Academy of Economics Studies
Doctoral School of Finance and Banking
Estimating equilibrium
exchange rate
- FEER vs BEER MCs student: Ana Simona Manu
Supervisor Professor: Moisă Altăr
July, 2010
Dissertation paper outline
The importance of the equilibrium real
exchange rate
 The aims of the paper
 Literature review
 Economic foundation: FEER and BEER
 Empirical evidence
 Concluding remarks

The importance of the
equilibrium real exchange rate



The stability of the exchange rate is an imperative condition
for a country that aims to join the European Monetary Union
while the competitiveness of an economy is a measure of the
real convergence process.
The fulfillment of Maastricht criterion regarding the
exchange rate stability depends on the optimal setting of the
central parity consistent with the economic fundamentals
One important indicator of the price competitiveness of a
country is represented by the real exchange rate
misalignment towards its equilibrium values
The aims of the paper




Assessing the equilibrium exchange rate for the Romanian
economy using two alternative approaches, respectively
Fundamental Equilibrium Exchange Rate (FEER) and
Behavioral Equilibrium Exchange Rate (BEER)
Evaluating the price competitiveness through real effective
exchange rate (REER) misalignment using the two models
Calculating the nominal equilibrium exchange rate using
bilateral EUR/RON exchange rate in an attempt to find an
optimal central parity by applying the two methodologies
Comparing FEERs vs. BEERs results
Literature review
The first attempts to model equilibrium exchange rate are based
on Purchasing Power Parity first developed by Gustav
Cassel (1922), however the empirical evidence hardly validates
this theory and only over the long term horizon.
In this context it became necessary to develop alternative
approaches for modeling equilibrium exchange rate:






FEER: introduced by Williamson (1994) the equilibrium value is defined
as that level of the exchange rate that assures simultaneous achievement
of the internal and external balance
IMF macroeconomic balance approach used as a variant of FEER, which
is based on a direct estimation of the sustainable level of the current
account deficit considering the investment – savings relation
BEER: first introduced by Clark and MacDonald (1998), aims to asses
the equilibrium exchange rate by using a more empirical approach based
on fundamental variables affecting the evolution of the exchange rate on
short and medium term.
for CEEC countries the most employed models are FEER and BEER
adjusted to the particularities of transition countries ( note Egert and
Lahrèche-Révil (2003), Bulir and Smidkova (2005), Michael Rubaszek
studies on FEER)
Economic foundation of the models
A. The FEER model
Determines the ERER consistent with both
internal and external equilibrium
 Internal equilibrium is usualy defined as that
level of output consistent with full employment
 External
equilibrium is achieved when
structural current account adjust to its
norm/target level

Structural current account



It is defined as the level of the current account
which is not affected by cyclical fluctuation of the
explanatory variables
It is based on describing the external sector
activity, respectively, the estimation of the
exports/imports equations
It is computed by imposing internal equilibrium
condition and accounting for exchange rate
variations
The current account could be expressed based on the following
equations:
 Px


X 
 P / NER 
 f

 Pm 
M  
P
 1
1
 Yf
Y
2
2
(1)
Pm  P   ( Pf / NER )(1  )
(2)
TB  X  Px  M  Pm
Px  P  ( Pf / NER )(1 )
(3)
(4)
(5)
( Px  X  Pm  M )  TR _ trend  INC _ trend
CA _ structural 
PY  Y
(6)
Current account norm

For estimating the current account norm it was employed
the methodology proposed by IMF researchers (Faruqee
şi Debelle (1998), Masson (1998)), the key element of
this approach consisting in defining the current account
norm as the difference between saving and investment
long term values.



Fiscal balance - positive relation, higher public spending
triggering a lower level of national savings.
Demographic factors – negative relation, a higher level of
population dependency ratio reduces savings and the current
account balance.,
Net foreign assets. – ambiguous effect, economies with high
NFA can support higher level of current account deficits without
having negative implication in terms of solvability, while a solid
investment position triggers higher revenues from abroad
improving the current account balance




The balance of fuel products - this variable is introduce in
order to account for terms of trade shocks associated with oil
prices.
The relative income per capita. It is expected that countries
with lower level of capital to recall to external resources in
order to finance the internal investments, triggering the
deterioration of the current account.
Economic growth. A higher level of this indicator generates
a higher current account deficit if the economic growth is
fuelled by foreign investments or if it is perceived as being
permanent, with a negative potential on saving ratio.
Foreign direct investments. The growth of foreign direct
investments is associated with higher imports, having a
negative impact on CC.
Fundamental equilibrium exchange rate
Stylized figure





The exchange rate is expressed as units of
foreign currency per unit of domestic
currency, an increase of the indicator being
equivalent with an appreciation
For a given level of output , the relation
between the exchange rate and the current
account is indirect, a depreciation leading
to a deterioration of the current account
If the domestic output increases above the
potential value, the curve will translate
towards the left side, as we will have a
permanent deterioration of the current
account given the increase of imports
The equilibrium exchange rate is that level
consistent with simultaneous achievement
of internal and external equilibrium, both
being impose exogenously.
This model gives us a trajectory of the
ERER on medium term trough the
adjustment of the current account trend to
its norm value but it doesn’t capture the
short term adjustment towards equilibrium
value
Economic foundation of the models
B. The BEER model




The observed level of the real exchange rate can be expressed as a
function of its expected value Et (qt 1 ) and the real interest rate
differential: qt  Et (qt 1 )  (rt  rt* )
Et (qt 1 ) is an unobserved variable will be determined solely by a
vector of fundamental economic variables Z t which act on the
medium and long term: qtBEER  f ( Z t , (rt  rt* ))
The empirical analysis considered testing the relation between the
real exchange rate and variables like the productivity differential
between the tradable and non-tradable sector of the economy, private
and government consumption, the openness of an economy, net
foreign assets, terms of trade: Et (qt 1)  f ( proddif, cons, openess, nfa, tot)
Considering this framework, we can define the total misalignment
as: tmt  qt  Z t
Empirical evidence
1.The data




Quarterly data extracted from Eurostat, Bank of International
Settlements, National Bank of Romania databases for the period
2000Q1- 2009Q4 (40 observations). First, all series were seasonally
adjusted using Demetra software, developed by Eurostat.
It was used both effective and bilateral EUR/RON real exchange
rate. The REER was extracted from the BIS database and is
computed by using HICP as a deflator. The same method is applied
in the case of bilateral EUR/RON real exchange rate.
all the variables are in constant prices (2000=100).
For determining current account norm it was employed a panel
data analysis, the data sample comprising data from 5 countries
(Romania, Hungary, Poland, Czech Republic and Bulgaria) for the
period 2001Q1-2009Q4. The decision regarding the countries
included in the analysis was motivated by the relatively similar
characteristics of the countries given the geographic position and
the development stage, while the choice of the period was
conditioned by the data availability. The source of data is Eurostat
database.
FEER empirical approach



This step consist in modelling the trade sector of
Romanian economy by identifying long term relation
for the considered variables. For this purpose I’ve
employ a Engle Granger methodology
For estimating the cointegration equation we used
the FMOLS estimator, as an alternative to static
OLS, considering the significant errors that could
appear given the reduce sample of data
The ADF and PP test are presented in Appendix 1
indicate that all the variables are I(1). All the
estimated relations are cointegrated ones according to
Engle-Granger tests (see Appendix 2)
Volume of import and export equations
Import price and export price equations
GDP deflator equation
Internal equilibrium
Chart 1 : The evolution of potential GDP
34,000
Chart 2: The evolutionofdomestic demandtrend
50,000
32,000
45,000
30,000
40,000
28,000
35,000
26,000
30,000
24,000
22,000
25,000
20,000
20,000
18,000
2000
2001
2002
2003
2004
GDP_HP
2005
2006
2007
2008
15,000
2009
2000 2001 2002 2003 2004 2005 2006 2007 2008 2009
GDP_RO
DD_HP
Chart 3: The evolution the labor productivity trend
1.5
1.4
1.3
1.2
1.1
1.0
0.9
2000
2001
2002
2003
2004
W_IND
2005
2006
W_IND_HP
2007
2008
2009
DD_R
O
Structural current account
Chart 4:The trend of the transfer
Chart 5: The trend of income balance
7,000
0
6,000
-1,000
5,000
-2,000
4,000
-3,000
3,000
-4,000
2,000
-5,000
1,000
-6,000
0
-7,000
2000
2001
2002
2003
2004
2005
TRANSFERURI
2006
2007
2008
2009
2000
2001
2002
2003
TRANSFERURI_HP
VENITURI
Chart 6: Actual current account vs s tructural current account
0
-2
-4
-6
-8
-10
-12
-14
-16
2004
2000 2001 2002 2003 2004 2005 2006 2007 2008 2009
Current
_ account
Current
_ account_structural
_
2005
2006
2007
VENITURI_HP
2008
2009
Current account norm
I’ve considered the fundamental variables presented in the theoretical part, the empirical evidence
indicating the following statistical significant variables fiscal balance, GDP growth per capita,
population growth, fuel products balance and direct foreign investment.
Before running the regression all the variable were tested for unit root process, resulting that all variables
are stationary (Appendix 3)
External equilibrium
( Px  X  Pm  M )  TR _ trend  INC _ trend
 CA *
PY  Y
CC norm
Structural CC
Chart 7: Structural current account vs current account norm
-5
-6
-7
-8
-9
-10
-11
2000
2001
2002
2003
2004
2005
CC_STRUCTURAL
2006
2007
CC_NORM
The results indicates a current account norm between -8,5 percent of GDP at the
beginning of the period and -7,45 percent at the end of 2009.
2008
2009
Chart 8: The evolution of the FEER equilibrium exchange rate and REER misalignment
110
-5
100
2009Q1
0
2008Q1
120
2007Q1
5
2006Q1
130
2005Q1
10
2004Q1
140
2003Q1
percent
15
2002Q1
index, 2000=100
2001Q1
150
-10
90
FEER (REER)
REER
-15
REER mis alignment
2009Q2
2008Q3
2007Q4
2007Q1
2006Q2
2005Q3
2004Q4
2004Q1
2003Q2
2002Q3
2001Q4
2001Q1
80
-20
Sursa: BIS, own calculation




In the period 2001Q1-2009Q4 the misalignment of the REER from the equilibrium
value varied between – 16,11 percent and 10,69 percent.
in 2001-2004 the REER was undervalued in average by 10 percent given that the
structural current account deficit was lower then the current account deficit norm.
Starting 2005, once with the deterioration of the structural current account deficit,
REER becomes overvalued, in order to restore the equilibrium being necessary a
depreciation of REER between 1 and 10,7 percent.
This trajectory reversed at the end of the analyzed period, the excessive correction
of the external position leading in 2009 to a level of REER slightly undervalued
(-1,46 percent).
Chart 9: FEER (RER_EUR) evolution and the RER_EUR vs REER misalignment
index, 2000=100
percent
15
10
140
2009Q1
2008Q1
2007Q1
2006Q1
2005Q1
2004Q1
-5
2003Q1
0
120
2002Q1
5
130
2001Q1
150
110
-10
100
-15
90
-20
2009Q1
2008Q1
2007Q1
2006Q1
2005Q1
2004Q1
2003Q1
2002Q1
2001Q1
80
REER mis alignment
FEER (RER_EUR)
RER_EUR
RER_EUR mis alignment
-25
source: own calculation



In the period 2001Q1-2009Q4 the misalignment of the RER_EUR from the
equilibrium value varied between – 21,16 percent and 11,54 percent.
In 2001-2004 the degree of the RER_EUR undervaluation was in average with 2,45
percentage points lower then that associated with REER
In 2005-2008 the overvaluation of RER_EUR was in average with 0,9 percentage
points higher than in the case REER.
Chart11: The impact of 1 pp. lower current account norm
on REER/RER_EUR misalignment
index, 2000=100
20
20
10
140
5
130
90
-25
-20
2009Q1
2008Q1
2007Q1
2006Q1
2009Q12009Q1
2008Q12008Q1
2007Q12007Q1
2006Q12006Q1
2005Q12005Q1
REER mis alignment
REER_SEZ mis alignment
2005Q1
2004Q12004Q1
2009Q1
2008Q1
-10
-15
-20
2004Q1
2003Q1
2002Q1
-30
-10
FEER (RER_EUR)
RER_EUR
REER mis alignment
2001Q1
-20
80
2007Q1
2006Q1
2005Q1
2004Q1
2003Q1
2002Q1
-10
2001Q1
100
-50
2003Q12003Q1
0
120
2002Q12002Q1
10
10
0
110
percent
15
2001Q1
150
Chart
9: FEER (RER_EUR) evolution and the RER_EUR vs REER misalignment
percent
percent
30
2001Q1
30
RER_EUR mis alignment
RER_EUR_SEZ
mis alignment
RER_EUR mis alignment
-30
source: own calculation
Source: own calculation



there are no important changes in the periods of under/over valuation of the real
exchange rate, but the magnitude of misalignment is significantly higher
In the case of REER the misalignment of the current values from the equilibrium
increases in average with around 6 percentage points, while the RER_EUR
misalignment is even more sensitive to this hypotheses, growing in average by 7,7
percentage points
towards the end of 2009 the sensitivity analysis indicate an equilibrium value
around the actual value, and not an undervalued one
Chart 12: The impact of e lasticitie s variation on REER/RER_EUR misalignme nt
-10
-25
-10
-15
-15
-20
-5
2009Q1
2009Q1
2008Q1
2007Q1
2006Q1
2005Q1
2004Q1
2003Q1
2002Q1
2001Q1
-5
0
2008Q1
5
2007Q1
5
2006Q1
10
2005Q1
10
2004Q1
15
2003Q1
15
0
percent
20
2002Q1
percent
2001Q1
20
-20
RER_EUR_SEZ1 mis alignment
REER_SEZ1 mis alignment
-25
RER_EUR mis alignment
REER_SEZ2 mis alignment
-30
REER mis alignment
RER_EUR_SEZ2 mis alignment
-30
Source: own calculation



For period 2001q1-2009q4, the increase of elasticises by 10% implies a higher misalignment
of REER in average with 1,5 pp. compared with the initial situation.
 in 2001q1-2004q4 the level of undervaluation was lower with around 1pp. (of-9,15%)
 2005q1-2008q4 the level of overvaluation was higher in average with around 2 pp.(8,85
%)
The decrease of the elasticises by 10% triggered for the entirely analyzed period a lower level
of REER misalignment in average with 1,8 pp.
 for 2001q1-2004q4 the undervaluation is higher with 1,2 pp. (of -11, 3%),
 for 2005q1-2008q4 it can be seen a lower level of the overvaluation with 2,3 pp.(4,62 %).
For the end of 2009 the sensitivity analysis indicates that the REER undervaluation
is between 3 and 8 percent.
BEER empirical approach



is based on the estimation of a long term equilibrium relation between the real exchange rate and the
fundamental variables: REER, net foreign liabilities, relative price of non-tradables versus
tradables, terms of trade
It were performed ADF and PP tests (Appendix 5) showing that all the variables have a unit root.
The first step in implementing Johansen 's test consists in the estimation of a VAR model with a
number of lags determined by the information criteria.. The quality test of VAR are presented in
Appendix 6.

The cointegrating relationship is given by:

log(REER)= -0,1623*log(NFL) +0,8803*log(TNT) +1,9739*log(TOT) + 0.507370
(0.0493)
(0.1234)
(0.029)
[3.2939]
[-7.1334]
[14.8208]
The equilibrium exchange rate was obtained by filtering the explicative variables
Chart 13: The evolution of the BEER and REER misalignment
percent
index, 2000=100
100
-5
2009Q1
REER
2007Q1
2006Q1
2005Q1
2004Q1
2003Q1
2002Q1
2001Q1
2000Q1
80
BEER (REER)
2008Q1
90
-10
2009Q1
0
2008Q1
110
2007Q1
5
2006Q1
120
2005Q1
10
2004Q1
130
2003Q1
15
2002Q1
140
2001Q1
20
2000Q1
150
REER mis alignment
-15
Source: BIS, own calculation





REER misalignment in the 2001Q1-2009Q4 period varies between -9,9 per cent and 13,9 per cent.
at the beginning of the analyzed period, REER was around its equilibrium value
starting with 2002, REER becomes clearly undervalued with a maximum misalignment in 2004Q2.
In the 2005Q1-2008Q4 period , the overvaluation of REER was on average 5,9 per cent
In 2009Q4 we can observe an undervaluation of 1,51 per cent.
BEER vs FEER
Chart 15:The comparative pre se ntation of the re sults obtain for equilibrium REER
FEER vs BEER
percent
15
10
10
-5
BEER
100
REER
-10
FEER
-15
2009Q1
2008Q1
2007Q1
2006Q1
2005Q1
2004Q1
2003Q1
2002Q1
80
2001Q1
90
2009Q1
0
2008Q1
0
110
2007Q1
5
2006Q1
5
2005Q1
120
15
2004Q1
130
20
2003Q1
140
20
2002Q1
index, 2000=100
2001Q1
150
FEER-BEER
FEER mis alignment
-5
-10
-15
BEER mis alignment
-20
-20
Source: BIS, own calculation






Important differences between the two approaches appear only at the beginning of the analyzed period
The FEER model indicates an equilibrium real exchange rate more appreciated by an average of 15 pp.
2001Q1-2002Q4. This is mainly due to significantly lower CA deficit than the one supported by the
norm level as indicated by fundamental values of savings and investments (structural CA was on average
-5,72% of GDP compared to a 8,4% deficit supported by the CA norm)
The modified hypothesis of a lower sustainable current account deficit by a single percentage point (to 7,4%) leads to significantly lower gaps between the misalignments predicted by FEER and BEER.
Starting with 2003, given the rise of the structural deficit, the undervaluation for REER indicated by
FEER was reduced, with an average gap over the level indicated by BEER of 5,82 per cent on average
(2003Q1-2004Q4).
FEER and BEER indicate for the 2005-2008 period an overvaluation for the real exchange rate, with an
average misalignment of 6,92% for the fundamental approach and one of 5,94% for the behavioral one.
The maximum misalignment was 10,7 per cent as indicated by FEER and 13,9% as pointed by BEER
In 2009, it can be observed an undervaluation for REER with a misalignment of 1,46% (FEER) or 2,56%
(BEER)
Chart 16: The comparative pre se ntation of the re sults obtain for e quilibrium RER_EUR
FEER vs BEER
150
percent
index, 2000=100
140
30
30
20
20
10
10
130
RER_EUR
90
2009Q01
2008Q01
2007Q01
2006Q01
2005Q01
2004Q01
2003Q01
2002Q01
2001Q01
80
2009Q01
2008Q01
2007Q01
0
-10
FEER-BEER
-20
FEER
2006Q01
2005Q01
2004Q01
-10
2003Q01
BEER
100
2002Q01
0
110
2001Q01
120
BEER mis alignment
-20
FEER mis alignment
-30
-30
Source: BIS, own calculation
Chart 17: The nominal RON/EUR exchange rate vs the level implied by
BEER and FEER
4.50
4.00
3.50
3.00
2.50
2.00
1.50
NER_EUR
BEER
FEER
20
01
Q
20 1
01
Q
20 3
02
Q
20 1
02
Q
20 3
03
Q
20 1
03
Q
20 3
04
Q
20 1
04
Q
20 3
05
Q
20 1
05
Q
20 3
06
Q
20 1
06
Q
20 3
07
Q
20 1
07
Q
20 3
08
Q
20 1
08
Q
20 3
09
Q
20 1
09
Q
3
1.00
Source: own calculation
According to FEER, in Q4 2009 the EUR/RON equilibrium value was around 4,02 RON/EUR
while BEER indicates 4,17 RON/EUR
Concluding remarks





The equilibrium real exchange rate, a fundamental indicator when judging the
competitiveness of an economy and its ability to match the nominal
convergence criteria was assessed using the method of fundamental
equilibrium exchange rate (FEER) and of behavioural equilibrium real
exchange rate (BEER)
Both FEER and BEER models revealed the same three periods in the
evolution of the real exchange rate misalignment towards equilibrium
The sensitivity analysis performed on the FEER model revealed that the
results are more sensitive to the hypothesis of the structural current account
than the one related to export/import elasticises.
The assessment of the equilibrium real exchange rate is also useful in the
determination of the nominal equilibrium exchange rate. According to FEER
method the in last quarter of 2009 the nominal equilibrium exchange rate was
4,02 while BEER suggests an equilibrium value of 4, 17.
In this context, for transition countries, BEER and FEER should be used as
complementary methodologies rather then substitutable