Download Exchange rate misalignment

Estimating Equilibrium Real
Exchange Rate
MSc.Student: Petcu C@t@lin
Supervisor: Mois@ Alt@r
Topics
Introduction
 Overview of Literature
 Theoretical Framework and Models
 Empirical Analysis
 Conclusion

Introduction



Important for future economic development
Exchange rate misalignment
- direct effects on the economy
- EU admission
VECM - Cointegration
Overview of literature
PPP equilibrium
 Cassel (1922)
 Chinn (1999)
 Sarno and Taylor(2002)
“Reduced Form” approach
(single equation)
 MacDonald(1997)
 Clark & MacDonald(1998)
 Elbadawi(1999)
 Halpern & Wyplosz(1997)
Macroeconomic Equilibrium
approach
 normative models:
FEER, DEER
 positive models:
NATREX, BEER, PEER
Studies on EU accession countries
 Alberola et al.(1999)
 Egert (2002),
 Elbadawi(1999)
 Halpern & Wyplosz(2001)
 Filipozzi(2000)
 Kemme & Tang (2002)
 Barlow & Radulescu (2002)
 Jörg Rahn(2003)
Theoretical framework and models
RER measure
Combines nominal exchange rate (S) with measures of
domestic(P) and overseas prices(P*).
S P*
RER 
P
ln( RER )  s  p *  p
Multilateral real exchange rate (REER):
( Si  Pi *)
REER  
P
i 1
n
wi
n
ln (REER)   ln( RER )  wi
i 1
BEER - PEER approach

Theoretical background:
- a country with a small open economy with two sectors of goods
(tradable and non-tradable)
- two fundamentals : - foreign asset position
- sectoral productivities - relative prices
Real exchange rate components:
qt =[((st + ptT*) – ptT ] + [α(ptN – ptT) – α*(ptN* - ptT*)]
qtX
qt
X

i

 NFAt
qtI
I
qt  qt   ( Pt
I
NT
 Pt
NT
)
α, γ<0
The real exchange rate becomes:
q t  β0  β1  ΝFΑt  β2 P NT 
β1 , β2  0
The econometric methodology:
- Cointegration
- Vector error correction
Estimation of equilibrium values of the variables:
Time series approach: (BEER)
- the transitory part of each series is eliminated by applying an econometric
filter to smooth the series
-the obtained series are used in the model
Hodrick- Prescott filter:
- computes the smoothed series “s” by minimizing the variance of initial series around the
computed one, subject to a penalty that constrains the second difference of it.
- in the estimation I use an smoothing parameter value of 50, because is very similar to the 2
year moving average
Orthogonal decomposition: (PEER) (Gonzalo - Granger (1995))
- the transitory component does not Granger cause the permanent component
- the permanent component is a linear combination of observed variables
p 1
xt      i xt i     ' xt 1   t
i 1
where xt is the vector of fundamentals=[REERt,NFAt,PNTt]’ and will be decompose
into permanent: xtP=[REERtperm, NFAtperm, PNTtperm]’ and transitory xtT=[REERttrans,
NFAttrans, PNTttrans]’ components.
xt  A1  ' xt    ( '   )1 ' xt
P
xt  A2  ' xt   (  ' ) 1  ' xt
T
where α┴,β┴ are the orthogonal components, defined as the eigenvectors
associated with the unit eigenvalues of the matrices:
(
I  ) and
( '( ) 1) '.
I   (  '  ) 1  '
Three equation system cointegration
- more complete model
- based on Montiel(1999) model extended by Egert (2002)
- internal and external balances are estimated trough their own
determinants
– internal balance:
PNT+ β1SALACT (β1<0)
– external balance:
NFA+ β1CA (β1<0)
– equilibrium real exchange rate: REER+ β1PNT+ β2NFA(β1,β2>0)
The monetary approach
Exchange rate is considerate the relative price of two monies: the
domestic money and the foreign money
Changes in relative magnitudes of foreign and domestic monetary
aggregates ,inflation differentials, or interest rate differentials
The methodology is based on VECM model:
REERt  β0  β1  LNCRt  β2 LNCF  β3 IRDIF
Equilibrium values of determinants are estimated with Hodrick Prescott filter
Empirical analysis

Data set

Results
Data set
lnREER - the real effective exchange rate
It is defined as the log of a CPI-deflated index based on German mark and US dollar bilateral exchange rates.
The weights used for computing the effective real exchange rate correspond to the structure of foreign trade
in terms of openness to the EU-15 (for the German mark), 60%, and to the rest of the world (for the US
dollar), 40%.
ln PNT - the relative price (productivity level differential)
Defined as the ratio of the domestic consumer price index to the domestic producer price index relative
to the corresponding foreign ratio, using the same trade weights as for the real effective exchange rate.
NFA_PIB - the net foreign asset stock
It is defined as the stock of net foreign assets from the banking system. In order to adjust for the size of
the country, net foreign assets were normalized by nominal GDP.
Back
SALACT - Real salaries - are obtained from nominal salaries deflated
with CPI
CONTCURENT_PIB - Current account balance - normalized to GDP
LNCR - Currency reserves - the log of the stock hold by National Bank
CAPITALFLOW - Foreign capital flow - the log of the foreign capital in
the banking system
RDID - The real interest rates differential - determined as a difference between the real interest rate
on the Romanian market and an international real interest rate for Germany and US using
the same weights as before.
Back
Results
Unit root tests:
ADF
PERRON
REER
-2.03 (I(1))
-2.20 (I(1))
PNT
-2.02 (I(1))
-2.02 (I(1))
NFA
-2.43 (I(1))
-2.91 (I(1))
Real Salaries
-3.18 (I(1))
-3.05 (I(1))
CA
-4.37 *
-3.85 (I(1))
Currency Reserves
-2.19 (I(1))
-2.19 (I(1))
Capital Flow
-2.42 (I(1))
-3.34 (I(1))
Real Interest differ
-5.51*
-5.59*
BEER Approach
Test for lag length criteria:
VAR Lag Order Selection Criteria
Endogenous variables: LNREERW LOG(PNT) NFA_PIB
Exogenous variables: C DUM972 DUM973
Date: 07/02/03 Time: 07:18
Sample: 1995:01 2002:12
Included observations: 77
Lag
LogL
LR
FPE
AIC
SC
HQ
0
1
2
3
4
5
6
7
55.50318
319.0405
343.5227
355.4200
368.6261
370.9319
379.0483
381.8692
NA
486.0039
43.24134
20.08631
21.26686*
3.533633
11.80562
3.883368
6.00E-05
8.07E-08
5.41E-08
5.04E-08
4.56E-08*
5.48E-08
5.70E-08
6.84E-08
-1.207875
-7.819234
-8.221370
-8.296624
-8.405872*
-8.231997
-8.209046
-8.048551
-0.933924
-7.271332
-7.399516*
-7.200819
-7.036115
-6.588290
-6.291387
-5.856940
-1.098297
-7.600078
-7.892636*
-7.858312
-7.857981
-7.574529
-7.441999
-7.171926
* indicates lag order selected by the criterion
Test for cointegration:
Hypothesized
No. of CE(s)
None **
At most 1
At most 2
Eigenvalue
Trace
Statistic
5 Percent
Critical Value
1 Percent
Critical Value
0.326261
0.153603
0.000213
44.38944
13.19141
0.016854
29.68
15.41
3.76
35.65
20.04
6.65
*(**) denotes rejection of the hypothesis at the 5%(1%) level
Trace test indicates 1 cointegrating equation(s) at both 5% and 1% levels
Hypothesized
No. of CE(s)
None **
At most 1
At most 2
Eigenvalue
Max-Eigen
Statistic
5 Percent
Critical Value
1 Percent
Critical Value
0.326261
0.153603
0.000213
31.19804
13.17455
0.016854
20.97
14.07
3.76
25.52
18.63
6.65
*(**) denotes rejection of the hypothesis at the 5%(1%) level
Max-eigenvalue test indicates 1 cointegrating equation(s) at both 5% and 1%
levels
Cointegration relationship (t-statistic in brackets):
ln REERW t   0.11 ΝFΑt  1.18 P  7.45
NT
(3.4398) (6.58846)
Error correction:
Error Correction: D(LNREERW) D(LOG(PNT)) D(NFA_PIB)
CointEq1
-0.076753
(0.03130)
[-2.45179]
-0.067213
(0.02525)
[-2.66241]
-1.784380
(0.73546)
[-2.42620]
Estimated behavioral equilibrium exchange rate
7.6
.20
7.5
.15
.10
7.4
.05
7.3
.00
7.2
-.05
7.1
-.10
-.15
7.0
95
96
97
98
ECHILIBRUBEER
99
00
01
HPLNREERW
02
95
96
97
98
99
MISABEER
00
01
02
PEER Approach
Orthogonal components:
Orthogonal
components
α
LNREERW
PNTT
NFAT
┴
-0.82668540.5624809 0.0143719
β
┴
0.5964793-0.5605464 0.5744564
Estimated permanent equilibrium exchange rate
.16
7.7
7.6
.12
7.5
.08
7.4
.04
7.3
7.2
.00
7.1
-.04
7.0
-.08
6.9
95
96
97
98
EQPEER
99
00
01
LNREERW
02
95
96
97
98
99
MISAPEER
00
01
02
System cointegration
Restriction on the coefficient matrix
 SALACT

a1


0


0

PNT
1
0
c3
NFA CA REER 

0
0
0 
1
b2
0 

c4
0
1 
Cointegration test:
Date: 07/02/03 Time: 08:42
Sample(adjusted): 1996:01 2002:04
Included observations: 76 after adjusting endpoints
Trend assumption: Linear deterministic trend
Series: SALARIIACT LOG(PNT) NFA_PIB CONTCURENT_PIB LNREERW
Lags interval (in first differences): 1 to 3
Unrestricted Cointegration Rank Test
Hypothesized
No. of CE(s)
Eigenvalue
Trace
Statistic
5 Percent
Critical Value
1 Percent
Critical Value
None **
At most 1 **
At most 2 *
At most 3
At most 4 *
0.445467
0.295226
0.236968
0.068262
0.056207
101.7272
56.91529
30.32450
9.769942
4.396464
68.52
47.21
29.68
15.41
3.76
76.07
54.46
35.65
20.04
6.65
*(**) denotes rejection of the hypothesis at the 5%(1%) level
Trace test indicates 3 cointegrating equation(s) at the 5% level
Trace test indicates 2 cointegrating equation(s) at the 1% level
System cointegration vectors:
– internal balance: PNT +β1SALACT [1;-0.473]
– external balance: NFA+ β1CA
[1;-0.203]
– equilibrium real exchange rate: REER+ β1PNT+ β2NFA [1;1.83;0.02]
.2
7.5
.1
7.4
.0
7.3
-.1
7.2
-.2
7.1
-.3
-.4
7.0
1996
1997
1998
EQVEC3EQ
1999
2000
2001
HPLNREERW
1996
1997
1998
1999
MISA3EQ
2000
2001
Monetary approach
Test for lag length criteria:
VAR Lag Order Selection Criteria
Endogenous variables: LNREERW LNCR LOGCAPITALFLOW RDID
Exogenous variables: C DUM973
Date: 07/02/03 Time: 09:10
Sample: 1995:01 2002:12
Included observations: 77
Lag
LogL
LR
FPE
AIC
SC
HQ
0
1
2
3
4
5
6
7
-30.80059
180.0310
221.9911
241.6095
259.0219
267.0418
274.1678
282.8091
NA
388.8064
73.02142
32.10283
26.68395*
11.45692
9.439626
10.54918
3.22E-05
2.04E-07
1.05E-07
9.63E-08
9.46E-08*
1.20E-07
1.58E-07
2.04E-07
1.007808
-4.052754
-4.727042
-4.821026
-4.857712*
-4.650435
-4.419942
-4.228808
1.251320
-3.322218
-3.509481*
-3.116441
-2.666102
-1.971801
-1.254282
-0.576124
1.105210
-3.760546
-4.240028*
-4.139207
-3.981087
-3.579005
-3.153706
-2.767766
* indicates lag order selected by the criterion
Test for cointegration:
Hypothesized
No. of CE(s)
Eigenvalue
Trace
Statistic
5 Percent
Critical Value
1 Percent
Critical Value
None *
At most 1
At most 2
At most 3
0.314505
0.206554
0.021858
0.004182
50.18676
20.35522
2.076979
0.331037
47.21
29.68
15.41
3.76
54.46
35.65
20.04
6.65
*(**) denotes rejection of the hypothesis at the 5%(1%) level
Trace test indicates 1 cointegrating equation(s) at the 5% level
Trace test indicates no cointegration at the 1% level
Hypothesized
No. of CE(s)
Eigenvalue
Max-Eigen
Statistic
5 Percent
Critical Value
1 Percent
Critical Value
None *
At most 1
At most 2
At most 3
0.314505
0.206554
0.021858
0.004182
29.83154
18.27824
1.745943
0.331037
27.07
20.97
14.07
3.76
32.24
25.52
18.63
6.65
*(**) denotes rejection of the hypothesis at the 5%(1%) level
Max-eigenvalue test indicates 1 cointegrating equation(s) at the 5% level
Max-eigenvalue test indicates no cointegration at the 1% level
Cointegration relationship (t-statistic in brackets):
ln REERW t   0.30  LNCRt  0.26 CAPITALFLOW  1.53RDID  19.78
(6.93) (3.50)
(4.51)
Error correction:
Error Correction: D(LNREERW
)
CointEq1
-0.048883
(0.02370)
[-2.06223]
D(LNCR)
D(LOGCAPIT
ALFLOW)
D(RDID)
-0.292074
(0.14100)
[-2.07143]
0.030231
(0.29506)
[ 0.10245]
-0.390529
(0.11280)
[-3.46227]
Estimated behavioral equilibrium exchange rate in monetary approach
.3
7.8
.2
7.6
.1
7.4
.0
-.1
7.2
-.2
7.0
-.3
6.8
-.4
-.5
6.6
95
96
97
98
EQMONETARY
99
00
01
HPLNREERW
02
95
96
97
98
99
00
MISAEQMONETARY
01
02
Conclusion
The equilibrium real exchange rate is the level to which the
RER will tend in the long run.
If at EMU entry Romanian currency will be undervalued or
overvalued against euro the adjusting to equilibrium will
involve significant costs.
Even in the case of an exchange rate very much consistent
with internal and external balance it will still exist the
danger of real appreciation over the future fixed parity