., 2005), the central bank of Spain (Andrés, Burriel and Estrada, 2006), Reserve
bank of New Zealand (Beneš et al., 2009) and Czech National Bank (Andrle et al.
2009). Similar research departments can also be found at prestigious European and
American universities and research institutions.
We analyse the possible drifting of structural parameters in a complex DSGE model
estimated on Czech data. To do this, we let structural parameters drift and subsequently
identify their trajectories via a non-linear filtration method on the second-order
approximation of the model. This issue might be more important for developing countries,
because such economies go through frequent structural changes. Twenty years
after the "Velvet Revolution", Czech economy remains on a convergence path towards
the more developed countries of Western Europe. It has been hit by various shocks,
some of which have generated structural changes. Fast liberalization of capital account
of the Czech Balance of Payments before the entry of the Czech Republic to
OECD, economic slump at the end of the 1990s or European Union (EU) entry are
good examples. In this respect, a question naturally arises about the projection of
these changes and shocks into the parameters of the DSGE model and the drift in
those parameters over time.
In our previous work1 we found out that models designed for monetary policy analysis
and forecasting of an economy that is undergoing structural changes must include
time-varying parameters. These parameters can be either structural parameters
or other exogenous processes (technologies) showing specific characteristics of individual
sectors. From the perspective of monetary policy analysis and forecasting, it
seems more convenient to assume that the structural parameters are stable and use
sectoral technologies owing to their aggregate form. In this work, we would like to
carry out the analysis on the second order approximated model.
1
See [40] for details.
4
2 Solution
This work deals with model construction. Consequently, the main methodology is
constructivism.2 We must always bear in mind the limits of this approach. Models are
consistent structures, and so their analytical conclusions result from the assumptions
we use to construct them. Positivism is then used to interpret the results and their
implications for economic theory and economic policy.
Models are simplified descriptions of real systems. We create them in order to
learn about principles that exist in reality. We want to analyse past decisions and predict
the future. When evaluating modelling results, we should be aware of the assumptions
of the model. All models are subjective from this point of view. The mainstream of
economic theory teaches us that we should regard economic systems as dynamic systems
that are capable of returning to equilibrium after being hit by stochastic shocks.
Economic agents are viewed as being rational in their behaviour and expectations.
The general modelling framework is therefore built from DSGE models with rational
expectations.
2.1 Model Development
The model development is a crucial part of the process of time-varying parameter estimation.
We need to have sufficiently rich and complex model to avoid capturing a
possible model misspecification through time-varying parameters (see [16]). We start
building the model in the paper [43]. The paper provides an analysis of the baseline
New Keynesian DSGE model for a closed economy. The model is estimated with a
Bayesian technique using quarterly Eurozone data. The estimation results are discussed
and compared with related papers. We analyze the behaviour of the model
via impulse responses to unanticipated shocks, which an analysis we carry out in
three steps. First, in order to understand essential model mechanisms, we analyze
the model behaviour without any rigidities. Then, we add separately real and nominal
rigidities to investigate their impacts within the model. In our contribution [42], we analyze
fully anticipated shocks in a medium-scale closed economy DSGE model and
compare them to unanticipated shocks. An anticipated shock might bring about significant
adjustments of agents’ behaviour before the moment a shock hits the economy.
From a practical policy side, modelling of anticipated shocks can be a useful tool for a
policy forecasting since we admit relevance of rational expectations in reality.
Then we construct a suitable model and check its properties (see [41] and [40]).
For our purposes, we need a sufficiently rich small open economy (SOE) model to fit
the main Czech stylized facts. The model is based mainly on the framework of Burriel
et al. [8] which we alter in several sectors (export, government, monetary policy) to
be closer to the Czech data.3 Then, we incorporate several technology processes into
the model, following Andrle et al. [2]. The technologies are designed directly for the
stylized facts of the Czech economy.4
2
Ullm’s understanding of the scientific reflection as a construction without metaphysical existence, see
[24].
3
For the analysis, we use post-1996 data. The data set before 1996 is incomplete.
4
Some sectors of the framework are modelled in a parsimonious way, as we do not aim to use the
model for regular forecasting. In such case, the model would converge more closely to the CNB’s g3
model developed for this objective.
5
Figure 1: Structure of the Model
2.2 Time-varying Parameter Estimation
Our motivation for time-varying parameter estimation is to identify changes in DSGE
model structure related implicitly with changes in productivity between tradable and
nontradable sectors, with deregulation, reexports, government transformation or changes
of monetary regimes (e.g. transition of fixed exchange rate to floating in the Czech
economy in 1997). We expect that it must be represented by an essential change of
DSGE structure which is given by parameters values.5
The method of time-varying parameter estimation is described in details in [41].
After the Bayesian estimation and checks, we allow several structural parameters to
drift in time. We extend the methods proposed in [16]. First, we run the Kalman
filter on the first-order approximated model. This procedure is the two-step problem
where the former consists of adding technologies into the framework whereas the
latter in endogenizing deep parameters via AR processes. Adding technologies helps
us to get the model to data. Endogenizing deep parameters then shows us a timevarying
structure of the model. Second, we run a Particle filter on the second-order
5
In works [45], [46] and [47], we find out that the method of time-varying parameter estimation by
Bootstrap filter can be applied only to models which are well-determined. In case of overcompleteness
or undercompleteness the estimation fails because of mutual interactions (overcompleteness) and an
insufficient base (undercompleteness). Simply said, the mutual interactions bring about instability of
the estimated paths of parameters and states; they differ in every repeated experiment with the same
Bootstrap filter setting. On the other hand, the poor base causes that we are not able to sufficiently fit the
data. The well-determined model is recognized as stabilized estimated paths of parameters and states
in every repeated Bootstrap filter estimation.
6
approximated model.6 Nonlinear filtration is necessary to capture nontrivial influence
of structural changes on model agents’ behaviour.
First, we carry out a simulation study to test a Particle filter. Then we filter technologies
which can also be seen as time-varying parameters and filter structural parameters
which were inverted to model variables. We are interested in mutual invertibility
of these two possible understanding of time-varying parameters. The introduction of
the trade openness and export-specific technology into the model might serve as an
example. Is filtration of these technologies not only reflection of time variability of the
import intensity parameters?
2.2.1 Simulation Study
We thus perform a simulation study to verify the functionality of the methodology. This
study consists of several steps. First of all, we simulate data using the estimated
model, and simultaneously set an arbitrary parameter as a time variable (we choose
parameter nx for the simulation study).
nx,t = ρnx nx,t−1 + (1 − ρnx )nx,ss + ξnx
t .
As in the first exercise, we carry out a time-varying parameter estimation allowing
the drifting of parameters when these movements are unanticipated by agents in the
model. The functional form of the linearized model is obtained via the Dynare Toolbox7.
yt = ys + Ayht−1 + But
where ys is the steady state value of y and yht = yt − ys.
The next step consists of a time-varying parameter estimation allowing the drifting
which is anticipated by model agents due to the higher order approximation. In such
case, one needs to use a nonlinear filter because the model structure is nonlinear as
well. We use the Particle filter.8 For obtaining the second order approximation, we
again employ the Dynare Toolbox.
The second order approximation is
yt = ys + 0.5∆2
+ Ayht−1 + But + 0.5C(yht−1 ⊗ yht−1) + 0.5D(ut ⊗ ut) + E(yht−1 ⊗ ut)
where ys is the steady state value of y, yht = yt − ys, and ∆2 is the shift effect of the
variance of future shocks.
From the simulation, we know the exact trajectory of parameter nx,t. Through
non-linear filter, we try to find the parameter path. We chose several types of time variability.
Firstly, the parameter was chosen as a constant (ρnx = 0, σξnx
t
= 0), but the
filter was set for time-varying parameter (ρnx = 0, σξnx
t
= 0). From a comparison of
simulation and filtering it can be seen that the filter did not detect temporal variability.
Second, time-varying parameter was simulated as a random deviation from long-term
6
The particle filter is very similar to the Bootstrap filter. These algorithms represent the same realizations
of Monte Carlo method. However, the Particle filter software is more user friendly for the
second-order approximated models.
7
See dynare manual [13]
8
See [1] and [46].
7
Figure 2: Simulation study - parameter filtration
2003:1 2008:1
0.35
0.4
0.45
0.5
constant nx
2003:1 2008:1
0.35
0.4
0.45
0.5
AR = 0 n
x
2003:1 2008:1
−3
−2
−1
0
1
2
Regulated prices tech.
2003:1 2008:1
−10
−5
0
5
10
Trade openness tech.
simul Kalman 1st 1std
(steady state) value (ρnx = 0, σξnx
t
= 0). Result for 5000 samples in each time step is
again depicted in Fig. 2.
The same exercise was done for model technologies. Experiment results indicate
good identification of the regulated prices technology and trade openness technology.
2.2.2 Structural Parameters
For the time-varying parameter estimation, we need to choose candidate parameters
for the drifting. Our first guess comes from the incentive experiment (nx, nc, ni, ρg, α)
and from the Bayesian estimation. Figure 3 shows parameters posterior distributions
of which are considerably bimodal9. The candidate is particularly the parameter for
the import intensity of export because we can expect that the openness of the Czech
economy was changing during the analyzed period.10
An exercise is performed in the following procedure. Gradually, each parameter is
separately controlled as time-varying, and then its model filtrations are compared11.
We compared the Kalman filter and particle filters (see [1]), while in the case of particle
filter, we still choose between the first and second approximations of the model. Be-
9
Bimodality can also signify problems in Bayesian estimation of the model.
10
In fact, we did not resist the temptation and tried to estimate all parameters as time-varying.
11
Technologies are switched on.
8
Figure 3: Bimodal posterior distributions parameters
6 6.98 7 7.02 7.04
eta
0.4 0.5 0.6
0
5
10
15
20
theta_p
05 0.1 0.15
theta_x
0.3 0.4 0.5 0.6
0
5
10
15
theta_w
0.4 0.6 0.8 1
chi_M
0.2 0.4 0.6
0
10
20
chi_x
7.4 7.6 7.8
0
6.96 6.98 7 7.02 7.04
0
0.4 0.5 0.6
0
0.6 0.8 1
0
5
10
15
theta_M
0.05 0.1 0.15
0
10
20
30
theta_x
0.3 0.4 0.5 0.6
0
5
10
15
theta_w
0.4 0.6 0.8 1 1.2
0
5
10
15
20
chi_p
0.2 0.4 0.6 0.8 1
0
5
10
15
20
chi_M
0.2 0.4 0.6
0
10
20
chi_x
0.7 0.8 0.9 1
0
5
10
15
chi_w
0.2 0.3 0.4 0.5
0
5
10
n_c
0.1 0.2 0.3
0
5
10
15
20
n_i
0.35 0.4 0.45
0
10
20
30
n_x
0.9995 1 1.0005
0
1000
2000
3000
4000
Lambda_mu
1.0085 1.009 1.0095
0
1000
2000
3000
4000
Lambda_A
0.9995 1 1.0005
0
1000
2000
3000
4000
Lambda_L
0.9935 0.994 0.9945
0
1000
2000
3000
4000
dot_ex_ss
0.998 1 1.0021.0041.0061.008
0
100
200
300
400
alphaO
0.7 0.8 0.9 1
0
5
10
15
chi_w
0.2 0.3 0.4 0.5
0
5
10
n_c
0.1 0.2 0.3
0
5
10
15
20
n_i
0.35 0.4 0.45
0
10
20
30
n_x
0.9995 1 1.0005
0
1000
2000
3000
4000
Lambda_mu
1.0085 1.009 1.0095
0
1000
2000
3000
4000
Lambda_A
0.9995 1 1.0005
0
1000
2000
3000
4000
Lambda_L
0.9935 0.994 0.9945
0
1000
2000
3000
4000
dot_ex_ss
0.998 1 1.0021.0041.0061.008
0
100
200
300
400
alphaO
1 1.005 1.01 1.015
0
100
200
alphaX
1 1.01 1.02
0
50
100
150
wedge_euler
1 1.005 1.01
0
100
200
300
400
wedge_uip
1 1.005 1.01
0
100
200
300
400
target_pi
0.4 0.5 0.6
0
10
20
rho_g
0.06 0.08 0.1 0.12
0
20
40
60
80
rho_b_W
0.8 0.85 0.9
0
10
20
30
rho_R_W
0.7 0.75 0.8
0
10
20
rho_y_W
0.25 0.3 0.35
0
10
20
30
40
rho_pi_W
0.14 0.16 0.18 0.2 0.22 0.24
0
20
40
60
alpha
0.7 0.75 0.8 0.85
0
10
20
30
gamma_R
0.18 0.2 0.22 0.24 0.26
0
10
20
30
40
gamma_y
1.12 1.14 1.16 1.18 1.2
0
20
40
gamma_pi
4.9 5 5.1
0
10
20
epsilon
8.8 9 9.2
0
5
10
15
20
epsilon_M
9.2 9.4 9.6
0
10
20
30
epsilon_x
1 1.5 2 2.5
0
5
10
15
epsilon_W
7.5 7.6 7.7
0
10
20
30
epsilon_c
cause the particle filtrations are very time-consuming12, we came to non-linear filtering
after the linear filtration had promised an interesting result. The results are reported
in Figure 4 and Figure 5. The nonlinear estimation confirms significant movements in
imports intensity parameters. It is especially during 2002 and 2003 that we do identify
a big increase of such parameters which indicate an increase of domestic component
in producing consumption and export. Other parameters seem to be stable over time.
12
The trajectories on Figure 5 are computed averages among 10 rerunned non-linear filtrations, where
each non-linear filtration has 6000 samples for each time step.
9
Figure 4: Parameters suspected to be time-varying, but they are not
2001:1 2006:1
0.5
0.55
0.6
0.65
thetap
2001:1 2006:1
0.65
0.7
0.75
0.8
0.85
chip
2001:1 2006:1
0.4
0.45
0.5
0.55
rhog
2001:1 2006:1
1
1.05
1.1
1.15
1.2
1.25
gammap
i
2001:1 2006:1
0.85
0.9
0.95
1
1.05
1.1
gammaR
2001:1 2006:1
0.05
0.1
0.15
0.2
0.25
alpha
Kalman 1st 1std
Figure 5: Nonlinear parameter filtration - Particle filter
2001:1 2006:1
0.25
0.3
0.35
0.4
0.45
0.5
nc
2001:1 2006:1
0.3
0.4
0.5
0.6
nx
2001:1 2006:1
−0.05
0
0.05
0.1
0.15
0.2
0.25
ni
2001:1 2006:1
1.1
1.2
1.3
1.4
1.5
epsilonW
Kalman 2nd data 1std
10
To complete the analysis, we need a tool for finding out which observables are
responsible for the parameter drifting. The first idea about how to verify the accuracy
of filtering dwells in confrontation of the development of time-varying parameters with
the data, i.e. to find the true development of import-intensive exports, and compare
it with nx trajectories, for example. Unfortunately, the Czech Statistical Office has no
such time series, and furthermore, published papers on this topic do not exist either.
Therefore, we decided to construct time series very simply as the share of real exports
to real imports in the case of nx parameter, and as the proportion of real consumption
to real imports in the case of parameter nc. These time series are of course only a
rough approximation of the parameters because they always consider all imports and
not only that portion that was used in the production of final goods. We put up with
the fact that at least the direction is intuitive, i.e. if there are increases of the import
intensity, both time series have to decline, which also corresponds to the definition of
parameters in the model, i.e. the lower the parameter, the higher the share of imports.
Moreover, we choose a traditional tool like endogenous variables decompositions
into observables. The Figure 6 presents decompositions of deviations of time-varying
parameters from their steady state into observables using linear13 approximation of
the model. Both decompositions show great influence of the exchange rate (obs_EX).
Its effect is intuitive, higher than the steady state appreciation (1999-2002 and 2004-
2006) and implies lower rate parameters nx and nc, i.e. the share of imports in the
production of exports and consumption is increasing, because imports are cheaper
and vice versa. We observed strong depreciation in 1997 (Q2 6.5, Q3 4, Q3 2.5),
1999 (Q1 5.6, Q2 1.2), 2002 (Q4 2.0, Q1 2003 2.5), 2008 (Q4 5.0, Q1 2009 8.5) and
related increases in nx and nc in these periods. Another interesting observation is that
the export prices (obs_PX) and import prices (obs_PM) compensate each other in a
decomposition of a specific parameter.
13
Individual filtrations are not additive because of a nonlinear world in the case of the second order
approximated model
11
Figure 6: Decomposition of the import intensity into observables
1998:1 2000:1 2002:1 2004:1 2006:1 2008:1 2010:1
−0.12
−0.1
−0.08
−0.06
−0.04
−0.02
0
0.02
0.04
0.06
0.08
n_c
obs_PI
obs_PX
obs_PM
obs_W
obs_L
obs_EX
obs_C
obs_I
obs_X
obs_M
obs_YW
obs_PIW
obs_R
obs_RW
obs_CPI
obs_GP
1998:1 2000:1 2002:1 2004:1 2006:1 2008:1 2010:1
−0.06
−0.04
−0.02
0
0.02
0.04
0.06
n_x
obs_PI
obs_PX
obs_PM
obs_W
obs_L
obs_EX
obs_C
obs_I
obs_X
obs_M
obs_YW
obs_PIW
obs_R
obs_RW
obs_CPI
obs_GP
12
In the case of the second order approximated model, we employ a simple correlation
analysis which shows lead and lag correlations between the drifting and observed
time series. We find out a negative correlation between current exchange rate and
current import intensity parameters. Higher domestic component of consumption and
export implies lower import and thus positive net foreign assets, and an appreciated
exchange rate. This finding is also in line with negative correlation between import
and intensity parameters (mainly in case of the second order approximation). Moreover,
we find out a positive correlation between future exchange rate movements and
intensity parameters. The depreciation anticipation, in this case, is a strong incentive
for consumption and export goods producers to increase the domestic component.
Our hypothesis that established technologies are merely a reflection of variability
of structural parameters was tested in two experiments. To avoid mutual interaction,
we switched on the export specific technology and switched off time-varying import
intensity parameters in the first experiment; in the second experiment it was vice versa.
The comparison of trajectories can be seen in Figure 7. We conclude that technology
capturing Balass Samuelson effect is, at least in its cyclical component, a reflection of
time-varying import intensity parameters.
I/98 I/00 I/02 I/04 I/06 I/08 I/10
−5
0
5
10
Export specific tech. and parameter
tech parameter
Figure 7: Comparison of export specific technology and import intensity parameter in
the second-order-approximated model
13
2.3 Monetary Policy Relevance
Our results indicate that the central banks can use sufficiently rich DSGE models for
a long period without frequent recalibrations, even during later phases of economic
transformation. For the case of the Czech Republic, we show that structural parameters
are stable in the model with added exogenous technology processes. We can
consider these technologies to be time-varying processes which capture the gradually
changing behaviour of an economy. The stability of the model parameters allows to
use the core model for several years till the substantial structural break occurs, or the
economy’s convergence moves forward.
However, if the central bank expects structural changes in the future, this assumption
should be incorporated into their forecasts. In this section, we will therefore evaluate
the relevance of the dissertation for monetary policy. We currently have the tools
to incorporate expert assumptions into the forecasts. In this case, it is necessary to
analyze the situation when the central bank is assuming a structural change. To analyze
the impulse responses to anticipated shocks, as in the work [42], represents a
good start.
Reactions of the Monetary Authority to an unexpected export-specific technology
is described in the Appendix well enough. Recall that the export-specific technology
captures the evolution of relative productivity in tradable sector to productivity in nontradeable
sector. A positive shock to this technology must necessarily lead to a rate
hike despite the strong appreciation. A similar response also brings the shock to the
import intensity parameter. In the event that the monetary authority is expecting a decrease
in import intensity of exports, its response should be in the direction of lower
rates, as shown by the expected shock to the export-specific technology and to the
import intensity parameter. Contemporary low rates should offset the disinflationary
pressures resulting from the current exchange rate strengthening. Appreciation of the
exchange rate in turn will partly compensate for inflation at the moment of the shock
realization (see Figures 8 and 9).
14
Figure 8: Export specific technology shock
5 10 15
−0.2
0
0.2
0.4
0.6
Investment deflator
5 10 15
−0.6
−0.4
−0.2
0
Export deflator
5 10 15
−0.3
−0.2
−0.1
0
Import deflator
5 10 15
−0.2
0
0.2
Nominal wages
5 10 15
−1
0
1
Hours worked
5 10 15
−1.5
−1
−0.5
0
Exchange rate
5 10 15
−5
0
5
10
x 10
−3Consumption
5 10 15
−0.02
0
0.02
Investment
5 10 15
−1
0
1
Export
5 10 15
−2
−1
0
1
Import
5 10 15
0
0.5
1
Foreign demand
5 10 15
−1
0
1
Foreign inflation
5 10 15
−0.04
−0.02
0
0.02
Interest rates
5 10 15
−1
0
1
Foreign int. rates
5 10 15
−0.2
0
0.2
0.4
CPI inflation
5 10 15
−5
0
5
10
x 10
−3Government spending
Unanti Anti
Figure 9: Import intensity of exports parameter shock
5 10 15
−0.1
−0.05
0
Investment deflator
5 10 15
−0.8
−0.6
−0.4
−0.2
0
0.2
Export deflator
5 10 15
−0.15
−0.1
−0.05
0
Import deflator
5 10 15
0
0.1
0.2
Nominal wages
5 10 15
−1
0
1
2
3
Hours worked
5 10 15
−0.6
−0.4
−0.2
0
Exchange rate
5 10 15
0
0.01
0.02
Consumption
5 10 15
0
0.1
0.2
Investment
5 10 15
−0.5
0
0.5
1
Export
5 10 15
−4
−2
0
2
Import
5 10 15
−1
0
1
Foreign demand
5 10 15
−1
0
1
Foreign inflation
5 10 15
0
0.02
0.04
Interest rates
5 10 15
−1
−0.5
0
x 10
−14Foreign int. rates
5 10 15
−0.1
0
0.1
CPI inflation
5 10 15
0
0.01
0.02
Government spending
Unanti Anti
15
Conclusion
We investigated possible drifting of structural parameters in an estimated small open
economy DSGE model. We run a particle filter on the second-order approximated
model. Nonlinear filtration is necessary for model agents to capture nontrivial influence
of structural changes on model agents’ behaviour. In our previous work, we found
out that models designed for monetary policy analysis and forecasting of an economy
that is undergoing structural changes must include time-varying parameters. These
parameters can be either structural parameters or other exogenous processes (technologies)
showing the specific characteristics of individual sectors. From the perspective
of monetary policy analysis and forecasting, it seems more convenient to assume
that the structural parameters are stable, and use sectoral technologies owing to their
aggregate form. In this work, we confirmed the previous results but on the secondorder
approximated model. We added to it that parameters capturing import intensity
drift even in framework with added technologies. We also analysed the source of such
drifting through decomposition of drifting parameters into observables. We found out
that their drifting is mainly caused by export and import prices and exchange rate
changes. We also confirmed that the technology capturing Balassa-Samuelson effect
is, at least in its cyclical component, a reflection of time-varying import intensity
parameters.
We carried out a comparison of first and second order approximated models. The
biggest differences represent a positive investment technology shock that increases
consumption in the case of an overheated economy, a positive foreign inflation shock
that increases nominal wages and consumption in the case of economy in crisis, and
positive exchange rate shocks that decrease nominal wages and consumption in case
of an economy in crisis. We also explained how these results can be used for monetary
policy analysis through impulse responses analysis of anticipated shocks.
Because the work deals with many issues, it offers a lot of questions and unsolved
problems. In my opinion, we have not exhausted all the opportunities offered by the
second order approximation. For example, it would be nice to check whether the
identification of the economy’s position in the business cycle would be more accurate
in times of crisis in the case of the second order approximated model. Let us remember
that the bigger a distance from the steady state, the worse is the approximation, and
during the crisis, we were far away. It also appears that the third order approximation of
a model is better suited to capture nontrivial influence of structural changes (changes
of structural parameters) on model agents’ behaviour. The new version of the toolbox
DYNARE already offers third-order approximation as standard, and therefore it will be
less difficult to verify this thesis.
The model itself offers another major challenge. It is a very simple but comprehensive
form of a small open economy. In future research we will have to focus on better
incorporating of labour market, government and financial frictions.
16
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19
List of author’s publications related to the work
[37] TONNER, J., AND VAŠÍ ˇCEK, O. Financial Frictions Relevance during the Crisis:
Czech Case. Q. Zhou (Ed.): ISAEBD 2011, Part II, CCIS 209, pp. 339-344, 2011,
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Dolina, Slovakia, 2011.
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frictions on Czech data. Proceedings of the 29th International Conference
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Estimated on Czech Data. In opposition procedure for publication in Czech Journal
of Economics and Finance (2011). This work was supported by funding of
specific research at Faculty of Economics and Administration.
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Methods in Economics 2009, University of Life Sciences, Praha, 2009.
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DSGE Model: Kalman or Bootstrap Filter? Proceedings of the 26th International
Conference Mathematical Methods in Economics 2008, Technical University of
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in Economics 2007, Technical University of Ostrava, 2007.
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[48] Tonner, J. Faktory konkurenceschopnosti (Komparace zemí V-4). CVKS,
Masarykova univerzita, Brno, 2007, ch. Odhad ˇcasovˇe promˇenných parametr˚u
v DSGE modelech s racionálním oˇcekáváním, pp. 210–213.
20
[49] Tonner, J., and Vašíˇcek, O. Odhad ˇcasovˇe promˇenných parametr˚u v modelech
ˇceské ekonomiky. Tech. rep., CVKS ˇCE MU, Brno, 2007. Working Paper, ISSN
1801-4496.
21
Appendix
The Appendix presents behaviour of the model. Impulse responses are expressed
as deviations from the steady state in percentage points of q-o-q growths, except for
interest rates which are expressed as deviations from the steady state in percentage
points.14 The shocks are of one-standard-deviation size and unanticipated. An impulse
responses simulation of the first-order approximated model is easy because it
does not depend on the position of the economy in the business cycle. In case of the
second-order approximated model, three different impulse responses are presented:
2+ for overheated economy behaviour (Q3 2008), 2- for the economy behaviour in
crisis (Q1 2009) and 2 for the economy in the ’second-order’ steady-state.
14
For example, one-standard-deviation neutral technology shock increases foreign demand from
2.25% q-o-q growth steady state value to 3.25% q-o-q growth. See Figure 10.
22
Figure 10: Neutral technology shock
5 10 15
−0.04
−0.03
−0.02
Investment deflator
5 10 15
−0.04
−0.02
0
0.02
Export deflator
5 10 15
−0.04
−0.02
Import deflator
5 10 15
0.2
0.4
0.6
0.8
Nominal wages
2 2 + 2 − 1
5 10 15
−0.4
−0.2
0
Hours worked
5 10 15
−0.2
−0.15
−0.1
−0.05
Exchange rate
5 10 15
0.15
0.2
0.25
0.3
0.35
Consumption
5 10 15
0.2
0.4
0.6
Investment
5 10 15
0.2
0.4
0.6
0.8
Export
5 10 15
0.2
0.4
0.6
0.8
Import
5 10 15
0.5
1
Foreign demand
5 10 15
−2
0
2
x 10
−14
Foreign inflation
5 10 15
−0.06
−0.04
−0.02
0
Interest rates
5 10 15
−2
−1
0
x 10
−14
Foreign int. rates
5 10 15
−0.04
−0.02
0
CPI inflation
5 10 15
0.2
0.3
0.4
Government spending
Figure 10 shows a positive neutral technology shock ξA
t of one standard deviation
size. The neutral technology shock is considered to be a shock to the productivity of
both the foreign economy and the small open domestic economy (information symmetry).
Therefore, the shock leads to growth of foreign GDP and thus to demand growth
for domestic production. The increased demand for domestic production strengthens
the domestic currency in comparison to the foreign currency. Stronger exchange rate
allows goods to be imported more cheaply and in greater quantity. This supports
production in sectors which use imports as an input, i.e. production of consumption
(both private and governmental) and investment goods. Exports fall as a result of
the stronger exchange rate, but this effect is outweighed by a higher foreign demand.
Nominal wages respond to higher productivity with higher-than-steady-state growth.
Wages represent a cost item of all manufacturing sectors in the model, i.e. the consumption,
investment and export goods manufacturing sectors. Higher wage growth is
outweighed by lower import prices which are also the prices of inputs in manufacturing
sectors. Consequently, consumer price inflation is below its steady-state level and the
monetary authority responds by lowering interest rates.
23
Figure 11: Investment - specific technology
5 10 15
−0.3
−0.2
−0.1
0
Investment deflator
5 10 15
−0.2
−0.1
0
0.1
Export deflator
5 10 15
−0.3
−0.2
−0.1
0
Import deflator
5 10 15
0
0.2
0.4
Nominal wages
2 2 + 2 − 1
5 10 15
−1
0
1
2
Hours worked
5 10 15
−1
−0.5
0
Exchange rate
5 10 15
−0.05
0
0.05
0.1
0.15
Consumption
5 10 15
0
0.2
0.4
0.6
0.8
Investment
5 10 15
0
1
2
Export
5 10 15
0
0.5
1
Import
5 10 15
0
1
2
3
Foreign demand
5 10 15
0
1
2
x 10
−14
Foreign inflation
5 10 15
−0.2
−0.1
0
0.1
Interest rates
5 10 15
−4
−2
0
x 10
−14
Foreign int. rates
5 10 15
−0.3
−0.2
−0.1
0
CPI inflation
5 10 15
−0.05
0
0.05
0.1
0.15
Government spending
The response of the model economy to an investment-specific technology shock
ξµ
t can be seen in Figure 11. This technology, together with the previous technology,
makes up the aggregate technology, which is used to stationarize the model equations.
For the same reason as for the neutral technology shock, the shock to investmentspecific
technology has an international dimension given perfect transmission of information,
and thus will be reflected in growth of foreign GDP and even in growth of
foreign demand for domestic goods. This again leads to higher-than-steady-state exchange
rate appreciation, although in contrast to the previous technology shock, this
is a one-off appreciation, and in other periods the rate of appreciation is lower than
the steady state. Growth rates of wages and price of capital15 in response to higher
productivity are above the steady state, however, in this case these the effects as
cost items are greater than the effect of the one-off appreciation, which implies CPI
inflation above its steady state. Because the reaction of the monetary authority is
forward-looking, interest rates will be increased so that the inflation target is hit at the
monetary policy horizon. This shock, of course, increases real investment and then
indirectly affects imports and exports. Note that in case of an overheated economy, a
positive shock increases consumption.
15
Change of the price of capital depends on the setting of the capital adjustment costs.
24
Figure 12: Population growth shock
5 10 15
−12
−10
−8
−6
−4
−2
x 10
−3
Investment deflator
5 10 15
−20
−10
0
x 10
−3
Export deflator
5 10 15
−12
−10
−8
−6
−4
−2
x 10
−3
Import deflator
5 10 15
−10
−5
0
x 10
−3
Nominal wages
2 2 + 2 − 1
5 10 15
−1
−0.5
0
Hours worked
5 10 15
−0.1
−0.05
0
Exchange rate
5 10 15
0
0.5
1
Consumption
5 10 15
0
0.5
1
Investment
5 10 15
0
0.2
0.4
0.6
0.8
Export
5 10 15
0
0.5
1
Import
5 10 15
0
0.5
1
Foreign demand
5 10 15
−1
0
1
Foreign inflation
5 10 15
0
0.01
0.02
0.03
Interest rates
5 10 15
−1
0
1
Foreign int. rates
5 10 15
−10
−8
−6
−4
−2
x 10
−3
CPI inflation
5 10 15
0
0.5
1
Government spending
Shock to population growth ξL
t , analysed in Figure 12, is another shock included
in the model. This variable is also used to stationarize the model, i.e. it converts
all variables to variables expressed in terms of per capita. The arrival of new workers
implies growth of consumption, investment and imports, and that is because the
growing population requires more consumption and higher investment, thus putting
upward pressure on imports. On the contrary, wage growth pressure is lower than
in the steady state because the newcomers are competitors for existing employees.
The downward pressure on wages implies a lower consumer price inflation, which
might, ceteris paribus, lead to lower-than-steady-state rates. In this case, however,
the demand effect of newcomers is very strong, and the monetary authority is forced
to prevent an overheating of the economy at the cost of failing to achieve the inflation
target.
25
Figure 13: Labour supply shock
5 10 15
0
2
4
6
8
x 10
−4
Investment deflator
5 10 15
0
5
10
x 10
−4
Export deflator
5 10 15
0
2
4
6
x 10
−4
Import deflator
5 10 15
0
1
2
x 10
−3
Nominal wages
2 2 + 2 − 1
5 10 15
−15
−10
−5
0
5
x 10
−4
Hours worked
5 10 15
0
1
2
x 10
−3
Exchange rate
5 10 15
−15
−10
−5
0
x 10
−5
Consumption
5 10 15
−10
−5
0
x 10
−4
Investment
5 10 15
0
5
10
15
x 10
−4
Export
5 10 15
−1
0
1
2
x 10
−3
Import
5 10 15
−1
0
1
Foreign demand
5 10 15
−1
0
1
Foreign inflation
5 10 15
2
4
6
8
x 10
−4
Interest rates
5 10 15
−1
0
1
Foreign int. rates
5 10 15
0
5
10
x 10
−4
CPI inflation
5 10 15
−15
−10
−5
0
x 10
−5
Government spending
A shock to the labour supply ξϕ
t , as depicted in Figure 13, reduces labour supply,
implying a reduction in hours worked. It results, ceteris paribus, in higher-than-steadystate
wages. Domestic production of intermediate goods, inputs of which are labour
and capital, is reduced. The lower domestic production of intermediate goods is an input
in production of final consumption (private and government) and investment goods,
and is only partially substituted in the production of these goods by imported goods.
Higher imports lead to a balance of payments deficit, which implies a weakening exchange
rate. This supports exporters. Depreciation leads to a cost increase because
imports enter the final production of all sectors with the exception of the government
consumption goods production sector. Higher wages and import prices imply higherthan-steady-state
consumer goods price inflation and an appropriate response of the
monetary authority in the direction of higher rates. We add that the labour supply
shock reduces the number of hours worked at all wage levels, and therefore works
very much like a shock to population growth (see Burriel et al. in [8]).
26
Figure 14: Monetary - policy shock
5 10 15
−0.3
−0.2
−0.1
Investment deflator
5 10 15
−0.8
−0.6
−0.4
−0.2
0
0.2
Export deflator
5 10 15
−0.3
−0.2
−0.1
0
Import deflator
5 10 15
−0.3
−0.2
−0.1
0
Nominal wages
2 2 + 2 − 1
5 10 15
−1
−0.5
0
Hours worked
5 10 15
−3
−2
−1
0
Exchange rate
5 10 15
−0.03
−0.02
−0.01
0
Consumption
5 10 15
−0.2
−0.1
0
Investment
5 10 15
−2
−1
0
Export
5 10 15
−0.2
0
0.2
Import
5 10 15
0
2
4
x 10
−14
Foreign demand
5 10 15
−1
0
1
Foreign inflation
5 10 15
0
0.2
0.4
0.6
Interest rates
5 10 15
−1
0
1
Foreign int. rates
5 10 15
−0.3
−0.2
−0.1
CPI inflation
5 10 15
−0.03
−0.02
−0.01
0
Government spending
Assuming nominal rigidities, effectiveness of a monetary policy shock is nontrivial.
A one-off increase in rates, therefore, does not merely reduce inflation and has a zero
effect on real variables. The response of the model economy to an unexpected monetary
policy shock ξm
t is shown in Figure 14. A one-off rate increase leads, ceteris
paribus, to exchange rate appreciation in accordance with the uncovered interest parity
condition. This leads to a high current account deficit because a stronger exchange
rate will allow more and cheaper goods to be imported, which, however, is a disadvantage
for exporters. Higher interest rates reduce domestic production of intermediate
goods, and, despite higher imports, production of consumer products (household and
government) and investment goods falls below its steady state level. Reduction in
production of domestic intermediate goods also results in a decrease in hours worked
and a corresponding decline in nominal wages. Lower nominal wages, together with
the stronger exchange rate, lead to lower consumer goods price inflation, so the initial
intention of the monetary authority is realized.
27
Figure 15: Real government consumption shock
5 10 15
0
2
4
x 10
−4
Investment deflator
5 10 15
0
5
10
x 10
−4
Export deflator
5 10 15
0
2
4
x 10
−4
Import deflator
5 10 15
2
4
6
8
x 10
−4
Nominal wages
2 2 + 2 − 1
5 10 15
−0.02
0
0.02
Hours worked
5 10 15
0
10
20
x 10
−4
Exchange rate
5 10 15
−3
−2
−1
0
x 10
−5
Consumption
5 10 15
−20
−10
0
x 10
−5
Investment
5 10 15
0
5
10
x 10
−4
Export
5 10 15
−1
0
1
2
3
x 10
−3
Import
5 10 15
−1
0
1
Foreign demand
5 10 15
−1
0
1
Foreign inflation
5 10 15
2
4
6
8
x 10
−4
Interest rates
5 10 15
−1
0
1
Foreign int. rates
5 10 15
0
2
4
6
8
x 10
−4
CPI inflation
5 10 15
−0.05
0
0.05
Government spending
An increase in real government consumption caused by shock ξg
t is shown in
Figure 15. The reaction of model agents to the growth in government spending is
simplified in order to reflect the response of agents in the real economy as much as
possible. In particular, higher-than-steady-state government spending is viewed as a
demand shock which leads to crowding out of private consumption and private investment
through a reduction of inputs in each sector. Shortage of domestic intermediate
goods (government final consumption is produced exclusively from domestic intermediate
goods) leads to higher imports. This results, ceteris paribus, in depreciation of
currency, because the balance of payments goes into a significant deficit. Exports are
partially supported, but not enough (crowding out of exports). Depreciation, coupled
with higher wages, leads to increased costs in all production sectors, and thus implies
a higher-than-steady-state consumer price inflation. This leads to the appropriate response
of the monetary authority, namely an increase in interest rates, which is the
likely reaction of the monetary authority when government spending is higher than
steady state.
28
Figure 16: Foreign demand shock
5 10 15
−20
−10
0
x 10
−3
Investment deflator
5 10 15
−0.02
0
0.02
Export deflator
5 10 15
−0.03
−0.02
−0.01
0
Import deflator
5 10 15
−0.01
0
0.01
Nominal wages
2 2 + 2 − 1
5 10 15
−0.2
0
0.2
Hours worked
5 10 15
−0.2
−0.1
0
Exchange rate
5 10 15
0
2
4
x 10
−3
Consumption
5 10 15
0
0.02
0.04
Investment
5 10 15
0
0.5
1
Export
5 10 15
0
0.2
0.4
Import
5 10 15
0
0.5
1
1.5
Foreign demand
5 10 15
−1
0
1
Foreign inflation
5 10 15
−0.02
−0.01
0
Interest rates
5 10 15
−1
0
1
Foreign int. rates
5 10 15
−10
−5
0
x 10
−3
CPI inflation
5 10 15
0
2
4
6
x 10
−3
Government spending
An increase in foreign demand realized by the shock ξyW
t is illustrated in Figure
16. First, we must say that foreign countries are modelled exogenously (not even as
a VAR model), so a shock to foreign demand (a shock to foreign GDP growth) does
not lead to an increase in foreign inflation and foreign rates. A single shock to foreign
demand leads mainly to higher-than-steady-state exchange rate appreciation through
a positive trade balance. Stronger exchange rate is detrimental for exporters, but this
effect is outweighed by the direct effect of higher foreign demand. Due to the strong
appreciation, consumer price inflation declines below the inflation target, as imports
as inputs in the production of consumer goods get much cheaper. The reaction of
the monetary authority is intuitive again – there is a reduction in interest rates which
leads to depreciation pressure on the exchange rate in order to steer inflation to the
target at the monetary policy horizon. The lower rates stimulate production in other
sectors (consumption and investment) but only very slightly. There will also be moderate
growth in nominal wages, but the growth in wages as a cost item cannot offset the
impact of the appreciation.
29
Figure 17: Foreign interest rates shock
5 10 15
0
0.02
0.04
Investment deflator
5 10 15
−0.05
0
0.05
0.1
Export deflator
5 10 15
0
0.02
0.04
Import deflator
5 10 15
0
0.01
0.02
0.03
Nominal wages
2 2 + 2 − 1
5 10 15
0
0.1
0.2
Hours worked
5 10 15
0
0.2
0.4
Exchange rate
5 10 15
−2
−1
0
1
x 10
−3
Consumption
5 10 15
−0.02
−0.01
0
0.01
Investment
5 10 15
0
0.2
0.4
Export
5 10 15
−0.1
−0.05
0
0.05
Import
5 10 15
−1
0
1
Foreign demand
5 10 15
−1
0
1
Foreign inflation
5 10 15
0
0.02
0.04
Interest rates
5 10 15
0.05
0.1
0.15
Foreign int. rates
5 10 15
0
0.02
0.04
CPI inflation
5 10 15
−3
−2
−1
0
1
x 10
−3
Government spending
Higher-than-steady-state foreign interest rates are realized by the shock ξRW
t ,
whose model implications are captured by Figure 17. The logics of uncovered interest
rate parity implies that an increase in foreign rates leads to a widening differential between
interest rates in the domestic and foreign economy. This automatically leads to
upward pressure on domestic interest rates and significant exchange rate depreciation
in the domestic economy. This weakening of the exchange rate supports domestic
exporters and dampens imports. Since the export sector is highly import-intensive,
production in other manufacturing sectors, i.e. consumption and investment, will be
muted. Missing imports will be partially substituted by domestic intermediate goods.
This will lead to growth of hours worked and also to growth of nominal wages, but the
rise in domestic production of intermediate goods will initially be unable to completely
offset the outflow of imports to the export-producing sector. Together with higher nominal
wages, depreciation will lead to growth of prices in the final consumption goods
production sector. The reaction of the monetary authority – higher nominal rates – is
in line with the anticipated higher inflation.
30
Figure 18: Foreign inflation shock
5 10 15
−0.04
−0.02
0
Investment deflator
5 10 15
−0.5
0
0.5
Export deflator
5 10 15
−0.06
−0.04
−0.02
0
Import deflator
5 10 15
−0.03
−0.02
−0.01
0
Nominal wages
2 2 + 2 − 1
5 10 15
−0.3
−0.2
−0.1
0
0.1
Hours worked
5 10 15
−4
−2
Exchange rate
5 10 15
−15
−10
−5
0
x 10
−4
Consumption
5 10 15
−6
−4
−2
0
2
x 10
−3
Investment
5 10 15
−0.6
−0.4
−0.2
0
0.2
Export
5 10 15
−0.05
0
0.05
0.1
0.15
Import
5 10 15
−1
0
1
Foreign demand
5 10 15
1
2
3
Foreign inflation
5 10 15
−20
−10
0
x 10
−3
Interest rates
5 10 15
−1
0
1
Foreign int. rates
5 10 15
−0.04
−0.02
0
CPI inflation
5 10 15
−20
−10
0
x 10
−4
Government spending
The response of the domestic economy to an increase in foreign inflation above
its steady state value is realized with shock ξπW
t and shown in Figure 18. According
to the model equations showing the identity between inflation in import prices in the
domestic currency and the product of inflation of foreign prices in foreign currency
and the exchange rate, the endogenous exchange rate must respond by appreciating
strongly. Economically, this relationship could be interpreted as the reaction of the
domestic economy to growth in foreign demand as a result of increased competitiveness
of the domestic economy. The domestic economy thus avoids an overheating
due to increased foreign demand and imported inflation through a strengthening of
the exchange rate. In this case, the exchange rate more than offsets the increase in
foreign prices in foreign currency and implies a reduction in monetary policy rates so
that consumer price inflation hits the inflation target at the monetary policy horizon.16
Note that a positive shock increases nominal wages and consumption in the case of
the economy in crisis.
16
Note that if the appreciation was not so strong, the effect of higher international prices could outweigh
the effect of the stronger exchange rate and import prices in the domestic currency would rise above their
steady state level. In this case, consumer price inflation would rise above its steady state level, and the
monetary authority would have to raise rates.
31
5 10 15
0
5
10
x 10
−3
Investment deflator
5 10 15
−0.1
0
0.1
Export deflator
5 10 15
0
5
10
15
x 10
−3
Import deflator
5 10 15
0
2
4
6
x 10
−3
Nominal wages
2 2 + 2 − 1
5 10 15
−0.1
0
0.1
Hours worked
5 10 15
−0.2
0
0.2
Exchange rate
5 10 15
−1
0
1
2
x 10
−4
Consumption
5 10 15
−1
0
1
x 10
−3
Investment
5 10 15
−0.2
0
0.2
Export
5 10 15
−0.04
−0.02
0
0.02
0.04
Import
5 10 15
−1
0
1
Foreign demand
5 10 15
−1
0
1
Foreign inflation
5 10 15
0
2
4
x 10
−3
Interest rates
5 10 15
−1
0
1
Foreign int. rates
5 10 15
0
5
10
x 10
−3
CPI inflation
5 10 15
−1
0
1
2
3
x 10
−4
Government spending
Figure 19: Debt elastic premium shock
A one-period shock to the debt elastic premium is realized by shock ξprem
t and is
captured by Figure 19. This shock can be viewed as a fundamental shock to the exchange
rate, i.e. in the case of a positive shock it leads to depreciation of the exchange
rate. Weakening of the exchange rate obviously favours domestic exporters exporting
to foreign countries, so we observe an increase in domestic exports. On the other
hand, imports are significantly more expensive, so they fall below their steady-state
growth. Because exports are set as very import-intensive in the domestic economy,
imports are replaced by domestic intermediate goods as inputs, i.e. substituted by
goods produced by labour and capital. This leads to an increase in hours worked
and also to growth of nominal wages. The considerably weakened exchange rate,
combined with the growth of nominal wages, leads to a rise in consumer price inflation,
which forces the monetary authority to increase interest rates so that inflation
will hit the inflation target at the monetary policy horizon. Note that a positive shock
decreases nominal wages and consumption in the case of the economy in the crisis.
32
Figure 20: Exchange rate shock - persistent
5 10 15
0
0.05
0.1
Investment deflator
5 10 15
−0.2
0
0.2
0.4
Export deflator
5 10 15
0
0.05
0.1
Import deflator
5 10 15
0
0.02
0.04
0.06
Nominal wages
2 2 + 2 − 1
5 10 15
−0.2
0
0.2
0.4
0.6
Hours worked
5 10 15
0
1
2
Exchange rate
5 10 15
−2
0
2
x 10
−3
Consumption
5 10 15
−0.01
0
0.01
Investment
5 10 15
−0.5
0
0.5
1
1.5
Export
5 10 15
−0.2
0
0.2
Import
5 10 15
−1
0
1
Foreign demand
5 10 15
−1
0
1
Foreign inflation
5 10 15
0
0.02
0.04
0.06
Interest rates
5 10 15
−1
0
1
Foreign int. rates
5 10 15
0
0.02
0.04
0.06
0.08
CPI inflation
5 10 15
−1
0
1
2
x 10
−3
Government spending
Figure 21: UIP shock
5 10 15
0
1
2
3
x 10
−4
Investment deflator
5 10 15
−2
0
2
x 10
−3
Export deflator
5 10 15
0
2
4
x 10
−4
Import deflator
5 10 15
0
5
10
15
x 10
−5
Nominal wages
2 2 + 2 − 1
5 10 15
−2
0
2
x 10
−3
Hours worked
5 10 15
−5
0
5
10
x 10
−3
Exchange rate
5 10 15
−2
0
2
4
6
x 10
−6
Consumption
5 10 15
−2
0
2
x 10
−5
Investment
5 10 15
−5
0
5
x 10
−3
Export
5 10 15
−1
0
1
x 10
−3
Import
5 10 15
−1
0
1
Foreign demand
5 10 15
−1
0
1
Foreign inflation
5 10 15
0
5
10
15
x 10
−5
Interest rates
5 10 15
−1
0
1
Foreign int. rates
5 10 15
0
1
2
x 10
−4
CPI inflation
5 10 15
−2
0
2
4
6
8
x 10
−6
Government spending
33
Figure 22: Regulated prices shock
5 10 15
−0.02
−0.01
0
0.01
Investment deflator
5 10 15
−0.05
0
0.05
Export deflator
5 10 15
−0.03
−0.02
−0.01
0
0.01
Import deflator
5 10 15
−0.04
−0.02
0
Nominal wages
2 2 + 2 − 1
5 10 15
0
0.2
0.4
Hours worked
5 10 15
−0.4
−0.2
0
Exchange rate
5 10 15
−0.1
−0.05
Consumption
5 10 15
−0.2
−0.1
0
Investment
5 10 15
−0.4
−0.2
0
Export
5 10 15
−0.1
0
0.1
0.2
0.3
Import
5 10 15
0
2
4
x 10
−14
Foreign demand
5 10 15
−1
0
1
Foreign inflation
5 10 15
0.04
0.06
0.08
0.1
0.12
Interest rates
5 10 15
−1
0
1
Foreign int. rates
5 10 15
0.2
0.4
0.6
CPI inflation
5 10 15
0
0.2
0.4
0.6
0.8
Government spending
Figure 22 captures an unanticipated one-period positive shock to the growth of
regulated prices, which is implemented by exogenous variable ξaR
t . This shock directly
increases consumer price inflation. Consumer basket is composed of both nonregulated
goods and goods prices of which are heavily regulated (rents and energy
prices being good examples for the Czech Republic). The monetary authority must respond
by raising interest rates so that inflation will hit the inflation target. Government
consumption will increase because the income from the increased regulated prices is
income of the government. Since the only input into production of government consumption
goods are domestic intermediate goods, domestic intermediate goods are
replaced by imports in other production sectors but not sufficiently so that they could
maintain real consumption, investment and exports at their steady state growth levels
(crowding-out effect). Balance of payments deficit increases, which implies exchange
rate depreciation. We should add that regulated prices are approximated by an exogenous
process in this model, i.e. there is no link to the observed regulated prices.
34
Figure 23: Intertemporal preference shock
5 10 15
0.1
0.2
0.3
Investment deflator
5 10 15
0.2
0.4
Export deflator
5 10 15
0
0.1
0.2
0.3
Import deflator
5 10 15
0.2
0.4
0.6
Nominal wages
2 2 + 2 − 1
5 10 15
0
0.5
1
Hours worked
5 10 15
0
0.2
0.4
0.6
0.8
Exchange rate
5 10 15
0
0.5
1
1.5
Consumption
5 10 15
−1
−0.5
0
Investment
5 10 15
0
0.2
0.4
Export
5 10 15
−0.5
0
0.5
1
Import
5 10 15
−4
−2
0
2
4
x 10
−14
Foreign demand
5 10 15
0
1
2
x 10
−14
Foreign inflation
5 10 15
0.2
0.4
0.6
Interest rates
5 10 15
0
1
2
x 10
−14
Foreign int. rates
5 10 15
0.2
0.4
CPI inflation
5 10 15
0
1
2
Government spending
An increase in intertemporal preference implemented by shock ξd
t is shown in
Figure 23. This demand shock increases private consumption and government consumption
in particular. By contrast, investment activity will be crowded out. The increased
demand for inputs in consumption sectors leads to substitution of domestic
intermediate goods for imports. As a result of the increased imports, balance of payments
falls into deficit and exchange rate depreciates, which partly boosts export activity.
On the other hand, growth in demand for domestic intermediate goods leads to
an increase in demand for inputs in this sector, i.e. for labour and capital. It therefore
increases number of hours worked and nominal wages. Depreciation, combined with
a higher nominal wage, increases inflation in prices of final consumption, to which the
monetary authority reacts by increasing monetary policy rates. We should add that
this shock alongside with the shock to government consumption are the only domestic
demand shocks in the model. The difference between them lies in the crowding-out
effect. While the shock to government consumption also crowds out private domestic
consumption, the domestic demand shock crowds out only private investment.
35
Figure 24: Export specific technology shock
5 10 15
0
0.2
0.4
Investment deflator
5 10 15
−0.8
−0.6
−0.4
−0.2
0
Export deflator
5 10 15
−0.2
−0.1
0
Import deflator
5 10 15
0
0.05
0.1
Nominal wages
2 2 + 2 − 1
5 10 15
−0.5
0
0.5
1
1.5
Hours worked
5 10 15
−1.5
−1
−0.5
0
Exchange rate
5 10 15
0
5
10
15
x 10
−3
Consumption
5 10 15
0
0.05
0.1
Investment
5 10 15
−0.2
0
0.2
Export
5 10 15
−2
−1
0
1
Import
5 10 15
0.2
0.4
0.6
0.8
1
Foreign demand
5 10 15
−1
0
1
Foreign inflation
5 10 15
−0.05
0
0.05
Interest rates
5 10 15
−1
0
1
Foreign int. rates
5 10 15
0
0.1
0.2
0.3
CPI inflation
5 10 15
0
10
20
x 10
−3
Government spending
Growth in export-specific technology realized by shock ξaX
t is shown in Figure
24.17 Growth in this technology increases productivity in tradable goods production
sector relative to non-tradable goods production sector, but the less productive workers
in the non-tradable sector will demand an increase in wages so that the wage gap
between the tradable and non-tradable sectors in the domestic economy does not increase.
This, of course, leads to inflation because the wage growth in the non-tradable
sector is not supported by a corresponding increase in productivity. On the other hand,
the exchange rate appreciates because the tradable sectors are able to produce more
goods at lower cost, so the balance of payments moves into surplus, which implies a
strengthening of the exchange rate. The response of the monetary authority is ambiguous
and depends on whether the effect of exchange rate or higher wages prevails
at the monetary policy horizon. In our case, the effect of stronger exchange rate prevails
and the monetary authority sets lower rates.
17
This technology should capture the relative effectiveness of the tradable sector w.r.t. the non-tradable
sector in the domestic economy. This effect is known as the Harrod-Balassa-Samuelson effect. See more
in Andrle et al. in [2].
36
Figure 25: Wedge Euler shock
5 10 15
−0.03
−0.02
−0.01
0
Investment deflator
5 10 15
−0.03
−0.02
−0.01
0
Export deflator
5 10 15
−0.03
−0.02
−0.01
0
Import deflator
5 10 15
−0.04
−0.02
0
Nominal wages
2 2 + 2 − 1
5 10 15
−0.06
−0.04
−0.02
0
Hours worked
5 10 15
−0.1
−0.05
0
Exchange rate
5 10 15
−10
−5
0
x 10
−3
Consumption
5 10 15
−0.08
−0.06
−0.04
−0.02
0
0.02
Investment
5 10 15
−0.1
−0.05
0
Export
5 10 15
−0.06
−0.04
−0.02
0
0.02
0.04
Import
5 10 15
−1
0
1
Foreign demand
5 10 15
−1
0
1
Foreign inflation
5 10 15
−0.03
−0.02
−0.01
Interest rates
5 10 15
−1
0
1
Foreign int. rates
5 10 15
−0.03
−0.02
−0.01
0
CPI inflation
5 10 15
−10
−5
0
x 10
−3
Government spending
In transition economies, there is a difference between real output growth and real
interest rates. In the Czech Republic, for example, real GDP growth is around 5%,
while real interest rates are hovering around 1% (the difference between 3% nominal
rates and 2% inflation). This difference is due to poorly developed financial markets
in emerging economies. An increase in this difference in the Euler equation is simulated
by a positive shock ξeuler
t and the response of domestic economy is shown in
Figure 25. This shock mainly reduces domestic nominal interest rates and increases
future inflation so that the difference between real economic output and real interest
rates widens. At the same time, it increases the shadow price of wealth in the economy,
which results in decline in domestic consumption (private and government) and
private investment.
37