REVIEW OF ECONOMIC PERSPECTIVES – NÁRODOHOSPODÁŘSKÝ OBZOR,
VOL. 11, ISSUE 3, 2011, pp. 168–191, DOI: 10.2478/v10135-011-0012-0
STRUCTURAL DIFFERENCES AND ASYMMETRIC SHOCKS BETWEEN
THE CZECH ECONOMY AND THE EURO AREA 12
Martin Slanicay
Masaryk University, Faculty of Economics and Administration, Department of
Economics, Lipová 41a, Brno 602 00, slanicay@mail.muni.cz
Abstract: The goal of this paper is to determine whether there exist asymmetric shocks
and structural differences between the Czech economy and the Euro Area 12. A New
Keynesian DSGE model of a small open economy is used for this purpose. Asymmetric
shocks and structural differences are examined in two ways. At first, I examine
asymmetry of shocks and sources of structural differences, using model comparison
based on the Bayes factor. I do not find substantial evidence in favor of heterogeneity in
household preferences. I find slight differences in price and wage formation and
substantial difference in interest rate smoothing. However, the main differences are in
timing, persistence and volatility of structural shocks. I also investigate impact of
structural differences and differences in persistence and volatility of structural shocks
on the behavior of both economies, using analysis of impulse-response functions. I find
no substantial differences in responses of the main variables to preference shocks. On
the other hand, I find much larger volatility and persistence of domestic technology
shocks. This contributes to the fact that responses of domestic variables to technology
shocks are much larger, and display more gradual and hump-shaped pattern than
responses of foreign variables. I also find that responses of foreign variables to labour
supply shocks are much more gradual and sluggish than responses of domestic variables.
As regards monetary shocks, I find that there is almost no response of foreign inflation
to foreign monetary shock while response of domestic inflation to domestic monetary
shock displays substantial decline followed by gradual recovery. Responses of foreign
variables to cost-push shocks are larger and more volatile than responses of domestic
variables.
Key words: New Keynesian, DSGE model, Bayes factor, Bayesian estimation,
structural differences, asymmetric shocks, model comparison.
JEL Classification: C51, E32, E52
DOI: 10.2478/v10135-011-0012-0
REVIEW OF ECONOMIC PERSPECTIVES
168
STRUCTURAL DIFFERENCES AND
ASYMMETRIC SHOCKS BETWEEN THE CZECH
ECONOMY AND THE EURO AREA 121
Martin Slanicay2
Introduction
Asymmetric shocks and structural differences are regarded as the main causes of a
potential suboptimality of common monetary policy. Asymmetry of shocks is defined as
differences in timing, magnitude or persistence of structural macroeconomic shocks.
Structural differences are then defined as differences in propagation mechanisms of
structural shocks. In case of asymmetric shocks and (or) structural differences in a
monetary union, applied monetary policy facing structural shocks must be suboptimal
for some countries. Therefore, analysis of asymmetric shocks and structural differences
plays an important role in evaluating benefits and costs of common currency.
The goal of this paper is to investigate the asymmetric shocks and structural differences
between the Czech economy and Euro Area. A New Keynesian DSGE model of a small
open economy developed by Justiniano and Preston (2010) is used for this purpose. The
model is built on the framework of Galí and Monacelli (2005), and Monacelli (2003),
who developed an elegant model of small open economy with price rigidity modelled in
Calvo style, see Calvo (1983). The latter paper, building directly on the former, extends
the former by introducing an incomplete pass-through. Another extension is brought by
Justiniano and Preston (2010a) who extended this framework by allowing for habit
formation, price indexation and incomplete asset market. The model of Justiniano and
Preston (2010b) used in this study extends the previous one by introducing wage
rigidity modelled in Calvo style, following a benchmark for staggered wage contracts
from Ergeg, Henderson and Levin (2000). I have altered this model in a few aspects.
Following Adolfson et al. (2008), I have modified the uncovered interest rate parity
condition (UIP condition) by giving a positive weight to the lagged real exchange rate.
Following Kolasa (2009), I also allow for correlations between corresponding shocks in
both economies.
Asymmetric shocks and structural differences are examined in two ways. Firstly, I
examine asymmetry of shocks and sources of structural differences, using model
comparison based on a Bayes factor. In the context of DSGE models, we can view
structural differences (asymmetric shocks) as significant differences in values of some
structural parameters (parameters related to shocks). Following Kolasa (2009), I use
Bayesian approach for testing significance of these differences. A difference in
parameter value is regarded as significant if the data fit of models which allow for
different values of this parameter in both economies are better than the data fit of those
1
This work was supported by funding of specific research at ESF MU, project
MUNI/A/0943/2009 and by MŠMT project Research centers 1M0524.
2
Masaryk University, Faculty of Economics and Administration, Department of Economics,
Lipová 41a, Brno 602 00, slanicay@mail.muni.cz
Volume 11, Issue 3, 2011
169
models with common value of this parameter in both economies. The data fit measure is
a Bayes factor (BF) calculated from marginal likelihood, which are acquired from
estimation. Secondly, I examine how structural differences and differences in
persistence and volatility of structural shocks influence behavior of both economies. I
analyze differences in responses of the main macroeconomic variables in both
economies to corresponding shocks in these economies, using impulse-response
functions.
Related Papers
Much economic research deals with these issues because of their important role in
evaluating benefits and costs of common currency. Pauer (1996) provides a nontechnical
overview of a role of asymmetric shocks in a debate about benefits and costs
of common currency.
Several authors try to determine to what extent are the shocks within EU asymmetric.
Bayoumi and Eichengreen (1992) find that shocks are significantly more idiosyncratic
across EU countries than across US regions, which may indicate that the EU will find it
more difficult to operate a monetary union. On the other hand, Verhoef (2003) shows
that symmetries of demand and supply shocks increase over time within EMU.
Some studies deal with an adjustment process to asymmetric shocks. Alexius and Post
(2008) examine how floating exchange rates respond to asymmetric shocks, and find
out that exchange rates display some stabilizing properties but can mainly be
characterized as disconnected from the rest of the economy. Amisano, Giammarioli and
Stracca (2009) examine the adjustment process to asymmetric shocks in Italy and argue
that joining EMU does not alter the adjustment process to idiosyncratic demand and
cost push shocks, and that the EMU system is not hit by idiosyncratic monetary shocks
anymore. Driver and Wren-Lewis (1999) try to quantify the costs imposed by
asymmetric shocks under EMU compared to free floating. Their results suggest that
these costs are significantly higher under EMU than under free floating.
Several papers discuss the presence and relative importance of asymmetric shocks and
structural differences. Jondeau and Sahuc (2007, 2008) test the structural heterogeneity
within Euro Area and come to the conclusion that asymmetric shocks are the main
sources of a different behavior of countries in Euro Area, while structural differences
play almost no role. Kolasa (2009) investigates structural heterogeneity between Poland
and Euro Area and finds out that volatility and synchronization of shocks hitting both
economies are the main sources of structural heterogeneity. Pytlarczyk (2005) estimates
a two country DSGE model of Germany and the rest of Euro Area. He finds out that the
unrestricted model with the stochastic heterogeneity and a different composition of
consumption and investment baskets across the regions fits the data better than the
restricted model with the stochastic homogeneity and identical composition of these
baskets.
Many authors examine structural differences alone. Benigno and López-Salido (2006)
find differences in inflation dynamics between Germany on the one side, and France,
Italy, the Netherlands and Spain on the other. They discover that inflation dynamics in
Germany is characterized by a forward-looking nature of price setting and average
duration of prices of about 5 quarters, while the other group of countries is characterized
REVIEW OF ECONOMIC PERSPECTIVES
170
more by a backward-looking nature of price setting and average duration of prices of
about 8 quarters. Fabiani and Morgan (2003) examine differences in the relationship
between wage growth, inflation and tightness of the labor market across Germany,
France, Italy, the Netherlands and Spain. They provide empirical evidence that there
exist large differences even across these "core" countries. Angeloni and Ehrmann (2004)
try to explain why differences in national inflation rates and growth rates arise within
the Euro Area. They find out that the main explanation can be ascribed to differences in
inflation persistence. Campa and González Minguez (2006) investigate exchange rate
pass-through in Euro Area countries. They find substantial differences across Euro Area
countries in the way how a common exchange rate movement gets transmitted into
prices. Most of these differences are caused by a distinct degree of openness of each
country to non-euro area imports rather than by heterogeneity in the structure of imports.
Demertzis and Hugues Hallett (1998) investigate differences in unemployment rates in
Europe. They show that disparities in unemployment rates are brought about mainly by
differences in labor market fundamentals causing natural rate of unemployment to differ.
Asymmetric shocks and policy differences, both causing differences in unemployment
gap, play a limited role in explaining unemployment disparities. Cecchetti (1999)
provides the evidence that differences in a financial structure influence the transmission
mechanism of the monetary policy. He shows that countries with poorer direct capital
access, less concentrated and less healthy banking systems display a greater sensitivity
of inflation and output to policy changes.
Model
Derivation of the model from microfoundations can be found in Justiniano and Preston
(2006, 2010b). The model is in the log-linear form, so all variables are in the form of
log-deviations from their respective steady state, formally XXx tt loglog= − ,
where X is a steady state value. Variables and parameters with the superscript “*”
hold for the foreign economy.
Domestic Block
Log-linear approximation of Euler equation for intertemporal decisions of domestic
households is in the form
( )tgtgttttttttt EEi
h
hccEhcc ,1,111
1
= εεπ
σ
−+−
−
−−− +++− , (1)
where ttt ic π,, is consumption, nominal interest rate and inflation in the period t , tE
denotes expectations in the period t , h is a parameter of habit formation in
consumption, σ is an inverse elasticity of intertemporal substitution in consumption
and tg,ε is a preference shock in the period t in the form of AR1 process. Goods
market clearing condition requires
*
,
**
))(1(=)(1 ttFttt ysyc αψαηααηαηα −−−+−− , (2)
Volume 11, Issue 3, 2011
171
where ttt syy ,, *
denotes domestic and foreign output and terms of trade in the period t ,
α is a parameter of the openness of a domestic economy,
*
,ηη is an elasticity of
substitution between domestic and foreign goods, and tF ,ψ is a law of one price gap
defined as
tFtttF ppe ,
*
, )(= −+ψ ,
where te is a nominal exchange rate,
*
tp is a foreign price index and tFp , is a price
index of imported goods. Terms of trade tS are defined standardly as tHtFt PPS ,, /= ,
and after log-linearizing and time differencing we get
tHtFts ,,= ππ −∆ , (3)
where tF ,π is inflation of imported goods and tH ,π is inflation of domestic goods.
Terms of trade ts , law of one price gap tF ,ψ and the real exchange rate tq are related
in an identity
.)(1= , ttFt sq αψ −+ (4)
Firms maximize their profits subject to a set of demand constraints and to the Calvo
constraint on the frequency of price adjustment. According to the Calvo constraint, only
pθ−1 portion of producers reset their prices optimally every period, while a fraction
pθ adjust their prices according to an indexation rule
1,1,, )(log=)(log −− + tHptHtH iPiP πδ . The result of optimal price settings of firms is a
rule for development of domestic inflation
tcptttptHptHttHptH swE ,,1,1,, )()(= εψξπδπβπδπ ++++−− +− , (5)
where
,
)(1
))(1(1
=
ppp
pp
p
εωθ
βθθ
ξ
+
−−
,)(1= , tptapt yωεωψ −+ (6)
pθ is a parameter of domestic price stickiness, pδ is a parameter of domestic price
indexation, β is a discount factor, pε is an elasticity of substitution among domestic
goods, 0>)/(= 2''
fYfp
′
−ω , f is a production function of domestic producers
which satisfies usual Inada conditions, tw is a real wage, ta,ε is a domestic technology
REVIEW OF ECONOMIC PERSPECTIVES
172
shock in the form of AR1 process, and tcp,ε is a firm’s cost-push shock in the form of
IID process, added for estimation purposes.
Importers maximize their profits subject to a set of demand constraints and to the Calvo
constraint on the frequency of price adjustment. According to the Calvo constraint,
every period only Fθ−1 portion of importers reset their prices optimally, while a
fraction Fθ adjust their prices according to the indexation rule
1,1,, )(log=)(log −− + tFFtFtF iPiP πδ . The result of optimal price settings of
importers is a rule for development of imported inflation
tcftFFtFFtFttFFtF E ,,,1,1,, )(= εψξπδπβπδπ ++−− +− , (7)
where
,
))(1(1
=
F
FF
F
θ
βθθ
ξ
−−
Fθ is a parameter of import's price stickiness, Fδ is a parameter of import's price
indexation and tcf ,ε is a cost-push shock in the form of AR1 process.
Households maximize their utility function subject to a set of labor demand constraints
and to the Calvo constraint on the frequency of wage adjustment. According to the
Calvo constraint, only wθ−1 portion of households reset their wages optimally every
period, while a fraction wθ adjust their wages according to the indexation rule
11 )(log=)(log −− + twtt kWkW πδ . The result of optimal wage settings of households
is a rule for development of wage inflation
)()(= 11 ttwtw
w
tttw
w
t wvE −+−− +− ξπδπβπδπ , (8)
where
,
)(1
))(1(1
=
ww
ww
w
ϕεθ
βθθ
ξ
+
−−
),(
1
)(= 1, −−
−
+− tttltt hyy
h
yv
σ
εϕ (9)
wθ is a parameter of wage stickiness, wδ is a parameter of wage indexation, ϕ is an
inverse elasticity of labor supply, tl,ε is a labor supply shock in the form of AR1
process. Price inflation, wage inflation and the real wage are connected in an identity
.= 1−+− tt
w
tt ww ππ (10)
Volume 11, Issue 3, 2011
173
Terms of trade, inflation of domestic goods and overall domestic inflation are connected
in an identity
.= , ttHt s∆+αππ (11)
Following Adolfson et al. (2008) I used a modified version of the uncovered interest
rate parity condition1
tsttqttqtttttt aqqEEiEi ,1
*
1
*
1 )(1=)()( εχφφππ +−∆−∆−−−− +++ , (12)
where χ is an elasticity of foreign interest rate to debt, qφ is a parameter of modified
UIP condition, ts,ε is a risk premium shock in the form of AR1 process and ta is a real
net foreign asset position expressed as a fraction of domestic output steady state which
has to satisfy flow budget constraint condition in the form
ttFt
t
tt ys
a
ac ++−+ −
)(= ,
1
ψα
β
. (13)
Domestic block of the model is completed with a monetary policy rule in the form of
modified Taylor rule, for the evolution of domestic nominal interest rates
tMtytitit yii ,1 ])[(1= εψπψρρ π ++−+− , (14)
where iρ is a parameter of interest rate smoothing, πψ is an elasticity of interest rate
to inflation, yψ is an elasticity of interest rate to output, and tM ,ε is a monetary shock
in the form of IID process.
Foreign Block
Foreign block is a closed economy version of that presented above. All variables and
parameters have the same interpretation as in the domestic economy, and are
distinguished from those of domestic economy by superscript "*". Intertemporal
decisions of foreign households are described by Euler equation
).(
1
= *
,
*
1,
*
1
*
*
*
***
1
*
1
**
tgtgttttttttt EEi
h
yhyEyhy εεπ
σ
−+−
−
−−− +++− (15)
Price setting behavior of foreign firms is described by the price Phillips curve
*
,
******
1
*
1
**
)()(= tcpttptptttpt wE εψξπδπβπδπ ++−− +− , (16)
where
1
If I set 0=qφ I obtain the usual UIP condition.
REVIEW OF ECONOMIC PERSPECTIVES
174
,
)(1
))(1(1
= *
**
*
*
ppp
pp
p
εωθ
βθθ
ξ
+
−−
.)(1= **
,
*
tptapt yωεωψ −+ (17)
Wage setting behavior of foreign households is described by the wage Phillips curve
)()(= ******
1
*
1
**
ttw
w
tw
w
tt
w
tw
w
t wvE −+−− +− ξπδπβπδπ , (18)
where
,
)(1
))(1(1
= **
**
*
ww
ww
w
εϕθ
βθθ
ξ
+
−−
).(
1
)(= *
1
**
*
*
*
,
***
−−
−
+− tttltt yhy
h
yv
σ
εϕ (19)
Inflation, wage inflation and the real wage in the foreign economy are connected in an
identity
.= *
1
***
−+− tt
w
tt ww ππ (20)
Foreign block of the model is completed with the monetary policy rule in the form of
modified Taylor rule, for the evolution of foreign nominal interest rates
*
,
******
1
**
])[(1= tMtytitit yii εψπψρρ π ++−+− . (21)
Estimation
Data
Quarterly data of CZ and EA 12 from 1st
quarter 1999 to 3rd
quarter of 2010 were
downloaded from the database of Eurostat, http://ec.europa.eu/eurostat. Figure 1
displays demeaned data which enter the estimation.
•
*
1
**
1 =,= −− −− ttt
obs
ttt
obs
yyyyyy : demeaned 100*log differences of real GDP per
capita. As a measure of GDP "Gross Domestic Product at Market Prices, Millions of
Euro, Chain-linked Volumes, Reference Year 2000 (at 2000 Exchange Rates),
Seasonally Adjusted and Adjusted Data by Working Days" is used, and as a measure of
population "Total Population" is used.
Volume 11, Issue 3, 2011
175
•
**
=,= tt
obs
tt
obs
ππππ : demeaned 100*log differences of price index, as underlying
index "HICP (2005=100), All Items" is used. Seasonally Adjusted by Tramoseats, using
Demetra software.
•
**
=,= w
t
w
t
obsw
t
w
t
obs
ππππ : demeaned 100*log differences of wage index. An
underlying index for wage inflation is "Labour Cost Index (Nace Rev.2) (2008=100) Wages
and Salaries, Business Economy, Seasonally Adjusted and Adjusted Data by
Working Days". This index starts at 1.Q 2000 so the first four values are computed from
"Labour Cost Index (2000=100) - Wages and Salaries, Industry and Services (excluding
Public Administration), Seasonally Adjusted and Adjusted Data by Working Days".
•
**
=,= tt
obs
tt
obs
iiii : demeaned data of nominal interest rate (quarterlized, i.e. divided
by four), as the measure "Money Market Interest Rates, 3-Month Rates" is used.
• 1= −− ttt
obs
qqq : demeaned 100*log differences of real exchange rate, "Euro/ECU
Exchange Rates - Quarterly Data, Average, National Currency (including 'euro fixed'
series for euro area countries), Czech Koruna" is used as the measure of nominal
exchange rate.
• 1= −− ttt
obs
sss : demeaned 100*log differences of terms of trade. Terms of trade are
calculated as a ratio of the deflator for imports to exports, "Exports of Goods and
Services, Seasonally Adjusted and Adjusted Data by Working Days, Price index,
2000=100, Based on National Currency (including 'euro fixed' series for euro area
countries)" is used as the measure of export prices , as a measure of import prices
"Imports of Goods and Services, Seasonally Adjusted and Adjusted Data by Working
Days, Price index, 2000=100, Based on National Currency (including 'euro fixed' series
for euro area countries)" is used.
Calibration and Priors
The model is formed by equations (1) - (21) and contains 21 endogenous variables, tc{ ,
ty , ti , ta , tq , ts , tπ , tH ,π , tF,π , tF,ψ , tw ,
w
tπ , tv , }tψ in the domestic
economy and
*
{ ty ,
*
ti ,
*
tπ ,
*
tw ,
*
tψ ,
*w
tπ , }*
tv in the foreign economy. The model
also contains 8 AR1 processes for exogenous shocks ta,{ε , tg,ε , tl,ε , ts,ε , tcf ,ε ,
*
,taε ,
*
,tgε , }*
,tlε and 4 shocks in the form of IID process tM ,{ε ,
*
,tMε , tcp,ε , }*
,tcpε . There
are 45 parameters in the model. Interpretation of the parameters is presented in the
Table 3. Except six parameters ( β , pε , wε , χ , pω and α ) which are difficult to
identify, all parameters are estimated using Metropolis-Hastings algorithm (using
Dynare toolbox for Matlab). Discount factor β is calibrated to be 0.9975, which
implies an annual steady state real interest rate of 1%. This value roughly corresponds
to the long term mean of an annual real interest rate in both economies. Elasticities of
substitution between various goods pε and labor inputs wε are both set equal to 8,
REVIEW OF ECONOMIC PERSPECTIVES
176
following results reported in Woodford (2003, ch. 3) and imply average price and wage
mark-up of 14%. Following Benigno (2009), the parameter χ governing the debt
elastic interest rate premium is fixed at 0.01. Parameter pω is calibrated to be 0.33,
following Justiano-Preston (2010b). Parameter of openness of the Czech economy α is
calibrated to be 0.35, according to the share of export to the production1
.
Prior setting of estimated parameters as well as their estimated values in the unrestricted
variant are presented in Table 4. Prior means for Calvo parameters of price and wage
stickiness pθ , Fθ , *pθ , wθ and *wθ are set to be 0.6, which implies average price
(wage) contract duration of 7.5 months. Because of no microeconomic evidence on
price and wage indexation I set very loose priors for these parameters, prior means
equal to 0.5 and prior std. deviations equal to 0.2. Parameter qφ in modified UIP
condition is estimated with prior mean equal to 0.2 and prior std. deviation equal to 0.1.
Priors for parameters in Taylor rule are set consistently with Taylor (1999). Although
prior means for elasticities of interest rate to output yψ and
*
yψ are set to be a little bit
higher (0.2 instead 0.125) and thus take into account changes in the behavior of central
banks in recent crisis. In my opinion, at this time central banks (ECB and CNB) pay
more attention to development in output than they did before crisis. Inverse elasticities
of intertemporal substitution σ *
σ are estimated with relatively loose priors with prior
means set to be 1.0, following Galí (2008), and prior std. deviations equal to 0.7.
Inverse Frisch elasticities of labor supply ϕ *
ϕ are estimated with prior means set to
be 2.0 and std. deviations equal to 0.7, which are values commonly found in the
business cycle literature. Parameters of habit formation h and *
h are estimated with
prior means set to be 0.7 and prior std. deviations equal to 0.1, as in Smets and Wouters
(2003). Backward-looking parameters in AR1 processes for exogenous shocks are
estimated with very loose priors, prior means equal to 0.5 and std. deviations equal to
0.2.
Model Comparison
Asymmetry of shocks and structural differences can be seen (in our context) as
significant differences in values of some structural parameters. The question is when
some difference can be regarded as significant. We adopt the approach presented in
Kolasa (2009) which is based on a model comparison using Bayes factor. The idea
which lies beneath this approach is as follows: structural parameters can be modeled as
common for both economies, or as different for both economies. If there truly exists a
significant difference in values of some parameters, than models which allow for
difference in these parameters should fit the data better than models with common
values of these parameters. I can compare unrestricted model with restricted model
where selected parameters are modeled as common, and hence find out which model fits
the data better. If I find that the unrestricted model fits the data better, I can say that
1
http://www.czso.cz/csu/tz.nsf/i/statistika_upresnuje_predstavy_o_otevrenosti_ceske_ekonomiky
Volume 11, Issue 3, 2011
177
there exist structural differences in those parameters. Next subsection describes the
method adopted for the model comparison.
Bayes Factor
The model comparison is based on the Bayes factor (BF). The Bayes factor is a specific
case of posterior odds (PO), when prior probabilities of competing models are set as
equal. The Bayes factor of model i and j ( ijBF ) is a Bayesian statistic calculated
from (log) marginal likelihood 1
(acquired from Bayesian estimation) as
)))|((log))|((log(exp=
)|(
)|(
= jTiT
jT
iT
ij MYpMYp
MYp
MYp
BF − , (22)
where )|( iT MYp is a marginal likelihood of model i and ))|((log iT MYp is a log
marginal likelihood of model i .2
The Bayes factor shows us how much more probable
model i is than model j . DeJong and Dave (2007, p. 242) show an interpretation3
of
BF values
• 1–3 – "very slight evidence"
• 3–10 - "slight evidence"
• 10–100 - "strong to very strong evidence"
• 100 and higher - "decisive evidence"
This interpretation shows us how strong the evidence of the Bayes factor about that
whether model i explains the data better then model j is. It is obvious that it holds
ijji BFBF // 1/= .
Sources of Structural Differences
Table 1 displays calculated Bayes factors of unrestricted model versus restricted
variants, where selected parameters are modeled as common.
We can see that there is almost no evidence in favor of heterogeneity in structural
parameters related to household preferences. Although Bayes factor slightly favors the
unrestricted variant before the variant with restriction on the inverse elasticity of labor
supply ϕ (BF=1.29) and before the variant with restriction on the elasticity between
domestic and foreign goods η (BF=1.15), these values of Bayes factor bring only very
slight evidence in favor of heterogeneity in these parameters. Moreover, Bayes factor
also favors the variant with restriction on all parameters related to household
1
Calculation of log marginal likelihood is based on the Laplace approximation.
2
It is more convenient to use log marginal likelihood because their numerical computation is
much easier. In the following text I display my results using log marginal likelihood.
3
Similar interpretation can be found in Jeffreys (1961) or Kass and Raftery (1995).
REVIEW OF ECONOMIC PERSPECTIVES
178
preferences before unrestricted variant (BF=0.28). This value of Bayes factor brings
slight evidence in favor of homogeneity in household preferences.
Table 1: Bayes Factors and Log Marginal Likelihood - Structural Parameters
i restriction BF0,i log(p(YT|Mi))
0. unrestricted 1 -417.16
1. *
= σσ - inv. elasticity of intertemporal subs. 0.61 -416.67
2. *
= ϕϕ - inv. elasticity of labor supply 1.29 -417.42
3. *
= hh - habit formation in consumption 0.49 -416.44
4. *
=ηη - elasticity between dom. and for. goods 1.15 -417.30
5. household preferences (1-4) 0.28 -415.88
6. *
= pp θθ - price stickiness 1.34 -417.46
7. *
= pp δδ - price indexation 5.41 -418.85
8. *
= ww θθ - wage stickiness 1.96 -417.84
9. *
= ww δδ - wage indexation 1.23 -417.37
10. price formation - stickiness and indexation (6,7) 2.29 -417.99
11. wage formation - stickiness and indexation (8,9) 2.56 -418.10
12. price and wage formation (10,11) 6.06 -418.96
13. *
= ii ρρ - interest rate smoothing 3.32*103
-425.27
14. *
= ππ ψψ - elasticity of interest rate to inflation 2.28 -417.99
15. *
= yy ψψ - elasticity of interest rate to output 0.70 -416.80
16. monetary policy rule (13-15) 2.31*103
-424.91
Note: Own calculations
Nevertheless, we should be careful to interpret this result as an evidence of quite
homogenous household preferences. Parameters related to household preferences are
known to be weakly identifiable, and the result of homogeneity can be just a reflection
of common priors. A look on credible intervals of these parameters, see Table 4,
confirms this weak identifiability of parameters related to household preferences,
especially in the case of inverse Frisch elasticities of labor supply ϕ and
*
ϕ . Therefore,
Volume 11, Issue 3, 2011
179
results should be rather interpreted as I did not find substantial evidence in favor of
heterogeneity in household preferences.
I found out that there are some differences between the Czech economy and Euro Area
in the price and wage formation (BF=6.06), the greatest one being the degree of price
indexation pδ , as suggested by Bayes factor (BF=5.41) and by the difference in their
estimated values in the unrestricted variant ( pδ = 0.17 in CZ vs.
*
pδ = 0.51 in EA). It
seems that Czech firms index their prices less than their foreign counterparts do. It also
suggests that inflation dynamics in the Euro Area is more adaptive and backwardlooking
while inflation dynamics in the Czech economy is more characterized by
forward-looking nature of price setting. Although Bayes factor favors the unrestricted
variant before all variants with some restriction on price and wage formation, these
values provide only slight evidence in favor of heterogeneity in price and wage
formation.
As regards monetary policy rules, I find substantial difference in the degree of interest
rate smoothing. Bayes factor brings the decisive evidence for this conclusion
(BF=3.32*103
), although estimated values of this parameter in the unrestricted variant
do not differ so much ( iρ = 0.93 in CZ vs.
*
iρ = 0.84 in EA). It seems that the ECB
does not smooth their interest rates as much as the CNB does.
Asymmetry of Shocks
Table 2 presents results for restrictions connected with structural shocks. Bayes factors
bring strong evidence for difference in volatility of labor supply shocks (BF=39.62),
and a very slight evidence for difference in volatility of preference shocks (BF=2.95).
These two differences also contribute to almost strong evidence in favor of overall
heterogeneity in volatility of structural shocks (BF=9.97).
The results for persistence of structural shocks are rather mixed. Estimated values of
these parameters in the unrestricted variant seem to be substantially different between
both economies, see Table 4. Nevertheless, Bayes factor favors variants with restriction
on the persistence of structural shocks before the unrestricted variant, which should
suggest that there are no differences in persistence of structural shocks. However,
adding restriction on persistence of structural shocks to the variant which also has a
restriction on volatility of structural shocks significantly worsens the empirical data fit
of this variant and leads to decisive evidence (BF=2.88*105
) in favor of the unrestricted
variant. It seems that there are substantial differences in overall persistence and
volatility of structural shocks, however, this result reveals itself only in testing this joint
hypothesis.
REVIEW OF ECONOMIC PERSPECTIVES
180
Table 2: Bayes Factors and Log Marginal Likelihood - Structural Shocks
i Restriction BF0,i log(p(YT|Mi))
0. Unrestricted 1 -417.16
1. *
= aa σσ - volatility of technology shocks 0.83 -416.98
2. *
= gg σσ - volatility of preference shocks 2.95 -418.25
3. *
= ll σσ - volatility of labor supply shocks 39.62 -420.84
4. *
= MM σσ - volatility of monetary shocks 0.17 -415.39
5. *
= cpcp σσ - volatility of cost-push shocks 0.41 -416.27
6. volatility of shocks (1-5) 9.97 -419.46
7. *
= aa ρρ - persistence of technology shocks 0.49 -416.45
8. *
= gg ρρ - persistence of preference shocks 0.43 -416.33
9. *
= ll ρρ - persistence of labor supply shocks 0.72 -416.83
10. persistence of shocks (7-9) 0.17 -415.37
11. persistence and volatility of shocks (4,10) 2.88*105
-429.73
12. no correlations of shocks 168.29 -422.29
13. almost perfect correlations of shocks 7.76*1048
-529.73
Note: Own calculations
I also compare the unrestricted variant with the variant, where corresponding shocks in
both economies are modelled as uncorrelated, and with the variant where corresponding
shocks in both economies are modelled as almost perfectly correlated.1
Bayes factor
favors the unrestricted variant before the variant with uncorrelated shocks (BF=168.29),
and also strongly favors the unrestricted variant before the variant with almost perfectly
correlated shocks (BF=7.76*1048
). It seems that allowing for correlations between
corresponding shocks in both economies (and estimating these correlations) improves
the data fit of DSGE models significantly.
According to the estimations of correlations between corresponding shocks, see Table 4,
we can say that the most correlated shocks are monetary shocks (cor=0.39) and
preference shocks (cor=0.38). Correlations of these shocks are statistically significant
1
Almost perfect correlation means correlation equal to 0.95. It is impossible to estimate this
model (using all previously mentioned time series) with correlation of structural shocks equal to
1. I decided to use this approximation, following Kolasa (2009).
Volume 11, Issue 3, 2011
181
on the significance level α = 0.01. Correlations of other shocks are not statistically
significant even on the significance level α = 0.1. These results suggest that there exists
a big asymmetry between shocks in the Czech economy and the Euro Area 12. However,
we should be careful with this interpretation. Except for the monetary shocks and costpush
shocks, the correlations are not between whole shocks (represented by AR1
processes) but only between innovations in these shocks. If I calculate correlations
between smoothed AR1 processes representing these shocks, I get slightly different
results. Correlations are now a little bit higher. Preference shocks are now highly
correlated with correlation equal to 0.62, correlations of technology shocks and labor
supply shocks are also higher, and for technology shocks it is equal to 0.34 and for labor
supply shocks it is equal to 0.21. However, these values are still rather low which
suggest a big asymmetry between shocks in the Czech economy and the Euro Area 12.
Impact of Structural Differences
Structural differences can be also seen as differences in the behaviour of both
economies. I can compare the behaviour of both economies in responses to various
shocks, by using impulse-response functions. Figure 2 displays impulse-response
functions of selected variables to various shocks. I restrict my analysis to the three most
important macroeconomic variables: output, inflation and interest rate. Every subfigure
displays a response of the domestic variable to the domestic shock and a response of the
foreign variable to the foreign shock of the same type.1
I find it more meaningful to
compare responses of domestic and foreign variables to shocks of the same type, where
magnitude and persistence of these shocks is given by their estimated posterior means.
Loosely speaking, I compare responses to shocks of the same type, with their average
magnitude and persistence. This comparison covers structural differences as well as
differences in persistence and volatility of structural shocks.
As regards preference shocks, it seems that there are no substantial differences in the
behaviour of the main macroeconomic variables. Although magnitude of preference
shocks is two times larger in the Czech economy than in the Euro Area 12, responses of
examined variables show a very similar pattern. Nevertheless, the initial response of
domestic output is larger than the initial response of foreign output, response of
domestic inflation is a little bit larger and more persistent than response of foreign
inflation, and response of domestic interest rate is a little bit more persistent than
response of foreign interest rate.
On the other hand, responses of the main macroeconomic variables to technology
shocks show substantial differences. Responses of domestic variables are much larger
and display more gradual and hump-shaped pattern than responses of foreign variables.
It is influenced by much larger volatility and persistence of domestic technology shocks.
Responses of the main macroeconomic variables to labor supply shocks are also
different between both economies. Responses of foreign variables are much more
gradual and sluggish than responses of domestic variables.
1
I consider the Czech economy as the domestic economy and Euro Area 12 as the foreign
economy.
REVIEW OF ECONOMIC PERSPECTIVES
182
As regards monetary shocks, the response of the domestic output is larger than the
response of the foreign output but the adjustment of the domestic output is more rapid.
There is almost no response of the foreign inflation to foreign monetary shock while the
response of domestic inflation to domestic monetary shock displays substantial decline
followed by gradual recovery.
Volatility of cost-push shocks in the domestic economy is much larger than in the
foreign economy. This contributes to the fact that responses of foreign variables to costpush
shocks are larger and more volatile than responses of domestic variables.
Conclusion
I investigated asymmetric shocks and structural differences between the Czech economy
and the Euro Area 12. At first, I examined asymmetry of shocks and sources of
structural differences, using model comparison based on the Bayes factor. I did not find
any substantial evidence in favor of heterogeneity in household preferences. I did find
though some slight differences in price and wage formation and a substantial difference
in interest rate smoothing. However, the main differences are in timing, persistence and
volatility of structural shocks.
Apart from that, I also examined impact of structural differences and differences in
persistence and volatility of structural shocks on the behavior of both economies, using
analysis of impulse-response functions. As regards preference shocks, I found no
substantial differences in the behaviour of the main macroeconomic variables. On the
other hand, I did find much larger volatility and persistence of domestic technology
shocks. This contributes to the fact that responses of domestic variables to technology
shocks are much larger and display more gradual and hump-shaped pattern than
responses of foreign variables. I also found out that responses of foreign variables to
labour supply shocks are much more gradual and sluggish than responses of domestic
variables. As regards monetary shocks, I discovered that there is almost no response of
foreign inflation to foreign monetary shock while response of domestic inflation to
domestic monetary shocks displays substantial decline followed by gradual recovery.
Responses of foreign variables to cost-push shocks are larger and more volatile than
responses of domestic variables.
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Volume 11, Issue 3, 2011
185
Tables and Figures
Table 3: Interpretation of Parameters
parameter Interpretation restriction
β discount factor 〉〈0,1
α openness of the economy 〉〈0,1
pε elasticity of substitution among goods )1, ∞〈
wε elasticity of substitution among labor types )1, ∞〈
pω 2
)/( fYf ′′′− )0, ∞〈
χ elasticity of interest rate to debt )0, ∞〈
*
,σσ inv. elast. of intertemporal substitution )0, ∞〈
*
,ϕϕ inv. elast. of labor supply )0, ∞〈
*
,hh habit formation 〉〈0,1
*
,ηη elast. of subst. among H/F goods )0, ∞〈
*
, pp θθ Calvo parameter for producers 〉〈0,1
Fθ Calvo parameter for importers 〉〈0,1
*
, ww θθ Calvo parameter for households 〉〈0,1
*
, pp δδ indexation of producers 〉〈0,1
Fδ indexation of importers 〉〈0,1
*
, ww δδ indexation of households 〉〈0,1
*
, ππ ψψ elasticity of interest rate to inflation )0, ∞〈
*
, yy ψψ elasticity of interest rate to output )0, ∞〈
*
, ii ρρ interest rate smoothing 〉〈0,1
*, aa ρρ AR1 parameters for technology shocks 〉〈0,1
REVIEW OF ECONOMIC PERSPECTIVES
186
*, gg ρρ AR1 parameters for preference shocks 〉〈0,1
*, ll ρρ AR1 parameters for labor supply shocks 〉〈0,1
cfρ AR1 parameter for importer’s cost push shock 〉〈0,1
sρ AR1 parameter for risk premium shock 〉〈0,1
*, aa σσ std. dev. of technology shocks )0, ∞〈
*, gg σσ std. dev. of preference shocks )0, ∞〈
*, ll σσ std. dev. of labor supply shocks )0, ∞〈
*, cpcp σσ std. dev. of producer’s cost-push shocks )0, ∞〈
*, MM σσ std. dev. of monetary shocks )0, ∞〈
cfσ std. dev. of importer’s cost push shock )0, ∞〈
sσ std. dev. of risk premium shock )0, ∞〈
acor correlation of technology shocks
*
,, , tata εε 〉〈−1,1
gcor correlation of preference shocks
*
,, , tgtg εε 〉〈−1,1
lcor correlation of labor supply shocks
*
,, , tltl εε 〉〈−1,1
cpcor correlation of cost-push shocks
*
,, , tcptch εε 〉〈−1,1
mcor correlation of monetary shocks
*
,, , tMMl εε 〉〈−1,1
Volume 11, Issue 3, 2011
187
Table 4: Estimated Parameters - unrestricted variant
par. prior
mean
prior
std.
dev.
prior
dist.
post.
mean
CZ
90% cred.
interval
CZ
post.
mean
EA
90% cred.
interval
EA
*
,σσ 1.0 0.7 G 0.79 0.25 1.29 0.78 0.23 1.30
*
,ϕϕ 2.0 0.7 G 1.75 0.80 2.66 2.40 1.19 3.56
*
,hh 0.7 0.1 B 0.81 0.69 0.93 0.79 0.69 0.89
*
,ηη 0.5 0.15 G 0.47 0.29 0.65 0.42 0.30 0.53
*
, pp θθ 0.6 0.05 B 0.63 0.56 0.70 0.67 0.60 0.74
Fθ 0.6 0.05 B 0.67 0.61 0.73
*
, ww θθ 0.6 0.05 B 0.57 0.52 0.63 0.67 0.61 0.73
*
, pp δδ 0.5 0.2 B 0.17 0.02 0.31 0.51 0.22 0.82
Fδ 0.5 0.2 B 0.54 0.26 0.82
*
, ww δδ 0.5 0.2 B 0.54 0.24 0.84 0.34 0.13 0.53
*
, ππ ψψ 1.5 0.15 G 1.62 1.40 1.84 1.38 1.15 1.60
*
, yy ψψ 0.5 0.15 G 0.19 0.11 0.26 0.16 0.09 0.23
*
, ii ρρ 0.8 0.05 B 0.93 0.92 0.95 0.84 0.80 0.87
*, aa ρρ 0.5 0.2 B 0.93 0.87 0.99 0.54 0.22 0.86
*, gg ρρ 0.5 0.2 B 0.58 0.34 0.82 0.70 0.57 0.82
*, ll ρρ 0.5 0.2 B 0.23 0.07 0.39 0.36 0.17 0.54
cfρ 0.5 0.2 B 0.88 0.82 0.94
sρ 0.5 0.2 B 0.93 0.88 0.98
*, aa σσ 3.0
0.5
∞ I 3.71 2.37 4.98 1.03 0.11 2.58
REVIEW OF ECONOMIC PERSPECTIVES
188
*, gg σσ 6.0
2.0
∞ I 7.91 3.62 12.63 2.82 1.55 4.10
*, ll σσ 25.0
12.0
∞ I 37.66 27.72 50.0 11.19 5.33 17.02
*, cpcp σσ 0.05
0.3
∞ I 0.14 0.01 0.47 0.36 0.21 0.49
*, MM σσ 0.1 ∞ I 0.10 0.08 0.11 0.10 0.08 0.11
cfσ 0.3 ∞ I 0.97 0.64 1.28
sσ 0.5 ∞ I 0.16 0.07 0.26
acor 0 0.4 N 0.21 -0.31 0.75
gcor 0 0.4 N 0.38***
0.18 0.59
lcor 0 0.4 N 0.11 -0.11 0.33
cpcor 0 0.4 N 0.19 -0.41 0.77
mcor 0 0.4 N 0.39***
0.19 0.58
Note: G – gamma, B – beta, I – inverse gamma, N - normal
Volume 11, Issue 3, 2011
189
Figure 1: Data
2000 2002 2004 2006 2008 2010
-1
0
1
Inflation EA12 - deviations from mean
2000 2002 2004 2006 2008 2010
-1
0
1
2
Inflation CZ - deviations from mean
2000 2002 2004 2006 2008 2010
-3
-2
-1
0
1
GDP EA12 - deviations from mean
2000 2002 2004 2006 2008 2010
-4
-2
0
GDP CZ - deviations from mean
2000 2002 2004 2006 2008 2010
-0.5
0
0.5
Interest Rate EA12 - deviations from mean
2000 2002 2004 2006 2008 2010
-0.5
0
0.5
1
Interest Rate CZ - deviations from mean
2000 2002 2004 2006 2008 2010
-0.5
0
0.5
Wage Inflation EA12 - deviations from mean
2000 2002 2004 2006 2008 2010
-6
-4
-2
0
2
Wage Inflation CZ - deviations from mean
2000 2002 2004 2006 2008 2010
-2
0
2
4
Terms of Trade CZ - deviations from mean
2000 2002 2004 2006 2008 2010
-5
0
5
Real Exchange Rate CZ - deviations from mean
REVIEW OF ECONOMIC PERSPECTIVES
190
Figure 2: Impulse-Response Functions
Note: solid line – responses of domestic variables to domestic shocks, dashed line –
responses of foreign variables to foreign shocks
Volume 11, Issue 3, 2011
191
STRUCTURAL DIFFERENCES AND ASYMMETRIC SHOCKS BETWEEN
THE CZECH ECONOMY AND THE EURO AREA 12
Martin Slanicay
Masaryk University, Faculty of Economics and Administration, Department of
Economics, Lipová 41a, Brno 602 00, slanicay@mail.muni.cz
Abstract: The goal of this paper is to determine whether there exist asymmetric shocks
and structural differences between the Czech economy and the Euro Area 12. A New
Keynesian DSGE model of a small open economy is used for this purpose. Asymmetric
shocks and structural differences are examined in two ways. At first, I examine
asymmetry of shocks and sources of structural differences, using model comparison
based on the Bayes factor. I do not find substantial evidence in favor of heterogeneity in
household preferences. I find slight differences in price and wage formation and
substantial difference in interest rate smoothing. However, the main differences are in
timing, persistence and volatility of structural shocks. I also investigate impact of
structural differences and differences in persistence and volatility of structural shocks
on the behavior of both economies, using analysis of impulse-response functions. I find
no substantial differences in responses of the main variables to preference shocks. On
the other hand, I find much larger volatility and persistence of domestic technology
shocks. This contributes to the fact that responses of domestic variables to technology
shocks are much larger, and display more gradual and hump-shaped pattern than
responses of foreign variables. I also find that responses of foreign variables to labour
supply shocks are much more gradual and sluggish than responses of domestic variables.
As regards monetary shocks, I find that there is almost no response of foreign inflation
to foreign monetary shock while response of domestic inflation to domestic monetary
shock displays substantial decline followed by gradual recovery. Responses of foreign
variables to cost-push shocks are larger and more volatile than responses of domestic
variables.
Key words: New Keynesian, DSGE model, Bayes factor, Bayesian estimation,
structural differences, asymmetric shocks, model comparison.
JEL Classification: C51, E32, E52
DOI: 10.2478/v10135-011-0012-0