1
A DSGE Model View of the
Czech Business Cycle
WORKING PAPER č. 01/2011
Tomáš Motl, Osvald Vašíček
Červen 2011
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Řada studií Working Papers Centra výzkumu konkurenční schopnosti
české ekonomiky je vydávána s podporou projektu MŠMT výzkumná
centra 1M0524.
ISSN 1801-4496
Vedoucí: prof. Ing. Antonín Slaný, CSc., Lipová 41a, 602 00 Brno,
e-mail: slany@econ.muni.cz, tel.: +420 549491111
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A DSGE MODEL VIEW OF THE CZECH
BUSINESS CYCLE
Abstract:
This paper uses a simple New Keynesian DSGE model as a means to
examine the sources of the Czech business cycle from 1996 to 2010,
focusing on the output gap. We estimate the DSGE model in order to
obtain trajectories of exogenous shocks. Based on the model, we
decompose the deviation of Czech output from trend into contributions
of these shocks. We show that since 2000, the foreign demand shock
and exchange rate shock have been increasingly important for the
domestic business cycle.
Overall, domestic shocks account for more than a half of the variance
in the domestic output gap. We contrast the recession of 1997-1998,
caused primarily by domestic shocks, to the recession of 2009, which
was caused by a drop in the foreign demand. We also find that the
Czech economy is sensitive to the exchange rate movements, as
documented by the year 2002.
Abstrakt:
Tento článek používá jednoduchý neokeynesiánský DSGE model
k určení příčin českého hospodářského cyklu mezi lety 1996 a 2010,
se zaměřením na mezeru výstupu. DSGE model je odhadnut, čímž
dostáváme trajektorie exogenních šoků. Na základě modelu poté
dekomponujeme odchylky české mezery výstupu mezi příspěvky
exogenních šoků. Analýza ukazuje, že od roku 2000 mají zahraniční
šoky a šok ve směnném kurzu rostoucí význam pro český
hospodářský cyklus.
Domácí šoky vysvětlují více než polovinu variability české mezery
výstupu. Zatímco recese z let 1997-1998 a následné oživení lze přičíst
zejména domácím šokům, recese roku 2009 byla téměř zcela
způsobena prpadem zahraniční poptávky. Dále také ukazujeme, že
česká ekonomika je citlivá na pohyby směnného kurzu, jak
dokumentuje rok 2002.
Recenzoval:
Ing. Karel Musil, Ph.D.
Introduction
Since the beginning of the transition to market based economy, the Czech economy
has experienced two recessions and several years of moderate growth around three
per cent but also a few years of a rapid economic growth over six per cent (figure 1).
What were the causes of these events? We use a simple dynamic stochastic general
equilibrium (DSGE) model to answer this question.
The DSGE model is derived from microeconomic principles. It is estimated by
Bayesian methods and tested for its data matching properties. The advantage of the
DSGE model is that it provides a structural view of the economy. It decomposes
data volatility into primitive drivers such as technological shocks, demand shocks or
monetary policy shocks. The model is replicated from Justiniano and Preston (2010).
Figure 1: Annualized quarterly growth rates of the seasonally adjusted Czech GDP.
Shaded areas indicate recessions.
In this paper, we estimate the trajectories of domestic and foreign technological
shocks, demand shocks, monetary policy shocks and an exchange rate shock. We decompose
the output gap fluctuations in terms of these shocks. Our analysis provides
an insight into which of these shocks can explain recession, recovery or expansion
in the domestic output. Based on the model, our assumptions and observed data,
4
we shed light on the basic factors that could influence the stability and growth of the
Czech economy.
Our analysis suggests that the two recessions mentioned earlier had different
sources. The recession of 1997-1998 was triggered by a domestic monetary policy
shock, which however resulted from monetary crisis and we do not interpret it as a
monetary policy error. The monetary shock was then followed by a negative contribution
of domestic technological shock which suggests that the recession was caused by
problems on the supply side of the Czech economy. On the other hand, the recession
of 2009 was caused primarily by a negative foreign demand shock. We therefore see
the first recession as caused primarily by internal shocks and the second recession as
caused primarily by shocks from abroad.
We also find evidence for increasing importance of foreign shocks. Since 2000,
foreign shocks and the exchange rate shock played an important role in determining
the domestic business cycle. Starting in 2008, the foreign sector has been the most
important source of output dynamics. We also find evidence suggesting that the exchange
rate shock has been also important, in particular in the economic slowdown
of 2002. Overall, we find that the output gap fluctuations are not driven primarily by
foreign factors, and more than a half of the volatility in the output gap is related to the
domestic shocks.
The rest of the paper is organized in the following way: section 2 presents the
DSGE model used for the analysis and discusses the interpretation of the structural
shocks. Section 3 discusses the identification of the model, parameter estimation and
data fit. Section 4 presents the main findings and section 5 concludes the paper.
5
The Model
The DSGE model used in this paper is a simple New Keynesian small open economy
model presented in Justiniano and Preston (2010), which is closely related to a model
in Monacelli (2005). The model consists of two economies – a small open economy
and a large foreign economy. The large economy has a strong influence over the small
one, whereas the small economy does not affect the large economy. We refer to the
small open economy as to the domestic (Czech) economy. The large foreign economy
will be approximated by the EA121 group of countries, as the foreign trade with these
countries accounts for a crucial share of the Czech foreign trade.
The model is derived from the first principles using optimal decision rules of economic
agents. Each of the two economies consists of households, firms and a monetary
authority. The domestic firms are divided into producers and importers. Both
types of firms operate on monopolistically competitive markets.
The domestic economy is influenced by the foreign economy in two ways. First,
the foreign interest rate and exchange rate influence the domestic interest rate through
the uncovered interest parity condition. Second, foreign goods are imported to the domestic
economy and constitute a part of the domestic consumption. Here, we assume
incomplete exchange rate pass-through.
Following Monacelli (2005), we model the foreign economy as a closed version of
the small economy with identical structural parametrization. Therefore we introduce
only the description of the domestic economy and the way the economies are linked
together. In order to distinguish foreign and domestic variables inthe text, the variables
originating in the domestic economy are denoted by subscript H and variables
originating abroad by subscript F. The foreign sector variables are denoted by ’*’.
1.1 Households
The domestic economy consists of a continuum of identical infinitely-lived households.
The representative agent maximizes his lifetime welfare represented by a utility func-
tion
E0
∞
t=0
βt
˜εG,t
(Ct − hCt−1)1−σ
1 − σ
−
N1+φ
t
1 + φ
. (1.1)
Here, Ct denotes household consumption, Nt denotes hours worked, σ is the inverse
intertemporal elasticity of substitution between the present and future consumption
1
The EA12 group consists of Austria, Belgium, Finland, France, Germany, Greece, Ireland, Italy,
Luxembourg, Netherlands, Portugal and Spain.
6
and φ is the inverse Frisch elasticity of labour supply. The parameter h denotes exogenous
habit in consumption and ˜εG,t is a preference shock.
The consumption basket is given by domestically produced goods CH and foreign
produced goods CF aggregated by Dixit-Stiglitz aggregator
Ct = (1 − α)
1
η C
η−1
η
H,t + (α)
1
η C
η−1
η
F,t
η
η−1
, (1.2)
The parameter η is the elasticity of substitution between CH and CF and α is a share
of foreign goods in total consumption.
The representative agent faces a budget constraint
CtPt + EtQt,t+1Dt+1 = Dt + WtNt + Tt. (1.3)
where Dt is a nominal income from one period bonds bought in time t − 1 maturing in
time t, and Qt,t+1 is the price of the bond. The financial markets are complete here. Wt
is the nominal wage, Pt is a price of the consumption basket and Tt are the lump-sum
transfers.
The first order conditions of this problem are summarized by the labor supply
Nφ
t
(Ct − hCt−1)−σ =
Wt
Pt
.
and the Euler equation
(Ct − hCt−1)
(Ct+1 − hCt)
−σ
˜εG,t
˜εG,t+1
Pt+1
Pt
= βRt.
where we define Rt = (EtQt,t+1)−1.
1.2 Producers
We assume domestic sector to be populated by a (0, 1) continuum of monopolistically
competitive producers. Each producer makes a decision about how much to produce
and how much to charge. Producers share the same production technology
Yt(i) = AtNt(i),
where Nt(i) denotes the amount of labour hired by the i-th producer and At is an
economy specific technological process.
Firms are assumed to set prices a la Calvo such that in every period a fraction
(1 − θH) of domestic producers is able to set optimal price.
The producers maximize profit given by
Et
∞
T=t
θT−t
H Qt,T yH,T (i) [PH,t(i) − PH,T MCT ] , (1.4)
where yH,T (i) is the demand for the production of the i-th producer, PH,t(i) is the
optimal price set by the i-th producer in period t and MCT are marginal costs given as
a derivative of the total costs.
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Differentiating with respect to PH,t(i), we acquire following optimality condition:
Et
∞
T=t
θT−t
H QT,tyH,T (i) PH,t(i) −
θH
θH − 1
PH,T MCT = 0.
1.3 Real exchange rate, law of one price relation
The real exchange rate is defined in log terms by
qt = et + p∗
t − pt = et + p∗
t − pF,t + (1 − α)st = ψt + (1 − α)st
where qt is the log of the real exchange rate, et = log ˆet is the log of the nominal
exchange rate, p∗
t is the log of the foreign CPI, st = pF,t − pH,t are log terms of trade
and ψt is the log of the law of one price gap ψF,t = et + p∗
t − pF,t.
The uncovered interest parity condition requires that
it − i∗
t = Et(et+1) − et
which after plugging for et, defining inflation as πt = pt − pt−1 and adding exchange
rate shock εQ,t gives
it − i∗
t + Etπ∗
t+1 − Etπt+1 = Et(qt+1) − qt + εQ,t
1.4 Importers
In the domestic economy there is a (0, 1) continuum of monopolistically competitive
importers. Each importer imports a unique good denoted by the index j bought for the
price ˆetP∗
F,t(j) which holds "at the docks".
Firms are also assumed to set prices a la Calvo such that in every period a fraction
(1 − θF ) of importers is able to set optimal price.
The problem of the importers is to maximize
Et
∞
T=t
Qt,T θT−t
F CF,T (i) PF,t(i) − ˆetP∗
F,t(i)
given the demand for their goods CF,T (i).
The first order condition to this problem is
Et
∞
T=t
Qt,T θT−t
F CF,T (i) PF,t(i) −
θF
θF − 1
ˆetP∗
F,t(i) = 0.
1.5 General equilibrium
The domestic consumption demand is given in a log-linearised form by
cH,t = −η(pH,t − pt) + ct = ηαst + ct.
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Similarly, the foreign demand for domestic goods is given by
c∗
H,t = −η(pH,t − p∗
t ) + c∗
t = η(st + ψF,t) + c∗
t .
where c∗
t is the overall foreign consumption and c∗
H,t is the foreign consumption of
domestic goods. The market clearing requires
yt = (1 − α)cH,t + αc∗
H,t. (1.5)
Plugging the demands into 1.5 and employing some additional identities gives the
final form of the goods-market clearing condition
(1 − α)ct = yt − αη(2 − α)st − αηψF,t − αy∗
t .
where y∗
t is the foreign output.
1.6 Monetary policy
Monetary policy in the foreign economy described by a Taylor rule with a lagged interest
rate and a focus on the output and the inflation:
i∗
t = ρ∗
i∗
t−1 + (1 − ρ∗
)(ψ∗
ππ∗
t + ψ∗
yy∗
t ) + ǫ∗
M,t
Here ρ∗ is parameter of interest rates smoothing, ψ∗
π (ψ∗
Y ) measures the magnitude of
the reaction of the monetary authority to the inflation (output), and ǫ∗
M,t is an exogenous
monetary policy shock.
Monetary policy in the domestic economy focuses only on the inflation:
it = ρit−1 + (1 − ρ)ψππt + ǫM,t
1.7 Exogenous shocks
The model features seven exogenous stochastic shocks. We describe only the domestic
shocks and the exchange rate shock. The foreign shocks are identical to their
domestic counterparts.
• The shock in preferences εG increases the present household utility, which makes
the households more impatient and causes them to shift their consumption from
future to present. This shift increases present demand and output. This shock
can be interpreted as a demand shock.
• The technological shock εA enters the firms’ production function, increases the
labor productivity and lowers the marginal costs of producers which in turn affect
the inflation. This shock is sometimes referred to as a cost-push shock, but
because it is present in the production function, we call it the technological shock.
This shock can be interpreted as a supply shock.
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• The monetary policy shock εM enters the Taylor rule and relates to the nominal
interest rate dynamics. If the monetary policy shock becomes positive, the
nominal interest rate is above the appropriate level given by the Taylor rule.
• The exchange rate shock εQ affects the uncovered interest parity.
The monetary shocks are modelled as iid. Other shocks are introduced as exogenous
stochastic AR(1) processes with innovations ǫ. The innovations have zero
mean and finite variance. Note that the shocks that are not introduced as iid are not
exogenous variables, but their innovations are.
εG,t = ρGεG,t−1 + ǫG,t
ε∗
G,t = ρ∗
Gε∗
G,t−1 + ǫ∗
G,t
εA,t = ρAεA,t−1 + ǫA,t
ε∗
A,t = ρ∗
Aε∗
A,t−1 + ǫ∗
A,t
εQ,t = ρZεQ,t−1 + ǫQ,t.
1.8 Log-linear equations
The model presented in previous subsections is approximated by the following set of
log-linear equations
1. Market clearing condition
(1 − α)ct = yt − αη(2 − α)st − αηψF,t − αy∗
t
2. Terms of trade
st − st−1 = πF,t − πH,t
3. Terms of trade, real exchange rate, law of one price gap relation
qt = ψF,t + (1 − α)st
4. Domestic producers price setting
πH,t = (1 − θH)
(1 − βθH)
θH
mct + βEt(πH,t+1)
5. Dometic real marginal costs
mct = ϕyt − (1 + ϕ)εA,t + αst +
σ
1 − h
(ct − hct−1)
6. Importers price setting
πF,t = (1 − θF )
1 − βθF
θF
ψF,t + βEt(πF,t+1)
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7. Complete markets assumption
ct − hct−1 = y∗
t − hy∗
t−1 +
1 − h
σ
(ψF,t + (1 − α)st) + εG,t
8. Uncovered interest parity
(it − Et(πt+1)) − i∗
t − Et(π∗
t+1) = Et(qt+1) − qt + εQ,t
9. Dometic monetary policy rule
it = ρit−1 + (1 − ρ)ψππt + εM
10. Domestic inflation
πt = πH,t + α(st − st−1)
11. Foreign Euler equation
y∗
t − hy∗
t−1 = Et(y∗
t+1) − hy∗
t −
1 − h
σ
i∗
t − Et(π∗
t+1) + (ε∗
G,t − ε∗
G,t+1)
12. Foreign producers price setting
π∗
t = (1 − θ∗
)
(1 − βθ∗)
θ∗
mc∗
t + βEt(π∗
t+1)
13. Foreign real marginal costs
mc∗
t = ϕy∗
t − (1 + ϕ)ε∗
A,t + αst +
σ
1 − h
(y∗
t − hy∗
t−1)
14. Foreign monetary policy rule
i∗
t = ρ∗
i∗
t−1 + (1 − ρ∗
)(ψ∗
ππ∗
t + ψ∗
yy∗
t ) + ε∗
M
15. Exogenous stochastic process for the domestic shock in preferences
εG,t = ρGεG,t−1 + ǫG,t
16. Exogenous stochastic process for the foreign shock in preferences
ε∗
G,t = ρ∗
Gε∗
G,t−1 + ǫ∗
G,t
17. Exogenous stochastic process for the domestic technological shock
εA,t = ρAεA,t−1 + ǫA,t
18. Exogenous stochastic process for the foreign technological shock
ε∗
A,t = ρ∗
Aε∗
A,t−1 + ǫ∗
A,t
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19. Exogenous stochastic process for the monetary policy shock
εQ,t = ρQεQ,t−1 + ǫQ,t
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Estimation and data fit
We estimate the model using Bayesian techniques in order to acquire the estimated
trajectories of structural shocks. In this section, we describe the data and their link to
the model variables, then discuss prior and posterior distribution of parameters and
potential issues with the model identification. Finally, before presenting our analysis,
we assess the data matching properties of the model.
2.1 The Data
The model is estimated on Czech and EA12 economy data. The sample ranges from
1996Q1 to 2010Q2. We measure quarterly domestic and foreign real GDP per capita,
domestic and foreign consumer price inflation, domestic and foreign nominal interest
rate and real exchange rate. Table 2.1 summarizes the mapping between the model
variables and the observed variables.
Model variable Observed time series
y Czech real GDP per capita
y∗ EA12 real GDP per capita
π annualized Czech HICP inflation
π∗ annualized EA12 HICP inflation
i annualized three months PRIBOR
i∗ annualized three months EURIBOR
q real exchange rate
Table 2.1: Link of observed time series to the model variables.
The observed data are detrended using the Hodrick-Prescott filter and all variables
are expressed in percentage deviation from the HP trend. To avoid the beginning-ofsample
filtration problem, we estimate the HP trend using observations from 1994Q1.
For output and HICP inflation, historical(pre 1996) data are not available – we construct
dummy observations assuming GDP and HICP evolved similarly to the four earliest
observations. To avoid the end-of-sample problem, we add dummy observations to
the ends of the observed time series using the Czech National Bank forecast as of
2010Q4. Except for nominal interest rates and real exchange rate, all time series were
seasonally adjusted using X-12 ARIMA. The plot of model consistent data and details
on data preparation can be found in the appendix.
We equal the output gap to the detrended output. An alternative and perhaps
better method would be to use dynamic steady state. Such method would not be
13
subject to potential problems arising from using Hodrick-Prescott filter. However, due
to practical difficulties with modelling dynamic steady state, it is common to use the
Hodrick-Prescott filter. We check the estimated values of output gap with the ones
reported by Czech National Bank and find a good correspondence. Specifically, the
CNB reports tightening of the output gap in 2000-2001 and subsequent widening. The
CNB also reports that the output gap became positive in the second half of 2005 and
turned negative again in 2009Q12.
2.2 Parameter identification and estimation
The estimation of parameters is an important step in our analysis because the realisation
of exogenous shocks depends on the values of structural parameters. For
example, we could observe different trajectories of exogenous shocks with equal likelihoods
and no guidance on how to qualify these two results. We therefore use the
methodology by Iskrev (2010) to assess whether there are potential identification is-
sues.
The methodology is based on two matrices of first derivatives with respect to the
parameters. The first matrix is based on derivatives of the vector of entries that determine
the solution of the model. The second matrix is based on derivatives of the
vector of entries that determine model implies restrictions on the first two moments
in data. A column of zeros in any of these matrices indicates that the corresponding
parameter does not affect the solution of the model or the implied restrictions on the
data. Such parameter can not be identified. High multicollinearity among individual
columns of the matrices indicates weak identification. For detailed description of the
method, the reader is encouraged to consult Iskrev (2010).
The results of the analysis show that all parameters are identified both structurally
and from the data. The analysis of multicollinearity in figure 7 in the appendix indicates
that there might be weak identification issues concerning the estimation from data.
We therefore check the quality of identification using Gelman-Brooks convergence
diagnostics, which show that the estimates of the parameters in the Random Walk
Metropolis Hastings Algorithm are stable and the model is well identified (figure 9 in
appendix).
The method by Iskrev (2010) also allows us to check pairwise correlation of columns
in matrices introduced above. High correlation suggests similar effects of the corresponding
parameters and thus potential identification issues. Figure 8 shows that
there are possible issues with three pairs of parameters: σ and h and domestic and
foreign Taylor rule parameters ρ and ψπ. The effects of these parameters partially
"overlap" and the parameters might be difficult to distinguish. Our findings are partly
similar to Iskrev (2010), who provides the Taylor rule coefficients as an example of
known identification issues.
2
CNB Inflation report III/2010
14
2.3 Priors and estimates
The bayesian methodology requires specification of prior distributions over parameters
and standard deviations of shocks. Priors affect the posterior values of the parameters.
Before discussing our posterior estimates, let us first discuss our motivation for the
choice of priors.
For the elasticity of substitution between domestic and foreign goods η and habit
parameter h we set prior means to 0.6 and 0.8 according to Remo (2008), who estimated
similar model for the Czech economy. Also according to Remo (2008), we set
prior means of inverse elasticity of substitution σ and inverse Frisch elasticity φ to 0.5
and 2.0. For Taylor rule parameters, we set priors according to Justiniano and Preston
(2010). Price stickiness parameters priors have means 0.7 to reflect high price stickiness
both in Czech economy and the eurozone. AR parameters for shocks ρ have
prior means equal to 0.5 to bear no special information about the nature of the AR
processes for shocks.
We decided to calibrate two parameters: the economy openness α is calibrated to
the value of 0.65 which equals the average share of nominal imports to nominal GDP
in Czech economy over the estimated period. It has been documented in the literature
(among others by Justiniano and Preston) that the cross-equation restriction within the
model push the estimates of this parameter towards zero – the closed economy case.
The estimation of this parameter would likely result in a lower estimate of the openness
which would understate the influence of the foreign economy on the domestic
economy. We also calibrate β to 0.9935 implying data consistent real interest rate of
2.65 per cent, which corresponds to the average real output growth in the estimated
period.
Now turning to the posterior estimates, the estimation results are summarized in
the table 2.2. The estimates are based on two runs of the Random Walk Metropolis
Hastings Algorithm implemented in DYNARE3. We generate 1,500,000 draws in each
run and discard first 60%. There are few estimates worth closer look.
The estimates of the parameters θH, θF and θ∗ show fairly high degree of price
stickiness. This indicates that the volatility of inflation will be captured in technological
shocks, which seems to be true according to the standard errors of the shocks.
Similarly, a high value of habit parameter h shows that there is a significant habit
in consumption. The standard errors of the technological shocks and the domestic
preference shock are notably larger than the other standard errors. However, the
variance decomposition discussed in the next subsection shows that these shocks do
not dominate the model.
2.4 Data fit and variance decomposition
To add to the credibility of the model, we assess the data matching properties of the
model. In our strategy, we compare the performance of statistical models on both real
3
Version 4.1.3
15
Parameter Distribution Prior mean Prior std Posterior mean Conf. interval
θH beta 0.70 0.10 0.7104 0.6473 0.7754
θF beta 0.70 0.10 0.7811 0.7000 0.8666
θ∗
beta 0.70 0.05 0.8971 0.8744 0.9211
h beta 0.80 0.20 0.8508 0.7612 0.9438
σ gamma 0.50 0.30 0.4899 0.1466 0.8094
φ gamma 2.00 0.50 2.3724 1.5875 3.1662
η gamma 0.60 0.10 0.3228 0.2363 0.4063
ψπ gamma 1.50 0.25 1.5122 1.1259 1.8628
ψ∗
π gamma 1.50 0.25 1.4358 1.0386 1.8089
ψ∗
y gamma 0.25 0.10 0.1527 0.0716 0.2316
ρ beta 0.50 0.15 0.8036 0.7498 0.8598
ρ∗
beta 0.50 0.15 0.8101 0.7519 0.8700
ρG beta 0.50 0.20 0.2801 0.1146 0.4397
ρ∗
G beta 0.50 0.20 0.3732 0.2012 0.5412
ρA beta 0.50 0.20 0.5452 0.3770 0.7144
ρ∗
A beta 0.50 0.20 0.3902 0.1764 0.5920
ρQ beta 0.50 0.20 0.6863 0.5747 0.7996
σǫG inv. gamma 1.00 ∞ 3.6177 2.7652 4.4271
σǫ∗
G
inv. gamma 1.00 ∞ 0.8932 0.7399 1.0431
σǫA inv. gamma 1.00 ∞ 3.4833 1.8931 5.0679
σǫ∗
A
inv. gamma 1.00 ∞ 4.9174 2.2733 7.4778
σǫQ inv. gamma 1.00 ∞ 1.0114 0.6488 1.3725
σǫM inv. gamma 1.00 ∞ 0.3638 0.3032 0.4241
σǫ∗
M
inv. gamma 1.00 ∞ 0.1353 0.1176 0.1511
Table 2.2: Prior and posterior distributions of parameters.
data and artificial data generated by the estimated model.
We estimate a VAR(1) model on original data and on artificial data and take fitted
values. For each time series, we compute model implied autocorrelation and crosscorrelation
with respect to the GDP. The results are summarized in tables 5 and 6 in
the appendix. We can see that the DSGE model approximates well the autocorrelations
in output, interest rates and real exchange rate, but fails to replicate the high
autocorrelation of inflations.
The cross-correlation coefficients in table 6 show similar results. The cross-correlation
between domestic output and foreign output, domestic interest rate and real
exchange rate is similar for both original and artificial data. We find it particularly
encouraging that the model matches the data in the international dimension well. The
cross-correlation between domestic output and foreign output is satisfactory. However,
the model can not replicate the relationship between output and inflations.
The variance decomposition in table 4 in the appendix shows a breakdown of variance
of endogenous variables into contribution of exogenous shocks. All variables are
driven by appropriate shocks with the exception of the real exchange rate where there
is a large influence of the domestic preference shock.
16
Shock decomposition
The goal of this paper is to analyse the structural sources of the Czech business cycle.
Based on the estimated model we compute relative contributions of structural shocks
to the domestic output gap identified by Hodrick-Prescott filter. We acquire the model
view on which factors influence the stability of the Czech economy and which factors
stood behind periods of economic growth.
The outcome of our analysis is depicted in figures 3.2, 3.3 and 3.4. The black line
shows the values of the output gap. The coloured columns denote the contributions of
structural shocks to this deviation. Foreign shocks are summed together for simplicity
because the contributions of foreign monetary and technological shock are negligible
(see variance decomposition in table 4).
The shocks influence the output in two ways. First, a rapid change in the contribution
of a shock induces a change in the output gap, typically in recessions (e.g.
domestic technological shock in 1997Q1 - 1997Q3). Second, a lasting positive or negative
influence of a shock pushes the output gap into positive or negative values (e.g.
foreign demand shock in 2007Q1 - 2008Q3).
Our analysis presents one of the possible interpretations of the history, which is
conditioned on the model use and the simplifying assumptions we make. The overall
picture is one of gradually rising importance of the foreign shocks for the Czech business
cycle. The recession of 1997 is attributed mainly to the technological shock. In
the following years, the foreign shocks become increasingly important. The exchange
rate shock had a significant impact in 2002 and the foreign demand shock was the
main driver of the Czech business cycle in 2006-2010.
An overview of the relative importance of individual shocks is given by the variance
decomposition in table 4 in the appendix. Half of the variance of the Czech output gap
is attributed to the domestic shocks. However, the most influential shock is the domestic
demand shock responsible for 36 per cent of the variance. The foreign demand
shock and the exchange rate shock together account for 40 per cent of the variance.
The foreign technological and monetary policy shocks have negligible influence on the
Czech business cycle.
The following subsections present the analysis divided into two time periods:
3.1 1996-2004
The period from 1996 to 2004 brought the first recession, recovery and then moderate
growth to the Czech economy.
In 1996, the Czech economy enjoyed moderate growth of about 4 per cent, although
with a number of warning signs such as growing external imbalances. In May
17
1997, after a run on the Czech currency, the Czech National Bank (CNB) was forced to
change the exchange rate regime from fixed to floating. The Czech currency devalued
by more than 10 per cent. The CNB tightened monetary policy in response to the devaluation
and resulting inflationary pressures, while the government enacted austerity
measures. Interest rates remained elevated for another 6 periods. As the result, the
Czech economy plunged into recession. The real GDP was falling in two consecutive
years and did not recover to its previous level until 1999.
Comprehensive discussion of the events was provided by Dˇedek (2003), who argues
that the monetary crisis and subsequent recession was partly the result of structural
and institutional problems in the Czech economy that were not properly dealt with
by the government.
Figure 3.2: Domestic output gap shock decomposition 1996-2001.
Figure 3.2 shows how this period is viewed using the DSGE prism. What does it
tell us about the causes of the recession? The early periods are strongly influenced
by the initial values, which can be interpreted as the overall effect of unidentified past
shocks. This fact makes the year 1996 harder to interpret but we still find the evidence
consistent with the hypothesis presented by Dˇedek (2003). The technological shock
had a decreasing tendency already since the last quarter of 1996 and was the main
reason why output fell in 1997 and 1998. The supply side problems helped to trigger
the monetary crisis, which then in turn unfolded the supply side problems in the Czech
economy.
In the second quarter of 1997, the influence of the domestic monetary shock turned
quickly from slightly positive into fairly negative. This sudden change in monetary
policy stance was probably induced by monetary crisis that can not be explained using
our model. For this reason, we do not see it as an evidence of an error made by the
Czech National Bank.
18
The domestic demand shock contributes to the fall in output in the second quarter
of 1997, probably as a results of the austerity measures. On the other hand, the
depreciation of the exchange rate had positive influence on the output.
Which factors brought the recovery? The recovery in 1999 was the result of the
vanishing negative effect of domestic technological shock and increasing positive influence
of the foreign demand shock. The recovery was countered by the domestic
demand shock. It is important to notice that foreign shocks play no role in the causes
of the recession and only a limited role in the recovery – the 1997-1998 recession and
the 1999 recovery had primarily internal sources.
The period of 2000-2004 saw a rise in the importance of the shocks outside of
the Czech economy, namely the foreign demand and exchange rate shock. While in
2000 the Czech GDP grew by solid 3.6 per cent annually, in 2001 and 2002 the growth
slowed to 2.6 and 1.8 per cent.
Given the model view, we find that in 2000 and early 2001 the foreign demand
shock contributed significantly to the renewed growth, more than any other shock.
However, the shock’s effect faded during 2001 and between 2003 and 2006 the effect
was negative.
The exchange rate shock also pushed the output gap into negative values in 2001
and in 2002 it was the main driver of the output slowdown. Looking at figure 6 in
the appendix, we can compare this model view with historical data on the nominal
exchange rate. The exchange rate appreciated from 36 CZK/EUR to 34 CZK/EUR
in 18 months from the second quarter of 2000 on. In the beginning of 2002, the
appreciation was even faster. The years 2001 and 2002 document the sensitivity of
the Czech economy to the exchange rate movements.
Although the years 2003 and 2004 saw GDP growth of 3.5 per cent and 4.5 per
cent annually, our analysis shows that in this period the Czech output gap was still
negative. As discussed before, this fact is consistent with the view of the Czech National
Bank. As figure 3 shows, weak foreign and domestic demand were responsible
for the negative output gap.
3.2 2005-2010
The years 2005-2010 saw another period of economic growth and recession. Contrary
to the previous period, however, the dynamics of the domestic output was given mainly
by foreign shocks. This is in line with conventional wisdom, but we also find that
domestic shocks still have had a role in the domestic business cycle.
The 2005-2007 period was very successful in terms of growth of the output, when
the Czech economy grew by over 6 per cent annually. The output gap turned positive
in late 2005. The causes of this development can be found both inside and outside
of the Czech economy. Figure 3.3 shows that in 2005, closing of the output gap was
likely caused by the demand factors. The decreasing negative contributions of both
domestic and foreign demand shocks were also important. Subsequently, since 2006
the foreign demand shock positively contributed to the output gap until the third quarter
of 2008. We can see in figure 3.4 that the foreign demand was especially influential in
the 2007-2008 period.
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Figure 3.3: Domestic output gap shock decomposition 2001-2006.
The domestic shocks also played significant role in the post-2005 period. Untill
2008, the domestic technological shock was an important determinant of the output
gap.
There is an interesting correlation between the domestic technological shock and
corporate taxes in the 2005-2008 period. The czech corporate tax rate was stable
during early 2000s at the level of 31 per cent. Since 2004, the tax rate was lowered
in several steps to the final value of 20 per cent in 2009. In 2005, we observe positive
contribution of the domestic technological shock which lasts until 2008. The cuts in
the corporate tax rate seem to have produced positive boost to the output.
The year 2008 brought a slowdown in output growth to 2.8 per cent annually. We
identify two main reasons. First, the exchange rate appreciation by some 15 per cent
in one year depressed exports and lowered the output. as obvious from the exchange
rate shock. Second, the foreign demand shock turned from a positive contribution in
third quarter of 2008 to a significantly negative one in the first quarter of 2009 as the
world-wide recession hit the foreign economy before it transpired into the domestic
economy. The Czech crown in turn depreciated in 2008Q4 and the exchange rate
shock decreased its negative contribution. Thus the main reason for positive, although
decreasing output gap in 2008 was the domestic demand shock.
The foreign demand shock transferred the recession to the Czech economy as can
be seen from its large negative contribution through the whole 2009 and early 2010.
Domestic demand and technological shocks also partly contributed to the recession,
20
Figure 3.4: Domestic output gap shock decomposition 2006-2010.
but we identify the foreign demand shock as the main cause of the 2009 recession.
This is in sharp contrast with the recession of 1997-1998 which was caused by domestic
shocks.
21
Conclusion
Based on the analysis in this paper, we provide several conclusions:
• The recession of 1997-1998 was caused entirely by domestic shocks. The domestic
technological shock was the key factor that stood behind the negative
GDP growth in 1997-1998. On the contrary, the recession of 2009 was almost
entirely caused by a drop in foreign demand. Given the fact that foreign shocks
were crucial for the Czech economy in the 2007-2010 period, it is likely that its
recovery is dependent on the recovery of the foreign demand.
• Since 2000, the foreign shocks have had increasing importance in determining
the domestic output. Most notably, the exchange rate shock was particularly
important in 1997 and 2002. Starting in 2007, the foreign demand was the most
significant outside factor that determined the domestic output, especially in the
late 2008 and early 2009. In general, the Czech economy is sensitive to the
foreign shocks.
• Although the Czech economy is sensitive to the foreign shocks, the domestic
shocks have played significant role in determining the Czech business cycle. Domestic
shocks explain approximately 60 per cent of the variance in the domestic
output.
There are several possible extensions to our research. Using more elaborate
model with broader set of structural shocks, one can get more information about what
shocks drive the dynamics of a given variable. In particular, using a model that incorporates
government and investment might result in a detailed description of effects
that we summarize as the effects of demand shocks and technological shocks.
The knowledge of the relative importance of particular shocks, namely the distinction
between foreign and domestic influences, is necessary for a conditional forecast
using DSGE models. Using the information about the relevance of shocks to the domestic
output, one can make a forecast based on expected paths of foreign GDP and
exchange rate.
22
Bibliography
[1] Dˇedek O (2003): The Currency Shake-Up in 1997: A Case Study of the Czech
Economy. In Griffith-Jones, S., Gottschalk, R., Cailloux, J.: International Capital
Flows in Calm and Turbulent Times. Michigan, The University of Michigan Press,
p. 231-266, ISBN 0-472-11309-7.
[2] Iskrev N (2010): Local identification in DSGE models. Journal of Monetary
Economics., 57(2):189-202.
[3] Justiniano A, Preston B (2010): Monetary Policy and Uncertainty in an Empirical
Small Open Economy Model. Journal of Applied Econometrics, 25(1):93-128.
[4] Monacelli T (2005): Monetary Policy in a Low Pass-through Environment. Journal
of Money, Credit and Banking, 37:1047-1066.
[5] Remo A (2008): Monetary Policy and Stability of Czech Economy: Optimal Commitment
Policy in NOEM DSGE Frame-work. CVKS MU, Brno, working paper no.
25/2008.
23
Figures and tables
Output per capita Real GDP was seasonally adjusted by X12-ARIMA and
divided by total population.
Real exchange rate Nominal exchange rate was multiplied by ratio
of seasonally adjusted HICP indices.
Inflation HICP index was seasonally adjusted by X12-ARIMA,
taking logs and first differences.
Quarterly HICP index Quartely HICP indices were computed
as averages of monthly indices.
Table 3: Preparation of the time series downloaded from Eurostat.
Figure 5: Data before estimation in percentage deviations from trend. All growth rates
are annualized QoQ.
24
ǫG ǫA ǫQ ǫM ǫ∗
A ǫ∗
G ǫ∗
M
Domestic consumption 84.06 2.03 7.93 2.80 0.01 3.15 0.01
Domestic interest rate 20.37 12.84 34.02 23.01 0.04 9.66 0.04
Domestic inflation 28.94 21.76 27.30 12.95 0.05 8.95 0.05
Domestic output gap 36.43 21.50 15.14 4.58 0.40 21.55 0.41
Terms of trade 56.96 26.19 7.23 3.17 0.32 5.88 0.25
Law of one price gap 2.13 1.01 70.99 20.51 1.09 2.56 1.71
Domestic marginal cost 51.38 34.88 6.25 1.63 0.01 5.84 0.01
Inflation in imports 6.75 3.33 51.33 29.30 0.67 7.99 0.63
Inflation in domestic goods 43.78 32.03 11.74 4.71 0.03 7.67 0.04
Real exchange rate 23.05 9.95 50.26 13.47 1.34 0.07 1.85
Table 4: Infinite horizon variance decomposition. Variances of endogenous variables
are divided into percentage contributions of exogenous shocks. Rows sum to 100%.
Original data Model
Domestic output gap 0.8805 0.8540
0.7019 0.6825
Foreign output gap 0.8278 0.8518
0.6378 0.6508
Domestic inflation 0.5359 0.4382
0.4858 0.1739
Foreign inflation 0.8236 0.4982
0.6583 0.2675
Domestic interest rate 0.8366 0.7821
0.6876 0.5871
Foreign interest rate 0.8708 0.8200
0.6517 0.6362
Real exchange rate 0.6931 0.6405
0.3097 0.4000
Table 5: Implied autocorrelation of 1st and 2nd order. Orders correspond to rows.
25
lag/lead of -2 -1 0 1 2
output gap
Foreign output gap Data 0.3546 0.5326 0.6713 0.6227 0.5307
Model 0.3732 0.4610 0.5245 0.4320 0.3216
Domestic inflation Data 0.4235 0.4080 0.5374 0.4716 0.4243
Model 0.0932 0.2166 0.4719 0.3825 0.2942
Foreign inflation Data -0.2597 -0.1306 0.0654 0.1500 0.2355
Model -0.2848 -0.3156 -0.3333 -0.2954 -0.2567
Domestic interest rate Data 0.5474 0.4558 0.3153 0.1479 0.0092
Model 0.3440 0.3987 0.4359 0.3481 0.2685
Foreign interest rate Data 0.5746 0.6614 0.6727 0.5247 0.3465
Model -0.0170 -0.0160 -0.0340 -0.0797 -0.1137
Real exchange rate Data -0.2610 -0.2708 -0.2097 -0.0476 0.0922
Model -0.1513 -0.1150 -0.0297 -0.0621 -0.0731
Table 6: Implied cross-correlation of Czech output gap with other time series.
Figure 6: Nominal exchange rate CZK/EUR. Source: Czech National Bank.
26
Figure 7: Results from identification analysis. The left column concerns identifiability
given the model structure, the right column concerns identifiability from data. Box plots
show values of collinearity coefficients obtained in Monte Carlo sampling, red circles
indicate outliers. Values close to one indicate potential identification issues.
27
Figure 8: Partial correlations between parameters. Box plots show values of collinearity
coefficients obtained in Monte Carlo sampling, red circles indicate outliers. Values
close to 1 indicate potential identification issues.
28
Figure 9: Brooks-Gelman convergence diagnostics. Both runs of Metropolis Hastings
algorithm converge and are stable over the last 40% of samples that we use for
computing the estimates of parameters.
29