275 ECONOMIC AND BUSINESS REVIEW | VOL. 21 | No. 2 | 2019 | 275-308
INFLATION – THE HARROD-BALASSA-
SAMUELSON EFFECT IN A DSGE MODEL 
SETTING
 Received: February 26, 2018 
ČRT LENARČIČ
1
 Accepted: September 15, 2018
ABSTRACT: This paper sets up a two-country two-sector dynamic stochastic general 
equilibrium model that introduces sector specific productivity shocks with quality 
improvement mechanism of goods. It provides a model-based theoretical background 
for the Harrod-Balassa-Samuelson phenomenon that describes the relationship between 
productivity and price inflation within different sectors in a particular economy. Both, the 
calibrated and the estimated model are able to show that the Harrod-Balassa-Samuelson 
effect is confirmed by inducing tradable sector productivity shocks as they drive the non-
tradable sector price inflation higher than the tradable sector price inflation. By doing this, 
we overcome the problem that the tradable productivity increase in a typical open economy 
specification reduces the relative price of domestic tradable goods relative to the foreign ones.
Key words: Harrod-Balassa-Samuelson effect, DSGE model, inflation, productivity, quality improvement
JEL classification: C32, E31, E32
DOI: 10.15458/ebr.86
1 INTRODUCTION
The relationship between productivity and price inflation is described by the theory 
of the Harrod-Balassa-Samuelson phenomenon (henceforth HBS). Harrod (1933), 
Balassa (1964) and Samuelson (1964) independently developed and formulated the HBS 
productivity approach in order to explain the purchasing power parity
2
. The HBS effect 
represents a tendency for countries that experience higher tradable-sector productivity 
growth compared to non-tradable sector productivity growth to have higher overall price 
levels (Obstfeld and Rogoff, 1996). In more detail, the basic idea behind it is that the growth 
in the productivity of a tradable sector influences the growth of wages in the tradable and 
later on in the non-tradable sector. W age growth in the tradable sector consequently affects 
the growth of prices in the non-tradable sector. Depending on the nominal exchange rate 
regime of a particular economy, it affects the real exchange rate as well. However, Betts 
and Kehoe (2008) studied the relationship between the real exchange rate and the relative 
price of non-tradable to tradable goods. Their conclusion is that the relation between the 
1 Bank of Slovenia, Ljubljana, Slovenia, e-mail: crt.lenarcic@bsi.si
2 Baumol and Bowen (1967) developed a similar model that only describes the relationship between productivity 
and wages, and presents an important part of the HBS hypothesis, as discussed by W agner and Hlouskova (2004).

ECONOMIC AND BUSINESS REVIEW | VOl. 21 | No. 2 | 2019 276
two variables is stronger in an intense trade environment. Therefore, the basic assumption 
is that the relationship between the relative growth in the productivities of the tradable to 
non-tradable sector and the relative price of non-tradable to tradable goods is relatively 
straightforward if we include sectoral data for European countries, for example. In 
addition to the close trade environment, the sole Euro area integration process suppresses 
the ability of economies to adjust through the nominal exchange rate channel, which could 
consequently put more pressure on non-tradable price inflation.
The HBS hypothesis can be tested on different entities, which in general represent countries, 
regions, or in many cases, sectors. In our case, we divide these entities into a tradable sector 
and a non-tradable sector; we use a similar principle as the De Gregorio, Giovannini, and 
Wolf's (1994) methodology by using the ratio of exports to total production to define 
both sectors. In order to do that we include and combine the NACE Revision 2 10-sector 
breakdown statistical classification time series data of economic activities, which provides 
data on labour productivity and price levels across the two sectors, and the ratio of exports 
to total production data calculated from the input-output tables, which are available at 
the World Input-Output Database (WIOD)
3
. By obtaining the relevant tradable and non-
tradable data for further analysis and adding other observable macroeconomic data, we 
estimate the constructed DSGE model. 
The problem of permanent tradable productivity increase in a typical dynamic open 
economy specification is reducing the relative price of domestic tradable goods relative 
to the foreign ones. This implies worsening the terms of trade for the domestic economy 
and consequently, its real exchange does not increase. These dynamics are not consistent 
with empirical evidence found for the new European Union member states. The main 
contribution of the paper is to overcome the typical dynamic open economy setting by 
constructing and estimating a two-country two-sector DSGE model with the quality 
improvement extension, proposed by Masten (2008), in a smaller calibrated version of a 
dynamic model. The basic assumption is therefore the separation of the economy into a 
tradable and a non-tradable sector. The tradable sector is open and allows domestic goods 
to be exported and foreign goods to be imported, whereas the non-tradable sector is closed 
to foreign markets (a similar structure was used by Masten, 2008; Rabanal, 2009; Micaleff 
and Cyrus, 2013). The assumption is that the tradable and non-tradable sectors are 
exposed to different productivity shocks; this means that non-stationary real variables can 
grow at a different pace, thus providing a case for the HBS effect. In specifying technology, 
we allow a quality improvement mechanism, which is needed to replicate the appreciation 
of prices, without resorting to the unrealistic assumption of perfect competition in the 
tradable sector (Masten, 2008).
We find evidence for the HBS effect, based on an augmented technology process that 
considers a quality improvement mechanism, which affects marginal costs by requiring 
3 In defining the tradable and the non-tradable sector we differ from the standard approach used in the literature 
by excluding the not distinctively tradable or non-tradable sectors from the analysis.

Č. LENARČIČ | INFLATION – THE HARROD-BALASSA-SAMUELSON EFFECT ... 277
the use of more advanced inputs in the production process. The quality improvement 
of goods overcomes the typical open economy theoretical specification that reduces the 
relative prices of domestic tradable goods relative to foreign prices, and consequently 
worsens the terms of trade for the domestic economy. By introducing a sector-specific 
domestic tradable technology shock, the modelled economy responds by increasing price 
differential of non-tradable relative to tradable prices and the overall domestic inflation. 
Doing this we are able to theoretically explain why the economies with higher economic 
and productivity growth during the catching-up phase experienced higher inflation.
In Section 2, a review of the HBS related literature is presented and discussed. Section 3 
provides a theoretical framework for the DSGE model. In section 4, the classification and 
definition of economic activities into a tradable and a non-tradable sector is presented, 
obtaining sectoral price indices and time series of sectoral labour productivity growths. 
The calibrated model is presented in Section 5, while the estimation results of the DSGE 
model are given and discussed in Section 6. Section 7 presents the conclusions.
2 LITERATURE REVIEW
Despite treating the HBS theory as an old idea, in which the sectoral productivity 
differential is seen as the driver for price inflation in the non-tradable sector (Harrod, 1933; 
Balassa, 1964; and Samuelson, 1964), the empirical testing of the HBS effect only became 
more popular in recent years as econometric methods advanced and new (or additional) 
time series data became available. This availability was largely due to the establishment 
of the EU and later on its enlargement process, together with advances and convergence 
of methodologies in collecting data by the national statistical offices. At the same time, 
addressing the HBS issue became relevant from the economic policy perspective trying to 
identify the different sources of (structural) inflation. Betts and Kehoe (2008) show that a 
close trade environment lowers the significance of the nominal exchange rate adjustment. 
This was (and can still be) especially important for the future EU and euro area countries, 
which are obliged to satisfy the Maastricht criterion of low and stable inflation, as well as 
for other emerging economies in trying to stabilise their overall inflation.
In their comprehensive survey, Tica and Družić (2006) gather empirical evidence 
regarding the HBS effect. They point out that most of the empirical work supports the HBS 
effect. Especially strong evidence comes from the work based on cross-section empirical 
studies, similar to Balassa's (1964) work. A large number of papers focus on studying the 
magnitude of the HBS effect in accession countries in the EU. Čihák and Holub (2001) for 
instance study the presence of the HBS effect in the Czech Republic vis-à-vis EU countries, 
while allowing for differences in structures of relative prices. Jazbec (2002) considers 
Slovenia as the HBS case of an accession country, while Dedu and Dumitrescu (2010) 
test the HBS effect using Romanian data. Papers by Cipriani (2000), Coricelli, and Jazbec 
(2004), Halpern and Wyplosz (2001), Arratibel, Rodríguez-Palenzuela, and Thimann 
(2002), Breuss (2003), Wagner and Hlouskova (2004), Mihaljek and Klau (2008) consider 

ECONOMIC AND BUSINESS REVIEW | VOl. 21 | No. 2 | 2019 278
a larger accession country panel. Some of the work focuses also on emerging economies. 
Jabeen, Malik, and Haider (2011) test the HBS hypothesis on Pakistani data, while Guo 
and Hall (2010) test the HBS effect on Chinese regional data.
These empirical strands of the HBS effect related literature opened up new questions 
regarding data issues and were related mostly to availability in reliability of sectoral 
data. As databases, especially in Europe, became more complete, new available data 
enabled studying the HBS effect between individual tradable and non-tradable sectors 
of a particular economy. Since it is difficult to clearly divide tradable and non-tradable 
commodities in the real world, some of the early papers tried to identify the tradability/
non-tradability of commodities. Officer (1976) proposed that manufacturing and/or 
industry combine a tradable sector, while the services represent the non-tradable sector. 
De Gregorio, Giovannini, and Wolf (1994) used a ratio of exports to total production of 
each sector to define both sectors.
In empirical studies, mostly total factor productivity (TFP) or average productivity of 
labour are used. Marston (1987), De Gregorio, Giovannini, and Wolf (1994), De Gregorio 
and Wolf (1994), Chinn and Johnston, (1997), Halikias, Swagel, and Allan (1999), Kakkar 
(2002), and Lojshová (2003) use total factor productivity as a productivity proxy, while due 
to the lack of data on TFP , many others, i.e., Coricelli and Jazbec (2004) and Žumer (2002), 
use average productivity of labour. Comparing total factor productivity and average 
productivity of labour, the argument against the use of average productivity of labour is 
that it is not completely clear if average labour productivity should be regarded as a reliable 
indicator for representing a sustainable productivity growth, which has a long-term effect 
on the economy (De Gregorio and Wolf, 1994). However, according to Canzoneri, Cumby, 
and Diba (1999), the argument against TFP is that TFP is a result of a possibly unreliable data 
collection of sectoral capital stocks comparing to data collection of sectoral employment 
and sectoral gross value added, especially in the case of the shorter-term series. Sargent 
and Rodriguez (2000) also conclude that if the intent of the research is to examine trends 
in the economy over a period of less than a decade or so, labour productivity would be a 
better measure than total factor productivity. According to Kovács (2002), another setback 
of using TFP is that during the catching-up phase the capital accumulation intensifies 
faster in the transition/accession countries than in the developed countries, due to the 
lower starting point in fundamentals of transition/accession countries. Therefore, the HBS 
effect might be overestimated. Listing some of the arguments against using TFP , we rather 
include the average labour productivity as a productivity proxy in the model.
Comparing to the vast HBS literature in the 2000s in the accession process of the countries 
to the EU and the monetary union, less theoretical work was done with regards to the 
HBS effect in more structural and more complex models. Rogoff (1992) was the first 
to implement a general equilibrium framework, introducing the demand side of the 
economy within the HBS theory. This opened the possibility to further investigate the 
effects of relative productivities of production factors and the effects of the demand side 
of the economy on price levels. For instance, Mihaljek and Klau (2002) conclud that the 

Č. LENARČIČ | INFLATION – THE HARROD-BALASSA-SAMUELSON EFFECT ... 279
HBS effect could have important policy implications for the EU accession countries in 
order to satisfy the Maastricht inflation criterion. To further investigate Mihaljek's point, 
Masten (2008) constructs a two-sector DSGE model to see whether the HBS effect could 
represent an issue in satisfying the Maastricht inflation criterion. Further on, Natalucci 
and Ravenna (2002) compare the magnitude of the HBS effect within different exchange 
rate regimes in the general equilibrium model, while Restout (2009) allows for varying 
mark-ups in its general equilibrium framework. However, Asea and Mendoza (1994) 
conclude that the proof of the HBS theory within the framework of general equilibrium 
cannot reliably asses the relationship between output per capita and domestic relative 
prices. In other words, conclusions regarding the HBS theory from cross-country analyses 
can only be conditionally accepted since it is difficult to account for cross-country trend 
deviations from purchasing power parity (PPP). Even more, Bergin, Glick, and Taylor 
(2004) show that the relationship between output per capita and domestic relative prices 
had historically oscillated too much for the HBS theory to be proved by cross-section 
empirical studies. In order to test the HBS theory their suggestion is that it should be tested 
with a sector-specific analysis. 
Following the general equilibrium strand of the HBS related literature, Rabanal 
(2009) offers three explanations for studying sectoral inflation dynamics in Spain in a 
DSGE model structure. The first explanation relates to the role of productivity growth 
differentials, which directly brings the possibility to study the HBS effect. Altissimo et al. 
(2005) introduced a seminal paper on productivity growth differentials in a DSGE model 
setting. The second explanation adds the role of the demand-side effects in shaping the 
inflation dynamics (López-Salido et al., 2005). The third explanation suggests that, due to 
different product and labor market structures, there is heterogeneity of inflation dynamics 
processes in each country of the union (Angeloni and Ehrmann, 2007; Andrés et al., 2003). 
Rabanal (2009) concludes that even when economies are hit by symmetric external shocks, 
such as for example oil prices, world demand, or nominal exchange rate, the response 
of sectoral inflation will be different across countries. The Rabanal's model was adopted 
by Micaleff and Cyrus (2013) as well. They analyse the relative importance of the three 
main determinants of inflation differentials in Malta. Based on these considerations, a 
structured theoretical framework is presented in the following section.
3 MODEL
In this section, we present the theoretical framework for the two-country two-sector 
DGSE model. The DSGE framework follows the Rabanal (2009) model, but the main 
contribution of the theoretical model is its extension for sectoral wage rigidites, thus 
making the model more realistic. Additionally, we introduce an augmented technology 
process with quality improvement (Masten, 2008). In order to investigate the HBS effect 
phenomenon, different sectoral productivity shocks have to be introduced providing 
assymetricity between sectors. The monetary union is made of two economies; a domestic 
and a foreign country with the common monetary policy rule. They are indexed on 
intervals [0,s] and [s,1], respectively, where s denotes the size of the domestic country with 

ECONOMIC AND BUSINESS REVIEW | VOl. 21 | No. 2 | 2019 280
respect to the two-country universe. In our case, we relate to Slovenia and the rest of the 
euro area. The following section only gives a structural domestic economy description 
since the foreign economy block is analogous to the domestic economy, which is in our 
case Slovenia.
3.1 Households
The assumption is that the representative household maximizes its utility function, given 
by
where C
t
 (i) and L
t
 (i) present consumption and quantity of work effort of a particular 
household. The parameter 0< β<1 is the discount factor of household. We assume that 
households value the current consumption more than the future one. The parameter 
0<ϖ<∞ is the inverse of the elasticity of work effort with respect to the real wage (Frisch 
elasticity parameter). We assume consumption habits as well, which is represented by the 
parameter 0<h <1.
The consumption index C
t
 (i) is defined by the constant elasticity of substitution (CES) 
function between tradable and non-tradable goods and holds for all households, so that 
C
t
 (i)=C
t
4
 
where the parameter ω
TN
 presents the share of the tradable goods in the aggregate 
consumption basket. The parameter ν
TN
>1 presents the elasticity of substitution between 
tradable and non-tradable goods.
Since the demand for tradable goods is not dependent only on domestic goods but foreign 
as well, the index of the tradable consumption good is written analogously to the equation 
(3) with which the aggregate consumption index is defined 
4 We scale the variables in the model with  so that the variables enter the model 
detrended, for example, . The scaling variable ensures a constant steady-state level of utility and is 
determined by productivity dynamics (Masten, 2008).

Č. LENARČIČ | INFLATION – THE HARROD-BALASSA-SAMUELSON EFFECT ... 281
where ω
HF
 represents the share of domestic tradable goods in the tradable consumption 
basket. The parameter ν
HF
>1 is therefore the elasticity of substitution between domestic 
tradable goods and tradable goods produced abroad.
The indexes of individual goods are defined by the following equations and represent a 
continuum of differenced goods of the same type
and
The parameter ν>1 denotes the elasticity of substitution within one type of differentiated 
goods: c
t
H
, c
t
F
 and c
t
N
. The same principle can be applied to price indexes. The aggregate 
price index P
t
 is then given by
As above, the price index for tradable goods is given by
Households have a set of contingent riskless euro area bonds B
t
EA
 at their disposal that pay 
one unit of currency in every possible state of nature in t+1. The assumption is that 
households can trade these bonds that pay a gross interest rate of R
t
EA
. Since households 
are ex ante identical, they face the same budget constraint in each period:
where W
t
 represents the real wage, while ς
t
 represents other income sources of households. 
As shown in Chari, Kehoe, and McGrattan (2002), the real exchange rate is given by

ECONOMIC AND BUSINESS REVIEW | VOl. 21 | No. 2 | 2019 282
where the variables μ
t
 and μ
t
*
 represent the marginal utilities of domestic and foreign 
consumption, respectively.
Labour market is, in comparison to the Rabanal (2009) model, differentiated, thus provides 
a more realistic model assumption. Further on, the aggregation of work effort of both 
sectors (i.e., tradable and non-tradable) holds
Against this backdrop, each household working in the tradable or the non-tradable sector 
sets its own wage (Erceg et al., 2000; Christiano et al., 2005). Firms aggregate the 
differentiated supply of labour by transforming it into a homogenous input of labour L
t
j
, 
where j=N,T, in accordance with the Dixit-Stiglitz (1977) aggregator
The parameter ν
L,j
 is defined as the wage elasticity within different varieties of labour 
services in a particular sector, where j= N,T. Based on that the labour demand function for 
a particular is given by
Combining equations (12) and (13) we get the aggregate wage, which is obtained from 
differentiated labour
In order to introduce wage frictions in the model, we apply the Calvo (1983) principle. 
Each household has monopolistic power over the setting of its wage W
t
j
 (i), where j=N,T. 
Yet not all the households can set their optimal wage at any point of time, but only a 
fraction of households (1– α
L,j
), where the Calvo parameter is defined on the interval 
0<α
L,j
<1. The other part of households ( α
L,j
) indexate their wage according to inflation 
target and current inflation. The wage inflation of a non-optimizing household is then 
given by

Č. LENARČIČ | INFLATION – THE HARROD-BALASSA-SAMUELSON EFFECT ... 283
where the parameter 0< φ
L,j
<1 stands for the degree of wage indexation with respect to 
inflation target and current inflation, where j=N,T.
When reoptimizing their wage in period t, workers of a particular sector choose an optimal 
wage W
t
j,opt
 in order to maximize household utility as opposed to their individual utility, 
where j=N,T. The utility is subject to a sequence of iso-elastic demand schedules for their 
labour type, and the usual sequence of household flow budget constraints. The first order 
condition associated with that problem can be written as
where the expression Λ
t,t+k
=β
k
 λ
t+k
/ λ
t
 represents the stochastic discount factor. The wage 
dynamics should therefore be
where j=N,T. The average wage on an economy scale is then given by W
t
=(W
t
T
 )
ωTN
 (W
t
N 
)
1-ωTN
.
3.2 Firms
On the supply side, there are three types of firms, producing two types of tradable goods 
(indexed by H,H
*
) and domestic non-tradable goods (indexed by N). Each type of firm is 
facing price rigidities (Calvo, 1983). That means that only a fraction of firms (1– α
i
), where 
i=N,H,H
*
, can set their optimal price. Other firms ( α
i
), where i=N,H,H
*
, index their prices 
according to the inflation target and current inflation based on the parameter 0< φ
i
<1, 
where i=N,H,H
*
, which stands for the degree of price indexation with respect to inflation 
target and current inflation.
Domestic and foreign economies are facing the same deterministic technology process, 
providing a case for output growth. This means that all the real variables entering the 
model are non-stationary in levels, but stationary in first differences.
3.2.1 Tradable sector
In the tradable sector there are two types of firms. One type of firm produces tradable 
goods for the domestic market and tries to satisfy domestic consumption of tradable 

ECONOMIC AND BUSINESS REVIEW | VOl. 21 | No. 2 | 2019 284
goods, C
t
H
. The other type of firm produces tradable goods meant for export and tries to 
satisfy the foreign consumption of domestic goods, C
t
H, *
. Each firm in the tradable sector 
follows the Cobb-Douglas production function, where work effort is the only production 
factor
and
The variable A
t
T
 is a sector-specific productivity process that is characterised by quality 
improvement of higher-quality goods in the tradable sector index χ
t
=(Z
t
T 
)
θZ
 with quality 
improvement parameter θ
Z
>0 (Masten, 2008), so that
The variable χ
t
 represents a quality improvement of goods index that influences wages and 
marginal costs via positive productivity shocks. Masten (2008) finds that the problem of 
permanent tradable productivity improvement in a typical open economy specification 
reduces the relative price of domestic tradable goods relative to the foreign ones, thus 
worsens the terms of trade. Consequently, the real exchange does not increase and is not 
consistent with empirical evidence based on the new European Union member states. On 
the other hand, introducing quality improvement of higher-quality goods may require the 
use of more advanced inputs in the production process and will consequently increase 
the marginal costs and product prices. Sallekaris and Vijselaar (2004) introduce a similar 
mechanism, as they adjust capital with a simple quality correction.
5
The variable Z
t
T
 represents a tradable sector productivity shock, which is country-specific
We assume that productivity shocks of both sectors can be different and that their growth 
rates could be different. We let the tradable productivity process Z
t
T
 to be affected by two 
different productivity innovations ε
t
Z,T
, which are country and sector specific, and ε
t
Z
, which 
represents a euro-area wide innovation. For the labour supply it holds L
t
T
=L
t
T,H
+L
t
T,H,
*
.
5 The idea of adjusting prices with quality improvements goes back into the 90s, as the study of Gordon (1990) 
tried to empirically document these biases. Later research focused on constructing quality-adjusted price indexes 
(Hulten, 1992; Greenwood et al., 1997; Cummins and Violante, 2002), production based estimates (Bahk and 
Gort, 1993), and capital model (Hobijn, 2000).

Č. LENARČIČ | INFLATION – THE HARROD-BALASSA-SAMUELSON EFFECT ... 285
Tradable sector firms producing domestic goods for the domestic market maximize their 
profits according to
subject to
where the expression Λ
t,t+k
=β
k
 λ
t+k 
⁄ λ
t
 represents the stochastic discount factor, and 
is the tradable goods demand of a firm in time t+k. Y
t
H
 is the aggregate domestic-
made tradable goods demand.
Similarly , we can write the maximization profit function for tradable sector firms producing 
domestic goods for the foreign market
subject to
where the expression Λ
t,t+k
=β
k
 λ
t+k 
⁄ λ
t
 represents the stochastic discount factor, and  
(h ) is the tradable goods demand of a firm in time t+k. Y
t
H,
*
 is the aggregate domestic 
tradable goods demand from abroad.
Real marginal costs in the tradable sector for both types of firms are defined as MC
t
T
. 
Marginal costs are defined as the real wage normalized for augmented productivity

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Both types of tradable sector firms maximize their profit with respect to prices p
t
H
 (h) and 
p
t
H,
*
 (f) and demands (h )and (f), respectively. The tradable price dynamics of 
domestic produced goods for the domestic market is
where P
t
H,
*
,opt
 is the optimal price and . The tradable price dynamics of 
domestic goods for the foreign market is
where P
t
H,
*
,opt
 is the optimal price and .
3.2.2 Non-tradable sector
Analogously to the tradable sector, each non-tradable sector firm follows the Cobb-
Douglas production function, where work effort is the only production factor
The variable A
t
N
 is a sector-specific productivity process that is characterised by quality 
improvement index  so that 
In this respect, we assume that the sector-specific productivity process A
t
N
 is affected by 
quality improvement of goods χ
t
 in the tradable sector, while the variable Z
t
N
 represents a 
non-tradable sector productivity shock, which is again country-specific
where we let the non-tradable productivity process Z
t
N
 to be affected by a sector-specific 
innovation, ε
t
Z,N
.
Non-tradable sector firms maximize their profits

Č. LENARČIČ | INFLATION – THE HARROD-BALASSA-SAMUELSON EFFECT ... 287
subject to
where the expression Λ
t,t+k
=β
k
 λ
t+k
 ⁄ λ
t
 represents the stochastic discount factor, and  
is the non-tradable goods demand of a firm in time t+k. Y
t
N
 is the aggregate non-tradable 
goods demand. Real marginal costs in the non-tradable sector are defined as MC
t
N
. From 
the cost-optimization perspective, the marginal costs are defined as the real wage 
normalized for productivity
A non-tradable sector firm maximizes its profit with respect to price p
t
N
 (n) and demand
. The non-tradable price dynamics should therefore be
where P
t
N,opt
 is the optimal price and .
3.3 Monetary policy
Monetary policy is modelled as a Taylor rule (Taylor, 1993) and is the same for both 
economies
where ε
t
MP
 represents the monetary policy shock, while the interest rate R
t
EA
 responds to 
inflation and output gaps. The total output of the euro area is defined by Y
t
EA
=(Y
t
 )
s
 (Y
t
* 
)
1-s
, 
while the overall inflation in the euro area is defined by Π
t
EA
=(Π
t
 )
s
 (Π
t
*
 )
1-s
, where s is the size 
of the domestic country. The parameter is the weight parameter for the responsiveness 
of the past interest rate, while γ
π
 and γ
y
 are Taylor type paramaters for the response of the 
interest rate accordingly to both gaps.
3.4 Market clearing
The clearing conditions are

ECONOMIC AND BUSINESS REVIEW | VOl. 21 | No. 2 | 2019 288
and
where variables G
t
T
 and G
t
N
 represent exogenous government spending shocks. Combining 
equations (37) and (38), the real GDP is
What is left to do is to define the government sectoral spending process
where i=N,T.
4 TRADABILITY OF SECTORS AND DATA
As the theoretical model is divided into tradable and non-tradable sectors, some attention 
is needed for the specification and the sectoral definition of the data. The dataset consists 
of quarterly Slovene and euro area sectoral data, which is available from the Eurostat
6
  website. The time series data spans from 1998Q4 to 2018Q1 and includes sectoral gross 
value added data and sectoral price indexes data.
4.1 Tradability of sectors
To begin with, the tradability of the sectors has to be defined. Officer (1976) proposes 
the following sector division. Manufacturing and other industry activities represent the 
tradable sector, while the services represent the non-tradable sector. De Gregorio et al. 
(1994) use a ratio of exports to total production to define both sectors. Their division 
threshold is set to 10 percent, stating that the sector is defined as tradable if the ratio of 
exports exceeds the 10 percent threshold, and the sector is defined as non-tradable if the 
ratio of exports does not exceed the 10 percent threshold. Following the De Gregorio et 
al. (1994) sector division, we take a step further by strictly distinguishing between the 
tradable and the non-tradable sector. This means that we exclude those activities from 
the analysis that oscillate around the 10 percent threshold too much. We provide a more 
detailed specification below.
6 Available at the European Commmission's statistical database site http://epp.eurostat.ec.europa.eu/portal/
page/portal/eurostat/home/.

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First, data on the share of exports in total value added have to be extracted from the input-
output tables available at the World Input-Output Database (WIOD). We use a standard 
ISIC/NACE Revision 2 aggregation category, which is used for reporting data from the 
System of National Accounts (SNA) for a wide range of countries. We present a 10-sector 
breakdown in Table 1.
Table 1: NACE Revision 2 10-sector classification of economic activities
Source: European Commission, author's calculations.
*Note: Countries, such as Belgium, the Netherlands and Luxembourg, stand out with their ratio-of-export 
figures, thus driving up the average of ratio of exports in the agriculture sector.
**Note: Countries, such as Ireland, the Netherlands and Luxembourg, stand out with their ratio-of-export 
figures, thus driving up the average of ratio of exports in the professional services sector.
As mentioned above, to divide the 10 sectors into tradable and non-tradable sectors, we 
use a similar approach as De Gregorio et al. (1994). However, in the present paper we 
put emphasis only on strictly tradable and non-tradable sectors, meaning that the sectors 
which are not distinctively tradable or non-tradable are exluded from the analysis. A sector 
is then treated as tradable if its ratio of exports exceeds the 10 percent threshold for at least 
75 percent of time using the WIOD data in the 2000-2011 period. The same principle is 
applied for the definition of a non-tradable sector. A sector is treated as non-tradable if its 
ratio of exports is under the 10 percent threshold for at least 75 percent of time using the 
WIOD data in the 2000-2011 period. Applying stricter conditions regarding the division 
of sector means that NACE Rev. 2 sectors, such as agriculture, forestry and fishing (A), 
information and communication (J), financial and insurance activities (K), professional, 
scientific, technical, administration and support services (M and N), are excluded from 
the analysis. These excluded sectors account for around 20 percent in total value added. 
Based on this threshold the manufacturing, mining, quarrying and other industries (B, C, 
NACE Revision 2 Sector description
Ratio of exports 
(in %)
Tradability
A Agriculture, forestry and fishing 18.32*
B, C, D, E
Manufacturing, mining and quarrying and 
other industry
45.99 T
F Construction 2.20 N
G, H, I
Wholesale and retail trade, transportation and 
storage, accommodation and food services
17.25 T
J Information and communication 10.42
K Financial and insurance activities 12.63
L Real estate activities 0.56 N
M, N
Professional, scientific, technical, administrative 
and support services
16.39**
O, P , Q
Public administration, defence, education, 
human health and social work services
0.95 N
R, S, T, U Other services 6.27 N

ECONOMIC AND BUSINESS REVIEW | VOl. 21 | No. 2 | 2019 290
D and E), wholesale, retail, transportation, storage, accommodation and food services (G, 
H and I) are treated as tradable sectors, while construction (F), real estate activities (L), 
public administration, defence, education, human health, social work services (O, P and 
Q), and other services (R, S, T and U) are treated as non-tradable sectors.
4.2 Sectoral inflation and productivity
Based on quarterly data available from the Eurostat website and consideration of the 
classification of economic activities into a tradable and a non-tradable sector (as defined 
in Table 1), supported by time-varying sectoral gross value added weights expressed in 
millions of euros in 2015, growth rate in prices for the tradable and the non-tradable sector 
are obtained. We use the same principle that was applied to divide economic activities into 
the tradable and non-tradable sectors to divide sectoral growth rate of value added for 
both sectors, based on the aggregation done for sectoral inflation. This way we get growth 
rates for the output on a quarterly frequency basis for a separate sector, i.e. tradable and 
non-tradable.
4.3 Data entering the model
After defining and obtaining the sectoral data, we can provide a full description of the 
dataset entering the model in Table 2. There are 9 observable variables at a quarterly 
frequency in the period of 1998Q4-2018Q1, thus providing 78 observations. Tradable 
sector figures stand out the most and have the highest variability. Intuitively, this means 
that the tradable sector is more responsive to changes in different phases of business cycles. 
Additionally, Slovene data in comparison to the euro area data varies more, thus providing 
a case that small open economies are more vulnerable to macroeconomic imbalances.
Table 2: Descriptive statistics (in p.p. deviations from the steady state)
Variable description Data transformation Country Minimum Maximum
Standard 
deviation
Weighted tradable sector 
inflation 
demeaned log-differences SI -2.59 2.21 0.92
Weighted tradable sector 
inflation
demeaned log-differences EA -1.08 1.31 0.39
Weighted tradable sector 
gross value added
demeaned log-differences SI -10.17 3.02 1.64
Weighted tradable sector 
gross value added
demeaned log-differences EA -6.36 1.23 1.07
Weighted non-tradable 
sector inflation
demeaned log-differences SI -1.22 1.84 0.69
Weighted non-tradable 
sector inflation
demeaned log-differences EA -0.76 0.80 0.30

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Source: Eurostat, author's calculations.
5 CALIBRATION OF THE MODEL
We set the values of the calibrated parameters accordingly to known empirical facts from 
the existing literature and characteristics of the modelled economies, in our case Slovenia 
and the euro area. The discount factor β is set to 0.99, following Smets and Wouters’ 
(2003) paper. The degree of habit formation parameter h for Slovenia is set to 0.80 (as in 
Kilponen et al., 2015), while for the euro area it is set to 0.60 (as in Smets and Wouters, 
2003), thus making Slovenia’s consumption slower to respond and more persistent. The 
Slovene economy size parameter s is set to 0.01.
7
 The Frisch elasticity or the inverse of the 
elasticity of work effort for both economies has a typical parameter value of 2 (Smets and 
Wouters, 2003; Rabanal, 2009; Rabanal, 2012; Micallef and Cyrus, 2013). The elasticities 
of substitution between tradable and non-tradable goods for both, domestic ( ν
TN
) and 
foreign (ν
TN, *
), economies, take the value of 0.44, following the values set by Stockman 
and Tesar (1995). The elasticities of substitution between domestic produced and foreign 
produced goods for both, domestic ( ν
HF
) and foreign (ν
HF, *
) economies, take the value of 
1.5, following Chari, Kehoe, and McGrattan (2002). Furthermore, the shares of important 
economic variables are calibrated as well. The share of government spending relative to 
GDP in Slovenia is set to 0.17 and for the euro area it is set to 0.20, while the average share 
of tradable goods in the consumption basket is set to 0.58 in Slovenia and 0.61 in the euro 
area. The Calvo wage parameters for both areass and both sectors are set to 0.81, while the 
price stickiness is set to 0.75, following the values set for Slovenia in Clancy, Jacquinot, 
and Lozej (2014) and Kilponen et al. (2015). The wage indexation parameters are set to 
0.75, according to Rabanal (2012). The quality improvement parameters θ
Z
 and θ
Z,*
 for 
both economies are set to 0.25. The Taylor rule values inflation and output gap response 
parameters γ
π
= 1.5 and γ
y
= 0.1 take usual values when modelling the euro area monetary 
policy close to Fourçans and Vranceanu’s (2004) estimation of the euro area parameters.
7 In comparison to the euro area the size of the Slovene economy is even smaller. The reason behind a slightly 
bigger economy size parameter is that very small numbers of the parameters could represent numerical difficulties 
for the model. These are shown in a very slow convergence after shocking the model or even in the inability of 
computing the responses of the shocks. However, 0.01 economy size parameter does not significantly influences 
the universum of both economies, which would be the case for small open economies.
Variable description Data transformation Country Minimum Maximum
Standard 
deviation
Weighted non-tradable 
sector gross value added
demeaned log-differences SI -3.20 5.13 1.51
Weighted non-tradable 
sector gross value added
demeaned log-differences EA -0.73 1.02 0.41
3-month Euribor
Interest rate given by 
log(1+r
t
⁄400), demeaned 
log-differences
EA -0.55 0.78 0.42

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The calibrated model is able to produce the HBS type of productivity shock. The 
following figure shows the impulse responses of the main macroeconomic variables to 
a 1 p.p. domestic tradable sector productivity shock, based on the calibrated model. The 
productivity shock increases the production of both sectors, tradable and non-tradable. 
As the quality improvement mechanism takes place, firms are compelled to raise wages 
since more sophisticated labour force is needed with the productivity picking up. The 
pick-up in wages increases inflation and consumption in both sectors. What is noteworthy 
is that inflation in the non-tradable sector increases more than in the tradable sector, thus 
providing a case for the HBS effect.
Figure 1: Impulse responses of the main variables to a 1 p.p. domestic tradable sector 
productivity shock (deviations from steady state, in p.p.)
6 ESTIMATION OF THE MODEL AND COMPARISON WITH THE 
CALIBRATED MODEL
With the obtained dataset and the calibration parameters set, the two-country two-
sector DSGE model is ready to be estimated. Doing that, we use the Bayesian inference 
methodology. We set the prior distribution of the estimated parameters, given in Table 
3. The prior and the posterior distribution of the estimated parameters and the shocks 
is presented in Table 3, while the figures with comparisons between the prior and the 
posterior distribution of the parameters are presented in Appendix A, and in Appendix 
B the dynamics of the exogenous shocks is presented. The Metropolis-Hastings MCMC 
algorithm is used with 300,000 steps and two sequential chains with the acceptance rate 
per chain of around 30%.

Č. LENARČIČ | INFLATION – THE HARROD-BALASSA-SAMUELSON EFFECT ... 293
W e estimate the quality improvement parameters θ
Z
 and θ
Z,*
 for both economies. The priors 
of both parameters were set to 0.25, while the estimates of both parameters took the values 
of 0.1676 and 0.2127, respectively. The estimated values of both quality improvement 
parameters are below the calibrated value of the parameter for the domestic economy in 
Masten (2008). Since Slovenia was catching up the average of the euro area and experienced 
higher growth and inflation, the estimate of the quality improvement mechanism had to 
be stronger during this period. With respect to the other estimated parameters, the shock 
persistence parameters seem to suggest that the productivity persistence parameters show 
less persistence than the demand shocks entering both the non-tradable and the tradable 
sector. The parameter  of the monetary policy rule is estimated as well and takes the 
value of 0.6250, suggesting a relatively high persistence of the past interest rate.
In comparison to the calibrated model, the Calvo price and wage rigidity parameters ( α's) 
are estimated to be higher, meaning that the prices and wages respond slower to exogenous 
shocks. The values of the Calvo parameters are similar comparing the foreign or domestic 
economy.
Table 3: Prior and posterior distribution of the estimated parameters and shocks
Parameter
Calibration 
model 
values
Prior 
mode
Posterior 
mode
90% HPD interval
Prior 
distribution
Prior 
distribution
θ
Z
0.250 0.250 0.1676 0.1061 0.2268 inv. gamma 0.100
θ
Z,*
0.250 0.250 0.2127 0.1153 0.3393 inv. gamma 0.100
α
H
0.750 0.750 0.6259 0.5828 0.6676 beta 0.150
α
F
0.750 0.750 0.8955 0.8524 0.9355 beta 0.150
α
H,*
0.750 0.750 0.8742 0.7620 0.9975 beta 0.150
α
F,*
0.750 0.750 0.9200 0.8963 0.9412 beta 0.150
α
N
0.750 0.750 0.8519 0.8250 0.8746 beta 0.150
α
N,*
0.750 0.750 0.9550 0.9415 0.9686 beta 0.150
α
W, T
0.810 0.810 0.9010 0.8395 0.9659 beta 0.070
α
W ,T,*
0.750 0.750 0.8249 0.7279 0.9198 beta 0.070
α
W, N
0.810 0.810 0.8889 0.8392 0.9367 beta 0.070
α
W ,N,*
0.750 0.750 0.7920 0.6909 0.8920 beta 0.070
ν
TN
0.440 0.500 0.5471 0.1888 0.8864 gamma 0.200
ν
HF
1.500 1.500 1.1671 0.5602 1.7190 gamma 0.500
φ
H
0.500 0.500 0.2600 0.0614 0.4389 beta 0.200
φ
F
0.500 0.500 0.4762 0.2029 0.7278 beta 0.200
φ
H,*
0.500 0.500 0.4643 0.3093 0.6329 beta 0.100
φ
F,*
0.500 0.500 0.1014 0.0120 0.1864 beta 0.200
φ
N
0.500 0.500 0.3958 0.2158 0.6011 beta 0.100

ECONOMIC AND BUSINESS REVIEW | VOl. 21 | No. 2 | 2019 294
Source: Author’s calculations.
6.1 Impulse response functions and the historical shock decomposition
In this subsection, we present the historical shock decomposition and impulse response 
functions. The purpose of both is to provide a description of the severity of shocks that 
influence the macroeconomic variables. Figure 2 shows the contributions of the exogenous 
shocks onto the price differential between the non-tradable and tradable sectors through 
time. It is evident that the inflation differential between the non-tradable and tradable 
sectors has been influenced by productivity components. As the financial crisis lingered 
on in the second wave after 2010, the difference between the non-tradable and tradable 
dynamics turned to be negative, implying a slowdown in the tradable sector productivity. 
Only with the start of the recovery of the Slovene economy in 2015, the difference between 
the inflation of both sectors returned to positive figures and has continued the pattern 
from before the financial crisis in 2008 by being affected with positive tradable sector 
productivity shocks.
Parameter
Calibration 
model 
values
Prior 
mode
Posterior 
mode
90% HPD interval
Prior 
distribution
Prior 
distribution
φ
N,*
0.500 0.500 0.2926 0.1718 0.4120 beta 0.100
ρ
Z,T
0.750 0.750 0.3940 0.2721 0.5210 beta 0.100
ρ
Z,T,*
0.750 0.750 0.3958 0.2485 0.5370 beta 0.100
ρ
Z,N
0.750 0.750 0.5840 0.4225 0.7360 beta 0.100
ρ
Z,N,*
0.750 0.750 0.4358 0.2903 0.6000 beta 0.100
ρ
G,T
0.750 0.750 0.8392 0.6415 0.9662 beta 0.100
ρ
G,T,*
0.750 0.750 0.8468 0.7520 0.9511 beta 0.100
ρ
G,N
0.750 0.750 0.9030 0.6564 0.9918 beta 0.100
ρ
G,N,*
0.750 0.750 0.8062 0.6567 0.9330 beta 0.100
0.750 0.750 0.6250 0.4788 0.7758 beta 0.100
ε
MP
- 0.4000 0.1266 0.1113 0.1417 inv. gamma 0.1000
ε
Z
- 0.5000 0.1840 0.1509 0.2156 inv. gamma 0.2000
ε
Z,T
- 0.7000 0.2593 0.2211 0.2978 inv. gamma 0.2000
ε
Z,T*
- 0.5000 0.3710 0.2322 0.5064 inv. gamma 0.2000
ε
Z,N
- 0.7000 0.2472 0.2126 0.2803 inv. gamma 0.2000
ε
Z,N,*
- 0.5000 0.5192 0.2784 0.7470 inv. gamma 0.2000
ε
G,T
- 1.0000 0.5061 0.4420 0.5733 inv. gamma 0.2000
ε
G,T,*
- 1.0000 0.4088 0.3539 0.4595 inv. gamma 0.2000
ε
G,N
- 1.0000 0.6004 0.5109 0.6883 inv. gamma 0.2000
ε
G,N,*
- 1.0000 0.4032 0.3538 0.4484 inv. gamma 0.2000

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Figure 2: Historical shock decomposition in the inflation differential between the non-
tradable and the tradable sector (deviations from steady state, in p.p.)
*Note: Tradable productivity shocks are the sum of the contributions of the country-specific domestic 
tradable sector shocks ε
Z,T 
and ε
Z,T,
*
 and the common productivity shock ε
Z
. The non-tradable sector 
productivity shocks ε
Z,N
 and ε
Z,N, *
 are depicted separately. Other shocks are the sum of the contributions 
of the government spending shocks ( ε
G,T,
 ε
G,T,
*
,
 ε
G,N
 and ε
G,N, *
) and the monetary policy shock ε
MP
.  
Source: Author’s calculations.
It is more intuitive to look at the impulse response functions in order to understand 
the effects of productivity shocks. Figures (3-6) show the responses of the main 
macroeconomic variables to different exogenous shocks and depict a 20-period horizon. 
In studying the impulse responses, we will only consider the productivity shocks that 
hit the two economies. Figure 3 displays the impulse responses of the main variables to 
a 1 p.p. domestic tradable sector productivity shock ε
Z,T
. When a positive productivity 
shock hits the tradable sector, tradable and non-tradable inflation increases in Slovenia, 
causing the overall inflation to increase. This is due to a wage increase in the tradable 
sector via quality improvement mechanism that increases the need for more demanding 
inputs in the production process, thus increasing the marginal costs, as wages increase the 
marginal costs increase, causing the inflation to increase. The Harrod-Balassa-Samuelson 
type productivity shock causes the increase of output and consumption as well. Under 
the implementation of quality improvement mechanism and under the price and wage 
frictions the HBS effect seems to hold, based on the impulse responses, the effects on the 
euro area macroeconomic variables are small.

ECONOMIC AND BUSINESS REVIEW | VOl. 21 | No. 2 | 2019 296
Figure 3: Impulse responses of the main variables to a 1 p.p. domestic tradable sector 
productivity shock (deviations from steady state, in p.p.)
The same pattern is observed when we analyse a 1 p.p. common tradable sector technology 
shock ε
Z
, shown in Figure 4. Similar effects happen when a 1 p.p. foreign tradable sector 
productivity shock ε
Z,T,*
 hits the rest of the euro area (Figure 5). The difference is that 
this time the quality mechanism works abroad, so that spillovers come with a lag and 
in smaller magnitude. As a consequence, marginal costs do not increase in the domestic 
country, but positive effects from the price increase abroad make the tradable sector more 
profitable, increasing production, consumption, price and wages in the domestic country.

Č. LENARČIČ | INFLATION – THE HARROD-BALASSA-SAMUELSON EFFECT ... 297
Figure 4: Impulse responses of the main variables to a 1 p.p. common euro area tradable 
sector productivity shock (deviations from steady state, in p.p.)
Figure 5: Impulse responses of the main variables to a 1 p.p. foreign tradable sector productivity 
shock (in p.p. deviations from steady state)

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We are left to study the effects of the non-tradable sector productivity shocks, as they are 
depicted in Figure 6. In contrast to the tradable sector productivity shocks, the domestic 
non-tradable sector productivity shock ε
Z,N
 does not enter the quality improvement 
mechanism. Consequently, it acts more as a (classical productivity) shock that decreases 
marginal costs and lowers non-tradable sector inflation, while the tradable sector 
marginally increases since the labour supply moves from the non-tradable sector to the 
tradable sector. The sectoral and the overall output, as well as the consumption, increase.
Figure 6: Impulse responses of the main variables to a 1 p.p. domestic non-tradable sector 
productivity shock (deviations from steady state, in p.p.)
6.2 Policy implications and way forward
The HBS effect is typically used to explain inflation differentials for countries experiencing 
a catching-up process. As the relatively poorer countries adopt new technologies in those 
sectors that are open to international trade (i.e., the tradable sector), they will experience 
higher productivity growth in the tradable sector, increased wages via quality mechanism, 
and consequently a higher inflation in sectors that are not open to international trade, 
as is the non-tradable sector. Therefore, the HBS effect hypothesis could help to explain 
higher inflation rates in the non-tradable sector than in the tradable sector, hence leading 
to higher overall inflation. 
Another important issue to point out is that the HBS effect theory does not explain the 
possible sources of productivity differentials between different sectors and countries. As 

Č. LENARČIČ | INFLATION – THE HARROD-BALASSA-SAMUELSON EFFECT ... 299
the HBS is often associated with catching-up and convergence phases of less developed 
countries, there is a possibility that a catching-up process could take place without the 
HBS effect. This happens if productivity growth in both sectors (i.e., tradable and non-
tradable) is equally high. Additionally, some countries that already experience high 
productivity levels may for various reasons (i.e., economic policies that are conducive 
to technological innovation) also experience relatively high productivity growth in the 
tradable sector. Importantly, in those countries structural rigidities and different degrees 
of competition
8
 can affect productivity growth differentials between sectors and overall 
productivity growth in a way that favours either positive or negative inflation differentials. 
Despite wage setting being typical for the DSGE model setting, following Calvo (1983) 
and later on Christiano (2005) labour market frictions, some issues could still arise 
in that respect. The wage setting in the non-tradable sector could be to a large extent 
governed by the non-market forces and other structural rigidities since a large part of the 
non-tradeable sector is comprised of the public sector. In our case, the model does not 
structurally distinguish between the private and the public sector and would consequently 
not be able to consider various types of non-market forces. However, it does provide some 
distinction in a sense of having two different (estimated) rigidity parameters of the wage 
setting equation for the non-tradable and the tradable sector. Based on the estimation 
figures the non-tradable sector wages seem to be more rigid than those in the tradable 
sector. They are slower in responding to exogenous shocks, which would to some extent 
simulate the differences between the private and the public sector. This issue could go 
beyond the scope of the present paper, but it could represent an additional way forward 
to extend the model into a more complex one by additionally restricting and dividing the 
modelled labour market, as well as the government sector.
Nonetheless, the continued process of convergence processes in the euro area should lead 
to a decline in inflation dispersion amongst the euro area countries due to a price level and 
income convergence in the long-run. On the other hand, other structural factors such as 
differences in the degrees of wage and price rigidities and divergent degree of competition 
in domestic markets may have also contributed to the observed inflation differentials and 
their persistence. In this respect, the relative degree of market competition seems to be 
an important parameter in explaining the size and volatility of relative price responses to 
symmetric shocks across euro area countries.
7 CONCLUSION
This paper draws conclusions based on a construction of a theoretical two-country two-
sector DSGE model with both economies operating in a common monetary union. We 
were able to produce and show the existence of the HBS effect in a calibrated and estimated 
structural dynamic setting of the DSGE model by introducing a quality improvement 
mechanism that helps to explain why prices grow when productivity increases, especially in 
8 i.e., the private vs. the public sector.

ECONOMIC AND BUSINESS REVIEW | VOl. 21 | No. 2 | 2019 300
catching-up economies like the new EU member states in 2000. The quality improvement 
mechanism affects marginal costs by requiring the use of more advanced inputs in the 
production process. Quality improvement of goods overcomes a typical open economy 
theoretical specification that reduces the relative prices of domestic tradable goods relative 
to the foreign prices, and consequently worsens the terms of trade for the domestic 
economy. Despite showing the presence of the HBS effect, the effect per se is not large 
enough to pose significant risks to central banks in their quest for price stability.
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APPENDICES
Appendix A: Prior and posterior distribution
Figure A1: Prior (dashed line) and posterior distribution (solid line) of the estimated shocks
Figure A2: Prior (dashed line) and posterior distribution (solid line) of the estimated 
parameters

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Appendix B: Exogenous shocks
Figure B1: Exogenous shocks