NOMINAL RIGIDITIES AND WAGE-PRICE
DYNAMICS IN ESTIMATED DSGE MODEL:
APPLICATION FOR THE CZECH ECONOMY
WORKING PAPER 28/2008
Miroslav Hloušek
December, 2008
Řada studií Working Papers Centra výzkumu konkurenční schopnosti české
ekonomiky je vydávána s podporou projektu MŠMT výzkumná centra 1MO524.
Vedoucí prof. Ing. Antonín Slaný, CSc., Lipová 41a, 602 00 Brno, e-mail:
slany@econ.muni.cz, tel.: +420 549491111
NOMINAL RIGIDITIES AND WAGE-PRICE DYNAMICS IN
ESTIMATED DSGE MODEL: APPLICATION FOR THE
CZECH ECONOMY
Abstract:
The goal of this paper is to examine importance of nominal rigidities ­ especially of
wages and prices ­ in the Czech economy. As a tool, DSGE model of open
economy with nominal rigidities is used. The model is estimated on data of the
Czech economy using Bayesian techniques. The model is evaluated in terms how it
fits the data and the dynamical properties of the model are studied. The emphasis is
put on wage-price dynamics. Next, the relative importance of nominal rigidities is
examined using sensitivity analysis. The conclusion is that wages are more rigid
than prices and thus wage rigidity and price rigidity are interchangeable. This
outcome should be taken into consideration for forming of monetary policy by the
central bank and modelling of behaviour of the Czech economy.
Abstrakt:
Cílem této práce je prozkoumat význam nominálních rigidit ­ obzvláště mezd a cen
­ v české ekonomice. Jako nástroj je použit DSGE model otevřené ekonomiky
s nominálními rigiditami. Model je odhadnut na datech české ekonomiky pomocí
Bayesovských technik. Poté je model zhodnocen podle toho, jak vystihuje data, a
jsou studovány jeho dynamické vlastnosti. Důraz je kladen na dynamiku mezd a
cen. Pomocí analýzy citlivosti je zkoumán relativní význam nominálních rigidit.
Z výsledků vyplývá, že mzdy jsou rigidnější než ceny a tedy, že mzdová a cenová
rigidita nejsou vzájemně zaměnitelné. Tyto závěry by měl být zohledněny při
uskutečňování monetární politiky centrální bankou a pro modelování chování české
ekonomiky.
Recenzoval:
Ing. Petr Harasimovič, M.A.
4
1. INTRODUCTION
1.1. Motivation
The primary objective of monetary authority is to maintain price stability. The central
banks usually use model framework for analysis of the economy and governing its
policy. Their model approach is based on New Keynesian paradigm of which main
features are various types of nominal rigidities. These rigidities can stem from wages
or prices. Erceg et. al (2000) show for the baseline New Keynesian model with sticky
prices that the optimal monetary policy completely stabilizes the price level and the
output gap in reaction to shocks. Thus the central bank is able to replicate flexible
price equilibrium allocation without welfare losses. When only wages are sticky, the
natural allocation is also attainable, but requires full stabilization of nominal wages.
When both prices and wages are sticky the natural equilibrium can no longer be
attained. More importantly, monetary policy that focuses exclusively on stabilizing
price inflation, as most central banks do, is suboptimal. The policy should be aimed
at appropriate weighted average of price and wage inflation to mitigate welfare
losses relative to the optimal policy. These weights are functions of structural model
parameters that describe preferences and technologies. Some of these parameters
express degree of price or wage stickiness. Thus the importance of nominal
rigidities, especially of wages and prices, has significant impact for pursuance of
monetary policy and its stabilization effects.
1.2. Background
Nominal rigidities are the cornerstone of models with label New Keynesian
economics.
1
Methodologically, they build on the Real Business Cycle (RBC) theory
that has origins in the seminal papers of Kydland and Prescott (1982) and Prescott
(1986). Both theories are based on optimizing behaviour of agents (firms and
households), both include rational expectations and clearing markets. As a tool,
Dynamic Stochastic General Equilibrium (DSGE) models are extensively used for
macroeconomic analysis. They are calibrated or estimated and used for simulation
and evaluation of model economies.
However, New Keynesian approach introduces several new aspects such as
monopolistic competition and nominal rigidities which give rise to short run nonneutrality
of monetary policy. Contrary to RBC theory where monetary factors do not
play significant role, central bank in " New Keynesian world" can influence the real
interest rate (through controlling nominal interest rate) and subsequently other real
variables. But in the long run, all prices and wages adjust and economy returns to its
natural equilibrium. New Keynesian models are not only in the center of academic
research, but they are also widely used in central banks and other institutions for
forming and evaluating of economic policy.
Today's economies are open economies and they should be modelled in that way.
DSGE models with market imperfections and nominal rigidities that are extended to
open economy are referred to as New Open Economy Macroeconomics (NOEM).
This new class of models originates from Obstfeld and Rogoff (1995). But their
'Exchange Rate Dynamics Redux' model assumes stickiness in prices that lasts only
for one period. Recent DSGE models in NOEM tradition are more realistic. They
assume that rigidity lasts for more than one period and allow stickiness in both
1
Nice introduction and overview of New Keynesian models provides Gali (2008).
5
prices and wages. The question whether wages are more rigid than prices or other
way around remains a matter of empirical testing and can be country specific.
There is number of empirical studies on relative importance of price and wage
stickiness, for various countries using various estimation techniques. The results
show quite mixed picture. Bergin (2003) uses maximum likelihood for estimation of
the model with price and wage rigidities that are introduced in the form of adjustment
cost. He tests restricted models with flexible wages and/or prices relatively to the
benchmark model with both types of rigidies for Australia, Canada and the UK. He
concludes that nominal rigidities are key elements of the NOEM models in all three
countries. Regarding relative importance, price rigidity is more important than wage
rigidity. The version of model that assumes flexible prices is rejected for all three
countries, while the version with flexible wages is rejected only for Australia.
Contrary to Bergin, other authors introduce nominal stickiness in the form of Calvo
contracts implying that both rigidities are present from the beginning. Then the
relevant question is which of the contracts lasts longer and accounts best for model
fit. Ambler et al. (2003) combine GMM and SMM
2
for estimation of DSGE model for
Canada. Their model assumes Calvo pricing mechanism for domestic prices, import
prices and wages and the estimation results indicate that wage contracts last longer
than price contracts. Smets and Wouters (2003) estimate DSGE model for Euro
area using Bayesian techniques. Relative importance of nominal rigidities says in
favour of price stickiness. Adolfson et al. (2005) use ritcher model with more nominal
(and real) rigidities and estimate it also on Euro data using Bayesian methods. Their
results confirm findings of Smets and Wouters. Rabanal and Rubio-Ramirez (2005)
also report that sticky wages models for the Euro area are rejected by the data.
Christiano et al. (2005) estimate DSGE model for US economy by minimizing a
measure of the distance between the model and empirical impulse response
function. The length of Calvo contracts were quite similar but subsequent
quantitative analysis shows that sticky wages play a crucial role in the modeľs
performance while sticky prices play only limited role for good fit of the model. Del
Negro and Schorfheide (2008) argue that some degree of price rigidity is needed to
describe US data but the whole issue is much more complex and the results may be
influenced by the choice of priors for parameters and data sets. Finally, Maih (2005)
found out for Norwegian economy that wage contracts last longer than price
contracts but adjustment to stochastic shocks is faster for wages than for prices.
1.1. Czech data evidence
Cyclical behaviour of the real wage is crucial in helping to discriminate between
theories of business cycle. It can also help to determine the source of nominal
rigidity. Cyclical behaviour of the real wage in the Czech economy is not typical. The
business cycle and the correlation function of labor productivity and the real wage is
depicted in Figure 1 (left hand side).
3
Both time series are obtained by Christiano
and Fitzgerald (2003) band pass filter.
4
The values of cross-correlation coefficient
indicate that the real wage is rather acyclical. Correlation coefficient is not
statistically significant except of the lead of five periods. This negative value of
2
Generalized method of moments (GMM) and Simulated method of moments (SMM).
3
Labor productivity is calculated as ratio of GDP and number of workers, the real wage is
nominal wage divided by CPI.
4
The business cycle fluctuations are defined as those between six and thirty two quarters,
same as in Agresti and Mojon (2005).
6
correlation coefficient can be explained by looking on the cyclical behaviour over
time. There is evident procyclical behaviour at the beginning of the sample period,
but from 2000 the real wage behaves countercyclicaly. Right hand side of Figure 1
shows the same characteristics for shortened sample. The correlation coefficient
confirm strong countercyclical behaviour of the real wage lagging the cycle of output
(per worker) by three periods.
The real wage is usually found to be procyclical or acyclical in other countries.
5
Turning to the theories of business cycle fluctuations, stylized fact of countercyclical
real wage is in favour of Keynesian model with sticky wages rather than sticky
prices, as it is illustrated in e.g. Romer (2006). However, Romer uses only simple
static model. The lagging behaviour of the real wage suggests that staggered wage
contracts embedded into dynamic model should be appropriate feature of model of
the Czech economy. Next, there are many other factors at play, e.g. various types of
shocks, transmission mechanisms, openness of the economy and also mutual
relationship between wages and prices (wage-price spiral). This is quite complex
issue which also says in favour of using model approach with dynamics.
1.2. The goal of the paper
The research question of this paper is whether wages are more sticky than prices or
more broadly which type of nominal rigidities is the most important for modelling of
the Czech economy. The objective is not only to estimate parameters that captures
degree of nominal rigidity but also to investigate wage and price dynamics.
To provide answer to this question, the DSGE model of open economy with nominal
rigidities on various markets is used. The model is estimated on Czech data using
Bayesian techniques. The behaviour of model is studied along several dimensions
including impulse responses, variance decomposition or sensitivity analysis, with
emphasis put on relative importance of wage and price stickiness and their joint
dynamics.
The reminder of the paper is organized as follows. Section 2 describes the DSGE
model used for the analysis, its derivation from optimization problems of agents, and
symmetric equilibrium of the model. Next steps before estimation are loglinearization
around the steady-state and solution of the system using state-space
form. Section 3 deals with data, their transformation and estimation methodology.
Section 4 presents and discusses results of the estimation. The model is evaluated
in terms how it fits the data before the dynamical properties of the model are
studied. Some other model implications regarding exchange rate pass-through and
wage-price dynamics are covered in this section as well. Section 5 focuses on
sensitivity analysis. The relative importance of nominal rigidities is tested via
marginal likelihood and vector autocorrelation functions. Finally, the issue whether
wage rigidity and price rigidity are interchangeable is examined. Section 6 concludes
with prospects for further research.
2. THE MODEL
The model is borrowed from Maih (2005), extended (especially by export market
rigidities) and adjusted for Czech economy condition. The inspiration for extension
5
See e.g. Romer (2006), Kydland and Prescott (1990) or Stock and Watson (1998)
7
was found in Adolfson et al. (2005). Similar models are used in papers of Ambler et
al. (2003) or Smets and Wouters (2003).
The model differs from Maih (2005) in several aspects. The money are assumed
endogenous and are not explicitly modeled within the (money-in-the-utility)
framework. Second, the prices of export intermediate goods are assumed sticky and
are modeled in Calvo style. Resulting Phillips curve introduces new channel of slow
price adjustment. and can improve fit of the model. Some additional amendments
relates to specific features of the Czech economy or estimation procedure. The
interest rate rule is modified; besides interest rate smoothing includes only deviation
of inflation from target and output gap. This specification is more in accordance with
regime of monetary policy of the Czech National Bank. Next, elasticity of substitution
across differentiated foreign (imported) intermediate goods is time-varying and is
subject to shock. Introduction of markup shock to import prices allows to use
additional time series for estimation and thus to draw more information from data.
The derivation of the model is similar to Maih's work, but for readers convenience
and several modifications, I present it in this section.
2.1. Households
The model consist of continuum of households indexed on interval (0,1)i .
Households is endowed with a differentiated labor skill. They are choosing a
consumption plan and also chooses wage rate plan for all K3,2,1,,= +++ tttt
to maximize an expected discounted infinite stream of utility of the form






+
--
-
+-
-
-

 




 
 1
,
1
1,
=
)(
1
1
))((
1
1
ihZhabCiCZE lsc
t
t
t
where tE is the conditional expectations operator,
6
(0,1) is the discount factor,
)(iC is consumption, )(ih denotes hours worked by the household, tcZ , is
consumption preference shifter (or aggregate preference shock that is common to all
households) and tlsZ , is labor supply shock.  is the constant relative risk
aversion coefficient or the inverse of the elasticity of intertemporal substitution,
0> is the inverse of the (Frisch) elasticity of labor supply with respect to the real
wage and [0,1)hab is external habit persistence in the previous perioďs
aggregate consumption.
7
The householďs budget constraint is given by
)()()()()()(
)()(
)( *
11*
*
iDPihiWiBSiBiT
rpR
iBS
R
iB
iCP ttttttt
tt
tt
t
t
tt ++++++ -- (1)
6
)|(= 11 tttt xExE ++ denotes expectation of variable 1+tx made under information set
t available in time t .
7
This form of habit formation is called "catching up with Johneses" . It is motivated by
explaining empirical fact of hump-shaped gradual response of consumption and inflation to
shocks. For more details see e.g. Fuhrer (2000) or Ljungqvist and Uhlig (2000).
8
The right hand side of equation (1) expresses sources, the left hand side is usage of
the sources. tP is price level in the economy and hence )(iCP tt denotes nominal
consumption of the household. )(iBt and )(*
iBt are domestic-currency and foreigncurrency
bonds respectively purchased at time t , tS is nominal exchange rate
quoted as domestic currency per unit of foreign currency. tR and
*
tR denote the
gross nominal domestic and foreign interest rates between t and 1+t , respectively.
trp measures risk premium that reflects departures from uncovered interest parity
condition. )(iTt are taxes paid to government (or transfers when tT is negative).
)(iWt is nominal wage rate and thus )()( ihiW tt is wage income from supplying
)(ih units of labor (hours worked) to the various intermediate goods-producing
firms. Households own all firms thus they receive )(iDt units of consumption good
as dividends from equities of intermediate goods-producing firms.
The households can carry wealth between periods using domestic and foreign
bonds. Domestic bonds are denominated in the domestic currency and foreign
bonds are denominated in the foreign currency. At the beginning of the period t the
bonds mature and provide 1-tB and )(*
1 iBS tt - additional units of consumption. The
household decide to buy tB new units of domestic bonds at the cost tR1/ and
*
tB
new units of foreign bonds at the cost )1/( *
tt rpR . The endogenous (gross) risk
premium trp captures that international financial markets are incomplete. It is
negative function that depends on the ratio of foreign bond to domestic output.
8






+- )(logexp= ,
*
trp
tt
tt
t Z
YP
BS
rp  (2)
where tY is the aggregate level of output,
*
tB is the aggregate foreign bonds
holdings and trpZ , is a shock to the risk premium. This function has following
properties, 0<trp  and 1=(0)trp . If 0<*
tB , domestic households are charged a
premium to the foreign interest rate, if 0>*
tB they receive a lower interest return on
their international savings. If there are no bonds, the risk premium is equal to one.
Each household chooses consumption )(iCt , and portfolio that consist of domestic
and foreign bonds, )(iBt and )(*
iBt . The first order conditions for these
optimization problems are:
tttttc PihabCiCZ )(=])([ 1, - -
-

(3)
8
This ratio ensures stationary dynamic path for domestic consumption and wealth and thus a
unique steady state.
9
)]([=)( 1 iERi tttt +  (4)
])([=)]([ 11
*
1 +++  ttttttttt SiErpRiESR (5)
where t is Lagrange multiplier connected with budget constraint in time t .
Equation (4) is standard Euler equation. It states that households want to equalize
expected marginal utilities across time periods taking into account relationship
between (subjective) time preference factor and market rate of return on savings.
Equation (5) is risk-adjusted uncovered interest parity condition. Its meaning is the
same, the household only adds into consideration possibility of investing into foreign
assets.
The household is endowed with differentiated labor skill that offers in
monopolistically competitive labor markets. Labor services of households are
imperfect substitutes and thus the households can choose their nominal wage
subject to demand imposed by the firms. The households set their nominal wage
rate and stand ready to supply the quantity of labor demanded for that wage by
firms. However, not all households are able to select their wage rate each period.
Result of this wage setting implies existence of nominal rigidities that are modeled in
the form of Calvo (1983) contracts. In each period, there is a constant probability w
that a worker is not able to re-adjust her wage. If the workers do not have
opportunity to reset their wages, these wages are adjusted by wage inflation from
previous period as a result of indexation
ttwt WiW 1,1 =)( -+ 
where
1
, =
-t
t
tw
W
W
 (6)
Similarly, there is a probability w-1 that the household will be able to change her
wage. Then the worker takes into account that she may not re-optimize her wage in
the next periods. Thus, she indexes her wage to (price) inflation and technology
growth so that her wage t- periods after the wage is set as
)(=)( ,
1
=
iWiW new
tkzyk
tk







-



where )(iW new
t is the wage set in time t that remains fixed until the next opportunity
for wage setting, and where
1
=
-t
t
t
P
P
 (7)
1,
, =
-ty
yt
tzy
Z
Z
 (8)
10
where ytZ is the level of technology in the economy in time t .
As the markup for workers that revise their wages should be positive in the steady
state, we must impose restriction that the time-varying elasticity of substitution
across different types of labor, wt is greater than unity. The worker who sets new
wage solves optimization problem






+
- +-

 


 
 1,
=)(
)(
1
)(max ih
Z
E lst
w
t
t
inew
tW
subject to budget constraint (1) for + ,1,,= Ktt and labor demand from
aggregator
9
)(
)(
=),(=)(
,
1
0
jh
W
iW
djjihih
w





-







This optimization results in the following first order condition
0.=1)(
)(
)( ,,
1
=
1
,,,
=






-





+- 
-+
-









 h
iW
hZZ
E wkzyk
tk
new
t
hsctwt
w
t
t (9)
The negative term in equation (9) is the marginal disutility of labor effort (additional
hours worked) and the positive term is the marginal revenue from slight increase of
the wage rate. In the optimum, the expected sums of those expressions should be
equal. At the resulting wage rate, the workers are ready to supply any amount of
labor demanded from firms.
In equilibrium, there is a fraction w-1 of workers that changes their wages at time
t . The expected time between wage adjustments, or equivalently, the number of
periods for that the wage reamains fixed is
w-1
1
.
10
For example, if 0.75=w
then the wages are not changed for one year.
This structure of labor market implies that households are heterogeneous and their
labor income and thus consumption and assets holdings may differ. To ensure
identical consumption in equilibrium, we assume that households have access to
state contingent security markets which provides them full insurance against
idiosyncratic shocks in labor income. Consumption will be same for all households in
equilibrium and only the wage rate and labor supply will differ.
2.2. Production side of the economy
The production structure of the economy is depicted in Figure 2. Monopolistically
competitive markets are depicted by dashed lines. There are three types of firms in
the model economy: continuum of intermediate goods producing firms, continuum of
exporting firms that give brand names to intermediate goods and various
aggregators. Domestic intermediate firms uses labor and capital as factors of
9
Labor demand function is solution of aggregator's labor packing problem and is defined later.
10
The time between wage adjustments follows a geometric distribution.
11
production. Part of domestic intermediate goods is exported and the other part
together with imported intermediate goods is used for production of final goods.
Final goods is either consumed by households and government or used as capital
input in production of intermediate goods. Optimization problem of these firms is
described in following subsections.
2.2.1. Domestic intermediate goods
There is continuum of domestic intermediate goods firms indexed on interval
(0,1)j . The firm producing good )(, jY tH has following production function:
 -1
)(=)( ttytHt KjhZjY (10)
where ytZ is a productivity shock, tttt GCYK --= is part of final goods that is
not consumed (capital) and  is labor intensity of production function.
11
Domestic firm chooses level of labor and capital (for given prices) to minimize its
cost of production
tttt
tKjth
KPjhW +)(min
),(
subject to production function (10). The first order conditions of optimization problem
are
)(
)(
)(=
jh
jY
jW
t
Ht
tt  (11)
t
Ht
tt
K
jY
jP
)(
)()(1= - (12)
where the Lagrange multiplier t expresses the marginal cost of production. Then
these two equations imply following relationship )()(=)( jYjKPjhW Htttttt + .
12
The real profits, )( jDt , made by domestic intermediate goods firm j are
ttttHtHttt KPjhWjYjPjDP -- )()()(=)( (13)
Firms operate in monopolistically competitive markets. They produce differentiated
goods (imperfect substitutes) and thus are able to influence their prices. These
characteristics of markets allow firms to gain non-zero profits in equilibrium.
11
The model does not assume existence of capital in usual terms. Final good is perishable
and cannot be stored into next period. Therefore it is used in production in the same period. I
will denote it by tK as capital even it does not correspond to usual definition. This
specification comes from Ambler et al. (2003) and has following reason: first, without final
goods in the production function, the response of the real wage to demand shocks is too
highly countercyclical. Second, the presence of intermediates in the production function for
domestic goods affects the correlation between the nominal exchange rate and domestic
inflation.
12
The output is sum of remunerations to production factors.
12
The price setting problem for domestic intermediate goods producing firm is
analogous to that of households for wage-setting. With probability h the firm is not
allowed to reoptimize and its price is updated according to the scheme
)(=)( 1,1, jPjP HtthtH -+ 
with
1
, =
-Ht
Ht
th
P
P
 (14)
Fraction h-1 of firms that can adjust prices set the new prices (
new
tHP , ) as a result
of following optimization problem:






-






-

 )()]()([
1
)(max
=)(
jYjjP
PP
P
E HH
tt
t
h
t
t
jnew
HtP





subject to demand that faces from aggregator
,
)(
=)( 



 H
h
H
H
H Y
P
jP
jY
-






where the newly set price is indexed to inflation in the previous period
)(=)( ,
1
=, jPjP new
HtkhtkH 

-

and
tt
t
P
P

- 
 is stochastic discount factor that is derived from Euler equation for
domestic bonds. Households are owners of domestic firms and every agent has
access to a complete contingent asset market which implies a unique market
discount factor.
The first order condition is
[ ]
0=
)()(1)(
)()(
1
=1
=
1
=























 
--
×







-
-
-
---















P
Y
P
jjP
jP
P
P
E
H
h
H
hktk
hhktk
new
Hth
hnew
Ht
tt
t
h
t
t (15)
2.2.2. Importers
Analogously, the economy imports a continuum of foreign intermediate goods on the
unit interval. There is monopolistic competition in the market for imported
intermediates which are imperfect substitutes. For the sake of simplicity the price in
the foreign economy is assumed to be flexible. Thus foreign intermediate goods
firms set their prices as a markup over foreign marginal costs. The elasticity of
substitution across foreign intermediate goods, tf , is assumed to be same in both
countries. With additional assumption that foreign goods imported by firms can be
13
also consumed directly by foreigners, the price of imported goods abroad is the
foreign consumer price index in equilibrium. Finally, the Home discount factor is
used to discount the profits of foreign intermediate goods firms. Again, each firm
faces probability f-1 that it can change its price. The newly set price is solution to
the following optimization problem






-






-

 )()]()([
1
)(max
****
=)*(
jYjSjP
PP
P
E FtF
tt
t
f
t
t
jnew
FtP





subject to demand from aggregator




 F
f
F
F
F Y
P
jP
jY
-





 )(
=)(
*
*
where )(
1
=)( ****
jjP
ft
ft




,
and each firm ignores impact of its price setting
decision on the price index. The firms take into consideration past inflation of foreign
intermediate goods and make indexation to newly set price
)(=)( *
,
1
=
*
, jPjP new
FtkftkF 

-

where
.=
1
1,
-
-
Ft
Ft
tf
P
P
 (16)
The first order condition of their optimization problem is
[ ]
0=
)()()(1
)()(
1
=*1
=
1
=

























 
+-
×







--
-
---
















P
Y
P
jSjP
jP
P
P
E
F
f
F
fktk
ffktk
new
Ftf
fnew
Ft
tt
t
f
t
t (17)
Other firms that do not have opportunity to change the price follows pricing rule
given by
FttftF PjP 1,
*
1, =)( -+ 
2.2.3. Exporters
Exporting firm buy domestic composite goods and differentiate it by brand naming.
Then, they sell the continuum of differentiated goods at monopolistically competitive
markets in the foreign economy. Each exporting firm j faces the following demand
for its product
13
13
0> is scale parameter which is expected to be small. In steady state it corresponds to
the share of exports of domestic country in the total demand of the foreign country.
14




  X
x
X
X
X Y
P
jP
jY
-





 )(
=)( (18)
Export price )( jPX is invoiced in local currency of the export market, XY denotes
total demand of exported intermediate goods and x is price elasticity of exports.
Existence of product differentiation and monopolistic competition in the foreign
market allow firms to influence prices of their goods. It is again modeled in the Calvo
setup. Exporting firms that do not have opportunity to reset their prices follow pricing
rule and index it to last period (export price) inflation.
XttxtX PjP 1,1, =)( -+ 
with
1
, =
-Xt
Xt
tx
P
P
 (19)
Other part of firms that have opportunity to reset prices (with probability x-1 )
solve optimization problem













 
-






-

 )()(
~
)(
1
)(max *
=)(
jYj
S
jP
PP
P
E X
t
X
tt
t
x
t
t
jnew
XtP







subject to demand function (18). Marginal cost for exporting firm t
~
is actually the
price of domestic composite good HtP . The firms take into account that there might
not be a chance to optimally change in next period. They index the newly set price to
inflation of export goods
new
XtkxtkX PjP ,
1
=, =)( 

-

The first order condition of optimization problem is
0=
)(
~
)()(1
)()(
*
1
=1
=
1
=























 





 
+-
×







-
-
-
---

















P
Y
P
j
S
jP
jP
P
P
E
X
x
X
xktk
xxktk
new
Xtx
xnew
Xt
tt
t
x
t
t (20)
2.2.4. Aggregators
There are several aggregators on various positions of production process. One
aggregator demands differentiated types of labor from households, make bundels
and sells them to intermediate good producing firms. Another aggregators assemble
differentiated domestic and foreign intermediate goods to make composite goods.
Final aggregator packs domestic and foreign composite goods to make final good
that is distributed among private and government consumption and production of
15
home intermediates. The aggregators are benevolent and they do not make any
profit. Their optimization problem are described in following subsections.
Labor packing
The aggregator demands differentiated domestic labor inputs from households.
Each worker i posses different skill type and thus acts as monopolistic supplier of
labor ),( jiht to firm j . The aggregator bundles together those different types of
labor and supplies them to each (domestic) intermediate goods firm. The composite
labor has following form:
11
1
0
),(=)(
--









wt
wt
wt
wt
tt djjihjh




where wt is elasticity of substitution between different labor skills. This implies
labor demand
)(
)(
=),( jh
W
iW
jih t
wt
t
t
t
-






The number of workers is large so that each of them ignores impact of her wage
setting decision on the aggregate wage index which is defined as
wttw
tt diiWW
 --





1
1
,11
0
)(=
Domestic and Foreign composite goods
The aggregator assembles imperfectly substitutable intermediate goods from all
firms producing domestic intermediate goods. The constant returns to scale (CRS)
technology is expressed as:
Ht
ht
ht
ht
ht
Ht YdjjY 







 --

11
1
0
)(




where 1>ht is time-varying elasticity of substitution across differentiated domestic
intermediates. The aggregator solve cost minimization problem which results in
demand for each good j given by
Ht
ht
Ht
Ht
Ht Y
P
jP
jY
-





 )(
=)(
and with zero profit condition the price index is defined as
htht
HtHt dijPP
 --





1
1
11
0
)(=
16
Each firm j takes the aggregate price in the market HtP and the overall production
HtY as given and independent of its own decision.
The domestic composite intermediate good is used in the production of final good or
it is exported
.= Xt
d
HtHt YYY + (21)
The aggregator of foreign intermediate goods solves an analogous problem. CRS
production function is given by
Ft
ft
ft
ft
ft
Ft YdjjY 









 --

11
1
0
)(




where 1>ft is time-varying elasticity of substitution across differentiated foreign
intermediates. Optimization problem with zero-profit condition implies demand
function of the form
Ft
ft
Ft
Ft
Ft Y
P
jP
jY
-





 )(
=)(
*
*
and price index
ftft
FtFt dijPP
 --





1
1
11
0
)(=
Again, each firm
*
j ignores impact of its price setting decision on the price index.
Finished goods production
The final good tY is produced by competitive firm (aggregator) that uses domestic
and foreign (composite) intermediate goods
d
HtY and FtY as inputs subject to
constant-returns-to-scale technology:
t
Ft
d
Ht
Y
YY






-





-

1
1
She buys intermediate goods
d
HtY and FtY at nominal prices HtP and FtP
respectively, and sells final good tY at nominal price tP . Her profit maximization
problem can be described as follows:
17
][max
,
FtFt
d
HtHttt
FtYd
HtY
YPYPYP --
subject to the production function. The first order conditions are:
t
Ht
td
Ht Y
P
P
Y = (22)
t
Ft
t
Ft Y
P
P
Y )(1= - (23)
and with assumption of zero profit the final good price tP is given by:
 -1
)()(= FtHtt PPP (24)
The final good is used for domestic consumption tC , government consumption tG
and in the production of domestic intermediate goods tK
.= tttt KGCY ++
2.3. Government
The government budget constraint in the economy is given by
diiTGP ttt )(=
1
0 (25)
where tG is government consumption and tT denotes lump-sum taxes from
households. The government budget is balanced in every period. The government
spending is subject to random shocks that is defined by equation 2 in next text.
2.4. Monetary policy
The behaviour of monetary authority (central bank) is described by an instrument
rule. Central bank adjust the short term interest rate (more precisely, the deviation of
nominal interest rate from its steady state value
ss
tt RR / ) in response to deviations of
CPI inflation from the inflation target and the output gap. We also allow for interest
rate smoothing. This type of modified Taylor rule performs empirically quite well and
could be regarded as good approximation of optimizing behaviour of central bank.
Monetary policy reaction function has following form
tmp
y
h
ht
T
tt
t
ss
t
t
ss
t
t
Z
y
y
P
P
R
R
R
R
,
)(1
1
4
1
3
4
1
4
)(
= ×
































-
-
-
+-


(26)
where
18
T
t
zyss
tR 


= (27)
yt
Ht
ht
Z
Y
y = (28)
T
t is inflation target which is subject to shocks, tmpZ , is shock to interest rate rule.
2.5. Domestic stochastic processes
There are ten exogenous domestic shocks in the model for which law of motion
need to be specified. They are tlsytct ZZZ ,,, , rp
T
tmp ZZ ,, , ht , ft , wt and gtZ
where the last one comes from definition
yt
t
gt
Z
G
Z = (29)
The law of motion of shocks is modelled as autoregressive processes
tcZtczctc ZZ
,1,, )(ln=)(ln  +- (30)
ytZtzyzyzyzytzy  )(ln)(ln)(1=)(ln 1,, -+- (31)
tlsZtlszlslszlstls ZZZ
,1,, )(ln)(ln)(1=)(ln  ++- - (32)
T
t
ZT
T
t
TT
T
t







+










 -1
ln=ln (33)
trpZtrprptrp ZZ
,1,, )(ln=)(ln  +- (34)
ht
Z
ht
ht
h
h
h
h
ht
ht
 








+





-
+





-
-





- -
-
11
)(1=
1 1
1
(35)
ft
Z
ft
ft
f
f
f
f
ft
ft
 








+








-
+








-
-








- -
-
11
)(1=
1 1
1
(36)
19
wt
Z
wt
wt
w
w
w
w
wt
wt
 








+





-
+





-
-





- -
-
11
)(1=
1 1
1
(37)
tgZtggzgtg ZZZ
,1,, )(ln)(ln)(1=)(ln  ++- - (38)
where the AR parameters are restricted as zrpzlszyzc  ,,, , ,,,,
wfhT 

[0,1)yg . Shock to monetary policy is assumed i.i.d. to be distinguishable from
inflation target shock
.=)(ln
,, tmpZtmpZ  (39)
2.6. Foreign economy
Foreign economy is represented by exogenous process and is identified separately.
Thus the domestic economy cannot influence foreign economy. Given that the
Czech Republic is a small country, it is quite realistic assumption. Foreign sector is
modeled as three-equation structural vector autoregression (SVAR) model which
includes equation for output, inflation and gross nominal interest rate, respectively.
The system of equations can be written as:
ttt FxAxA +-110 = (40)
where
(0,1)==
*
*
*
*
*
*
1
*
*
*
*
N
R
R
P
P
Z
y
Y
x
tR
t
ty
t
t
t
t
yt
t
t ~
ln
ln
ln




















































-




 
and where
*
y ,
*
 and
*
R are values representing steady states of the variables.
This system resembled reduced form of basic New Keynesian model. First equation
(for output) can be thought of as aggregate demand of IS curve, second equation
(for inflation) is aggregate supply or Phillips curve and the last equation (for interest
rate) represents monetary policy reaction function. The productivity shock in foreign
economy is assumed to be same as in domestic country.
To identify the SVAR model we must impose some restrictions (which already
follows from ordering of the variables). The output does not respond
contemporaneously to both inflation and interest rate and inflation does not react
contemporaneously to interest rate. It means that matrix 0A is lower triangular. With
those restrictions, there are only three free parameters in 0A matrix and also in F
matrix, which is diagonal.
20






















*
*
*
****
**0
00
00
00
=
1
01
001
=
R
y
RyR
y
FA




 


2.7. Macroeconomic equilibrium and solution
The symmetric equilibrium of the economy allows to drop the indices ),( ji and
express all variables in per capita (or aggregate) term. The wage index and the
aggregate prices for domestic and foreign intermediates and exports are
[ ] wtwtnew
tw
wt
twtwt WWW 
 ---
-- -+ 1
1
)(11
11 )(1)(= (41)
[ ] hthtnew
Hth
ht
HththHt PPP 
 ---
-- -+ 1
1
)(11
11 )(1)(= (42)
[ ] ftftnew
Ftf
ft
FtftfFt PPP 
 ---
-- -+ 1
1
)(11
11 )(1)(= (43)
[ ] xtxtnew
Xtx
xt
XtxtxXt PPP 
 ---
-- -+ 1
1
)(11
11 )(1)(= (44)
Symmetry also implies that domestic bonds holdings for every home agent are zero
0=tB (45)
The equilibrium of the economy consists of 34 sequences of endogenous variables
tttttt GDCBB ,,,,, *
, tXtHtFt
new
Xt
new
Ht
new
Ftt PPPPPPPh ,,,,,,, , wtt  , , xtftht  ,, ,
zyt , XtFtHt
d
Htt
new
ttttt
ss
tt YYYYWWTSrpRR ,,,,,,,,,,,  , tY , hty . The equilibrium
implies that )(i households maximize their utility )(ii firms maximize profits or
minimize their costs, )(iii markets are cleared for each asset and each good and
(iv) the resource constraints are satisfied. The endogenous variables are driven by
13 stochastic shocks tlsytct ZZZ ,,, , rp
T
tmp ZZ ,, , ht , ft , wt ,
***
,,, tttgt RYPZ .
There is 47 sequences of variables and thus 47 equations are needed to solve the
system. These are the equations numbered from (1) to (45) where (40) is actually a
set of three equations.
The model is too complex and does not have an analytical (closed form) solution. It
possible to get only approximate solution that is derived from numerical simulation of
model log-linearized around its steady state. However, in equilibrium some of the
variables contain unit root that comes from the technology shock ytZ (equation
(31)) and from foreign inflation (second equation in (40)). Under such conditions the
log-linearization is not accurate. The stochastically detrended variables wtt  , ,
21
tzyxtftht ,,,,  , hty remain stationary. The nonstationary variables are put into
stationary form using following transformations:
,,, *
*
*
ytt
t
t
ytt
t
t
ytt
t
t
ZP
W
w
ZP
B
b
ZP
B
b 
yt
t
t
t
new
tnew
t
Z
C
c
W
W
w  ,
t
Ft
ft
t
Ht
ht
ytt
t
t
yt
t
t
yt
t
tg
P
P
p
P
P
p
ZPZ
D
d
Z
G
Z 

 ,,,,, 
yt
t
t
t
t
Ht
new
Htnew
ht
t
Xt
xt
Z
Y
y
PP
P
p
P
P
p 

 ,,,*

.,,,,
*
*
*
1
*
*
yt
t
t
t
t
t
yt
d
Htd
ht
yt
xt
xt
yt
Ft
ft
Z
Y
y
P
P
Z
Y
y
Z
Y
y
Z
Z
y 
-

After these transformations of the variables one can derive stationary form of the
system, compute steady state and solve it. The steady state behaves as an atractor
or equilibrium to which the system converges when any deviation occurs. Those
deviations comes from innovations in the shocks processes (equation (30) to (38)).
The aim of the analysis is to study dynamics of the system around the steady state,
therefore the log-linearized form of the system is computed. The log-linearized
system is presented in Appendix A. The variables are expressed as deviation from
steady state, )(log^
x
x
x t
 , where for any variable tx , the variable without time
index x denotes steady state and tx^ is log-linear approximation. The log-linearized
system includes, besides other equations, four hybrid New Keynesian Phillips
curves: for wage inflation (A.15), for domestic prices inflation (A.16) and for import
prices and export prices inflation (A.17 and A.18). These equations capture rigid
behaviour of (nominal) prices.
The system is transferred into state-space representation and is solved using
Blanchard and Kahn (1980) procedure or its modification outlined in Klein (2000).
State-space form consists of transition equation (46) and measurement equation
(47).
11 = ++ + ttt SS S (46)
ttftf + S= (47)








******,,
,,,
=
tRRttyytmpZT
ttrpZytZ
wtfthttlsZtgZtcZ
t 



 K
where tS is vector of state variables and tf is vector of flow variables, t is vector
of innovations to shocks and t is vector of measurement errors for which hold
22
VE tt =)( ' and RE tt
~
' =)(  . The vector of state variables includes all the
predetermined variables ( 111111
*
1
*
11
^,^,^,^,^,^,^,^,^
--------- wtxtfthtttttt pppwcpbR  ,
11
^,^ -- ftht  , 11
^,^ -- htxt y ) and the exogenous variables ( tlsct ZZ ,
^,^ , rpmp
T
t ZZ ^,^,^ , ht^ ,
ft^ , wt^ ,
*** ^,^,^,^,^
tttzytgt RyZ  ). The vector of flow variables contains
(
ss
tttt Rprhd ^^^^ ,,, , t
d
htftxtt yyyy ^,^,^,^,^ , wttYHtct  ^,^,^,^ , ht^ , tttxtft srer ^^^^^ ,,,,  )
where three auxiliary variables were added for estimation purposes. They are the
growth rate of consumption ct^ , the growth rate of production of intermediate goods
tHY^ and the real exchange rate trer^ .
Elements in matrices S of format ( 1313× ),  of format ( 1313× ) and f of
format ( 1319× ) are nonlinear functions of the structural parameters of the model.
They do not have analytical solution and thus numerical procedures must be
involved to derive it.
14
The requirement of unique solution imposes some restrictions
on the parameter space that also cannot be expressed analytically. The unique
solution requires that the Blanchard-Kahn condition must be satisfied, i.e. the
number of the predetermined variables must be equal to the number of stable
eigenvalues of the system, which can be calculated only numerically.
3. EMPIRICAL STRATEGY
3.1. Variables selection
The model includes thirteen exogenous shocks that drive behaviour of the
endogenous variables. The parameters of the model cannot be estimated using
more than thirteen observable variables. Trying so, the stochastic singularity
problem can arise as discussed e.g. in Ireland (2004). It means that the covariance
matrix of the data becomes singular and the maximum likelihood estimation breaks
down. This is caused by fact that the model predicts deterministic relationship
between some endogenous variables but this relationship does not need to hold in
the data.
As the number of variables used for estimation is limited, the estimation results can
be influenced by choice of them. Therefore the choice of variables has to be
restricted to those of direct interest. Specifically, the choice should be motivated by
the research question about dynamics of wages and prices within the DSGE model.
The variables should help to identify parameters describing nominal rigidity and also
parameters of the shocks that directly affects behaviour of wages and prices. The
following thirteen variables were chosen to match their empirical counterparts: wage
inflation wt( ), inflation in prices of domestic intermediates )( ht , inflation of
imported goods )( ft , CPI inflation )( t , consumption growth )( Ct , production
14
E.g. Blanchard and Kahn (1980) or Klein (2000).
23
growth )( tHY , the labor input )( th , the real exchange rate )( trer , government
expenditures )( gtZ , nominal interest rate )( tR , foreign inflation )( *
t , foreign
demand )( *
tY and foreign nominal interest rate )( *
tR .
3.2. Taking theoretical variables to the data
Theoretical variables do not need to have exact definition in terms of observable
variables. Therefore some compromises and amendments of observable variables
must be made to conform the theoretical model. This issue is particularly important
because answer to the question, whether wages are more rigid than prices or vice
versa, is very sensitive to the exact definition of wage and price indices.
The data used for empirical analysis are quarterly, spanning period from 1996:Q1 to
2007:Q4. Time series are obtained from databases of the Czech Statistical Office
(CZSO), the Czech National Bank (CNB) and the European Central Bank (ECB).
15
The data are seasonally adjusted from source or adjusted by Kalman filtersmoother.
Domestic output )( tY is measured by gross domestic product, final
consumption expenditures of households is empirical counterpart for consumption
)( tC . Government expenditures )( tG are measured by final consumption
expenditures of government. Labor input ( th ) is represented by number of worked
hours. The consumer price index ( tP ) has same definition as empirical measure,
total wages and salaries correspond to wage rate )( tW in the model. Prices of
imported goods )( FtP is expressed by import price index. The gross nominal
interest rate )( tR is measured by 3 months Prague Inter Bank Offered Rate
(PRIBOR). Nominal exchange rate tS is exchange rates against the ECU/Euro. As
the CZSO do not have records of producer prices from domestic sources, the best
proxy variable for prices of domestic intermediate goods )( HtP is implicit price
deflator of gross domestic product which excludes, by definition, prices of imported
goods. Foreign sector is represented by Eurozone that includes 12 countries.
Foreign demand )( *
tY is measured by gross domestic product, price level )( *
tP by
deflator of final consumption of households and NPISHs and nominal interest rate
)( *
tR is 3 months EURIBOR. The aggregate variables ( tC , tG , HtY , th and
*
tY )
are divided by total employment to obtain per worker values.
16
The model is estimated in stationary form, thus the observable variables should be
tranformed into stationary form to match the theoretical counterparts. Most of the
variables are expessed as growth rates, thus first differences (of logarithms) were
calculated. This procedure applies for all types of inflation and consumption and
15
Appendix B deals with data sources in more detail.
16
Usual approach is to divide the aggregate variables by working age population to get per
capita values. However, the model assumes that all people in the economy work, the
expression of variables per worker is more appropriate.
24
output growth. These time series were also demeaned where the mean of time
series corresponds to steady state value.
Another approach was chosen for other variables. First, there is structural break in
hours worked during year 2001 that can be ascribed to demographical changes
which are not captured by model. To circumvent this problem, the Hodrick-Prescott
(HP) filter
17
was used for estimation of smooth trend that was then extracted. Hours
worked are then expressed as gap (deviation from trend). Second, there is
downward trend in the real exchange rate which is common in all transition
countries. It is usually explained by catch-up effect (or Balassa-Samuelson effect).
18
Simply said, increase in productivity causes increase of relative prices of
nontradable goods (to tradable goods). It subsequently induces increase in the
overall price level and hence appreciation of the real exchange rate. The paper does
not treat tradable and nontradable goods in the model framework and thus is not
capable to explain this phenomenon. Again Hodrick-Prescott filter was used to
detrend data series of the real exchange rate. Third, nominal interest rate exhibits
peak in 1997 and then downward trend. Calculated mean of the series indicates that
nominal interest rate has been under its equilibrium value since 2000. This does not
correspond to view of the Czech central bank. Therefore HP filter was used for
extraction of smooth trend (that expresses steady state) to get more interpretable
time series. The processes for exogenous variables are estimated separately.
Government spendings are assumed to follow AR(1) process. Foreign sector is
modeled as SVAR(1) which should remind basic New Keynesian gap model. The
corresponding series (government spendings, foreign output, foreign inflation rate
and foreign nominal interest rate) are detrended by Hodrick-Prescott filter and
expressed in gap form.
After transformation of the time series used for estimation test for presence of unit
root was proceeded to ensure that the series are stationary.
19
Table 1 summarizes
results of the test. One could reject the null hypothesis of a unit root for nominal
interest rate, all types of inflation, the real exchange rate and consumption growth at
significance level of 1 %. On the other hand hours worked and output growth were
found to be (1)I . Despite the fact that all theoretical variables are assumed to be
stationary, these two time series were used for estimation without any additional
transformation. However, to mitigate the nonstationarity problem, measurement
errors were added to the measurement equation for these two variables. In the
state-space representation of the system, measurement errors are stacked in vector
t in equation (47).
Foreign nominal interest rate was also found to be (1)I , but this time series is used
in separate estimation using ordinary least squares (OLS) method. Even if the
parameters of the foreign sector model can be biased, I belive that it does not have
important influence for estimation results of the main model.
17
Hodrick and Prescott (1997)
18
Balassa (1964), Samuelson (1964)
19
Augmented Dickey-Fuller test was used.
25
3.3. Estimation methodology
A combination of three methods -- calibration, maximum likelihood and Bayesian
estimation -- is used for identification of structural parameters of the model. Several
parameters are kept fixed throughout the estimation procedure. Some of them
relates to steady state values of the observed variables, therefore they are
calibrated to match their sample mean. Some parameters are calibrated just for the
reason to reduce the number of parameters for estimation.
The state-space form representation of the log-linearized system allows to use
Kalman filter algorithm for estimation of the model parameter via maximum
likelihood. The maximization of the likelihood is sometimes difficult in large systems
due to overparametrization. The likelihood is flat in some directions and parameters
can take corner solution. Next, the iteration process do not need to find global
maximum of likelihood function. Those problems can be partly eliminated using
Bayesian approach. It combines the likelihood with some prior information on the
distribution of the parameters to form the posterior density function of those
parameters. The prior density of the parameters give a shape or curvature to the
likelihood function which makes the optimization algorithm more stable. The prior
information downweights the likelihood function in the regions that are implausible or
in dissonance with economic theory or other empirical studies. Prior information can
be acquired from microeconomic studies or from results of estimation of similar
macromodels. They can be also based on expertize analysis or personal judgement
that reflect strong beliefs about economic behaviour even if the raw data does not
carry such information. This kind of expediency allows to introduce information from
outside of the modelling framework. It is initial guess of the value of each parameter
and associated uncertainty that is held a priori. Then the uncertainty of the guess is
reduced by means of likelihood function to arrive at the posterior. Hence, the
Bayesian approach can be thought of as a combination of maximum likelihood and
calibration methods.
According to Bayes' rule the posterior density )|( yp  is related to the prior density
)(p , the likelihood function )|( yp and marginal data density )(yp ,
)(
)()|(
=)|(
yp
pyp
yp


where  is unknown vector of parameters and y denotes data. As we are
interested in unknown parameters  which are not involved in )(yp , this term can
be ignored. Then, the posterior is proportional to likelihood times prior
).()|()|(  pypyp
The formula shows that the Bayesian approach to estimation in some sense tries to
pull the estimates of parameters to the values possessing prior information while the
maximum likelihood approach pulls those parameters to the values with good fit of
the model. In the end, one should get estimates that are plausible from the
economic point of view and also fit well empirically.
There is important distinction between Bayesian and classical approach to
inferences. The classical approach considers parameters as fixed (and unknown)
and the observed data are treated as realizations of some stochastic (data
generating) process. The goal is whether the data could be generated by particular
26
model given certain values of parameters. On the other hand, the Bayesian
approach treat parameters as random variables, while the observed data are fixed.
This simple theoretical concept offers broad range of possibilities including e.g.
model comparison based on model probabilities.
To make inferences about the parameters, one needs to compute moments of
posterior distribution. The posterior distribution does not have analytical solution,
therefore numerical solution using stochastic simulation is employed. This sampling
procedure uses Random Walk Chain Metropolis-Hastings algorithm. It is kind of
Markov Chain Monte Carlo (MCMC) algorithm that draws sample parameters from a
candidate density with equal weights but do not accepts all candidates. The
candidates draws are chosen according to acceptance probability. Finally, moments
of the function of interest are obtained thought Monte-Carlo integration of the
simulated values.
20
All the computations regarding Bayesian estimation are done using Dynare toolbox
(see Juillard (2004)) in Matlab software.
4. ESTIMATION RESULTS
The estimation process for maximization of the posterior distribution is
computationally demanding: the model is solved for each observation in each
iteration of the optimization procedure for the likelihood function. It can be partly
simplified by estimating some parameters separately. It is possible for those shock
processes that directly involve observable variables, namely government spending
shocks and the foreign sector. Those two sets of parameters are estimated by
ordinary least squares method; government spending as simple AR(1) process,
foreign sector as SVAR model. Treating foreign sector as exogenous is reasonable
assumption. The Czech Republic is small open economy; it behaves as price taker
on the world market and cannot affect the world variables. As shown by Musil (2008)
there are not important differences between modelling of behaviour of the Czech
economy with endogenous or exogenous foreign sector.
4.1. OLS estimation
As mentioned above, the parameters of government spending shock and foreign
sector are estimated separately given that corresponding shock processes involve
observables. The productivity shock ( ytZ ) that is unobservable is assumed to be
included in both government spendings ( tG ) and foreign demand (
*
tY ). To remove
it from observable variables, the time series of government spending and the foreign
demand are detrended using Hodrick-Prescott filter. The same procedure was
applied to foreign inflation and foreign nominal interest rate.
The results of estimation is shown in Table 2 and 3.
21
The government spending
shock is not very persistent, the value of AR parameter is 0.58. The innovation to
shock is also quite modest with standard deviation of nearly 2 %.
The variables in SVAR model for foreign sector are lagged by only one period.
Number of lags was chosen according to information criterions; whereas AIC implied
20
More details about the algorithm can be found in Koop (2003).
21
For the sake of transparency, parameters pertaining to foreign sector are quoted in matrix
notation.
27
two lags, and SBC and HQ implied one lag. The matrix pertaining to independent
variables (without lag), 0A , is lower triangular. This restriction is imposed from
identification purposes and is based on Choleski decomposition. All parameters in
matrix 0A have correct signs, **y
 is negative (-0.0716) and thus confirm positive
relationship between inflation and output gap in the reduced form of Phillips curve.
Parameters **yR
 and **yR
 are also negative (-0.0869 and -0.0549, respectively)
and also correctly describe positive relationship between nominal interest rate and
inflation and output gap in the interest rate rule. Matrix of lagged variables 1A is
quite sparse because some of the parameters were not statistically significant.
Negatively signed parameter that catches relationship between contemporary
inflation and lagged output is difficult to interpret. However, its value is less than
value of **y
 thus the positive impact of contemporary output gap overweights.
Other statistically significant parameters in 1A are correctly signed. Standard
deviation of innovations to individual equations are shown on diagonal of matrix F .
The influence of shock to interest rate rule is negligible, only 0.05 %. It implies that
behaviour of (foreign) nominal interest rate is almost perfectly explained by inflation
and output gap. Standard errors in demand equation and Phillips curve equation are
around 0.2 %.
4.2. Calibration
Because number of variables used for estimation is limited, not all the parameters
can be estimated precisely. As it is common in the literature, the accuracy of the
estimation is increased if some parameters are kept fixed throughout the estimation.
Usually, the parameters are calibrated to match their long-run averages in the data
or they are set at " reasonable" values based on some prior knowledge from other
empirical studies. Most of calibrated parameters relates only to modeľs steady state.
The calibrated parameters are summarized in Table 4.
The shock processes with the steady state different from unity (zero in log-linearized
model) cause that the steady state of the whole model is not uniquely defined.
Therefore ten additional conditions regarding steady states are needed to add. )(i
Output, consumption and government spendings should grow at the same rate in
the steady state. This growth rate is equal to the growth rate of technology.
However, the data shows that this assumption is not maintained. The output growth
rate is similar to growth rate in consumption, 1.0079 and 1.0075, respectively.
22
The
growth rate of government spendings is only 1.0045. Against this background, the
steady-state gross growth rate of technology is calibrated to =zy 1.005 which is
roughly 2 % on annual basis. This choice comes from necessary condition that  ,
the time preference parameter, must be less than one. As shown below, the growth
rate of technology together with the real interest rate implies the value of  . Thus,
this choice has rather pragmatic reasoning. Another justification is that the model
does not take into consideration population growth. The calibrated value can be
thought of as mixture of technology growth and population growth which was
22
The growth rate is expressed as quarter-on-quarter.
28
actually negative in the Czech Republic. The lower value of zy is reasonable
compromise. )(ii and )(iii The steady state level of elasticity of substitution across
different types of domestic and foreign intermediate goods, h and f , are both set
to 8, which implies a gross steady state markup of 1.143.
23
There are not any
microeconomic studies of these elasticities for the Czech data. Value for these
parameters were simply borrowed from Maih (2005) for Norwegian economy. Same
approach was chosen for )(iv the steady state level of the elasticity of substitution
across different types of labor input, w , which is set to 6, implying gross steady
state markup of 1.2.
Generally, it is quite difficult to pin down the values of elasticity of substitution
(especially for foreign intermediates) because lack of enough empirical evidence.
Those elasticities appear only in the steady state of the model which makes
impossible to identify them econometrically. The value of likelihood is independent of
those parameters. It may be worth exploring the impact of different values of those
elasticities on the results of the estimations and implications for the modeľs
dynamics. Sensitivity analysis is a possible approach, but this paper does not deal
with this issue and leaves it for further research. )(v The steady state level of
inflation target,
T
 , is set to the sample mean of CPI inflation. The Czech National
Bank has been operating in regime of inflation targeting since January 1998 which
covers almost the whole data sample used for the estimation and offers possibility to
use official measure of inflation target. However, the ways of inflation target
announcements was altered several times, they were discontinuous and also the
targeting variable changed during the time. The mean of CPI inflation is better proxy
for the inflation target. )(vi The steady state level of foreign inflation,
*
 , is set to
the sample mean of consumer prices inflation in Eurozone, )(vii the steady state
level of the foreign gross nominal interest rate,
*
R , is set to match the sample mean
of EURIBOR. )(viii For determination of the steady state level of detrended foreign
output,
*
y , the paper uses fact of constant export-to-output ratio which can be
computed from the data, yxkx /= ;
24
)(ix the stationary model also implies
constant government spending-to-output ratio, gk (again calculated from data),
which can be used for computing of the steady state level of detrended government
spendings ykZ gg = . )(x The model implies that discount factor,  , is related to
the steady state real interest rate by following formula:



zyR
= . With calibrated
23
markup =
1-h
h


24
Even if the model implies constancy of export-to-output ratio, it does not hold in Czech data.
There is increasing trend of this ratio. Alternatively, it is possible to use consumption-to-output
ratio as Maih (2005) did.
29
value of zy and steady state real interest rate calculated from data,
25
the discount
factor is equal to 0.9993.
The elasticity of intertemporal substitution

1
is set to 1 because that is the only
value for which the model is consistent with a balanced growth path. This is a
consequence of the additively separable parametrization of the utility function as
shown e.g. by King, Plosser and Rebelo (1988). Necessary condition for the
identification of shocks is to have as many observable variables as the number of
shocks. However, this condition is not sufficient. Both labor supply and wage markup
shocks enter the system through and only through the wage Phillips curve, as can
be seen in equation (A.15). Without any further assumption about how those two
shocks are correlated, none of them can be identified. The paper assumes wage
markup shocks to be persistent and labor supply shocks to be only temporary. This
identification assumptions implies that labor supply shock is i.i.d. 0)=( zls while
wage markup shocks follow autoregressive processes.
4.3. Bayesian estimation
4.3.1. The prior distribution
This section deals with setting of priors of the parameters before Bayesian
estimation. Priors can be thought of as beliefs about the likely location of the
structural parameters in the parameter space. Some regions of that parameter
space are not in accordance with the theory or model equilibrium. The priors are
chosen so as to preclude those regions and thus restrict the parameters to lie within
the boundaries specified by the theory. Table 5 reports estimated parameters
together with parameters' domain, distribution, prior mean and the standard
deviation reflecting the uncertainty about prior beliefs.
For parameters that lie between 0 and 1, beta distribution is used. The prior mean of
the habit persistence parameter )(hab is set to 0.7, which is value commonly used
in the literature. Its prior standard derivation is set to 0.1. The prior mean for  is set
to 0.2669 so that )(1 - matches the average import-to-output ratio calculated from
data. The prior mean for the persistence parameters (
lsZT 
, ,
rpZ ,
wfhyZ   ,,, ) is set to 0.4 with standard deviation .1. Smets and
Wouters (2003), Maih (2005) or Adolfson et al. (2005) use higher values of priors for
autoregressive coefficients of the shocks, usually 0.85. Higher persistence of shocks
can usually improve the fit of the model. However, I decided to choose lower prior
values of AR parameters based on discussion with experts from the Czech National
Bank. The reasoning is as follows. When the shock hits the economy, the agents
usually do not assume that the shock is persistent and will last for many periods.
This is quite relevant assumption especially for the Czech economy that has
experienced many structural changes during the transformation process and people
expect variable economic environment. Excessively persistent shocks could
misleadingly catch some important features of the economy that are under our
25
Sample mean of the real interest rate is 2.3% on an annual basis.
30
interest. Following Adolfon et al. (2005) the prior for smoothing parameter of interest
rate in the monetary policy reaction function ( ) is set to 0.80 with a standard
deviation of 0.05. High degree of interest rate smoothing of the Czech central bank
was also found e.g. in Musil (2008).
Stickiness in wages and prices reflects frictions in goods and labor markets that
causes propagation of exogenous shocks into the real part of economy. Parameters
expressing degree of nominal rigidity are closely related to our research question.
Even if the data experience of the Czech economy suggests that nominal wages are
more sticky than prices the prior mean is set to same value. It allows us to reveal
ultimate conclusion without influences caused by prior setting. The Calvo
parameters for imported intermediates )( f , domestic intermediates )( h exported
intermediate composite good )( x and wages )( w are all set to 0.75, which
implies that contracts change on average every 4 quarters. Standard deviation of
0.10 means that contracts can vary between 3 and 6 quarters.
26
For parameters that are assumed to be positive, such as the standard deviations of
the shocks,  , inverted gamma distribution is used. The prior mean for standard
deviations of the shock processes is set to 0.01. The prior mean for the standard
deviations of the measurement errors is set to 0.01 for both hours worked ( h ) and
output growth (
HY ). The paper allows measurement errors only in these two
variables because they contain unit root, as disscused above. There are no
measurement errors on the other variables because they are stationary processes.
The inverted gamma distribution is also used for the risk premium parameter  .
This parameter is assumed to be positive but small, the prior mean was set to 0.01.
For two parameters, the price elasticity of exports ( x ) and the Frisch elasticity of
labor supply (

1
) that are assumed positive and larger, gamma distribution is
chosen. The prior mean for the price elasticity is set to 0.8 with standard deviation
0.05. The Frisch elasticity of labor supply is quite controversial and is usually
calibrated. References in Maih (2005) report values that vary from 1/3 to 1,
depending on the study. Since there is not any study about labor supply elasticity for
the Czech economy, the paper uses Maih's prior values: mean of  is set to 3 and
standard deviation to 1.
The remaining parameters are the coefficients of the monetary policy reaction
function for which the normal distribution is chosen. The parameter that describes
reaction of central bank to inflation (  ) has prior 1.70 and standard deviation 0.1.
Weight of reaction to output gap ( y ) is assumed much smaller, the prior mean is
set to 0.1 and standard deviation to 0.05.
26
Average length of contracts comes from formula:
-1
1
.
31
4.3.2. The posterior distribution
The joint posterior distribution of the vector of parameters is obtained in two steps by
using numerical algorithms. First, the posterior mode and Hessian matrix evaluated
at the mode are computed by standard numerical optimization routines (Christopher
Sims' csminwel function). The likelihood function is computed first by solving the
model and then using the Kalman filter. Figure 4 and 5 shows the curvature of the
objective function at the mode for each estimated parameter. The algoritm did not
find evident minimum for parameters  and w thus they are not properply
identified. Then, there is a second step that generates samples from joint posterior
distribution to carry out Bayesian inferences. Specifically, Random Walk Chain
Metropolis-Hastings algorithm is used. The algorithm starts from the mode and
generates 1,000,000 draws from the posterior distribution. 50 % of replications are
discarded so as to avoid influence of initial conditions. The moments of the posterior
distribution are computed through Monte-Carlo integration of the remaining draws.
The average acceptance probability of candidates was 0.32. Markov Chain Monte
Carlo diagnostics were used for convergence verification of the algorithm.
Figure 6 and 7 shows prior distribution (grey line) and posterior distribution (black
line) together with posterior mode (dashed green line) for each of the estimated
parameters. Table 4 shows the results from the Bayesian estimation. The structural
parameters and their domain are presented in the first and second column. The third
up to the fifth column summarizes moments of the prior distribution. The mode and
the standard deviation of the posterior maximization are reported in the sixth and
seventh column. The eighth column shows the posterior mean together with the 5th
and 95th percentile of the posterior distribution (ninth and tenth column). The last
two columns thus constitute the 90 % confidence interval.
Let us start interpretation of the results with the parameters describing preferences
of households. The habit formation ( hab ) seems not so important, its posterior
mean is 0.6937, lower than the prior value. The mean of the Frisch labor supply
elasticity (inverse of  ) is
2.7062
1
which indicates that labor adjust quite slowly to
the real wage movements. However, this estimated value should be taken with care
because time series of hours worked was found nonstationary and enter the
estimation with measurement error.
The estimated Calvo parameters ( f , h , w , x ) express degree of nominal
rigidities and are key element in answering the research question. The estimated
Calvo parameters express degree of nominal rigidity. The average duration of wage
contracts is nearly 7 quarters and that of price contracts for domestic intermediates
is only 1.7 quarters.
27
It indicates that wages adjust more sluggishly than domestic
prices. More importantly, according to this measure, wages are the most rigid and
domestic prices are the most flexible nominal prices. Calvo parameters (and
contracts duration) for other nominal variables lie between these two values.
Average duration of price contracts for imported intermediates is 4 quarters and for
exported intermediates 2.7 quarters. The point estimate of Calvo parameter for
27
Average duration of contract is calculated using formula
-1
1
.
32
domestic prices deviated from the prior value more than three times the standard
deviation. However, this result turned out to be robust outcome of the estimation
procedure. Parameter  expresses openness of the economy. More precisely
)(1 - should capture share of imports to output. Posterior mean of  is 0.1629
which indicates much higher openness than the prior value. Labor share in the
production function, parameter  , was estimated to 0.6498. It is quite reasonable
value, as the capital share
28
is usually calibrated to one third. However, it is higher
than value obtained from other sources; e.g. Hloušek (2007) reports average labor
share 0.59, calculated as total labor cost to gross value added.
The monetary policy reaction function shows very high interest rate smoothing.
Mean of the parameter corresponding to the lagged interest rate,  , is 0.8972. This
value seems to be too high in comparison with rhetoric of the Czech National Bank
about inflation targeting as the main strategy. However, similar values were found by
Musil (2008), and other authors. Weights on inflation and output in the reaction
function,  and yh , are very similar to the priors; emphasis on inflation targeting
is sixteen times higher than on output stabilization. But as can be seen from Figure 7
these two parameters were not identified appropriately from the data. The difference
between the prior and the posterior distribution was negligible which indicates that
the parameters are rather calibrated than estimated.
The price elasticity of export function, x , is rather high compared to the prior mean.
Risk premium was estimated to about 2 % p. q. Such high value should be attributed
mainly to the financial crisis in 1997.
Looking at the autoregressive parameters of the shocks, the most persistent shock
is the risk premium shock ( zrp = 0.5719). On the other hand, the least persistent
are the shocks to price markup of imported intermediates (
f = 0.1705) and
markup of domestic intermediates (
h = 0.3151). Other autoregressive shock
processes exhibit inertia not far from the prior value.
Looking at the volatility of the shocks, labor supply shock and shock to markup of
imported intermediates are the most volatile (
lsZ = 0.1415,
f = 0.1321.) Quite
substantial is also wage markup shock,
w . Productivity shock and monetary
policy shock are the least volatile,
yZ and
mpZ respectively. The measurement
error of output growth is relatively small, measurement error of hours worked is more
substantial but still acceptable. Their impact on the overall fit of the model could be
considered as negligible.
4.4. Assessing the fit
Although the DSGE model has firm economic foundations, it may have problems to
replicate the data, because it is too stylized. The assessing of the fit of the model is
carried out along three dimensions. Firstly, the fitted series are visually compared
28
Complement to one, )(1 - .
33
with the observed series. Secondly, the volatility and the autocorrelations implied by
the model are compared with the statistics calculated from the data. And thirdly,
estimated unobserved shocks should reflect important events in the Czech
economy.
4.4.1. Filtered vs. observed variables
Figure 8 provides qualitative fit of the DSGE model to the data. Observed time
series (solid line) can be compared with the one-period-ahead forecast obtained
from Kalman filter (dashed and dotted line). Filtered and smoothed variables are
computed at the mean of the posterior distribution. Overall fit of the model is more or
less satisfactory at the first sight. Nominal interest rate and CPI inflation has the best
fit. Nominal interest rate can be perfectly measured, the result is in accordance with
what one would assume. Other filtered variables mostly record the right direction,
however their volatility is smaller. But not always, the model predicted more
significant drop in consumption growth at the end of 90's than the data shows.
Model behaviour of wage inflation is in accordance with the data from 2000 or so.
Time series of output growth and hours worked were introduced with the
measurement error and thus poor fit of these model variables can be ascribed to this
fact. Prediction of hours worked looks like being lagged, especially in the mid of the
sample period. Very significant differences are in inflation of import prices. This
variable was introduced without measurement error, however the algorithm returned
quite substantial measurement error and filtered import inflation closely to CPI
inflation. This is the most severe problem of the model fit, however I belive that its
implications for wage-price dynamics is not so critical and it does not influence the
principal research question in important way.
4.4.2. Unconditional second-order moments
Common practice in the Real Business Cycle literature for model evaluation is
comparison of model statistics (mostly variances and correlations) with statistics
from the data. Here, I focus only on the volatility and autocorrelations (not crosscorrelation)
of the variables used for Bayesian estimation. Table 7 presents standard
deviations computed from the data and the theoretical standard deviation predicted
by the model (for the estimated vector of parameters). As the table shows, the most
volatile variable is the real exchange rate while nominal interest rate is the least
volatile. DSGE model succeeded in replication of these magnitudes pretty well. The
volatility of output growth is also almost the same. Differences in volatility of hours
worked, consumption growth and CPI inflation are not large. However, the model
overestimates volatilities in wage inflation and underestimates volatility in import
inflation and domestic inflation. Overall fit of the model regarding these statistics is
quite satisfactory.
The benchmark for comparison of autocorrelations is unrestricted first order VAR.
Figure 9 shows autocorrelations implied by DSGE model (dashed and dotted line)
and VAR model (solid line) for the same set of variables as above. The DSGE model
replicates autocorrelations of the real exchange rate, domestic inflation and
consumption growth quite well, but it fails in other variables. Magnitude of
autocorrelation of nominal interest rate is systematically higher than in the data.
DSGE also fails to capture short run autocorrelation of CPI inflation and output
growth and medium run autocorrelation of labor (hours worked). Autocorrelation
functions of VAR and DSGE model only intersect for wage inflation and import
inflation at lags of four. All these discrepancies can be caused by the fact that the
34
VAR is not the process that generates data and that, due to unobserved variables,
the DSGE does not have VAR representation.
4.4.3. Kalman smoothed unobserved shocks
Estimates of the unobserved variables (shocks) are presented in Figure 10. The
shocks are smoothed by Kalman filter and are also computed at the mean of the
posterior distribution. Most of the shocks follow autoregressive processes and their
behaviour can be linked with estimated values of AR parameters.
29
The AR
coefficients are quite small (around 0.4) and the degree of persistence is not so
visible. Risk premium shocks should be the most persistent ( =Zrp 0.59), but it is
apparent only at the end of time series. Consumption preference shocks and
productivity (technology) shocks have similar AR coefficients ( =Zc 0.44) and
=zy 0.42), but their behaviour is totally different. Productivity shocks look more
persistent.
The smoothed shocks can be related to events in the history of the Czech economy.
Most of the shocks exhibit higher volatility at the beginning of the sample period.
This is certainly connected with the crisis in 1997. This period was characterized by
high interest rates which can be detected in monetary policy and risk premium
shocks. The recession was characterised by negative output growth which can be
ascribed to negative technology shock. Regime of inflation targeting was introduced
in January 1998. Period before the transition to this regime and the first year of its
functioning is characterized by high volatility of inflation target shock. Higher inflation
at the end of 1990s can be associated with domestic prices markup shocks. It must
be mentioned that wage and import prices markup shocks are large in terms of
volatility compared to other shocks (look at the scale). However, their role in
explaining some economic events is limited. They do not exhibit any systematic
pattern and looks stationary. Government spendings were also negatively influenced
by the recession. But from 2001 onwards, the government budget benefited from
growing economy. Economic slowdown in 2002 in the Czech economy can be partly
explained by weak foreign demand. Similarly, negative foreign inflation shocks
contributed to low (or decrease of) CPI inflation before 2000 and after 2002.
4.5. Dynamical properties of the model
This section studies dynamical characteristics of the model using variance
decomposition and impulse response functions.
4.5.1. Variance decomposition
Variation of selected endogenous variables can be decomposed into contribution of
each shock using variance decomposition. It enables to infer the importance of the
thirteen exogenous shocks in fluctuations of the variables. Table 8 presents
unconditional asymptotic variance decomposition, i.e. forecast error variance of the
variables in the long run horizon. The considered variables are following: real and
nominal interest rate, real exchange rate, CPI inflation, domestic prices and wage
inflation, consumption growth, output growth and labor (hours worked). The shocks
are divided into three groups. Real shocks include consumption preference shock,
technology shock and labor supply shock; nominal shocks are wage markup shock,
price markup shocks (of domestic goods and imports), inflation target, risk premium
29
Monetary policy shock and labor supply shock are i.i.d. and thus are equal to innovations.
35
and monetary policy shocks. Last group contains shocks in foreign economy and
government spending shock.
Foreign shocks have negligible effect for behaviour of selected variables. Only
foreign output shock can explain 20 % of the variation of domestic output growth.
Government spending shock is also insignificant. On the other hand, the most
important shock is shock in markup of import prices. It has substantial effects not
only for nominal but also for real variables.
Shock to wage markup, which is assumed to be persistent, is then second most
important driving force in variation of hours worked. It comes as no surprise that
consumption preference shock explains most of the variation in consumption growth
(65 %) and productivity shock of the output growth (nearly 40 %). Risk premium
shock has significant impact on movements of the real exchange rate. Its
contribution to variation in hours, output growth and nominal interest rate is about
11 %.
Besides import prices markup shock, large part of variation in the domestic prices
and wage inflation are explained by (domestic) price markup and wage markup
shocks, respectively. Even if labor supply shock was assumed i.i.d. (not persistent) it
accounts for almost 11 % in variation of wage inflation.
As it was mentioned above, the import prices markup shock is principal mover in
nominal variables, especially in import and CPI inflation (more than 77 and 74 %
respectively). It indicates that the Czech economy must confront inflation pressures
mostly from abroad. Inflation target and monetary policy shocks are more or less
evenly spread among all analysed variables. Their contributions in explaining
variation of overall inflation are 4.6 and 7.4 % respectively. It shows that the Czech
National Bank pursue good monetary policy.
4.5.2. Impulse response function
The dynamic behaviour of the model can be also studied using impulse response
function. The model is hit by one-period unitary shock (innovation) and behaviour of
endogenous variables in reaction to that disturbance is simulated. Reported
variables are real and nominal interest rate, real exchange rate, CPI inflation,
domestic and wage inflation, consumption growth, output growth and labor (hours
worked) and, if appropriate, import inflation, imports and exports. In figures from 11
to 23, time horizon (in quarters) is measured on the horizontal axis, the vertical axis
expresses percentage deviation of the variable from steady state.
30
The size of the
shock is one standard deviation of the stochastic variable. The shocks can be
divided into two groups, similarly as in Juillard et al. (2006). Demand shocks
produce positive correlation between inflation and real GDP in the short run, while
supply shocks imply negative short run correlation between these two variables. Due
to this classification, demand shocks considered in this paper are: consumption
preference shock ( cZ^ ), the inflation target shock (
T
^ ), the risk premium shock
( trpZ ,
^ ), the monetary policy shock ( tmpZ ,
^ ) and the imported intermediates price
markup shock ( ft^ ) and all shocks in foreign economy (
*
^ty ,
*
^t and
*^
tR ). Group of
30
Used notation is e.g. 0.10 which means 10 %.
36
supply shocks includes the government spending shock ( tgZ ,
^ ), the domestic price
markup shock ( ht^ ), the wage markup shock ( wt^ ), the technology shock ( zyt^ ), the
labor supply shock ( tlsZ ,
^ ).
Consumption preferences shock [figure 11]
Higher consumption demand increases production and thus demand for labor input.
Increased labor demand induces wage inflation which pushes up also prices.
Central bank reacts by increasing interest rate. However, increase in inflation is
higher and the real interest rate decreases. Real exchange rates depreciates in
reaction to the (real) interest rate differential.
Technology shock [figure 12]
The productivity shock is not so persistent as one would expect. Production and
consumption increase, part of output (of intermediate goods) is exported. Higher
productivity is followed by increase of worked hours which pushes the wages up.
However, the total marginal cost of firms decreases (without reducing their profits)
and firms can reduce their markups. It lowers domestic inflation. Overall inflation
also decreases and the central bank reacts by decrease of nominal interest rate.
Decrease of inflation is more significant therefore the real interest rate increases and
the real exchange rate appreciates.
Wage markup shock and Labor supply shock [figure 13 and 14]
An increase in wages raises cost of production of domestic intermediates which
causes decrease of the demand for labor. Wage inflation is transmitted into price
inflation, but only for domestic good. Overall CPI inflation after initial small jump
decreases. Central bank lowers interest rate to stabilize the economy, because
production is also below its potential. In spite of it the real interest rate increases and
the real exchange rate appreciates to satisfy (real) UIP condition. The effects of
labor supply shock are qualitatively very similar to the wage markup shock, only the
size of deviations is smaller.
Monetary policy shock [figure 15]
The contractionary monetary policy represented by sudden increase in nominal
interest rate causes recession in the economy -- drop in output growth and inflation.
Decline of inflation is hump shaped because prices are sticky. Combination of high
nominal interest rate and fall in inflation implies that the real interest rate rises even
more and the real exchange rate appreciates. High real interest rate increases the
opportunity cost of consumption which depresses domestic demand as consumers
shift their consumption into the future. Weak demand for output forces domestic
produces to decrease demand for labor input.
Inflation target shock [figure 16]
Inflation target shock causes initial decrease of nominal interest rate which allows
inflation to increase. Decline in the real interest rate is connected with sharp
depreciation of the real exchange rate and increase of consumer demand (which is
more profitable today than in the future). Higher consumer (and export) demand is
satisfied by higher production which leads to increase of hours worked.
37
Risk premium shock [figure 17]
Risk premium shock induces large exchange rate depreciation (in real terms). It
enhances export of intermediates, because they are cheaper for foreigners. The
exchange rate depreciation is passed-through into import prices. Import price
inflation leads to fall in imports and to increase of the overall inflation. The central
bank reacts by increase of interest rate. Even if the real interest rate decreases,
consumers do not switch consumption form future towards today. Higher production
of output is rather exported than consumed. It follows that the number of hours
worked increases.
Government spending shock [figure 18]
Reaction of the economy is quite similar to consumption shock. There is an initial
increase in the aggregate output which is produced by employing more labor.
However, government spending crowds out private consumption which decreases.
All types of inflation increase and follow hump-shaped pattern. Central bank reacts
by increasing interest rate. Again, the real interest rate decreases which is
accompanied by real exchange rate depreciation.
Domestic price markup shock [figure 19]
An increase in the markup of domestic producers increases domestic and also
overall inflation. However, this increase is only one-shot and inflation switches into
negative values. The production follows similar but reversed pattern. Labor demand
decreased together with wage inflation. To restore the equilibrium in the economy,
central bank gradually lowers interest rate. However, as the inflation was below the
equilibrium, the real interest rate increased and the real exchange rate appreciated.
Appreation has negative effect on exports and higher consumption demand was
satisfied by higher imports.
Import price markup shock [figure 20]
An increase in the markup of importers is passed through import inflation into CPI
inflation. The amount of imported goods decreases. The central bank reacts to
inflation in the economy and increases interest rate. The increase in the nominal
interest rate is not sufficient and the real interest rate decreases which makes the
real exchange rate to gradually appreciate. Production increases only a little, but
allows a rise in worked hours. Consumption is negatively affected by decrease in
imports.
Foreign interest rate shock [figure 21]
Shock in foreign interest rate causes (through uncovered interest parity condition)
depreciation of the real exchange rate. It enhances domestic production and labor
demand. Output is rather exported than consumed by households. Depreciation of
the real exchange rate has negative effect on imports because they are more
expensive. Expansion in home economy is accompanied by increase in all types of
inflation. Central bank reacts by rising nominal interest rate to bring the economy
back to equilibrium.
Foreign output and foreign inflation shock [figure 22 and 23]
Shock to foreign output affects home economy through another channels, even if the
impacts are quite similar. Part of higher foreign production is imported and
consumed in home economy (increase in imports is long-lasting). Increase in output
growth is one-shot. Initialy higher labor demand returns to steady state more
38
sluggishly. Inflation in the economy forces central bank to increase nominal interest
rate. The real interest rate decreases as the real exchange rate depreciates.
Reaction of the economy to the shock in foreign inflation is qualitatively very similar
to the shock in foreign output. Exception is volume of imports that responds only
temporary for the foreign inflation shock. Quantitatively, the size of deviations is
smaller in case of foreign inflation shock.
4.6. Further implications of the model
4.6.1. Implications for exchange rate pass-through
Figure 24 shows how changes in the exchange rate slowly pass-through into
domestic prices, import prices and consumer prices. It must be mentioned that all
prices and exchange rate are endogenous variables, which means they are
interdependent. Adjustment of the prices following changes in exchange rate cannot
be interpreted as the exchange rate pulls the prices. The degree of exchange rate
pass-through can be inferred from the distance between the line representing
nominal exchange rate and the lines of corresponding variables (prices).
Exchange rate is flexible, it usually jumps and then gradually moves to new level.
Behaviour of prices is regulated by contracts, thus the prices evolve only gradually.
High flexibility of domestic prices is evident in the plots and is consistent with low
value of estimated Calvo parameter.
Exchange rate pass-through is very fast in case of monetary policy, inflation target
and risk premium shocks. The complete adjustment of all the prices is no longer
than fifteen periods.
31
Pass-through into the CPI is faster than into the other prices in
response to all shocks. This result is in contrast to findings of Maih (2005) and
Ambler et al. (2003). They found out that pass-through to import prices is the
quickest.
32
Quite surprising result is that the pass-through is not complete in the long
run horizon for domestic prices and even import prices for some types of shocks. It
can be explained by fact that domestic prices are quite independent of exchange
rate movements and are influenced only indirectly. Or from the other side, some
types of shocks have direct impact on domestic prices but exchange rate is subject
to other forces. This is certainly the case of domestic prices markup shock, wage
markup shock, labor supply shock and technology shock. Following three former
shocks, domestic prices initially increases but the nominal exchange rate
appreciates. It confirms the view that domestic prices " live their own life" . In case
of import prices markup shock, exchange rate and other prices behave similarly, but
domestic prices converge to different level in the long run. Why pass-through into
import prices is incomplete in the long run for some type of shocks remains puzzle.
Regarding foreign economy shocks, the speed of pass-through for import prices and
CPI is quite high (again around fifteen periods) with domestic prices approaching in
the long run horizon. Similarly for consumption preference shock. In case of
government spending shock, pass-through to all prices is complete after twenty five
periods.
31
The word "complete" is not accurate. There is still small gap between nominal exchange
rate and domestic prices, even in the long run. However, I neglect this discrepancy as it can
be covered in the confidence interval of impulse responses that are not shown here.
32
Import prices follow CPI very closely, but there remains small discrepancy between import
prices and exchange rate for some types of shocks.
39
This analysis shows that exchange rate pass-through is conditional on the stochastic
shocks which can influence prices and exchange rate in different way.
4.6.2. Implications for wage-price dynamics
The point estimates of Calvo parameters indicates how often the contracts change,
but they do not say anything about the dynamics of wages and prices. Again as in
the previous subsection, wages and prices are endogenous variables which means
that they do not affect each other directly and they are subject to many other
influences. Figure 25 shows impulse responses of wages (solid line) and consumer
price index (dashed line) in reaction to exogenous shocks. Overall impression is
similar to exchange rate pass-through analysis. Behaviour of the variables depends
on the type of shock and considered time horizon. Wages and prices behave almost
identically in case of monetary policy and inflation target shock. The prices change
quicker (lead) than wages for most of the shocks.
33
However, wages are significantly
more volatile than prices for labor supply, wage markup and technology shocks. It is
intuitive, because these shocks influence the process of wage setting directly.
Wages and prices do not need to move in the same direction in the short run.
Examples of such behaviour are responses to price markup shock and technology
shock. In the case of technology shock, prices and wages diverge even in the long
run (wages come to higher and prices to lower level than before the shock). At long
run horizon wages and prices do not converge to the qualitatively and quantitatively
same level for many shocks. The reasoning can stem from high openness of the
Czech economy. Wages are the main component of domestic prices, but large part
of CPI is composed of import prices and they are determined on different markets.
5. SENSITIVITY ANALYSIS
5.1. Relative importance of wage and price rigidity
This section focuses on assessment of relative importance of nominal rigidities in
the model. Special attention is devoted to wage and price rigidity.The subject of
interest is comparison of competing models in terms how they fit the data. These
competing models assume flexibility in some of the prices or combinations of them.
Marginal likelihood based on Bayesian estimation is first measure of fit. Second
measure looks at vector autocorrelation function.
5.1.1. Marginal likelihood
Quantitative measure of data fit provides marignal likelihood calculated from
Bayesian estimation. The Bayesian estimation overcomes maximum likelihood
estimation because it takes into account the uncertainty that comes from the models
or the estimates of shocks and parameters.
34
Because the priors play key role in
Bayesian estimation and can influence results in important way, it is necessary to
set the priors of all estimated parameters for all models to their initial values. It is
exceptionally important for the sensitivity analysis.
33
Leading behaviour is very subtle but is noticeable.
34
However, as Del Negro and Schorfheide (2008) pointed out standard setting of priors need
not be the right guide for discrimination among different theories. They suggest alternative
approach for choosing the priors that is based on quasi-likelihood function with the aim of
'levelling the playing fielď. However, I believe that this new approach do not have substantial
qualitative influence for the results presented here. Nevertheless it could be interesting topic
for further research if and how the results are quantitatively different.
40
The competing models are derived from the benchmark model (with all rigidities) --
they allow flexible prices in particular sector. The term flexibility (or no habit
persistence) means that corresponding parameter is set to 0.2.
35
The analysis considers following specifications: the benchmark model is denoted
BM, the model with flexible import prices FIP, the model with flexible domestic prices
FDP, the model with flexible wages FW and the model with flexible export prices
FEP. Then some combinations with rigidities in two or more sectors are: the model
with flexible domestic and export prices FDEP, the model with flexible domestic,
import prices and no habit formation FDIPH and model without nominal rigidities
FWDIEP.
36
Table 9 presents estimated parameters of competing models together with Laplace
approximation of the log data density. The models are ordered according to the
value of log data density which measures fit of the data.
The results of the analysis are quite surprising. The model with flexible domestic
prices fits the data better than the richer benchmark model. Also model with
assumption of flexible domestic and export prices overtook the benchmark model.
With focus on relative importance between price and wage stickiness it is obvious
that these rigidities are not interchangeable. Specifically, wage rigidity is more
important than price rigidity. It is confirmed both by triumph of FDP model and by
poor fit of FW model. It also corresponds to empirical fact that real wages behave
countercyclically in the Czech economy.
Next, the results indicate that extension of the model by rigidities in export market
(compared to Maih's (2005) original model) has only small effect. Difference
between benchmark model and that with flexible export prices is not so significant.
The model without nominal rigidities and with only real rigidity (habit in consumption)
has the worst fit of all models. It suggests that nominal stickiness is important
phenomenon. However, it is not universal for all prices. The most important nominal
frictions in the Czech economy are rigidities in wages and import prices.
Interesting fact is how the model parameters compensate the lack of rigidity in
particular sector (compared to the benchmark model). The most striking difference is
in estimates of Frisch elasticity of labor supply ( /1 ) which decreases from
1/2.7062 for the benchmark model to 1/3.9320 for the flexible wage model. It implies
that labor supply is more unresponsive to changes in the real wage. In other words,
the nominal rigidity in wages is transferred to rigidity in labor supply.
Another structural parameter that is highly volatile for different specifications is  . It
expresses openness of the economy; more precisely )(1 - should capture share
of imports to output. However,  also regards to the price index, it expresses weight
of domestic prices in the CPI. Because the nominal time series (inflation of domestic
prices, import prices and CPI) are used for estimation this influence is probably more
important for the results. Value of  fluctuates from 0.1629 for the benchmark
model (very open economy) up to 0.5128 for flexible import prices model. The
35
For behaviour of prices it means that the contract is changed once in 1.25 quarters.
36
Some other specifications as the models with flexible domestic and import prices FDIP plus
flexible export prices FDIEP were also analyzed. Their performance to fit the data is not
significantly different from FDIPH model, so they are not presented here.
41
domestic prices thus increased their ability in explaining (rigid) behaviour of CPI
index. Low value of 0.094 for flexible wage model shows extreme openness to
trade. This result is quite puzzle and can stem from mutual influence of more
parameters for this specification.
Autoregressive parameter of shock to import prices is also highly volatile. It
increases (from 0.17 ) to value around 0.52 for all models with flexible import
prices. The model tries to explain higher persistence in import prices by shock
behaviour.
This approach also enables to assess importance of measurement errors introduced
in the estimation. Measurement errors remain quite stable for all specifications of the
models; the only exception is measurement error in output growth which slightly
increased for models which include flexible import prices. However, in general the
results indicate that measurement errors have negligible effect for the fit of the
models.
Similar analysis could be applied to shocks and their volatility. The most important
shocks (with largest standard deviation) are labor supply shock and markup shocks
to import prices and to wages. These shocks also vary most of all which indicates
quite high sensitivity to the type of rigidity. It is quite hard to find some stable pattern
across the models. However, it seems that higher flexibility of particular prices
reduces the standard deviation of relevant shock. This is true e. g. for import prices
and shock to their markup.
5.1.2. Vector autocorrelation functions
This section looks at vector autocorrelations of the variables used in Bayesian
estimation. This is done for three specifications of the model: flexible domestic
prices model and flexible wages model are compared to each other and with
reference to the benchmark model. The considered variables are hours worked,
output growth, consumption growth and the real exchange rate as the real variables
and wage inflation, domestic inflation, import inflation, CPI inflation and nominal
interest rate as the nominal variables.
Figure 10 plots correlation up to tenth order of these variables for BM (solid line),
FDP (dashed and dotted line) and FW (dotted line) model. Persistence of the
variables is shown on the diagonal plots. Autocorrelations implied by FDP are pretty
much same as in the BM case for all the variables. FW model shows lower short-run
persistence
37
especially for wage inflation (plot(5,5)), but partly also for domestic
inflation, consumption and output growth and labor. In the medium run,
38
the
persistence of these variables is little bit higher for flexible wage model compared to
the benchmark. Looking at the off-diagonal correlations, there are many statistics,
but most of them provide similar picture. Flexible domestic prices model matches
correlations very closely to the benchmark model. Correlations implied by flexible
wages model are usually smaller and sometimes close to zero. Correlation of wage
inflation with the nominal variables is an illustrative example (fifth row). Similar
pattern shows also correlations of many variables with worked hours (first column).
Cross-correlation function of labor with wage inflation and domestic inflation follow
hump shaped pattern for FW model, but for FDP and BM it gradually decreases,
37
Up to 5 periods.
38
From 5 to 10 periods.
42
even into negative values (plot(1,5) and (1,6)). Neither FW nor FDP can match
medium run correlations of import and CPI inflation with consumption growth that is
present in benchmark model (plot (7,3) and (8,3)). Correlation of wage inflation and
domestic prices inflation with growth of consumption is different for all models and
for all lags (plot (4,3)).
To summarize it, assumption of flexible wages is at odd in matching the statistics of
benchmark model. This result further support the view that wage rigidity is more
important than price rigidity.
5.2. Is wage and price rigidity interchangeable?
This section further examine whether wage and price rigidity is interchangeable or
not. This is done by comparison of impulse responses for different model
specification, i.e. with different assumption about nominal rigidity. The considered
models are again the benchmark, the flexible wages and the flexible domestic prices
model. Figures 11 and 12 show impulse responses of these variables: labor, output
growth, consumption growth, CPI and wage inflation, the real interest rate and the
real exchange rate, to all shocks except the foreign shocks. The responses are
computed using the vector of parameters at the mean of posterior distribution.
The impulses response for the benchmark model (solid line) and flexible domestic
prices model (dashed and dotted line) are very similar. Significant differences are
evident only for the wage markup and labor supply shock (figure 12, fourth and fifth
row). For the latter shock, the variables in benchmark case are more volatile.
Differences between flexible wages and the benchmark model are apparent
especially in behaviour of hours worked and wage inflation. Under the assumption of
wage flexibility, responses of labor are not so hump shaped, return is faster and
initial reaction is sometimes opposite than in benchmark case (figure 11, first
column). Wage inflation is more volatile, but returns quickly to the equilibrium. Fast
adjustment of the variables is characteristic also for many other variables and
shocks in flexible wage model. These observations confirm that behaviour of the
variables in time is sensitive to the assumptions about the source of nominal rigidity
and that wage rigidity is not tantamount to price rigidity.
6. CONCLUSION
This paper examined importance of nominal rigidities in DSGE model of the Czech
economy with emphasis on wage-price dynamics. Results of estimation revealed
quite clear conclusion. Estimated length of Calvo contracts suggests that wage
stickiness is more important than price stickiness. The model approach allowed to
investigate the dynamics of wages and prices in more detail. The impulse response
funciton showed that adjustment of prices is faster than of wages for many
stochastic shocks. Next, prices and wages need not move in the same direction and
can converge to different levels. Their joint dynamics depends on type of the shock
and considered time horizon. Sensitivity analysis showed that assumption of flexible
nominal wages is flawed feature of the model and do not fit data well. On the other
hand, model specification with flexible prices are in accordance with the data. It
means that rigidity in wages is more important than in prices. Impulse responses for
alternative models (with different assumptions about nominal rigidities) illustrated
that the source of nominal rigidity has important impacts for behaviour of several
variables, especially in the short and medium horizon. It was also confirmed by
vector autocorrelations. The price rigidity is thus distinguishable from wage rigidity.
43
The analysis made in this paper naturaly suggests several ways for further research
on both theoretical and empirical level. The model can be extended by investment
sector with real rigidity expressed by adjustment cost, as in Adolfson et al. (2005).
Another interesting extension could be dividing the production into tradable and
nontradable goods, as it is modeled by Musil (2008).
On the empirical level, the sensitivity analysis can be carried out using Global
sensitivity analysis (GSA) techniques propagated by Ratto (2008). This approach
can more effectively show possible weaknesses of estimation process or
relationship between data series and parameters or between structural parameters
and parameters of the reduced form. Next, the setting of priors (quasi-likelihood
based priors) for Bayesian estimation as suggested DelNegro and Schorfheide
(2008) can have quantitative impacts for the result. They are worth to be examined.
44
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46
A Stationary log-linearized system
Definition of deviation of variable from trend: )(log^
x
x
x t
 .
The risk premium
( ) trptttt Zybrer
y
b
rerpr ,
*
*
= ^^^^^ +-+- (A.1)
The budget constraint
=1)( *
*
*
*
*
t
zy
t
zy
b
rerb
rer
rerb ^^



+(
)ttzttt
zy
ththhhthh prRb
rerb
yyyyppyp ^^^^^^^^ 

++--+-+ -
***
1*
*
(A.2)
The consumption demand
( ) ( )tzytt
zyc
tt
c
tC c
Z
chab
c
Z
c
Z ,1,
^^^^^=^ 




-+-+ - (A.3)
The Euler equation for domestic bonds
)^()^()^(^=^
1,1 ++ --+ tzyttttttt EEER  (A.4)
The uncovered interest rate parity condition
*
11
*
1 =)( +++ -++- tttttttttt ErerEprRErerR  ^^^^^^^ (A.5)
The home demand for home intermediates
tht
d
ht ypy ^^=^ +- (A.6)
The home demand for foreign intermediates
tftft ypy ^^=^ +- (A.7)
The aggregate price or CPI index
ftht pp ^)(1^=0  -+ (A.8)
Equilibrium condition for the Home production of intermediates
xt
h
xd
ht
h
d
h
ht y
y
y
y
y
y
y ^^=^ + (A.9)
Export demand equation
*
)(= thttxpxt yprery ^^^^ +- (A.10)
The production function for domestic intermediates






--
-
--
-
--
-+ ttttht g
gcy
g
c
gcy
c
y
gcy
y
hy ^^^)(1^=^  (A.11)
47
The labor demand equation
thttt hyw ^^^=^ -+ (A.12)
The other input (capital) demand equation
ttthtt g
gcy
g
c
gcy
c
y
gcy
y
y ^^^^^=0
--
+
--
+
--
-+ (A.13)
The profits
tttthththht ccyyhwwhypypdd ^^)^^()^^(=^ +-+-+ (A.14)
The Phillips curve for wages
11
^
1
1
^
1
=^ -+
+
+
+
wt
w
wtt
w
w
wt E 











-
-++--
+
--
+ wt
w
tlstCttt
ww
ww
ZZwh 



 ^
1
1^^^^^
)(1
))(1(1
,, (A.15)
The Phillips curve for domestic intermediates' prices






-
--
+
--
+
+
+
+
-+ ht
h
htt
hh
hh
ht
h
htt
h
h
ht pE 









 ^
1
1
^^
)(1
))(1(1
^
1
1
^
1
=^ 11
(A.16)
The Phillips curve for imported goods' prices
( )ftt
ff
ff
ft
f
ftt
f
f
ft prerE ^^^^^ -
+
--
+
+
+
+
-+
)(1
))(1(1
1
1
1
= 11







 (A.17)
The Phillips curve for exported goods' prices
( )xttht
xx
xx
xt
x
xtt
x
x
xt pspE ^^^^^^ --
+
--
+
+
+
+
-+
)(1
))(1(1
1
1
1
= 11








(A.18)
The monetary policy reaction function
+-1
^4=^4 tt RR 
tmpT
tttttt
hty
ss
t
Z
E
yR
,
123
1 ^
)^4^^^^(
^^4
)(1 +





-+++
+
-+
+++
-




(A.19)
The steady state for the gross nominal interest rate is
T
t
ss
tR ^=^ (A.20)
The definition of the real exchange rate
tttt ppsrer ^^^^ -+ *
= (A.21)
The definition of foreign inflation rate
48
*
1
**
^^=^ -- ttt pp (A.22)
The definition of inflation for the aggregate domestic intermediate goods price
thththt pp  ^^^=^ 1 +- - (A.23)
The definition of nominal wage growth
ttzyttwt ww  ^^^^=^ ,1 ++- - (A.24)
The definition of inflation for the aggregate imported intermediate goods price
tftftft pp  ^^^=^ 1 +- - (A.25)
The definition of inflation for the aggregate exported intermediate goods price
1
^^=^ -- xtxtxt pp (A.26)
The consumption preference shock
tcZtczctc ZZ
,1,,
^=^  +- (A.27)
The government spending shock
tgZtgzgtg ZZ
,1,,
^=^  +- (A.28)
Labor supply shock
tlsZtlsZlstls ZZ
,1,,
^=^  +- (A.29)
Domestic prices markup shock
ht
h
h
hthht  



2
1
1)(^=^ --
(A.30)
Import prices markup shock
ft
f
f
ftfft  



2
1
1)(^=^ --
(A.31)
Wage markup shock
wt
w
w
wtwwt  



2
1
1)(^=^ --
(A.32)
The technology shock
tyZtzyzytzy ,1,,
^=^  +- (A.33)
The monetary policy shock
tmpZtmpZ
,, =^  (A.34)
The risk premium shock
trpZtrpzrptrp ZZ
,1,,
^=^  +- (A.35)
Inflation targeting shock
49
T
t
T
tT
T
t 
 +-1^=^ (A.36)
Foreign sector's shocks (demand, price, interest rate)














+




















-
-
-
*
*
*
*
1
*
1
*
1
*
*
*
0
^
^
^
)(=
^
^
^
tR
t
ty
t
t
t
t
t
t
F
R
y
LA
R
y
A



 
(A.37)
The definition of consumption growth
1,
^^^=^ --+ tttzyCt cc (A.38)
The definition of production growth
1,
^^^=^ --+ hthttzyYHt yy (A.39)
The model consists of 41 equations; equation (37) is actually set of three equations.
There are 28 endogenous variables (prices and quantities) tttttt hdcpb ^,^,^,^,^,^ **
,
xtft  ^,^ , xtfthtwtht ppp ^,^,^,^,^  ,
ss
thttYHtCt RR ^,^,^,^,^  , tt srer ^^ , , tpr^ , ftttt yxw ^,^,^,^  ,
tht
d
ht yyy ^,^,^ together with the law of motion of 13 shocks trpthstgtc ZZZZ ,,,,
^,^,^,^ , tmpZ ,
^ ,
,^,^,^ ,twht
T
t  **
,
^,^,^ tttzy R ,
*
^ty . (Assuming that 0=tb for all t , it is dropped out.
And given that the paper focuses on the macroeconomic equilibrium
new
xt
new
ft
new
ht ppp ,, and
new
tw is also dropped.)
50
B Data description
The data are quarterly, spanning period from 1996:Q1 to 2007:Q4. If the data are
not seasonally adjusted from the source, when necessary, Kalman smoother is used
for seasonal adjusment.
* Gross domestic product / CZK mil., constant prices of 2000 / seasonally
adjusted / CZSO
* Gross domestic product / CZK mil., current prices / seasonally adjusted /
CZSO
* Final consumption expenditures of households / CZK mil., constant prices of
2000 / seasonally adjusted / CZSO
* Final consumption expenditures of government / CZK mil., constant prices
of 2000 / seasonally adjusted / CZSO
* Exports / Total / CZK mil., constant prices of 2000 / seasonally adjusted /
CZSO
* Total employment: hours worked / thousand hours / CZSO
* Total employment: persons / one-job holder / CZSO
* Wages and salaries: total / CZK mil., current prices / CZSO
* Import prices / Index, December 1999 = 100 / CZSO
* Consumer price index / Index, 2005 = 100 / seasonally adjusted / CZSO
* 3-month PRIBOR / per cent p.a. / CNB
* Exchange rates against the ECU/Euro (average) / Not seasonally adjusted
data / Czech Koruna / CNB
* Gross domestic product at constant prices, in millions of ECU/EUR at 1995
prices / seasonally adjusted, Euro 12 /ECB
* Total employment / thousands of persons / Seasonally adjusted / Euro 12 /
ECB
* Deflator of final consumption of households and NPISHs / Euro 12 / ECB
* 3-month EURIBOR / per cent p.a. / ECB
51
C Tables and figures
Table 1: Data and their transformation
Variable Symbol Transform. Test of
stationarity
Estimated
shock
Endogenous data
labor (hours worked)
th HP filter ***
(1)I tlsZ ,
nominal interest rate
tR HP filter ***
(0)I tmpZ ,
CPI inflation
t none ***
(0)I T
t
domestic inflation
ht none ***
(0)I
1-ht
ht


imported inflation
ft none ***
(0)I
1-ft
ft


wage inflation
wt none ***
(0)I
1-wt
wt


real exchange rate
trer HP filter ***
(0)I trpZ ,
consumption growth
ct none ***
(0)I tcZ ,
output growth
yht none ****
(1)/(0) II tzy,
Exogenous data
government spending
tg HP filter ***
(0)I tgZ ,
foreign CPI inflation *
t HP filter ***
(0)I *
t
foreign demand *
ty HP filter **
(0)I *
ty
foreign interest rate *
tR HP filter ***
(1)I *
tR
Test of stationarity is based on Augmented Dickey-Fuller (ADF) test. Maximum
number of lags was set to five. Symbols
******
,, denotes significance level, 10 %, 5
% and 1 % respectively. Data that are not filtered by HP filter are centered around
their mean before estimation.
52
Figure 1: Cyclical behaviour of the real wage
1996 1998 2000 2002 2004 2006 2008
-4
-2
0
2
%
Cycle
Productivity gap
Real w age gap
-5 -4 -3 -2 -1 0 1 2 3 4 5
-0.4
-0.2
0
0.2
k
corr.coef.
Y/Lt
x RWt+k
2000 2002 2004 2006 2008
-1
0
1
2
%
Cycle
-5 -4 -3 -2 -1 0 1 2 3 4 5
-0.8
-0.6
-0.4
-0.2
0
k
corr.coef.
Y/Lt
x RWt+k
Figure 2: Production side of the economy
53
Figure 3: Data for Bayesian estimation
1996 2000 2004 2008
-0.02
0
0.02
Hours w orked
1996 2000 2004 2008
-0.01
0
0.01
0.02
0.03
Consumption grow th
1996 2000 2004 2008
-0.01
0
0.01
Output grow th
1996 2000 2004 2008
-0.05
0
0.05
Real exchange rate
1996 2000 2004 2008
-0.02
0
0.02
Domestic prices inflation
1996 2000 2004 2008
-0.01
0
0.01
Wage inflation
1996 2000 2004 2008
-0.04
-0.02
0
0.02
0.04
Import prices inflation
1996 2000 2004 2008
-0.02
0
0.02
0.04
CPI inflation
1996 2000 2004 2008
-5
0
5
10
15
x 10
-3
Nominal interest rate
Table 2: Government spending shock
Parameter estimate standard deviation
zg
0.5812 0.2886
gZ 0.0199 Table
3: Foreign sector
ttt FxAxA +-110 =










-










--
-
0.68170.10950.0425
000.0618
000.8628
=
10.05490.0869
010.0716
001
= 10 AA


































*
*
*
*
*
*
=
0.000500
00.00180
000.0024
=
^
^
^
=
tR
t
ty
t
t
t
t
t F
R
y
x



 
54
Table 4: Calibrated parameters and steady states
Parameter Symbol Value
Structural parameters
Elasticity of intertemporal substitution

1 1
Discount factor  0.9993
Labor supply shock persistence
zls 0
Steady state parameters
Gross growth rate
zy 1.0050
Export-to-output ratio
ck 0.6989
Gov. spending-to-output ratio
gk 0.2167
Inflation target
T 1.0104
Real interest rate

R 1.0057
Domestic intermediates' price markup
1-h
h

 1.1429
Foreign intermediates' price markup
1-f
f

 1.1429
Wage markup
1-w
w

 1.2
Foreign gross nominal interest rate *
R 1.0091
Foreign inflation *
 1.0047
Table 5: Parameters
Para-
meter
Domain Density Prior
mean
Std Description
Nominal rigidities
f [0,1) beta 0.75 0.10 Calvo parameter, import prices
h [0,1) beta 0.75 0.10 Calvo parameter, domestic prices
w [0,1) beta 0.75 0.10 Calvo parameter, wages
x [0,1) beta 0.75 0.10 Calvo parameter, export prices
Miscellaneous
 [0,1) beta 0.40 0.10 weight of domestic goods in
output
 +
R invg 0.06 Inf risk premium (UIP condition)
55
Preferences
hab [0,1) beta 0.70 0.05 habit in consumption
 +
R gamm 3.00 1.00 (Frisch) elasticity of labor supply
Monetary policy reaction function
 [0,1) beta 0.75 0.10 interest rate smoothing
 +
R norm 1.50 0.10 weight on inflation
yh +
R norm 0.10 0.05 weight on output
Production and export function
 [0,1) beta 0.60 0.05 labor elasticity of production
x +
R gamm 0.03 0.02 price elasticity of exports
Shock persistence
T
 [0,1) beta 0.40 0.10 inflation target
h [0,1) beta 0.40 0.10 markup in domestic prices
f [0,1) beta 0.40 0.10 markup in imported prices
w [0,1) beta 0.40 0.10 markup in wages
cZ [0,1) beta 0.40 0.10 preferences
yZ [0,1) beta 0.40 0.10 technology
rpZ [0,1) beta 0.40 0.10 risk premium
Shock volatility
cZ +
R invg 0.01 Inf consumption preference shock
lsZ +
R invg 0.01 Inf labor supply shock
mpZ +
R invg 0.01 Inf monetary policy shock
T
 +
R invg 0.01 Inf inflation target shock
yZ +
R invg 0.01 Inf technology shock
rpZ +
R invg 0.01 Inf risk premium shock
h +
R invg 0.01 Inf markup shock in domestic prices
f +
R invg 0.01 Inf markup shock in imported prices
w +
R invg 0.01 Inf markup shock in wages
Standard deviation of measurement errors
yht +
R invg 0.01 Inf output growth
th +
R invg 0.01 Inf labor (hours worked)
56
Figure 4: Check plots
0.02 0.025 0.03
-1070
-1069
-1068
-1067
Z
c
4 5 6
x 10
-3
-1069.4
-1069.3
-1069.2
Z
ls
3 4 5
x 10
-3
-1070
-1069
-1068
-1067
Z
mp
5 6 7
x 10
-3
-1069.4
-1069.3
-1069.2

T
2 2.5 3 3.5
x 10
-3
-1069.5
-1069
-1068.5
-1068
Z
y
6 8 10
x 10
-3
-1070
-1069
-1068
-1067
Z
rp
0.01 0.012 0.0140.016 0.018
-1070
-1069
-1068
-1067

h
0.1 0.12 0.14
-1070
-1069
-1068
-1067

w
0.1 0.12 0.14 0.16
-1070
-1069
-1068
-1067

f
2.2 2.4 2.6 2.8 3 3.2 3.4
x 10
-3
-1069.5
-1069
-1068.5
-1068

yht
8 10 12
x 10
-3
-1070
-1069
-1068
-1067
h
t
0.7 0.8 0.9 1
-1
0
1
2
x 10
7

0.7 0.8 0.9 1
-2000
-1000
0
1000
f
0.35 0.4 0.45 0.5
-1070
-1065
-1060
h
0.7 0.8 0.9 1
-5
0
5
x 10
5 w
0.5 0.6 0.7
-1070
-1069
-1068
-1067
x
0.12 0.14 0.16
-1069.4
-1069.3
-1069.2

0.5 0.6 0.7 0.8
-1070
-1060
-1050
-1040
hab
57
Figure 5: Check plots
1.4 1.6 1.8 2
-1070
-1065
-1060

0.08 0.1 0.12
-1069.4
-1069.3
-1069.2
yh
0.5 0.6 0.7 0.8
-1070
-1065
-1060

0.35 0.4 0.45 0.5 0.55
-1069.4
-1069.2
-1069

T
0.2 0.3 0.4
-1069.4
-1069.2
-1069

h
0.35 0.4 0.45 0.5
-1069.5
-1069
-1068.5

w
0.12 0.14 0.16 0.18 0.2
-1069.4
-1069.2
-1069

f
0.35 0.4 0.45 0.5 0.55
-1069.5
-1069
-1068.5
Z
C
0.35 0.4 0.45 0.5 0.55
-1069.4
-1069.2
-1069
Z
y
0.5 0.6 0.7
-1070
-1068
-1066
-1064
-1062
Z
rp
2 2.5 3
-1069.4
-1069.3
-1069.2
-1069.1
-1069
-1068.9

0.014 0.016 0.018 0.02
-1069.4
-1069.2
-1069
-1068.8
0.18 0.2 0.22 0.24 0.26 0.28
-1069.35
-1069.3
-1069.25
-1069.2
-1069.15
-1069.1
x
58
Figure 6: Priors and posteriors
0 0.02 0.04 0.06 0.08
0
100
Z
c
0 0.1 0.2 0.3
0
100
Z
ls
0 0.02 0.04
0
500
Z
mp
0 0.02 0.04
0
100
200

T
0 0.02 0.04
0
500
Z
y
0 0.02 0.04
0
100
200
Z
rp
0 0.02 0.04 0.06
0
100

h
0 0.2 0.4 0.6 0.8
0
100

w
0 0.2 0.4
0
100

f
0 0.02 0.04
0
200
400
600
800

yht
0.01 0.02 0.03 0.04 0.05
0
100
200
300
h
t
0.7 0.8 0.9
0
10
20

0.4 0.6 0.8
0
5
10
f
0 0.2 0.4 0.6 0.8
0
2
4
6
h
0.4 0.6 0.8 1
0
5
10
w
0.2 0.4 0.6 0.8 1
0
2
4
x
0 0.2 0.4 0.6
0
2
4
6
8

0.2 0.4 0.6 0.8 1
0
2
4
6
hab
59
Figure 7: Priors and posteriors
1.2 1.4 1.6 1.8 2 2.2 2.4
0
2
4

-0.2 0 0.2 0.4
0
5
yh
0.4 0.6 0.8
0
5
10

0 0.5 1
0
2
4

T
0 0.2 0.4 0.6 0.8
0
5

h
0 0.2 0.4 0.6 0.8
0
2
4

w
0 0.2 0.4 0.6
0
5

f
0 0.5 1
0
2
4
Z
C
0 0.5 1
0
2
4
Z
y
0.2 0.4 0.6 0.8 1
0
1
2
3
4
5
Z
rp
0 5 10
0
0.1
0.2
0.3
0.4
0.5

0 0.05 0.1 0.15 0.2 0.25
0
20
40
60
80
-0.2 0 0.2 0.4 0.6 0.8
0
2
4
6
8
10
x
60
Table 6: Bayesian estimation results
Prior distribution Posterior max Posterior distribution
Dom. Density Mean S.D. Mode S.D. Mean 5 % 95 %
Nominal rigidities
f [0,1) beta 0.75 0.10 0.7523 0.0352 0.7530 0.6925 0.8159
h [0,1) beta 0.75 0.10 0.4025 0.0653 0.4181 0.3121 0.5263
w [0,1) beta 0.75 0.10 0.8258 0.0337 0.8569 0.7860 0.8910
x [0,1) beta 0.75 0.10 0.6179 0.0841 0.6329 0.5036 0.7584
Miscellaneous (CPI index, risk premium)
 [0,1) beta 0.27 0.10 0.1417 0.0529 0.1629 0.0703 0.2426
 [0,1) invg 0.05 Inf 0.0168 0.0045 0.0192 0.0107 0.0272
Preferences
hab [0,1) beta 0.75 0.10 0.6882 0.0710 0.6937 0.5772 0.8081
 +
R gamm 3.00 1.00 2.3532 0.7986 2.7062 1.3035 4.1225
Monetary policy reaction function
 [0,1) beta 0.80 0.05 0.9037 0.0148 0.8972 0.8728 0.9237
 +
R norm 1.70 0.10 1.7095 0.0963 1.7026 1.5427 1.8647
yh +
R norm 0.10 0.05 0.1044 0.0500 0.1070 0.0227 0.1859
Production and export function
 [0,1) beta 0.60 0.05 0.6546 0.0428 0.6498 0.5805 0.7222
x +
R gamm 0.10 0.10 0.2425 0.0785 0.2500 0.1025 0.3885
Shock persistence
T
 [0,1) beta 0.40 0.10 0.4302 0.1063 0.4184 0.2586 0.5794
h [0,1) beta 0.40 0.10 0.3086 0.0915 0.3151 0.1789 0.4577
w [0,1) beta 0.40 0.10 0.3846 0.0934 0.3918 0.2348 0.5256
f [0,1) beta 0.40 0.10 0.1576 0.0524 0.1705 0.0854 0.2554
zc [0,1) beta 0.40 0.10 0.4466 0.0955 0.4440 0.2962 0.5978
zy [0,1) beta 0.40 0.10 0.4211 0.1004 0.4193 0.2594 0.5724
zrp [0,1) beta 0.40 0.10 0.6019 0.0784 0.5719 0.4409 0.7062
Standard deviation of shocks
cZ +
R invg 0.01 Inf 0.0253 0.0062 0.0281 0.0166 0.0392
lsZ +
R invg 0.01 Inf 0.0046 0.0019 0.1415 0.0024 0.0153
mpZ +
R invg 0.01 Inf 0.0034 0.0006 0.0036 0.0026 0.0046
T
 +
R invg 0.01 Inf 0.0059 0.0024 0.0064 0.0029 0.0097
yZ +
R invg 0.01 Inf 0.0029 0.0005 0.0031 0.0022 0.0040
61
rpZ +
R invg 0.01 Inf 0.0079 0.0019 0.0091 0.0056 0.0125
h +
R invg 0.01 Inf 0.0139 0.0039 0.0163 0.0088 0.0235
w +
R invg 0.01 Inf 0.1223 0.0468 0.0878 0.0659 0.2624
f +
R invg 0.01 Inf 0.1158 0.0343 0.1321 0.0657 0.1962
Standard deviation of measurement errors
ht +
R invg 0.01 Inf 0.0028 0.0005 0.0031 0.0022 0.0039
th +
R invg 0.01 Inf 0.0096 0.0014 0.0102 0.0076 0.0125
Table 7: Standard deviation from the data and from the model
h c yh rer h w f  R
Data 1.24 0.87 0.59 3.50 0.99 0.52 1.97 1.05 0.43
Model 1.80 1.10 0.57 3.47 1.22 1.07 1.44 1.34 0.37
Figure 8: Filtered and observed variables
1996 2000 2004 2008
-0.02
0
0.02
ht
1996 2000 2004 2008
-0.04
-0.02
0
0.02
0.04
ct
1996 2000 2004 2008
-0.01
0
0.01
yht
1996 2000 2004 2008
-0.1
0
0.1
rert
1996 2000 2004 2008
-0.02
0
0.02
ht
1996 2000 2004 2008
-0.01
0
0.01
wt
1996 2000 2004 2008
-0.04
-0.02
0
0.02
0.04
ft
1996 2000 2004 2008
-0.02
0
0.02
0.04
0.06
t
1996 2000 2004 2008
-0.01
0
0.01
Rt
Data
Prediction
62
Figure 9: Autocorrelation from VAR and DSGE model
0 5 10
-0.5
0
0.5
1
ht
0 5 10
-0.2
0
0.2
0.4
ct
0 5 10
-0.5
0
0.5
1
yht
0 5 10
-0.2
0
0.2
0.4
0.6
rert
0 5 10
-0.2
0
0.2
0.4
0.6
ht
0 5 10
-0.5
0
0.5
1
wt
0 5 10
-0.2
0
0.2
0.4
0.6
ft
0 5 10
-0.2
0
0.2
0.4
0.6
t
0 5 10
-0.5
0
0.5
1
Rt
VAR
DSGE
Figure 10: Historical shocks
1996 2000 2004 2008
-0.05
0
0.05
0.1
Consumption pref.
1996 2000 2004 2008
-0.1
0
0.1
Labor supply
1996 2000 2004 2008
-0.02
0
0.02
Technology
1996 2000 2004 2008
-0.05
0
0.05
0.1
Monetary policy
1996 2000 2004 2008
-0.05
0
0.05
0.1
Risk premium
1996 2000 2004 2008
-0.02
0
0.02
Inflation target
1996 2000 2004 2008
-0.04
-0.02
0
0.02
0.04
0.06
Domestic prices markup
1996 2000 2004 2008
-1
0
1
Import prices markup
1996 2000 2004 2008
-0.4
-0.2
0
0.2
Wage markup
63
1996 2000 2004 2008
-2
0
2
4
x 10
-4
Foreign int. rate
1996 2000 2004 2008
-4
-2
0
2
4
x 10
-3
Foreign output
1996 2000 2004 2008
-2
0
2
4
x 10
-4
Foreign inflation
1996 2000 2004 2008
-8
-6
-4
-2
0
2
4
x 10
-3
Gov. spending
Table 8: Variance decomposition
real shocks nominal shocks other shocks
Variable
cZ lsZ yZ mpZ T
 rpZ h w f gZ *R
 *
 *y

real variables
th 1.8 8.9 1.7 3.8 2.3 11.0 2.9 26.1 35.6 0.4 0.1 0.1 5.3
ct 65.3 0.1 5.4 6.1 3.4 2.6 0.6 0.4 15.6 0.1 0.0 0.0 0.3
yht 2.6 1.3 39.8 3.7 2.1 10.6 7.1 3.8 7.1 0.8 0.1 0.1 20.8
trer 1.6 0.3 0.0 11.0 6.2 53.0 1.1 1.0 24.1 0.2 0.4 0.1 1.1
nominal variables
ht 2.1 3.0 1.7 7.7 4.8 5.7 29.7 7.5 36.4 0.1 0.1 0.0 1.1
wt 3.2 10.7 4.2 9.5 5.9 5.9 0.3 22.4 36.1 0.1 0.1 0.0 1.6
ft 1.6 0.1 0.1 6.6 4.1 8.9 0.3 0.3 77.2 0.1 0.1 0.1 0.6
t 1.8 0.1 0.1 7.4 4.6 9.0 1.1 0.3 74.7 0.1 0.1 0.1 0.7
tR 10.8 0.8 0.3 7.1 2.2 11.1 3.8 2.4 57.7 0.8 0.1 0.1 2.7
64
Figure 11: Impulse responses: shock to consumption preferences
0 20 40
0
2
4
6
x 10
-4
Hours
0 20 40
-4
-2
0
2
4
6
8
x 10
-4
Output grow th
0 20 40
-5
0
5
10
x 10
-3
Consumption grow th
0 20 40
-5
0
5
10
15
x 10
-4
Wage inflation
0 20 40
0
5
10
x 10
-4
Domestic inflation
0 20 40
0
5
10
x 10
-4
CPI inflation
0 20 40
0
2
4
x 10
-4
Nominal interest rate
0 20 40
-8
-6
-4
-2
0
2
4
x 10
-4
Real interest rate
0 20 40
-1
0
1
2
3
x 10
-3
Real exchange rate
Figure 12: Impulse responses: shock to technology
0 20 40
-5
0
5
10
15
x 10
-4
Hours
0 20 40
0
2
4
x 10
-3
Output grow th
0 20 40
0
10
20
x 10
-4
Consumption grow th
0 20 40
0
5
10
x 10
-4
Wage inflation
0 20 40
-10
-5
0
5
x 10
-4
Domestic inflation
0 20 40
-2
-1
0
x 10
-4
CPI inflation
0 20 40
-4
-2
0
x 10
-5
Nominal interest rate
0 20 40
-1
0
1
2
x 10
-4
Real interest rate
0 20 40
-4
-2
0
2
x 10
-4
Real exchange rate
65
Figure 13: Impulse responses: shock to wage markup
0 20 40
-4
-2
0
x 10
-3
Hours
0 20 40
-6
-4
-2
0
2
x 10
-4
Output grow th
0 20 40
0
2
4
x 10
-4
Consumption grow th
0 20 40
-2
0
2
x 10
-3
Wage inflation
0 20 40
-1
0
1
x 10
-3
Domestic inflation
0 20 40
-2
0
2
x 10
-4
CPI inflation
0 20 40
-2
-1.5
-1
-0.5
0
x 10
-4
Nominal interest rate
0 20 40
-1
0
1
x 10
-4
Real interest rate
0 20 40
-15
-10
-5
0
5
x 10
-4
Real exchange rate
Figure 14: Impulse responses: shock to labor supply
0 20 40
-2
-1
0
x 10
-3
Hours
0 20 40
-4
-2
0
2
x 10
-4
Output grow th
0 20 40
0
1
x 10
-4
Consumption grow th
0 20 40
-1
0
1
2
3
x 10
-3
Wage inflation
0 20 40
-1
0
1
x 10
-3
Domestic inflation
0 20 40
-1
0
1
x 10
-4
CPI inflation
0 20 40
-1
-0.5
0
x 10
-4
Nominal interest rate
0 20 40
0
1
2
x 10
-4
Real interest rate
0 20 40
-10
-5
0
x 10
-4
Real exchange rate
66
Figure 15: Impulse responses: shock to monetary policy
0 20 40
-20
-10
0
x 10
-4
Hours
0 20 40
-6
-4
-2
0
2
x 10
-4
Output grow th
0 20 40
-2
-1
0
1
x 10
-3
Consumption grow th
0 20 40
-15
-10
-5
0
5
x 10
-4
Wage inflation
0 20 40
-20
-10
0
x 10
-4
Domestic inflation
0 20 40
-20
-10
0
x 10
-4
CPI inflation
0 20 40
-4
-2
0
2
4
6
8
x 10
-4
Nominal interest rate
0 20 40
0
1
2
x 10
-3
Real interest rate
0 20 40
-8
-6
-4
-2
0
2
x 10
-3
Real exchange rate
Figure 16: Impulse responses: shock to inflation target
0 20 40
-5
0
5
10
15
x 10
-4
Hours
0 20 40
-4
-2
0
2
4
6
x 10
-4
Output grow th
0 20 40
-1
0
1
x 10
-3
Consumption grow th
0 20 40
-5
0
5
10
15
x 10
-4
Wage inflation
0 20 40
-5
0
5
10
15
x 10
-4
Domestic inflation
0 20 40
-5
0
5
10
15
x 10
-4
CPI inflation
0 20 40
-2
0
2
x 10
-4
Nominal interest rate
0 20 40
-15
-10
-5
0
5
x 10
-4
Real interest rate
0 20 40
-2
0
2
4
6
x 10
-3
Real exchange rate
67
Figure 17: Impulse responses: shock to risk premium
0 20 40
-1
0
1
2
3
x 10
-3
Hours
0 20 40
-1
0
1
2
x 10
-3
Output grow th
0 20 40
-1
0
1
x 10
-3
Consumption grow th
0 20 40
-5
0
5
10
15
x 10
-4
Wage inflation
0 20 40
-5
0
5
10
15
x 10
-4
Domestic inflation
0 20 40
-1
0
1
2
3
x 10
-3
CPI inflation
0 20 40
-2
0
2
4
x 10
-4
Nominal interest rate
0 20 40
-2
-1
0
1
x 10
-3
Real interest rate
0 20 40
-0.01
0
0.01
0.02
0.03
Real exchange rate
0 20 40
-1
0
1
2
3
x 10
-3
Import inflation
0 20 40
-2
-1
0
1
x 10
-3
Imports
0 20 40
-1
0
1
2
x 10
-3
Exports
Figure 18: Impulse responses: shock to government spending
0 20 40
0
0.5
1
x 10
-3
Hours
0 20 40
-4
-2
0
2
4
6
8
x 10
-4
Output grow th
0 20 40
-2
0
2
x 10
-4
Consumption grow th
0 20 40
0
1
2
3
x 10
-4
Wage inflation
0 20 40
0
1
2
3
x 10
-4
Domestic inflation
0 20 40
0
2
4
x 10
-4
CPI inflation
0 20 40
0
1
2
x 10
-4
Nominal interest rate
0 20 40
-4
-2
0
2
x 10
-4
Real interest rate
0 20 40
0
10
20
x 10
-4
Real exchange rate
68
Figure 19: Impulse responses: shock to domestic prices makrup
0 20 40
-1.5
-1
-0.5
0
x 10
-3
Hours
0 20 40
-15
-10
-5
0
5
x 10
-4
Output grow th
0 20 40
-2
0
2
4
x 10
-4
Consumption grow th
0 20 40
-4
-2
0
2
x 10
-4
Wage inflation
0 20 40
-5
0
5
x 10
-3
Domestic inflation
0 20 40
-1
0
1
x 10
-3
CPI inflation
0 20 40
-3
-2
-1
0
x 10
-4
Nominal interest rate
0 20 40
-2
0
2
4
x 10
-4
Real interest rate
0 20 40
-3
-2
-1
0
1
x 10
-3
Real exchange rate
0 20 40
-4
-2
0
2
x 10
-4
Import inflation
0 20 40
0
0.5
1
1.5
x 10
-3
Imports
0 20 40
-15
-10
-5
0
5
x 10
-4
Exports
Figure 20: Impulse responses: shock to import prices makrup
0 20 40
-2
0
2
4
6
x 10
-3
Hours
0 20 40
-1
0
1
x 10
-3
Output grow th
0 20 40
-4
-2
0
2
x 10
-3
Consumption grow th
0 20 40
-2
0
2
4
x 10
-3
Wage inflation
0 20 40
-2
0
2
4
6
x 10
-3
Domestic inflation
0 20 40
-5
0
5
x 10
-3
CPI inflation
0 20 40
-5
0
5
10
15
x 10
-4
Nominal interest rate
0 20 40
-10
-5
0
x 10
-3
Real interest rate
0 20 40
-10
-5
0
x 10
-3
Real exchange rate
0 20 40
-5
0
5
x 10
-3
Import inflation
0 20 40
-5
0
x 10
-3
Imports
0 20 40
-1
0
1
x 10
-3
Exports
69
Figure 21: Impulse responses: shock to foreign interest rate
0 20 40
-2
0
2
4
x 10
-4
Hours
0 20 40
-1
-0.5
0
0.5
1
x 10
-4
Output grow th
0 20 40
-10
-5
0
5
x 10
-5
Consumption grow th
0 20 40
-5
0
5
10
15
x 10
-5
Wage inflation
0 20 40
-5
0
5
10
15
x 10
-5
Domestic inflation
0 20 40
-1
0
1
2
x 10
-4
CPI inflation
0 20 40
-2
0
2
4
6
x 10
-5
Nominal interest rate
0 20 40
-2
0
2
x 10
-4
Real interest rate
0 20 40
-5
0
5
10
15
x 10
-4
Real exchange rate
0 20 40
-1
0
1
2
x 10
-4
Import inflation
0 20 40
-2
0
2
x 10
-4
Imports
0 20 40
-1
0
1
2
x 10
-4
Exports
Figure 22: Impulse responses: shock to foreign output
0 20 40
-1
0
1
2
3
x 10
-3
Hours
0 20 40
-1
0
1
2
3
x 10
-3
Output grow th
0 20 40
-2
0
2
4
x 10
-4
Consumption grow th
0 20 40
-5
0
5
10
x 10
-4
Wage inflation
0 20 40
-5
0
5
10
x 10
-4
Domestic inflation
0 20 40
-5
0
5
10
x 10
-4
CPI inflation
0 20 40
-2
0
2
4
x 10
-4
Nominal interest rate
0 20 40
-5
0
5
x 10
-4
Real interest rate
0 20 40
-1
0
1
2
3
x 10
-3
Real exchange rate
0 20 40
-5
0
5
10
x 10
-4
Import inflation
0 20 40
0
0.5
1
1.5
x 10
-3
Imports
0 20 40
-1
0
1
2
3
x 10
-3
Exports
70
Figure 23: Impulse responses: shock to foreign inflation
0 20 40
-2
0
2
4
x 10
-4
Hours
0 20 40
-2
0
2
4
x 10
-4
Output grow th
0 20 40
-4
-2
0
2
4
x 10
-5
Consumption grow th
0 20 40
-5
0
5
10
x 10
-5
Wage inflation
0 20 40
-5
0
5
10
x 10
-5
Domestic inflation
0 20 40
-5
0
5
10
15
x 10
-5
CPI inflation
0 20 40
-2
0
2
4
x 10
-5
Nominal interest rate
0 20 40
-10
-5
0
5
x 10
-5
Real interest rate
0 20 40
-5
0
5
10
x 10
-4
Real exchange rate
0 20 40
-5
0
5
10
15
x 10
-5
Import inflation
0 20 40
-1
0
1
2
x 10
-4
Imports
0 20 40
-2
0
2
4
x 10
-4
Exports
71
Figure 24: Exchange rate pass-through
0 20 40
0
2
4
x 10
-3
Consumption pref.
0 20 40
-1
0
1
x 10
-3
Technology
0 20 40
-2
0
2
x 10
-3
Labor supply
0 20 40
-8
-6
-4
-2
0
x 10
-3
Monetary policy
0 20 40
0
2
4
6
x 10
-3
Inflation target
0 20 40
0
0.01
0.02
Risk premium
0 20 40
-4
-2
0
2
4
6
x 10
-3
Domestic prices markup
0 20 40
0
0.01
0.02
Import prices markup
0 20 40
-4
-2
0
2
4
x 10
-3
Wage markup
0 20 40
0
1
2
x 10
-3
Foreign int. rate
0 20 40
-2
0
2
x 10
-3
Foreign output
0 20 40
0
2
4
6
x 10
-4
Foreign inflation
0 20 40
0
0.5
1
x 10
-3
Government spending
S
P
PH
PF
72
Figure 25: Wage-price dynamics
0 20 40
0
2
4
x 10
-3
Consumption pref.
0 20 40
0
2
4
x 10
-3
Technology
0 20 40
-4
-2
0
2
4
x 10
-3
Labor supply
0 20 40
-8
-6
-4
-2
0
x 10
-3
Monetary policy
0 20 40
0
2
4
6
x 10
-3
Inflation target
0 20 40
0
2
4
6
x 10
-3
Risk premium
0 20 40
-2
-1
0
1
x 10
-3
Domestic prices markup
0 20 40
0
0.01
0.02
Import prices markup
0 20 40
-5
0
5
x 10
-3
Wage markup
0 20 40
0
2
4
6
x 10
-4
Foreign int. rate
0 20 40
-2
0
2
x 10
-3
Foreign output
0 20 40
0
2
4
6
x 10
-4
Foreign inflation
0 20 40
0
0.5
1
x 10
-3
Government spending
W
P
73
Table 9: Comparison of the models
Param. Prior FDP FDEP BM FEP FDIPH FIP FW FWDIEP
Nominal rigidities
f 0.75 0.7596 0.7657 0.7530 0.7564 [0.2] [0.2] 0.7571 [0.2]
h 0.75 [0.2] [0.2] 0.4181 0.4242 [0.2] 0.4902 0.3988 [0.2]
w 0.75 0.8351 0.8579 0.8569 0.8299 0.8498 0.8382 [0.2] [0.2]
x 0.75 0.6323 [0.2] 0.6329 [0.2] 0.7007 0.7016 0.6745 [0.2]
Miscellaneous (CPI index, risk premium)
 0.27 0.1374 0.1351 0.1629 0.1508 0.5133 0.5128 0.0940 0.2172
 0.05 0.0203 0.0197 0.0192 0.0190 0.0238 0.0203 0.0230 0.0243
Preferences
hab 0.75 0.6892 0.7010 0.6937 0.6884 [0.2] 0.6537 0.5461 0.4972
 3.00 2.7051 2.7843 2.7062 2.8382 2.5112 2.5180 3.9320 3.7854
Monetary policy reaction function
 0.80 0.8991 0.8969 0.8972 0.8957 0.8281 0.8503 0.8964 0.8408
 1.70 1.7014 1.7002 1.7026 1.7036 1.7109 1.7174 1.6877 1.7384
yh 0.10 0.1025 0.1024 0.1070 0.1028 0.1105 0.1103 0.0988 0.0984
Production and export function
 0.60 0.6522 0.6406 0.6498 0.6370 0.6961 0.6724 0.6019 0.6094
xp 0.10 0.2521 0.1175 0.2500 0.1178 0.2283 0.2400 0.1453 0.0702
Shock persistence
T
 0.40 0.4167 0.4092 0.4184 0.4138 0.4446 0.4637 0.4159 0.4449
h 0.40 0.4448 0.4523 0.3151 0.3151 0.4903 0.2876 0.3182 0.4574
w 0.40 0.3824 0.398 0.3918 0.3817 0.3918 0.3751 0.6070 0.5972
f 0.40 0.1711 0.1722 0.1705 0.1707 0.5234 0.5223 0.1714 0.5464
zc 0.40 0.4491 0.455 0.4440 0.4487 0.5134 0.3803 0.5025 0.5160
zy 0.40 0.4207 0.4049 0.4193 0.4063 0.3524 0.3680 0.4198 0.3929
zrp 0.40 0.5785 0.5815 0.5719 0.5705 0.5919 0.5767 0.5807 0.6136
Standard deviation of shocks
cZ 0.01 0.0275 0.0297 0.0281 0.0285 0.0096 0.0236 0.0197 0.0167
lsZ 0.01 0.0401 0.2022 0.1415 0.0228 0.1405 0.0146 0.0064 0.0066
mpZ 0.01 0.0036 0.0037 0.0036 0.0037 0.0032 0.0030 0.0036 0.0033
T
 0.01 0.0065 0.0064 0.0064 0.0064 0.0058 0.0065 0.0064 0.0073
yZ 0.01 0.0031 0.0032 0.0031 0.0032 0.0029 0.0031 0.0032 0.0030
74
rpZ 0.01 0.0090 0.0088 0.0091 0.0090 0.0077 0.0078 0.0087 0.0069
h 0.01 0.0078 0.0079 0.0163 0.0170 0.0082 0.0227 0.0156 0.0082
w 0.01 0.1331 0.0168 0.0878 0.1417 0.0430 0.1452 0.0307 0.0303
f 0.01 0.1358 0.1526 0.1321 0.1352 0.0317 0.0318 0.1279 0.0264
Standard deviation of measurement errors
yt 0.01 0.0031 0.0034 0.0031 0.0033 0.0043 0.0041 0.0033 0.0034
t 0.01 0.0101 0.0101 0.0102 0.0101 0.0123 0.0123 0.0104 0.0117
log data
density
978.57 976.53 972.79 969.39 949.23 947.52 935.20 900.71
75
Figure 10: Vector autocorrelations for the benchmark, the flexible wage and the
flexible domestic prices models
76
Figure 11: Impulse responses of selected variables for various shocks under
different assumptions about nominal rigidity (Part1)
77
Figure 12: Impulse responses of selected variables for various shocks under
different assumptions about nominal rigidity (Part 2)