Estimating Equilibrium Real Estimating Equilibrium Real Exchange RateExchange Rate

MSc.Student: Petcu C@t@lin

Supervisor: Mois@ Alt@r

TopicsTopics

Introduction Overview of LiteratureTheoretical Framework and ModelsEmpirical AnalysisConclusion

IntroductionIntroduction

Important for future economic development Exchange rate misalignment

- direct effects on the economy - EU admission

VECM - Cointegration

Overview of literatureOverview of literature

PPP equilibrium Cassel (1922) Chinn (1999) Sarno and Taylor(2002)

Macroeconomic Equilibrium approach

normative models: FEER, DEER positive models: NATREX,

BEER, PEER

“Reduced Form” approach (single equation)

MacDonald(1997) Clark & MacDonald(1998) Elbadawi(1999) Halpern & Wyplosz(1997)

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 modelsTheoretical framework and models

ppsRER *)ln(P

PSRER

*

RER measure Combines nominal exchange rate (S) with measures of domestic(P)

and overseas prices(P*).

Multilateral real exchange rate (REER):

n

i

wii

P

PSREER

i

1

*)(

n

iiwRER(REER)

1

)ln(ln

BEER - PEER approachBEER - 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 + pt

T*) – ptT ] + [α(pt

N – ptT) – α*(pt

N* - ptT*)]

qtX qt

I

t

X

t NFAi

q )(

NT

tNT

t

I

tI

t PPqq α, γ<0

The real exchange rate becomes:

NTtt PβΝFΑβ β q 210 0, 21 ββ

The econometric methodology:

- Cointegration

- Vector error correction

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

Estimation of equilibrium values of the variables:

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

ttit

p

iit xxx

1

1

1

'

where xt is the vector of fundamentals=[REERt,NFAt,PNTt]’ and will be decompose

into permanent: xtP=[REERt

perm, NFAtperm, PNT

tperm]’ and transitory xt

T=[REERttrans,

NFAttrans, PNT

ttrans]’ components.

where α┴,

β┴ are the orthogonal components, defined as the eigenvectors

associated with the unit eigenvalues of the matrices:

( ) and ( ) .

ttT

t xxAx ')'(' 12

ttP

t xxAx

')'(' 11

')'( 1 I ')'( 1 I

Three equation system cointegrationThree 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 approachThe 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:

IRDIFβLNCFβLNCRβ β REER tt 3210

Equilibrium values of determinants are estimated with Hodrick - Prescott filter

Empirical analysisEmpirical analysis

Results

Data set

Data setData setlnREER - 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%.

NFA_PIB - the net foreign asset stockIt 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.

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.

Back

SALACT - Real salaries - are obtained from nominal salaries deflated with CPI

CONTCURENT_PIB - Current account balance - normalized to GDP

CAPITALFLOW - Foreign capital flow - the log of the foreign capital in the banking system

LNCR - Currency reserves - the log of the stock hold by National Bank

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

ResultsResults

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 ApproachBEER Approach

Test for lag length criteria:VAR Lag Order Selection CriteriaEndogenous variables: LNREERW LOG(PNT) NFA_PIBExogenous variables: C DUM972 DUM973Date: 07/02/03 Time: 07:18Sample: 1995:01 2002:12Included observations: 77

Lag LogL LR FPE AIC SC HQ

0 55.50318 NA 6.00E-05 -1.207875 -0.933924 -1.0982971 319.0405 486.0039 8.07E-08 -7.819234 -7.271332 -7.6000782 343.5227 43.24134 5.41E-08 -8.221370 -7.399516* -7.892636*3 355.4200 20.08631 5.04E-08 -8.296624 -7.200819 -7.8583124 368.6261 21.26686* 4.56E-08* -8.405872* -7.036115 -7.8579815 370.9319 3.533633 5.48E-08 -8.231997 -6.588290 -7.5745296 379.0483 11.80562 5.70E-08 -8.209046 -6.291387 -7.4419997 381.8692 3.883368 6.84E-08 -8.048551 -5.856940 -7.171926

* indicates lag order selected by the criterion

Test for cointegration:

Hypothesized Trace 5 Percent 1 PercentNo. of CE(s) Eigenvalue Statistic Critical Value Critical Value

None ** 0.326261 44.38944 29.68 35.65At most 1 0.153603 13.19141 15.41 20.04At most 2 0.000213 0.016854 3.76 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 Max-Eigen 5 Percent 1 PercentNo. of CE(s) Eigenvalue Statistic Critical Value Critical Value

None ** 0.326261 31.19804 20.97 25.52At most 1 0.153603 13.17455 14.07 18.63At most 2 0.000213 0.016854 3.76 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):

45.718.111.0ln NTtt PΝFΑ REERW

(3.4398) (6.58846)

Estimated behavioral equilibrium exchange rate

Error Correction: D(LNREERW) D(LOG(PNT)) D(NFA_PIB)

CointEq1 -0.076753 -0.067213 -1.784380 (0.03130) (0.02525) (0.73546)[-2.45179] [-2.66241] [-2.42620]

7.0

7.1

7.2

7.3

7.4

7.5

7.6

95 96 97 98 99 00 01 02

ECHILIBRUBEER HPLNREERW

-.15

-.10

-.05

.00

.05

.10

.15

.20

95 96 97 98 99 00 01 02

MISABEER

Error correction:

PEER ApproachPEER Approach

Orthogonal components:

Orthogonal components

LNREERW PNTT NFAT

α┴

-0.82668540.5624809 0.0143719

β┴

0.5964793-0.5605464 0.5744564

6.9

7.0

7.1

7.2

7.3

7.4

7.5

7.6

7.7

95 96 97 98 99 00 01 02

EQPEER LNREERW

-.08

-.04

.00

.04

.08

.12

.16

95 96 97 98 99 00 01 02

MISAPEER

Estimated permanent equilibrium exchange rate

100

0100

0001

43

2

1

cc

b

a

REERCANFAPNTSALACTRestriction on the coefficient matrix

Date: 07/02/03 Time: 08:42Sample(adjusted): 1996:01 2002:04Included observations: 76 after adjusting endpointsTrend assumption: Linear deterministic trendSeries: SALARIIACT LOG(PNT) NFA_PIB CONTCURENT_PIB LNREERWLags interval (in first differences): 1 to 3

Unrestricted Cointegration Rank Test

Hypothesized Trace 5 Percent 1 PercentNo. of CE(s) Eigenvalue Statistic Critical Value Critical Value

None ** 0.445467 101.7272 68.52 76.07At most 1 ** 0.295226 56.91529 47.21 54.46At most 2 * 0.236968 30.32450 29.68 35.65At most 3 0.068262 9.769942 15.41 20.04

At most 4 * 0.056207 4.396464 3.76 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

Cointegration test:

System cointegrationSystem cointegration

– 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]

System cointegration vectors:

7.0

7.1

7.2

7.3

7.4

7.5

1996 1997 1998 1999 2000 2001

EQVEC3EQ HPLNREERW

-.4

-.3

-.2

-.1

.0

.1

.2

1996 1997 1998 1999 2000 2001

MISA3EQ

Monetary approachMonetary approach

Test for lag length criteria:VAR Lag Order Selection CriteriaEndogenous variables: LNREERW LNCR LOGCAPITALFLOW RDIDExogenous variables: C DUM973Date: 07/02/03 Time: 09:10Sample: 1995:01 2002:12Included observations: 77

Lag LogL LR FPE AIC SC HQ

0 -30.80059 NA 3.22E-05 1.007808 1.251320 1.1052101 180.0310 388.8064 2.04E-07 -4.052754 -3.322218 -3.7605462 221.9911 73.02142 1.05E-07 -4.727042 -3.509481* -4.240028*3 241.6095 32.10283 9.63E-08 -4.821026 -3.116441 -4.1392074 259.0219 26.68395* 9.46E-08* -4.857712* -2.666102 -3.9810875 267.0418 11.45692 1.20E-07 -4.650435 -1.971801 -3.5790056 274.1678 9.439626 1.58E-07 -4.419942 -1.254282 -3.1537067 282.8091 10.54918 2.04E-07 -4.228808 -0.576124 -2.767766

* indicates lag order selected by the criterion

Test for cointegration:Hypothesized Trace 5 Percent 1 PercentNo. of CE(s) Eigenvalue Statistic Critical Value Critical Value

None * 0.314505 50.18676 47.21 54.46At most 1 0.206554 20.35522 29.68 35.65At most 2 0.021858 2.076979 15.41 20.04At most 3 0.004182 0.331037 3.76 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 Max-Eigen 5 Percent 1 PercentNo. of CE(s) Eigenvalue Statistic Critical Value Critical Value

None * 0.314505 29.83154 27.07 32.24At most 1 0.206554 18.27824 20.97 25.52At most 2 0.021858 1.745943 14.07 18.63At most 3 0.004182 0.331037 3.76 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):

78.1953.126.030.0ln RDIDFLOWCAPITALLNCR REERW tt

(6.93) (3.50) (4.51)

Estimated behavioral equilibrium exchange rate in monetary approach

Error Correction: D(LNREERW)

D(LNCR) D(LOGCAPITALFLOW)

D(RDID)

CointEq1 -0.048883 -0.292074 0.030231 -0.390529 (0.02370) (0.14100) (0.29506) (0.11280)[-2.06223] [-2.07143] [ 0.10245] [-3.46227]

Error correction:

6.6

6.8

7.0

7.2

7.4

7.6

7.8

95 96 97 98 99 00 01 02

EQMONETARY HPLNREERW

-.5

-.4

-.3

-.2

-.1

.0

.1

.2

.3

95 96 97 98 99 00 01 02

MISAEQMONETARY

ConclusionConclusion

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