The price block of Eesti Pank’s macro model:
Implications for the Estonian inflation
Aurelijus Dabušinskas, Martti Randveer, Märten Kress
Bank of Estonia
Abstract: The paper describes a system of price equations that form a new price
block of Eesti Pank’s macro model. The price block covers four kinds of prices: the
GDP deflator, the import deflator, the price of labor and several categories of
consumer prices: fuel, food and energy price indexes as well as the remaining HICP
core. The long-run equilibrium of the price block is built on the assumption that
convergence of various Estonian prices to the respective price levels in the EU-15
will be completed simultaneously with real income convergence. Simulations of
shocks to three exogenous prices – the US dollar exchange rate, the world oil price,
and the EU-15 price of food – are performed to investigate the nature of domestic
price responses to such disturbances and to infer the degree to which external forces
are likely to affect domestic inflation in the medium run. This analysis shows that
the influence of persistent shocks of “typical” size on the annual HICP inflation rate
is relatively strong, ranging from 0.3 to 0.45 p.p. Finally, several targeting exercises
illustrate how much some selected external variables must change, one at a time, to
make Estonian inflation be of a certain target rate over the two-year horizon.
Authors e-mails: aurelijus.dabusinskas@epbe.ee, martti.randveer@epbe.ee
1
1. Introduction
The paper presents an alternative system of price equations for the existing macro
model of the Estonian economy. The new price block differs from the previous one in
terms of its structure and the way individual prices are modeled, but the most important
distinguishing features of the new price block are imbedded in its long-run equilibrium
dynamics. Firstly, the new version of the price block posits that labor productivity is the
main determinant of real labor costs in the long run. Coupled with the markup-based
price setting by firms, this relationship is also used to model one of the central prices of
the module – the GDP deflator. Secondly, the long-run dynamics of the price block is
made to reflect our priors about income and price level convergence in the long run. As
will be seen later, these considerations impose a number of static and dynamic
restrictions that constrain the estimations a great deal, representing the cost of making
the price system have desirable long-run properties.
Current macroeconomic models tend to have neo-classical properties in the long run,
when the steady state (balanced growth path) of the economy is supply determined, but
maintain certain features of a demand-driven economy in the short run. Since price
developments play a crucial role in the adjustment of the real side of the economy to its
long-run equilibrium, the price block of the macro model must be consistent with the
supply section of it, at least in the long run. For this reason, a natural starting point in
developing the price block is to consider the behavior of profit maximizing firms.
Notably, under the now common assumption of monopolistic competition, optimality
conditions describing the behavior of firms contain a couple of relationships that are
essential for modeling prices. First, the optimal choice of labor input makes the real
wage anchored to labor productivity in the long run. Although this relationship alone
(without considering the labor market) is not sufficient to determine the equilibrium
level of real wage, the wage-productivity bond implied by firms’ demand for labor is
the link that later can be used to integrate the supply and price blocks of the macro
model. The second key relationship that follows from the optimizing behavior of firms
under monopolistic competition is that prices are set as markups over marginal cost. 1
This establishes a direct link between prices and costs and relates the nominal
dimension of the model economy to its real part. As a result, the price of domestic
production, the GDP deflator (at factor cost), becomes a central nominal variable around
which the rest of the price block can be built.2 For example, various consumer prices are
modeled as composites of the GDP deflator and relevant foreign prices.
In addition to explaining the real wage and GDP deflator, the price block covers four
categories of consumer prices (HICP): FOOD (approximately 20 percent of the
consumer basket), FUEL (about 5 percent of the basket), HOUSEHOLD ENERGY
(about 10 percent of consumer expenditures) and the remaining part, HICP CORE
(approximately 65 percent). There are several reasons for modeling them separately.
First, food and energy prices are known to be more volatile. Hence, although
movements in these prices may be quite important for overall inflation in the short run,
they are relatively less informative about longer-term inflationary developments
(Wynne, 1999; Vega and Wynne, 2001). Dropping the two components from HICP to
obtain HICP CORE may help us follow underlying inflation in the economy more
1
Given nominal wage and cost of capital, technology and the firm-specific demand.
The GDP deflator at factor cost is obtained from the GDP deflator by netting out the effect of indirect
taxes. This calculation is discussed in more detail later.
2
2
closely. Second, FOOD and FUEL represent relatively well-defined and homogenous
groups of goods, whose prices have rather distinct determinants. For example, FUEL is
strongly influenced by the international oil price and the US dollar exchange rate, while
FOOD follows the corresponding price index of EU-15 closely. Finally, some
disaggregation of consumer prices is needed for better understanding of actual and
future price developments as well as investigating more detailed scenarios in the
simulation analysis.
Another important feature of the modeled price system stems from the requirement that
the long-run dynamics of various prices and the relationships assumed between them in
levels be mutually consistent. For example, if some consumer price is modeled as a
weighted average of the price of domestic output and that of foreign production, the rate
of consumer price inflation must be related to the rates of inflation in the two production
prices accordingly. Moreover, in the context of error-correction specification that is
used to model all explicitly considered prices, such consistency of inflation rates in the
long run imposes restrictions on the short-run adjustment coefficients as well.
Perhaps most importantly, however, the long-run inflation rates that the price equations
are made consistent with, reflect our priors about the convergence of various Estonian
prices to the levels prevailing in the EU-15. In this regard, an operational assumption is
made that nominal price convergence and income convergence (vis-à-vis the EU-15
average) will proceed in parallel and will be completed simultaneously. Some empirical
basis for this prior is presented in Section 2, which investigates the relationship between
price and income levels in European countries. Section 3 builds upon this evidence and
provides a detailed account of how the assumption of parallel income and price
convergence was used in developing the long-run structure of the price block.
Once the overall structure of the price block is made clear in Section 3, Section 4
considers each price category individually and describes the estimation results for one
equation at a time. Section 5 discusses the performance of the price block as a whole
and presents simulated responses to shocks in selected exogenous prices: the US dollar
exchange rate, the international oil price and food prices in the EU-15.
3
2. The relationship between income and price levels
It is assumed in the inflation model that the price and income levels in Estonia will
converge to the average income and price levels of the so-called older EU member
states simultaneously.3 Thus Estonian consumer price inflation in the long run is subject
to the speed of convergence with income levels. In support of this assumption, the
present section provides (1) a brief survey of research on the relationship between
income and price levels in different countries, (2) an evaluation of the relationship
between income and price levels in the EU, and (3) an investigation of relative changes
in income and price levels in the new EU member states over the period 1995-2002.
Studies of the relationship between income and price levels in different countries show
that there tends to be a statistically significant positive correlation between the two
variables. The presence of this relationship is most clearly demonstrated using samples
with large cross-country variation in income levels. Table 2.1 summarizes the main
findings of several papers in this area of research. Generally, the evidence seems to
suggest that, all other conditions being equal, a 1 percentage point higher income is
associated with 0.5-0.9 percentage points higher price level.
Table 2.1. A summary of the research on the correlation between income and price levels in different
countries
Author
Randveer (2002)
IMF (2000)
Hansson-Helliwell (1990)
Kravis and Lipsey (1988)
Kravis and Lipsey (1988)
Kravis and Lipsey (1988)
Sample
Period
Result (1)
Comments
52 countries
EU15 + CEE
1996
1993-99
19 European, Asian, American
and African states
19 European, Asian, American
and African states
24 European, Asian, American
and African states
1960-83
0.5-0.7%
0.40%
0.40%
0.55-0.85%
Only tradable
1960-83
0.81-1.065%
1960-83
0.54-0.95%
Kravis (1985)
Only nontradable
0.60-0.87%
Notes:
(1)
In the result column the rise coefficient of the following regression equation is referred to as
Price leveli = Constant + Rise*Income leveli + ei .
As a more detailed example, Figure 2.1 compares relative price levels in European
countries, where the EU-15 price-level index equals 100. In particular, the figure shows
that the average price level of the EU candidate countries (currently the new EU
member states) amounted to about 53 percent of the average EU price level in 2002.
Among the new member states (NMS-10), the lowest price levels were in the Slovak
Republic and Lithuania, accounting for 42 and 45 percent of the average EU-15 price
level, respectively. The highest price level among NMS-10 was in Cyprus, which
amounted to approximately 82 percent of the EU-15 price level and was even higher
than the price levels in Portugal and Greece. The relative price level in Estonia was
3
These conclusions will not change significantly, but we anticipate that Estonian price and income levels
will conform at the same time as the average EU-25 price and income levels.
4
close to the average price level of the new EU member states (53% of the EU-15 price
level). From among the older EU member states, the highest price level was in Denmark
(126 percent). Finally, the average price level in the present European Union, or EU-25,
was equal to 96 percent of the EU-15 price level.
The relationship between price and income levels can also be observed across different
product groups. In new member states (including Estonia), the relative price levels
corresponding to the 12 product groups of the consumer basket are lower than the
respective price levels in the older EU member states. The price levels are most
different in the product groups ‘Gross rents, fuel and power’ and ‘Education,’ where the
average price levels in the new member states account for only 37 and 33 percent of the
EU-15 average price levels, respectively. The difference in price levels is smallest in
the case of category ‘Communication,’ where the average price level in the new
member states makes up 98 percent of the EU-15 average price. 4
Figure 2.1 Comparison of general price levels in European states,
December 2002 (EU15 =100)
BG
RO
SK
LT
LV
TR
CZ
EE
NMS10
PL
HU
MT
SI
PT
GR
CY
ES
IT
EU25
EU12
BE
FR
EU15
AT
NL
DE
UK
IE
FI
LU
SE
IS
DK
NO
CH
0
25
50
75
100
125
150
Notes:
NMS10 – 10 member states new in May 2004 (New Member States).
Source: Eurostat.
4
The smallest difference between the average price levels in the EU-15 and Estonia is in the product
group ‘Clothing and footwear’ where the Estonian price level constitutes 84 percent of the EU-15
average.
5
Figure 2.2 Comparison of price levels in major product groups in the old EU
member states (EU15), new EU member states (NMS10) and Estonia (EE), EU15
=100.
100
75
50
25
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Source: Eurostat.
Table 2.2 presents the implications of simple regression analysis of the strength and
statistical significance of the correlation between price and income levels in the EU
states in 2002. The strongest relationship between price and income levels can be
observed in the case of EU-25 (but Luxembourg excluded), where, all other things
being equal, a 1 percentage point higher income is associated with 0.88 percentage
points higher price level. The regression results also indicate that the relationship is
statistically and economically significant in all the sub-samples of Table 2.2. In order to
see whether fitting a linear regression is appropriate, Figure 2.4 plots the regression line
based on the EU-25 price and income levels (excluding Luxembourg) together with a
third-degree polynomial (with four parameters) in income. As can be seen from the
figure, the non- linearities captured by the polynomial are minor, indicating that the
linear regression provides a proper description of the data.
Table 2.2 The relationship between income and price levels in
European countries, 2002
Rise
EU25+IS,NO,CH,BG,RO,TR
EU25
EU25 excl. LU
EU15
EU15 excl. LU
NMS10
0.74
0.65
0.88
0.33
0.81
0.74
Notes:
(1)
Price leveli = Constant +Rise*Income leveli + ei .
6
Std.deviation t-statistics
0.07
0.08
0.06
0.12
0.15
0.16
10.60
8.53
15.60
2.76
5.43
4.72
R2
0.80
0.76
0.92
0.37
0.71
0.74
Relative price level, EU-15=100
Figure 2.3 The relationship between income and price levels in the European
Union (except for Luxembourg) in 2002.
GDP per capita relative to EU-15
Notes: The figure shows a linear regression curve and the 4-parameter Cubic spline curve.
In addition to the clear statistical link between income and aggregate price levels, there
is also a strong correlation between income and relative price levels in the majority of
different product groups in the EU states (see tables 2.3 and 2.4). In the case of EU-15
countries, which have relatively similar income levels, the correlations between income
and price levels in different categories of goods are weaker. The inclusion of the new
member states in the sample raises these correlations, however. In the sample of 25
European Union countries, the correlation is strongest in ‘Rent, fuel and power’,
‘Education’ and ‘Food and beverages’. The results are similar if we look at the
respective correlations in the sample of the new member states alone. As can be seen
from Table 2.4, a rise in income by 1 percent relative to the EU-15 average income
results in 0.4-1.5 percent increases in relative price levels in different product groups.
The only product category that does not show this positive relationship is
‘Communication’.
7
Table 2.3 The relationship between price and income levels in the European
Union, major product groups, 2002
Gross Domestic Product
Gross rents, fuel and power
Education
Food & non-alcoholic beverages
Final consumption by private households
Furnishings, equipment, maintenance
Health
Clothing & footwear
Recreation & culture
Restaurants & hotels
Miscellaneous goods & services
Transport
Alcoholic beverages & tobacco
Communications
Correlation, %
(EU25)
Correlation, %
(EU15)
Correlation, %
(NMS10)
87.2
87.2
81.5
81.1
80.9
80.4
79.7
74.4
73,4
71.1
71.0
66.3
50.0
-30.7
60.8
63.9
49.1
48.9
40.3
44.7
41.6
32.2
25.4
33.1
16.0
11.8
10.7
-50.5
85.8
80.0
83.1
73.0
81.2
68.0
78.4
57.5
65.7
45.4
67.3
76.9
61.4
-54.5
Table 2.4 The relationship between price and income levels in the European
Union (EU-25, except for Luxembourg), major product groups, 2002
Gross Domestic Product
Final consumption by private households
Food & non-alcoholic beverages
Alcoholic beverages & tobacco
Clothing & footwear
Gross rents, fuel and power
Furnishings, equipment, maintenance
Health
Transport
Communications
Recreation & culture
Education
Restaurants & hotels
Miscellaneous goods & services
Rise (1)
Std.deviation
t-statistic
R2
0.88
0.87
0.69
0.92
0.40
1.30
0.60
0.99
0.68
-0.15
0.63
1.54
0.83
0.87
0.06
0.07
0.07
0.19
0.08
0.11
0.06
0.09
0.08
0.15
0.08
0.18
0.12
0.09
15.60
13.00
10.20
4.77
4.90
12.20
9.32
10.80
8.42
-0.99
7.98
8.41
6.87
9.67
0.92
0.88
0.82
0.51
0.52
0.87
0.80
0.84
0.76
0.04
0.74
0.76
0.68
0.81
Notes:
(1)
Rise refers to the rise coefficient of the following regression equation:
Price level of the product groupi = Constant + Rise*Income leveli + ei .
Finally, we investigate whether the relationship between income and price levels in the
new EU member states carries over time. We find that during the period 1995-2002, the
income and price levels of the new member states grew one-to-one on average. In
particular, 1 percent economic growth was associated with a 1 percent rise in the
relative price levels over the period 1995-2002. At the same time, the relationship
tended to be weaker over shorter periods of time (see Table 2.5). For example,
8
economic growth of 1 percent was associated with only 0.7 percent rise in price levels
on average during 2000-2002.
Table 2.5 The relationship between price and income levels in the new member
states of the European Union (1)
Period
Sample
Rise
Std.deviation
t-statistic
R2
1995-2002
EE
CY
LV
LT
HU
SI
SK
NMS10 excl. CZ, MT, PL
NMS10 excl. CZ, MT, PL
NMS10 excl. CZ
NMS10
2.17
0.41
2.74
3.57
2.00
-0.03
0.40
1.01
0.92
0.81
0.71
0.29
0.14
0.63
0.93
0.43
0.12
0.28
0.10
0.11
0.09
0.11
7.60
2.81
4.36
3.83
4.64
-0.27
1.44
9.96
8.42
8.69
6.68
0.91
0.97
0.76
0.71
0.78
0.01
0.26
0.83
0.81
0.79
0.67
1998-2002
1999-2002
2000-2002
Notes:
(1)
Based on time series regression.
Similarly, there are differences in the evolution of income and prices across the
countries of the sample. For example, the convergence of price levels was relatively
faster in the Baltic States and Hungary and slower in the Slovak Republic and Cyprus.
Notably, the relatively rapid income growth did not result in price level convergence of
a similar magnitude in the Slovak Republic (see Figure 2.4).
Price level relative to EU-15
Figure 2.4 Convergence of price and income levels in CEE states for 1995-2002.
GDP per capita relative to EU-15
9
To sum up, the empirical evidence presented here suggests that Estonian consumer price
inflation is likely to be associated with income level convergence in the long run. If we
assume that Estonian income and prices are approaching the respective levels in the
older EU member states simultaneously, a 1 p.p. growth differential between Estonia
and the older EU member states will result in a 0.7 p.p. difference in inflation rates.
Thus, if long-term economic growth in Estonia amounts to 5 percent and that of the
older EU member states to 2 percent, Estonian consumer price inflation will exceed
inflation in the older EU member states by approximately two percentage points
(inflation rates should be 4 and 2 percent, respectively).
3. The structure of long-run relationships between prices
The new price block models six price series: the real wage, GDP deflator (GDP DEF),
import deflator (IMP DEF), and the three components of HICP – FOOD, FUEL and
HICP CORE.5 The focus of this subsection is on the set of long-run relationships upon
which the price module is built. In what follows, these relationships play at least two
important roles. Firstly, they determine the long-run dynamics of the price system and
therefore implement some of our priors about price level convergence into the model.
Secondly, these relationships represent the long-run components of the error-correction
specifications used in modeling each of the six endogenous prices.
By far the most important assumption made about the nature of price dynamics in the
long run is that nominal (price level) convergence will proceed together with real
(income) convergence and that the two will take approximately the same amount of
time. Table 3.1 summarizes the actual data and our priors used to calculate the duration
and speed of real and nominal convergence to the EU-15 average. To start from real
economic variables, the assumed scenario of Estonia’s income per capita convergence
to that of the EU-15 average is reported in the top panel of Table 3.1. In particular, two
things are assumed there: that the annual rate of income per capita growth is going to be
2 percent in the EU-15 and 5 percent in Estonia. According to the latest statistics of
PPP-based income differences by Eurostat, real GDP per capita in Estonia amounts to
44 percent of the EU-15 respective average. It is then easy to calculate that at the 3
percent growth differential assumed, it would take for Estonia 28.3 years to eliminate
the currently existing income gap.
5
Since by definition the real wage is equal to the ratio of the nominal wage to the GDP deflator, it could
be said that the price block models the nominal rather than real wage.
10
Table 3.1
EU-15 average
Estonia
Real convergence
Real GDP per
Assumed longcapita relative
run RGDP per
to EU-15
capita growth,
average, %
% p.a.
100
2
44
5
Implied time to
convergence, years
28.3
Nominal convergence
EU-15 average
All prices
Level relative to EU-15
average, %
100
Assumed long-run inflation, %
p.a.
2
Level relative to EU-15
average, %
GDP DEF
CONS DEF
INV DEF
GOV DEF
IMP DEF
52.6
56
85
30
100
Implied long-run inflation, % p.a,
if nominal convergence takes 28.3
years to complete
4.3
4.1
2.6
6.4
2
HICP, of which
HICP CORE a
FOOD
FUEL b
HOUSEHOLD
ENERGY c
60.2
57.3
69.7
63.5
50
3.8
4.0
3.3
3.6
4.5
Estonia
Source: Eurostat and author’s calculations
a
Excluding FOOD (HICP group 0110), FUEL (0722) and HOUSEHOLD ENERGY (0450).
b
HICP group 0722, Fuel for personal transport.
c
HICP group 0450, Electricity, gas and other fuels.
Following the assumption of simultaneous real and nominal convergence, the bottom
panel of Table 3.1 reports the inflation rates that must prevail in various Estonian price
categories if their levels are to reach the respective EU-15 average over the period of
28.3 years. As the time of converge is fixed, the current price level in various groups of
goods is the only determinant of the calculated inflation rates. For example, the
relatively high level of Estonian food prices warrants that the rate of inflation of 3.3
percent is sufficient for nominal convergence in this category of goods. In contrast,
household energy prices, which are mostly administratively regulated ones, would have
to grow at the higher annual rate of 4.5 percent to reach the EU-15 average level over
the same period of time. At this moment, it seems worth emphasizing the profound role
that these calibrated long-run average inflation rates are meant to play: they will be the
benchmark rates that the price module will be made to generate in its long-run (out-ofsample) equilibrium dynamics.
11
It is also important to realize that the calibrated long-run inflation rates have strong
implications for the relationships among prices in levels. Indeed, most of the prices in
the price block are modeled as weighted (geometric) averages of other price indexes, in
which case both (log) price levels and inflation rates are linked by the same linear
relationships. Table 3.2 presents all such relationships in the present price module. It
shows, for example, that the major component of consumer prices, HICP CORE, is
modeled as a weighted average of prices set by domestic and foreign producers. As a
result, the long-run average inflation rates of HICP CORE, GDP DEF and IMP DEF
discussed in Table 3.1 are consistent among themselves only if the weight of the GDP
deflator in HICP CORE is 0.865.
Table 3.2 Long-run linear relationships between various prices
HICP CORE = w*GDP DEF + (1-w)*IMP DEF
Weight, w
GDP DEF
IMP DEF
0.865
0.135
4.3
2.0
Inflation, %
Implied average
4.0
FOOD = w*GDP DEF + (1-w)*FOOD EU-15
Weight, w
GDP DEF
FOOD EU-15
0.559
0.441
4.3
2.0
Inflation, %
Implied average
3.3
FUEL = w*GDP DEF + (1-w)* OIL PRICE
Weight, w
GDP DEF
OIL PRICE
0.705
0.295
4.3
2.0
Inflation, %
Implied average
3.6
HICP by components
Weight, w
Inflation, %
FOO
D
0.206
FUEL
HICP CORE
0.055
HOUSEHOLD
ENERGY
0.082
3.3
3.6
4.5
4.0
Implied
average
0.657
3.9
IMP DEF = w*EP FIXED + (1-w)* (EP FLOAT/EER FLOAT)
EP FIXED
EP FLOAT/EER FLOAT
Weight, w
0.60
0.40
Inflation, %
2.0
2.0
Implied average
2.0
In fact, Table 3.2 shows that there are five such relationships in the price block. Four of
them involve different consumer prices: i) HICP CORE is a weighted average of GDP
DEF and IMP DEF; ii) FOOD prices are determined by the price of food in the EU
(FOOD EU-15) and domestic cost (GDP DEF); iii) FUEL prices depend on the world
price of oil (OIL PRICE) and domestic cost (GDP DEF), and iv) all these components
12
together with HOUSEHOLD ENERGY prices are combined to obtain the overall HICP.
Finally, the fifth relationship model IMP DEF as a weighted average of two foreign
price indexes. In all cases, the long-run average inflation rates discussed in Table 3.1
and the weights shown in Table 3.2 are consistent with each other. It remains to explain
how this consistency has been established.
In principle, if the error-correction framework is appropriate to model a certain
multivariate relationship, the long-run error-correction term of the model can be
estimated. Unfortunately, not a single attempt to estimate the long-run relationships of
the kind discussed in Table 3.2 has been successful. Neither simple OLS in levels nor
unrestricted autoregressive distributed lags or the Johansen cointegration procedure led
to robust and sensible long-run relationships between prices. Of course, this could be
caused by specification problems in the model equations. Alternatively, the failure to
pin down the long-run relations could be due to the shortness and turbulent nature of the
estimation period. As a way out, it has been decided to rely more on theoretical
considerations and our priors about real and nominal convergence than just the data to
ensure that the long-run dynamics of the price block are internally consistent.
As a result, the weights in all five equations of Table 3.2 are not estimated but
calibrated. In the case of the thirst three equations, the weights are calculated to make
the equations hold for the long-run inflation rates of Table 3.1. Without additional
information, it is difficult to come up with a normative assessment of how realistic the
calculated weights are, although the one of import prices in HICP CORE seems to be on
the low side. In such a situation, it remains to wait and see how well the model performs
in terms of dynamic in- and out-of-sample simulations.
The weights in the remaining two long-run relationships of Table 3.2, for HICP and
IMP DEP, have been obtained in a different way. The equation for HICP is in fact an
identity because its weights are the same as those used by Eurostat. Since Eurostat
adjusts the HICP weights annually, the table shows only the most recent, year 2004,
weighs, which will be extrapolated in the out-of-sample simulations. The import
deflator is modeled as being equal to the effective foreign price, that is, as a weighted
average of prices corresponding to two types of foreign trading partners: those whose
currencies have fixed exchange rates vis-à-vis the Estonian kroone, EP-FIXED, and
those whose currencies are floating against the Estonian kroone, EP-FLOAT. Since in
the case of the latter group changes in exchanges rates matter as well, EP-FLOAT enters
the equation divided by the effective nominal exchange rate, ER-FLOAT, expressed in
terms of a foreign currency per Estonian kroone. Given this setup, the weights of 60 and
40 percent applied to EP-FIXED and EP-FLOAT, respectively, are chosen to match the
empirical shares of the two trading partner groups in Estonian imports.
Before moving on to discuss the dynamic parts of error-correction equations, it needs to
be clarified what assumptions should be added concerning the long-run dynamics of the
price block to prevent Estonian prices from growing faster than their foreign
counterparts after the nominal convergence is completed. Given the simple and stylized
way in which the long-run of the price block is modeled, it can be assumed that the
long-run inflation rates of all domestic prices drop discontinuously to 2 percent at the
moment nominal convergence is completed. The 28.3-year convergence horizon
considered here is arguably long enough to make such discontinuities irrelevant for
modeling the medium run. A related but more general question is whether the log-linear
13
price convergence is a good enough approximation of reality for the purpose of this
work. An in-sample dynamic solution of the model is likely to shed some light on this
issue, but a more reliable assessment will be possible only when a large enough number
of out-of-sample observations become available.
4. Equations
Having introduced the long-run terms, it is now time to discuss the short-run dynamic
parts of individual price equations and complete the description of error-correction
specifications. The estimations of the dynamic parts were carried out with the restriction
imposed that the inflation rates of Table 3.1 satisfy the equations in the long-run
dynamics. The section is divided into seven sub-sections and covers one price category
at a time.
4.1 Real wage
The equation for the real wage follows from one of the first order conditions of firm’s
profit maximization problem. Assume, as it is standard in today’s macroeconomic
models, that an economy consists of a continuum of monopolistically competitive firms
indexed by i  0,1 that produce differentiated products Yi using Cob-Douglas
technology Yi  AK i (et Li )1  . If consumers’ utility depends on a CES composite of

 1 1   1
the differentiated products, Y    Yi di  , the solution to the intratemporal
0


P
consumer problem implies isoelastic demand curves of the form Yi    Y and the
 Pi 
1
 1 1  1
aggregate price index P    Pi di  , where Pi denotes the price of product Yi . In
0

this setup, the representative firm solves the following profit maximization problem:
1  1




max
Y

P
Y

WL

P
K

PY
Yi   WLi  Pk K i ,

Pi , Li , K i ,Y I  i
i i
i
k i

s.t.
Y  AK  (et L )1  ,
i
i
 i

where W is the nominal wage rate, Pk is the (nominal) cost of capital, defined as
Pk  P(r   ) , and r and  are the real interest rate and the depreciation rate,
respectively. Note that the second expression in the definition of profit establishes that
the firm faces its own downward-sloping demand curve. The first order condition for
the optimal choice of labor input implies that the firm equates the marginal revenue
  1 Yi
 W . Equivalently, this
product of labor with its marginal cost, Pi (1   )
 Li
condition can be interpreted as describing the pricing behavior of monopolistically
competitive firms, namely, that prices are set as markups over marginal cost,
14

1 WLi
. The most important implication of the optimality condition for
  1 1   Yi
this work is that in a symmetric equilibrium, the supply side of the economy makes the
real wage follow the marginal productivity of labor with unitary elasticity:
Pi 

W  1
Y

(1   ) .
P

L
(1)
It is this theoretical relationship between the real wage and labor productivity that gives
the basis for the real wage equation in the price module. In the empirical application, the
estimates for the elasticity of real wage with respect to productivity tended to be 10-15
percent lower unity, so the latter had to be imposed. The top panel of Table 4.1 shows
the resulting long-run term of the error-correction specification for real wage. In this
and further descriptions, such terms will be denoted by ECM, and the same acronym
will be used to refer to the adjustment coefficients next to ECM in the description of
dynamic parts of equations, as in the bottom panel of Table 4.1.
Table 4.1 Equation for real wage a
Long run for Log (REAL WAGE)
Error correction term, ECM
Constant
Log (LABOR PRODUCTIVITY)
Coefficient
4.95
1
t-statistic
693
-
Dynamic specification for Δ log (REAL WAGE)
Coefficient
0.02
-0.56
-0.12
-0.47
-0.18
Constant
Δ log (REAL WAGE(-1))
Δ log (REAL WAGE(-2))
Δ UNEMPL
ECM (-4)
t-stat
111.7
-5.90
-1.63
-1.88
-6.78
IV estimator, NOB=23, R2 = 0.72, DW = 1.84, St. error = 0.007
a
REAL WAGE =NOMINAL WAGE/GDP DEF at factor cost
As can be seen from Table 4.1, in addition to changes in the real wage, the dynamic
section of the equation includes the rate of unemployment, which makes the whole
relationship reminiscent of the Phillips curve. At the start, the unemployment rate was
included in levels, but initial estimation results showed that the restriction of having the
15
rate of unemployment in differences rather than levels was not binding. In addition,
when the rate of unemployment enters the right hand side in the form of changes, the
equation does not determine the long-run equilibrium rate of unemployment (NAIRU).
Given that the estimation period is that of very significant economic transformation, one
can hardly expect that an equation like this would lead to a reliable estimate of the
equilibrium unemployment rate. Hence, having the rate of unemployment in first
differences may be a preferable specification.
Finally, it remains to emphasize that the short-run dynamic part of the equation has been
restricted to be consistent with 5 percent annual growth in real wage in the long run.6
That the real wage must grow at 5 percent per year in the dynamic equilibrium follows
from equation (1) and the assumption that the long-run growth rate of real per capita
GDP is 5 percent per year (Table 3.1).7
4.2. Price of production – GDP deflator
As alluded to in the introduction, the GDP deflator plays a central role in the current
version of the price block: it links nominal price variables with the real side of the
model economy and serves as one of the main determinants of consumer prices.
Following the approach used in the French block of MCM, modeling of the GDP
deflator is based on the same theoretical relationship that guided the modeling of real
wage. As mentioned in the previous sub-section, one of the interpretations of equation
(1) is that it describes markup pricing by firms, that is, the way firms set prices for given
nominal wage. For this reason, in addition to being the long-run relationship bringing
the real wage and labor productivity together, equation (1) is also a legitimate
equilibrium expression for the GDP deflator, if nominal wage is treated as given. As a
result, the same error-correction term is used to model both the real wage and GDP
deflator. 8 The dynamic parts are different, however, as the GDP deflator equation treats
changes in the nominal wage as a separate determinant of changes in the price of
production in the short-run. These and other coefficients as well as some basic
estimation diagnostics are reported in Table 4.2. As before, a restricted estimation was
carried out to make the dynamic section of the equation be consistent with the long-run
inflation rates reported in Table 3.1.9
It remains to note that it is the GDP deflator at factor cost rather than the GDP deflator
itself that is modeled by the error-correction equation presented in Table 4.2.
That is, 0.012  0.02-0.012(0.56+0.12), where 0.012 is the quarterly rate corresponding to the annual
growth rate of 5 percent.
7
In fact, out-of-sample simulations will be based on the assumption that the labor force grows at 0.5
percent per year. This will require 5.5 percent growth in real GDP to have 5 percent income growth in per
capita terms.
8
More precisely, the two error correction terms will be equal to the negative of each other.
9
The 5 percent growth rate in real wage together with 4.3 percent inflation in GDP deflator imply that
nominal wage must grow at 9.5 percent annually. The dynamic section of the equation for GDP deflator is
restricted to be consistent with these inflation rates in the long run.
6
16
Table 4.2 Equation for GDP deflator
Long run for log (GDP DEF at factor cost)
Error correction term, ECM
Constant
Log (LABOR PRODUCTIVITY)
Coefficient
t-statistic
4.95
1
693
-
Dynamics for Δ log (GDP DEF at factor cost)
Constant
Δ log (GDP DEF at factor cost (-1))
Δ log (GDP DEF at factor cost (-3))
Δ log (NOMINAL WAGE)
Δ log (NOMINAL WAGE (-1))
ECM (-4)
Coefficient
-0.01
-0.36
0.20
0.53
0.41
-0.11
t-stat
-7.92
-2.75
1.61
4.80
3.94
-2.39
IV estimator, NOB=26, R2 = 0.72, DW = 2.71, St. error = 0.007
The difference between the two arises form the influence of indirect taxation on the
aggregate price level. To account for this effect, a proxy for the indirect tax rate was
calibrated by calculating the ratio of indirect tax revenues to GDP, and then GDP
deflator at factor cost was computed as
Log(GDP DEF factor cost) = Log(GDP DEF) + Log(1-IND. TAX RATE).
(2)
In this work, no issues related to indirect taxation will be explored, so the distinction
between the two price levels is innocuous here but may appear useful in other
applications.
4.3 Consumer prices
As discussed in Section 3 and tersely presented in Table 3.2, consumer prices are
modeled by splitting them into four components – FOOD, FUEL, HOUSEHOLD
ENERGY, and HICP CORE – which are then combined to obtain the predicted series
for the overall HICP. In the current version of the price block, the series for household
energy is taken as exogenous, while each of the remaining three sub-indexes is modeled
via a separate error-correction equation.
17
4.3.1 HICP core
In what follows, HICP core is viewed as a composite price of domestic and imported
foreign goods. Table 4.3 shows that the error-correction term expresses this idea directly
by positing that HICP core is equal to a weighted average of GDP and import deflators.
The calibration of weights for this long-run term relationship was described in Section
3, so this sub-section focuses mainly on the dynamic part of the error-correction
specification.
The equation for HICP core turned out to be the most difficult to estimate. First and
foremost, the point estimate of the adjustment coefficient next to the error-correction
term would almost always be positive, although never significantly so. Instead of
concluding that the equation is mispecified, it was decided to keep the same errorcorrection setup due to theoretical considerations and to set the value of the adjustment
coefficient at -0.1.
Table 4.3 Equation for HICP CORE
Long run for log (HICP CORE)
Error correction term, ECM
Coefficient
Constant
-0.007
Log (GDP DEF)
0.865
Log (IMP DEF)
0.135
t-statistic
-2.42
-
Dynamic specification for Δ log (HICP CORE)
Coefficient
t-stat
Constant
0.002
8.42
Δ log (HICP CORE (-1))
0.09
0.64
Δ log (HICP CORE (-2))
0.34
2.70
Δ log (GDP DEF (-2))
0.26
2.51
Δ log IMP DEF)
0.12
1.02
Δ log (IMP DEF (-1))
0.23
2.64
GDP GAP
0.13
1.93
ECM (-1)
-0.10
IV estimator, NOB=31, R2 = 0.80, DW = 1.67, St. error = 0.006
The second difficulty was associated with determining the lag structure of the model.
The need to make the dynamic part of the equation consistent with the long-run inflation
rates of Table 3.1 complicated matters even more because the restriction made the
equation less stable and weakened its ability to match the actual data. Given these
problems, selecting the best specification was far form straightforward. The final choice
presented in Table 4.3 is a compromise based on a number of criteria and the preference
not to exclude some variable form the dynamic part completely because all of them are
deemed to influence HICP core. One of them, GDP GAP, is measured as the deviation
of actual GDP from its potential, so the point estimate (0.13) corresponding to this
variable has the correct sign.
18
4.3.2 Food prices
Similarly to HICP core, the price of food is regarded as a composite price of domestic
and foreign food products. The index of food prices in the EU-15 is chosen to represent
the external price of food, while the GDP deflator is meant to proxy the domestic
component in food prices, which includes domestic food production costs and local
distribution costs. Both series for food prices were seasonally adjusted.
The fit and standard error of the regression indicate that somewhat bigger share of
variation in food prices is left unaccounted for, but that is hardly unexpected given that
food prices are known to be more volatile. On the other hand, the contemporaneous
elasticity of domestic food prices with respect to the EU-15 food price is estimated to be
0.79, which exceeds the 0.44 weight used in the error-correction term. This implies that
Estonian food prices tend to overshoot in response to changes in the foreign food price.
Table 4.4 Equation for food prices
Long run for log (FOOD)
Error correction term, ECM
Coefficient
Constant
0.04
Log(GDP DEF)
0.559
Log(FOOD EU-15)
0.441
Dynamic specification for Δ log (FOOD)
Coefficient
Constant
-0.004
Δ log (FOOD (-1))
0.41
Δ log (GDP DEF)
0.45
Δ log (FOOD EU-15)
0.79
ECM (-1)
-0.13
t-statistic
5.46
-
t-stat
-3.77
3.17
3.27
1.90
-1.69
OLS estimator, NOB=31, R2 = 0.69, DW = 2.08, St. error = 0.012
4.3.3 Fuel prices
The strategy used to model fuel prices is very similar to the one followed in the case of
food prices. As set in Table 3.2 and repeated in Table 4.5, the long-run price of fuel is
assumed to be determined by the world price of oil (Brent) and the domestic cost
component, proxied by the GDP deflator. In practice, the international oil price is
quoted in US dollars. Since it is the long-run that the error-correction term models, the
oil price in this term is expressed in Estonian kroons. In the dynamic part of the
equation, however, this variable is split into its two components, the price of oil in US
dollars and the dollar exchange rate.
19
Table 4.5 Equation for fuel prices
Long run for log (FUEL)
Error correction term, ECM
Coefficient
Constant
-1.93
Log (GDP DEF)
0.705
Log (OIL PRICE in EEK)
0.295
Dynamic specification for Δ log (FUEL)
Coefficient
Constant
0.08
Δ log (OIL PRICE in USD)
0.09
Δ log (OIL PRICE in USD (-1))
0.16
Δ log (EXCHANGE RATE USD)
0.61
ECM (-1)
-0.09
t-statistic
-85.95
-
t-stat
30.3
1.98
3.53
4.27
-1.90
OLS estimator, NOB=31, R2 = 0.64, DW = 1.70, St. error = 0.032
The inclusion of the dollar oil price and the dollar exchange rate separately seems to pay
off because the estimated short run elasticities are quite different (Table 4.5). In
particular, the short-run oil price elasticity is relatively small, 25 percent over two
quarters, while the exchange rate pass-through is stronger and more immediate,
amounting to 61 percent in the contemporaneous quarter. Since the latter exceeds the
weight of oil in the error-correction term, the reaction of domestic fuel prices to shocks
in the dollar exchange rate will feature overshooting. In contrast, the response of fuel
prices to changes in the dollar price of oil is estimated to be gradual convergence.
4.3.4 Administratively regulated prices (Household energy)
Until recently, the group of goods and services with administratively regulated prices
consisted mostly of three categories of items – fixed-line phone communication, rental
housing, and household energy (electricity, heating, etc.) – but in the very near future,
only energy prices will remain under administrative control. For this reason, the price
block identifies regulated prices with household energy prices, which currently account
for 8.2 percent of consumer expenditures.
As mentioned before, the present version of the price block takes household energy
prices as given and incorporates them into predicted consumer prices via the equation
(identity) that expresses HICP as a weighted average of its four sub-components (Table
3.2). Section 6 will look at the basic statistical properties of some exogenous series,
including the household energy price, in order to substantiate a discussion about
possible medium-run inflation scenarios. Unfortunately, the amount of knowledge we
can gain from looking at what would happen to consumer price inflation if regulated
prices changed is unavoidably negligible because in the current model, the contribution
of regulated prices to consumer prices is static and determined by the weight of
regulated prices in the overall HICP.
20
4.4 Import deflator
The effective foreign price index is assumed to be the only determinant of the import
deflator in the long run. As described in Section 3, the foreign price index is divided
into two parts, EP-FIXED and EP-FLOAT, which correspond to the trading partners
whose currencies are fixed with respect to the Estonian kroon and floating, respectively.
In the case of floating currencies, the foreign price index must be adjusted for changes
in the exchange rates because these are likely to affect foreign goods’ prices expressed
in the local currency. For this reason, EP-FLOAT enters the error-correction term
divided by the effective nominal exchange rate, ER-FLOAT. 10
Table 4.6 Equation for the import deflator
Long run for log (M DEF)
Error correction term, ECM
Coefficient
Constant
-0.02
Log (EP fixed)
0.60
Log (EP float / EER float)
0.40
t-statistic
-3.54
-
Dynamics for Δ log (M DEF)
Coefficient
Δ log (EP fix (-2))
0.84
Δ log (EER float)
-0.20
Δ log (EER float (-1))
-0.07
Δ log (EP float)
0.36
Δ log (EP float (-2))
0.08
ECM (-1)
-0.23
t-stat
15.3
-4.07
-1.92
3.18
1.27
-4.0
OLS estimator, NOB=31, R2 = 0.71, DW = 2.26, St. error = 0.011
When it comes to the dynamic part of the equation, the two effective price indexes, EPFIXED and EP-FLOAT, and the effective exchange rate, EF-FLOAT, are included
separately. This approach of combining a more stringent long-run relationship and a
more flexible short-run adjustment was already used in the case of fuel prices, when the
dollar price of oil and the dollar exchange rate were separated in the dynamic section of
the equation. Allowing for more flexibility for short-run adjustment seems to be
justified again because the response of import deflator to changes in the foreign price
index, EP-FLOAT, and the effective exchange rate, ER-FLOAT, is slightly different in
terms of both magnitude and timing. For example, the contemporaneous elasticity with
respect to EP-FLOAT is estimated to be 0.36, somewhat higher than that with respect to
ER-FLOAT of 0.20. Although the difference is not as large as in the case of fuel prices,
not restricting the elasticities to be the same is still preferable. Finally, the short-run
price elasticity with respect to EP-FIXED is estimated to be 84 percent, which exceeds
the weight of these prices in the error-correction term (60 percent) and therefore
signifies that overshooting is likely.
10
Recall that exchange rates are expressed in terms of foreign currency per Estonian kroon.
21
Before proceeding to the next section, it is worth emphasizing one important difference
in the way the import deflator is modeled here and in the French and Spanish macro
models. The equation above does not include the GDP deflator as a determinant of the
import deflator, neither in the short nor long run. In the Spanish model, the GDP
deflator appears among the determinants of import price after assuming that the real
exchange rate influences markups that foreign firms can charge. In the French model,
the presence of GDP deflator in the error-correction term is justified on the basis of
pricing-to-market. Although the first effect may be significant in Spain, it is difficult to
notice it in Estonia. At large, the real exchange rate continues to appreciate due to price
converge and the Balassa-Samuelson effect and this trend seems to overshadow the
more subtle effects raised in the Spanish case.
Pricing to market can certainly be a valid argument in the case of Estonia but the
suggestion to model it by including the GDP deflator into the long-run expression for
the foreign price is questionable. Firstly, the domestic cost component (like distribution
costs) is not relevant in the case of import deflator because this is the price measured at
the border. Secondly, pricing to market may be the result of different demand
elasticities in the domestic and foreign markets, but that leads to a constant difference in
the markups and has no connection with the GDP deflator. Finally, the PPP based price
level comparison reported by Eurostat assumes that the level of import and export prices
in Estonia is international. Given these considerations, it seemed more appropriate to
avoid including the GDP deflator among the explanatory variables of import prices but
model them as a function of foreign prices only.
5. Dynamic solution and simulations
The price block presented in the previous section consists of nine equations, six of the
error-correction form and three identities. It has nine endogenous and twelve exogenous
variables, which are listed in Table 5.1 for convenience. The aim of this section is to get
some sense of the performance of the price block. At the beginning, an in-sample
dynamic solution of the price block is presented. This kind of simulation takes the
actual start-of-period values of predetermined variables as a base and solves for
endogenous variables over the remaining sample period using the actual data on
exogenous variables. When the model is solved dynamically, prediction errors are
accumulated over time, so a graphical comparison of the predicted and actual
endogenous series is quite revealing about the performance of the model. In addition, a
very useful way to learn more about the dynamic implications of the model is to
simulate its responses to some shocks. Hence, a number of stylized 10 percent shocks to
selected exogenous variables will be performed.
22
Table 5.1 Endogenous and exogenous variables of the price block
Exogenous
Employment
Effective foreign price (euro)
Effective foreign price (non-euro)
USD exchange rate
Effective exchange rate(non-euro)
EU-15 Food price
GDP GAP
Regulated prices (Household energy)
Indirect tax rate
Oil price (Brent, $)
Real GDP
Unemployment
Endogenous
GDP deflator
GDP deflator at factor cost
HICP
HICP core
Fuel price
Food price
Import deflator
Nominal wage
Real wage
The results of the dynamic in-sample (1997Q1-2003Q3) solution of the price block are
presented in Fig. 5.1. The table contains eight figures – one for each of the endogenous
variables and the real wage – which show three kinds of graphs: the actual series
(Actuals), the dynamically simulated series (Baseline) and the percent deviation of the
latter from the former (Percent deviation). Given the simplicity of the model and the
presence of a number of non-data-determined parameters in it, the price block seems to
track the data rather well, although some deviations are quite substantial and persistent.
Judging on the behavior of percentage deviations, the model performs best in the case of
food prices (FOOD), the import deflator (IMP DEF), and the real wage (RW). In all
these cases, deviations tend to revert to zero within sample. For some variables,
especially the GDP deflator, fuel prices and the nominal wage, the deviations of
simulated series from the actual ones are very persistent. However, none of the
deviations is explosive, and even the largest and most persistent of them seem to be
rather stable (see, e.g., the graph for the nominal wage), suggesting that proper additive
adjustments might improve the performance of the price module in out-of-sample
simulations.
23
Fig. 5.1 In-sample dynamic solution of the model (baseline),
all endogenous variables, 1997Q1-2003Q3
GDP DEF factor cost
GDP DEF
G D EFN
Import DEF
GDEF
MD EF
1.0
1.2
1.08
0.9
1.1
1.04
1.00
1.0
0.8
0.7
5
5
0.6
0
0
-5
-5
0.96
0.9
4
0.8
3
0.88
0.7
2
0.84
1
0.80
0.92
0
-1
-10
-10
1996
1997
1998
1999
2000
2001
2002
2003
-2
1996
1997
1998
A ctual
GD EF N (B aseline)
P ercent Deviation
1999
2000
2001
2002
2003
1996
Food
Fuel
H PF_SA
HPE7
4
0
0.9
0.8
-10
-4
-15
2000
2001
2002
2003
1.2
1.1
0.8
1.0
0.9
-6
-8
1996
1997
1998
1999
2000
2001
2002
2003
1998
-4
-6
-8
2001
A ctual
H IC P (B aseline)
P ercent D eviation
2002
2003
1999
2000
2001
Actual
HPXEF_SA (Baseline)
Percent Deviation
Nominal wage
Real wage
2002
2003
RW
1.2
7000
7000
1.1
6000
6500
1.0
5000
6000
5500
4000
0.8
2
0.7
0
3000
5000
2
4500
0
2000
-2
2000
1997
W
-2
1999
1996
Actual
HPE7 (Baseline)
Percent Deviation
0.9
1998
0.7
-4
H ICP
1997
0.8
0
-2
HICP
1996
2
0.4
Actual
H PF_SA (Baseline)
Percent Deviation
0
2003
1.0
-20
1999
2002
1.2
-5
-2
1998
2001
0.6
0
-6
2000
HPXEF_SA
1.0
2
1999
HICP core
1.1
1997
1998
Actual
MDEF (Baseline)
Percent Deviation
1.2
1996
1997
Actual
GDEF (Baseline)
Percent Deviation
-4
-4
-6
-6
-8
-8
-10
-10
1996
1997
1998
1999
2000
2001
Actual
W (Baseline)
Percent Deviation
24
2002
2003
4000
-2
1996
1997
1998
1999
2000
2001
Actual
RW (Baseline)
Percent Deviation
2002
2003
Perhaps the most instructive way to analyze the performance and implications of the
price block is to simulate its responses to changes in exogenous variables. Of particular
interest here is the influence on Estonian inflation of three external prices: the price of
oil, foreign food prices and the US dollar exchange rate. 11 In order to prepare the model
for the shock simulation exercise, the long-run inflation rates of Table 3.1 were used to
extrapolate the exogenous series until 2011Q4. Although the timing of shocks is not
relevant, they are programmed to start in the first quarter of 2005, and the response of
endogenous variables is tracked until the last quarter of 2007. Positive 10 percent
shocks will be of two kinds, permanent and temporary, lasting for two quarters only,
and they will be applied to three exogenous variables: the US dollar exchange rate, the
oil price, and the EU-15 food price index.
5.1 Shock to the USD exchange rate
The shock to the US dollar exchange rate affects four price indexes: the price of fuel,
import deflator, HICP core, and the overall HICP. Simulated responses of these
variables to the permanent shock are presented in Fig. 5.2. Fig. 5.3 shows analogous
results for the temporary shock.
The US dollar exchange rate influences fuel prices because the world oil price is quoted
in this currency. It is convenient to think for a moment that this influence of the
exchange rate works through two channels: the error-correction term, where the value of
the dollar is an undistinguishable part of the oil price, and the direct exchange rate passthrough, which is captured by the dynamic part of the equation. Because the
contemporaneous pass-through of 0.61 exceeds the weight assigned to oil in the errorcorrection term, fuel prices overshoot in response to the shock. Fig. 5.2 shows that the
price of fuel increases by 6 percent in the same quarter the shock occurs and then
declines slowly to its new long-run equilibrium level, which is now approximately 3
percent higher than before.
The US dollar exchange rate affects the import deflator via the nominal effective
exchange rate, ER-FLOAT. The data on currency denomination of Estonian trade
indicate that about 17 percent of foreign trade is carried out in US dollars. This
corresponds to about 40 percent of ER-FLOAT, so the 10 percent shock to the US dollar
11
The impact of changes in regulated prices on the overall inflation is of equal interest. However, these
prices are introduced into the current version of price block in a static way, and therefore shocks to them
do not result in any dynamics but an immediate adjustment in the total HICP.
25
Fig. 5.2 Permanent 10 percent shock to the USD exchange rate
Fuel prices
Import deflator
MDEF (Percent Deviation)
HPE7 (Percent Deviation)
1.6
7
6
1.2
5
4
0.8
3
2
0.4
1
0.0
04Q1 04Q3 05Q1 05Q3 06Q1 06Q3 07Q1 07Q3
0
04Q1 04Q3 05Q1 05Q3 06Q1 06Q3 07Q1 07Q3
HICP core
HICP
HPXEF_SA (Percent Deviation)
HICP (Percent Deviation)
.28
.5
.24
.4
.20
.3
.16
.12
.2
.08
.1
.04
.00
04Q1 04Q3 05Q1 05Q3 06Q1 06Q3 07Q1 07Q3
.0
04Q1 04Q3 05Q1 05Q3 06Q1 06Q3 07Q1 07Q3
translates into a 4 percent disturbance in the effective exchange rate. Finally, the
estimated contemporaneous pass-through of 0.2 implies that one fifth of this shock
feeds into the import deflator. Hence, the deflator increases by 0.8 percent in the first
quarter, raises by another half a percent in the second quarter and then gradually
converges to its new long-run level which is 1.6 percent higher than before.
26
Fig. 5.3 Temporary 10 percent shock to the US dollar exchange rate
Fuel prices
Import deflator
MDEF (Percent Deviation)
HP E 7 (P e rc e nt D e v iati on)
7
1.4
6
1.2
5
1.0
4
0.8
3
0.6
2
0.4
1
0
0.2
-1
04Q1 04Q3 05Q1 05Q3 06Q1 06Q3 07Q1 07Q3
0.0
04Q1 04Q3 05Q1 05Q3 06Q1 06Q3 07Q1 07Q3
HICP core
HICP
HPXEF_SA (Percent Deviation)
HICP (Percent Deviation)
.5
.16
.4
.12
.3
.08
.2
.04
.1
.00
.0
-.1
04Q1 04Q3 05Q1 05Q3 06Q1 06Q3 07Q1 07Q3
-.04
04Q1 04Q3 05Q1 05Q3 06Q1 06Q3 07Q1 07Q3
The response of fuel prices and the import deflator to the change in the value of US
dollar is further carried into HICP core and total HICP. HICP core depends on the
deflator only, so its reaction is very similar to that of the deflator, just about seven times
weaker.12 Finally, the overall HICP combines the effects from fuel prices and HICP
core. A steep rise in the former together with a more gradual increase in the latter make
HICP move up by 0.4 percent, which brings it close to its new long-run equilibrium
level.
12
The weight of import prices in the error-correction term for HICP core is 13.5 percent.
27
The effects of the temporary 10 percent shock to the US dollar exchange rate are shown
in Fig. 5.3. The immediate response of the four price indexes is necessarily the same as
above, so it is only their paths of return to the former baselines that is of interest. With
the exception of HICP core, none of the prices shows significant inertia, so the
disturbance lasts for only two quarters after the shock ends. In contrast, HICP core stays
above its former baseline for almost two years, which is the result of low adjustment
coefficient next to the error-correction term. This does not have any significant
influence on the dynamics of the total HICP, however.
5.2 Oil price shock
Differently from the shock to the US dollar exchange rate, a disturbance in the world oil
price affects only two endogenous prices of the model: the price of fuel and HICP.
Moreover, since the oil price can influence HICP only indirectly, via fuel prices,
basically all implications of the shock can be understood from investigating the
simulated effect on the price of fuel alone.
The price of oil and the dollar exchange rate enter the equation for fuel price in a very
similar way, so it is natural to expect that they produce similar responses in the
dependant variable as well. In fact, the influence that they exercised through the errorcorrection term is exactly the same. However, some important differences are present in
the dynamic part of the equation, which shows that changes in the oil price have weaker
28
Fig. 5.4 Ten percent shock to oil price
Permanent shock
Fuel prices
HICP
HPE7 (Percent Deviation)
HICP (Percent Deviation)
2.8
.16
2.4
.14
.12
2.0
.10
1.6
.08
1.2
.06
0.8
.04
0.4
.02
0.0
04Q1 04Q3 05Q1 05Q3 06Q1 06Q3 07Q1 07Q3
.00
04Q1 04Q3 05Q1 05Q3 06Q1 06Q3 07Q1 07Q3
Temporary shock
Fuel prices
HICP
HPE7 (Percent Deviation)
HICP (Percent Deviation)
3.0
.14
2.5
.12
.10
2.0
.08
1.5
.06
1.0
.04
0.5
.02
0.0
04Q1 04Q3 05Q1 05Q3 06Q1 06Q3 07Q1 07Q3
.00
04Q1 04Q3 05Q1 05Q3 06Q1 06Q3 07Q1 07Q3
and more gradual short-run effects than changes in the dollar exchange rate. Simulations
shown in Fig. 5.4 illustrate that succinctly. The permanent shock to the oil price does
not lead to overshooting in the price of fuel. Rather, it rises by 2.4 percent over the two
quarters after the shock and by doing so covers almost all of the adjustment needed to
reach its new long-run equilibrium level. The resulting response in HICP is analogous
but scaled down by a factor of 20 because the share of consumer spending on fuel is
only 5.5 percent of total expenditures. Finally, simulations based on the temporary
shock to the oil price show that the resulting deviations in the price of fuel and HICP are
of the same amplitude as above but short-lived, it takes two quarters for the price
indexes to return to their previous baselines.
29
5.3 Shock to the EU-15 price of food
The error-correction term of the equation for food prices assigns 44 percent weight to
the index of food prices in the EU-15. Consequently, a 10 percent permanent increase in
the latter will make domestic food prices rise by 4.4 percent in the long run. Fig. 5.5
presents the simulation results, which show that domestic food prices are predicted to
overreact to the shock initially. Indeed, the estimated contemporaneous elasticity of the
domestic food price with respect to that of the EU is 79 percent, almost twice the weight
of the foreign price in the long-run relationship. This makes the domestic price of food
rise by 8 percent in the first quarter. The adjustment continues as the price of food
increases by additional 3 percentage points over the following two quarters but then
changes its course and starts declining to its new long-run level. Again, the response of
HICP to the shock is analogous but approximately 5 times weaker due to the fact that
consumer spending on food accounts for only 21 percent of total expenditures. Finally,
the simulation of the temporary shock to foreign food prices has no unexpected
implications but shows that the tendency of domestic food prices to overreact now
causes some undershooting in the aftermath of the shock, when the price index declines
below its long-run level.
It is legitimate to ask whether such overshooting in food prices is realistic and what
could be the reason for it. On the one hand, the “cause” of the strong initial response is
the relatively large estimate of short-run elasticity. Importantly, this result is not specific
to the lag structure of the equation or the time period used for estimation: the estimated
short-run elasticity tended to be high in all the runs carried out when choosing the lag
structure and also in recursive estimation. Hence, if the model is not contaminated by
some serious specification problems, the data are telling that the elasticity is high.
30
Fig. 5.5 Shock to EU-15 food prices
Permanent shock
Food prices
HICP
HICP (Percent Deviation)
HPF_SA (Percent Deviation)
12
2.4
10
2.0
8
1.6
6
1.2
4
0.8
2
0.4
0
04Q1 04Q3 05Q1 05Q3 06Q1 06Q3 07Q1 07Q3
0.0
04Q1 04Q3 05Q1 05Q3 06Q1 06Q3 07Q1 07Q3
Temporary shock
Food prices
HICP
HICP (Percent Deviation)
HPF_SA (Percent Deviation)
12
2.5
10
2.0
8
1.5
6
1.0
4
2
0.5
0
0.0
-2
-0.5
04Q1 04Q3 05Q1 05Q3 06Q1 06Q3 07Q1 07Q3
-4
04Q1 04Q3 05Q1 05Q3 06Q1 06Q3 07Q1 07Q3
On the other hand, the strong response of domestic food prices to changes in food prices
abroad could be resulted in by the price taking behavior of domestic food producers. If
food products are highly tradable, international arbitrage should make their prices move
together regardless of whether the products are produced domestically or abroad.
Indeed, the relatively high level of Estonian food prices in comparison with those in the
EU-15 could be indicating that the market for food products is somewhat more
integrated than other markets.
The latter argument could explain why the short-run elasticity of food prices is so high
but at the same time it would make the current specification of the model equation
31
questionable. The figures in Fig. 5.5 show that after the initial overshooting, the
domestic price of food declines to the level implied by the error-correction term. It is the
presence of the GDP deflator in the long-run relationship for the food price that causes
this downward adjustment. Since the deflator stays constant in the simulation, the price
of food remains anchored to it in accordance with its weight in the error-correction
term. Here the GDP deflator is meant to proxy the cost of domestic production, but if it
is not a good representation of the costs faced by domestic food producers, the
simulated food price response is likely to be misleading, especially in its long-run
implications.13 This issue is not investigated here but could be worth addressing in
future work.
6. Conclusions
Having presented both the workings of the new price module and its more practical
implications about inflation dynamics in detail, it seems useful to divide the concluding
remarks accordingly, into those related to modeling and policy-relevant ones.
On the modeling side, there are a number of dimensions along which the current version
of the price block could be improved. To start from a rather specific issue, for example,
the price of fuel that consumers face is currently modeled without taking into account
the effect of excise taxes. Difficulties with data have prevented us from modeling such
effects now but it would be worthwhile incorporating them into the model in the future.
A more fundamental issue that can be raised is the possibility that price convergence
may be nonlinear. Although this question may demand a more detailed analysis, the
evidence provided in the Appendix suggests that such non-linearities seem to be
insignificant. In fact, it was this conclusion that prompted us to carry on with the current
long-run structure of the price module. Finally, the price block is meant to be an integral
part of the overall macro model of the Estonian economy. It is because the new macromodel is under construction that we have not been able to link the price block with the
rest of the model yet. Analyzing the implications of the price block alone may entail
some risk that the picture we are getting is only partial, based only on the impact effects.
However, the fact that Estonia is a small and very open economy suggests that such
first-round effects must be by far of most importance and therefore we are not likely to
be missing much.
13
An alternative scenario could be that domestic food producers, being international price takers, attempt
to expand their production in response to the rise in the foreign price of food. As they do so, the
(marginal) cost of domestic food production rises, making the domestic component in the error-correction
term increase. As a result, differently from the simulation presented in the text, the price of food would
not have to adjust downwards so much (or at all) to reach it long-run level because the latter would be
higher than in the original simulation.
32
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33