Notes on Forecasting Nominal Equilibrium Exchange Rates of PLN Against USD

A C T A U N I V E R S I T A T I S L O D Z I E N S I S FOLIA OECONOMICA 192, 2005

W ł a d y s ł a w M i l o * , M a g d a l e n a R u t k o w s k a * *

N O T E S O N F O R E C A S T IN G N O M IN A L E Q U IL IB R IU M E X C H A N G E R A TES O F P L N A G A IN S T U S D

Abstract. Exchange rate is one of the most important prices in an open economy. For theoretical and practical reasons it is useful to calculate an equilibrium level of exchange rate. There is a wide range o f theories explaining exchange rate determinants. This article presents determinants o f exchange rates derived from monetary theory and balance o f payments theory. Upon these fundamental economic theories and defining different definitions of equilibrium we have calculated predictors o f nominal exchange rate of PLN against USD. We have also computed equilibrium level o f this exchange rate. Empirical results have shown that the theoretical equilibrium values do not statistically significantly differ on the method used in equilibrium computations and they are similar to the empirical trajectory o f PLN /U SD in the period 1995-2003.

Keywords: exchange rates, equilibrium, forecasting. JEL Classification: C62, D58, F31, F37.

1. INTRODUCTION

O ne o f the central prices in an open econom y is exchange rate. It influences so m any m ark e t m em bers th a t “ getting the currency rig h t” has becom e a critical objective purpose o f all decision m ak ers and m ark et players (R o senberg 1996, p. 2). F o r theoretical and practical reasons it is useful to calculate an equilibrium level o f exchange rate.

A rou nd this equilibrium level will fluctuate the value o f nom inal exchange ra te in th e long r u n .1 It is hard to define one theoretical con cep t o f the

* Prof. dr. hab. (Full Professor), Department o f Econometrics, University o f Łódź. ** Mgr (M.A.), Department o f Econometrics, University o f Łódź.

1 John Williamson (1985) - the pioneer in defining fundamental equilibrium exchange rate (FEER), recognized that PPP is not the satisfactory measure o f equilibrium. He defined the FEER as the exchange rate, which is “expected to generate a current-account surplus or deficit equal to the underlying capital flow over the cycle, given that the country is pursuing internal balance as the best as it can and not restricting trade for balance-of-payment reasons” - Williamson (1985) after Rosenberg (1996), p. 56.

d e te rm in a n ts o f exchange rate. A cco rd in g to lite ra tu re th e th eoretical equilibrium level can be obtain ed, e.g. either by the im plem entation of purchasing pow er parity PPP theory or balance o f paym en ts BOP theory. Existence o f equilibrium trajectory o f exchange ra te m ean s th a t exchange rate will n o t m ove random ly but it will gravitate tow ard its equilibrium path.

O n the basis o f fundam ental econom ic theories and theories o f equilibrium we will present som e em pirical exam ples o f forecasting equilibrium exchange rate o f P L N against U SD in the period 1995-2003.

O ur analysis will be based on two theoretical definitions o f d eterm inants o f nom inal exchange rate and two different approaches in defining equilibrium value o f o u r variable - this m eans th a t we will have fo u r definitions of n om in al value o f equilibrium level o f exchange rate.

We will exam ine w hether o u r theoretical trajectories o f equilibrium level o f exchange ra te are sim ilar to the em pirical values o f exchange rate o f PLN against U SD . We will also evaluate w hether using equilibrium m odels to forecasting exchange rates is b etter th an a trad itio n al ap p ro ach . We will try to answ er the question, w hether all obtained trajectories o f equilibrium exchange ra te o f PLN against U SD are com parable o r d o the results depend on th e used m eth o d . We also com pare the predicted values o f cxchangc ra te with its observed value.

2. EQUILIBRIUM PRICE

T here is a wide range o f m ethods o f calculating lon g-ru n level (or trajecto ry) o f equilibrium exchange rates. Every ap p ro ach m ay give different results. In this p ap e r we will focus o n the m eth o d s o f com p u tin g equilibrium values o f currencies based on the fundam ental theories (balance o f paym ents theory, m o n etary extension o f P PP theory) o f exchange ra te behavior in c o m b in atio n w ith the m eth o d s o f finding an equilibrium .

E xchange rate o f hom e currency is the price o f foreign currency expressed in the value o f dom estic currency. Because exchange ra te is a k ind o f price o u r concern will be focused o n th e m etho ds o f co m putin g price equilibrium . T here are several ways o f com puting equilibrium value o f variable P (price). W e will in tro d u ce two different definitions o f equilibrium value o f price P*.

Definition 1. T he equilibrium price P* is the price u n d er which dem and (Y f) equals supply ( Y’), both for the observable as well as fo r historical forecasts, i.e. Y?(P*) = Y?(P*), and f ? = Ý*t t = 1, ..., n. T h u s if

Y \ = a 0 + + X fa . + £я - _ Д , - a 0 Z,r ß - X / a

where X,7’ = ( X u , X 2„ X kt), Z J = ( Z lt, Z 2t, •••, Z kt) are row vectors of values o f exogenous variables th a t influence supply and d em and respectively, a , p are the vectors o f unkn ow n param eters, <£« ~ represents the w hite noise type e rro r o f specification for the eq uation i = s, d.

D efinition 2. T h e equilibrium price (P f) is th e price th a t corresponds to the situ ation when all forces (X) th a t influence P , keep balance and P, stays stable (AP, = 0) or alm ost stays stable ( A P ,» 0 ) .

T herefore, if

AP, = а 0 + а ,Р ,_ , + Х(г а + <!;,=>ДР, = 0 then

or r * _ , = P f =

OCj OEj И, '

w here a 0, ótj, á are lse(a 0), lse{a 1), Ise(tx).

3. THE THEORY OF EXCHANGE RATES

3.1. Balancc of Paym ents Theory

T h e first conventional way o f analyzing changes in exchange ra te is to study the changes in the cu rren t and capital accou nt tran sactio n s (R osenberg 1996, p. 68). S ta n d ard balance o f paym ents equilibrium co n d itio n is given by equality o f c u rren t (curracc) and capital accounts (capacc) o f balance o f paym ents (eq u atio n 1)

(1) capacc, = curracc

W e can define c u rren t acco unt as a sum o f net ex po rts (nex) and net interest paym ents on net foreign assets (M acD o n ald 2000, p. 3) (niponfa) (equation 2).

(2) curracc, = nex, + niponfa,.

F u rth e r, we can w rite, as in the eq u atio n 3 below , th a t ca p ital account is a functio n o f hom e interests rates (hir), foreign interest rates (fir) and expected first difference o f exchange rate (Aerf).

N et ex p o rt is a function o f exchange rate, difference in foreign (fp ) and hom e level (hp) o f prices and incom es (hgdp, f g d p ) (equ atio n 4):

F ro m eq u a tio n s (1) to (4) we can derive equilibrium exchange rates th at satisfy balance o f paym ents condition (equation 5):

P urchasing pow er parity (P P P) theory stipulates th a t th e long-term equilibrium value o f currency is determ ined only by the ra tio o f dom estic price level (U P ) relative to the foreign price level (FP) (R osen berg 1996, p. 8). T h e co ndition o f purchasing pow er parity m ay be w ritten by equation 6 (W illiam son 1994, p. 245-247):

PPP th eo ry is ad eq u ate to the econom ies w here dev iation s from equilib­ rium level are m onetarily in duced.3 D em and for m oney (M ) is a function o f incom e and interest rate. E q u atio n 7 and 8 describe a fu nction of d em and fo r m oney for hom e and foreign co u n try respectively:

By substitu tin g (7) and (8) in to (6) we o b tain n om inal exchange rate, which is driven by relative excess m oney supplies (eq u atio n 9):

2 To simplify the algebra, equations can be expressed in logarithms, lower case letters will represent the logs o f the variable.

3 PPP cannot be applied if disturbances are caused bz real factors (eg. productivity shocks) - Rosenberg (1996), p. 8.

(4) nex, = a 2(er, + f p , - hp,) - a 2hgdp, + a j g d p , .

(5)

er? = (hp, - f p , ) + — (hir, - f i r , + A erf) + — hgdp, - — f g d p , ---niponfa,.

3.2. The M onetary Extension of P P P Theory

(6)

(?)

(

)

M

=

4. EMPIRICAL RESULTS

T h e m entioned theories were applied in form ulating em pirical econom etric m odels o f exchange ra te o f PLN against U SD . E stim ation s were m ade on d a ta co ncerning Poland and USA from first q u a rte r o f 1995 till fou rth q u a rte r o f 2003.

E q u atio n s (5) and (9) enable us to derive exchange rates u n d er different theories o f equilibrium . We have tw o different equations describing equilibrium exchange rates con sistent with the first definition o f equilibrium prices and tw o o th er eq u a tio n s consistent w ith the second definition o f such prices.

C om bin ing (5) w ith D efinition 1 o f equilibrium gave us 3 different trajectories o f E R F (ERF__BOP, E R F B O P E C M , E R F B O P E C M R E S ), then using the sam e theoretical ap p ro ach bu t according to the second definition o f equilibrium we have com puted ERF_D BO P. F orecasts based on m onetary extension o f P P P are all denoted with letters M E P P P . W e have obtained 4 different paths of forecasts o f ER based on the first definition o f equilibrium ( E R F _ M E P P P , E R F _ M E P P P 2 , E R F _ M E P P P E C M , E R F _ M E P P P E R ) and tw o traje cto ries based on th e second defin itio n (E R F _ D M E P P P 1 , E R F _ D M E P P P 2 ). All this predictions are presented in F igu re A l (cf. A ppendix).

Table 1. Forecasts evaluation criteria

Forecast o f ER Mean R 2 (%) MAPE (%) SC (%) TPC (%) Deviation of mean (ER) from

mean (ERF) ER 3.59 ERF_BOP 3.65 93.47 2.26 48.57 70.59 0.07 E R F B O P E C M 3.73 97.10 2.21 51.43 52.94 0.14 ERF_BOPECMRES 3.59 96.27 2.34 68.57 58.82 0.00 ERF _D BOP 3.75 77.66 6.13 54.29 41.18 0.17 ERF_DMEPPP 1 3.77 80.67 4.74 62.86 17.65 0.19 ERF_DMEPPP2 3.75 88.37 4.53 48.57 47.06 0.17 ERF_MEPPP 3.73 91.84 2.44 68.57 23.53 0.14 ERF_MEPPP2 3.73 94.13 1.66 71.43 52.94 0.14 ERFJMEPPPECM 3.77 94.78 2.34 57.14 41.18 0.18 ERF_MEPPPER 3.73 94.51 2.36 57.14 47.06 0.14

L/\

О

Table 2. Descriptive statistics o f forecasts of equilibrium exchange rates (ERF_) in comparison with descriptive statistics o f ER

Forecast of ER Mean Median M axi­ mum M ini­ mum Standard deviation Skew­ ness Kurtosis Jarque-Bera Sum Sum square dev. ER 3.77 3.95 4.50 2.67 0.50 -0.77 2.68 3.08 112.99 7.15 ERF_BOP 3.76 3.95 4.39 2.65 0.48 -0.85 2.73 3.67 112.87 6.66 ERF_BOPECM 3.76 3.93 4.46 2.63 0.49 -0.89 2.89 3.94 112.72 7.01 ERF_BOPECMRES 3.76 3.92 4.44 2.64 0.49 -0.84 2.84 3.54 11Z87 6.89 ERFJDBOP 3.86 3.96 4.43 2.83 0.37 -1.03 3.80 6.10 115.91 4.00 ERF_DM EPPP\ 3.84 3.94 4.36 2.89 0.40 -0.95 2.94 4.50 115.29 4.58 ERF_DMEPPP2 3.82 3.92 4.48 2.76 0.43 -0.80 3.05 3.17 114.73 5.48 ERF_MEPPP 3.76 3.91 4.39 2.65 0.48 -0.90 2.86 4.03 112.66 6.60 ERFJAE PPP2 3.75 3.88 4.45 2.67 0.48 -0.81 2.80 3.32 112.62 6.80 ERF_MEPPPECM 3.76 3.93 4.40 2.67 0.48 -0.88 2.66 4.06 112.91 6.75 ERF_MEPPPER 3.76 3.92 4.37 2.65 0.48 -0.87 2.71 3.90 112.78 6.78 W ła d ys ła w M ilo , M a g d a le n a R u tk o w sk a

W e m ay observe th a t the values o f em pirical no m in al exchange rates and forecasts o f m o n etary and balance o f paym ents equilibrium rates arc relatively close to each o th er in the period 1999-2002. In 1995-1997, som e trajectories based on the BOP theory let us infer th a t P L N was in this period overvalued. In 2000 empirical nom inal value o f PLN was undervalued. In 2003, how ever, it starts a phenom enon o f grow ing difference between em pirical nom inal E R and any equilibrium nom inal E R tak en from the bundle o f equilibrium exchange rates, especially from M P P P theory. It m eans th a t U SD is q u ite undervalued (PLN overvalued) in 2003. We can see th a t equilibrium values received from each equatio n have close trajectories to the observed values. It m eans th a t the observed values o f exchange rates are m o st often co rresponding to their theoretical equilibrium values.

We can now com pare basic statistics o f tim e series o f predicted values o f equilibrium and em pirical exchange rates.

W e have ob tain ed 10 different p ath s o f equilibrium values o f exchange rate. I t is easily seen th a t equilibrium values received from each equ atio n have close trajectories to the observed values. It m ean s th a t the observed values o f exchange rates are m ost often co rrespo nd in g to th eir theoretical equilibrium values. D escriptive statistics o f all series o f E R F are also co m p arab le in values. C om p arin g forecasts based on th e first definition of equilibrium w ith the forecasts based on the second definitio n we can no t say th a t on e o f this ap p ro ach gave better historical forecasts. T h e same can be said a b o u t the predictors based on m o n etary extension o f PPP and balance o f paym ents theories. T herefore, we expect th a t o u r p redicto rs are good for m ak in g predictions o f equilibrium exchange rates o f P L N /U S D . W e m ay say th a t the values o f em pirical exchange rates are close to equilibrium values forecasts under M E P P P and BOP conditions.

It is also interesting to find com bined forecasts by the use o f obtained equilibrium exchange rates forecasts (F igure 1).

T h e com bined historical predictor is defined as the unweighted arithm etical m ean o f 10 p redictors o f equilibrium nom inal exchange rates. It m atches em pirical values o f E R o f P L N /U S D in 89% . It tu rn s o u t th a t under the assum ption th a t all o u r theoretical equations give som e in fo rm atio n ab o u t equilibrium exchange rates their com bination gives the best possible trajectory o f E R F . T his trajectory is sim ilar to the historical E R . C onsequently, we can suppose th a t the exchange rate o f P L N against U SD d u rin g 1995-2003 was shaped in accord ance with equilibrium conditio ns as well.

A fte r p u ttin g a shock to hom e interest ra te (i.e. we increased hir by 10% and 2 0 % ) in all equations, then, it tu rn ed o u t th a t all predictions cam e b ac k to th e ir p re v io u s values o b ta in e d w ith o u t th is d istu rb in g shock.

4.30

3.80

3.30

2.80

2.30

Fig. 1. Combined predictor (ERF_combined) o f empirical values o f nominal exchange rates o f PLN/USD (ER)

5. CONCLUSIONS

N om inal exchange ra te o f P L N against U SD was, in analyzed period, close to the equilibrium value of this rate. We have show n th a t the theoretical equilibrium values do no t statistically significantly differ o n the m ethod used in equilibrium com p u tatio n s, i.e. neither the applied econom ic theories as th e base fo r choosing determ in an ts for exchange rates, n o r th e definition o f equilibrium th at was used for com putations. Since bo th kinds o f definitions o f equilibrium gave sim ilar results we can suppose th a t o u r results are interesting from the theoretical and em pirical p o in t o f view.

Before P L N will be anchored into E R M 2, it is very im p o rta n t to find w h ether the em pirical value o f exchange rate is close to its equilibrium co u n te rp a rt (Lipiński and Słowiński 2003, p. 137). If it is n o t it will be necessary to answ er the question how to achieve the equilibrium exchange rates an d w hat are the im plications for the choice o f th e eu ro conversion rates. U n fo rtu n ately , p articu lar theoretical m odels d o n o t give clear answers fo r these questions (R aw danow icz 2003, p. 20). It is a very im p o rta n t issue in the aspect o f entering M o n etary U nion and an ch o rin g the zloty in the E R M 2 . I f we could find a p p ro p riate exchange ra te before anch orin g, then we could expect th a t the in tro d u ctio n o f E uro zo n e in P o la n d will be carried o u t “u n o b serv ed ” and Polish currency will jo in eu ro very softly.

U ) U) i n i i ) ( 0 ( D ( O a ) S N N N e O C O O ) C O O > < 3 ) 0 ) 0 ) 0 0 0 0 « — T - T - r - N N N N P ) M f O f O о>сг>с7>а>ст>о>о>о><ла>о)слст>ст>спо>ст>ст>ст>а>оооооооооооооооо

APPENDIX 1. BOP ér = 2.23 + 1.90 (hp, —fp ,) — 0.lHfgdp,_} — 0.005(to'r,_, + 0.80er,_, MUt (2 .5 9 ) ( - 3 . 2 9 ) ( - 2 . 2 5 ) (7 .8 3 ) R2 = 0.97 D-W = 2.6 /(0) n = 34 2. BOPECM

M r, = -20.7 + 25 ( hp,_ , - f p , _ ,) + 1 -57fgdp,_A- O.llfgdp, _ , + 0.038(tor,_4 - f i r , _ J - 0.48£CJVi,. , H U ( - 2 . 4 6 ) (2 .1 3 ) (2 .3 ) ( 3 .5 1 5 ) ( - 3 . 8 5 ) R 2 = 0.52 D - W = Z 38 /(0) n = 32 3. BOPECMRES Aér, = 6.64 + \(h p,_l —f p , - ,) — 0-9bhgdp,_2 +Q 39fgdp,_2 4-0.0218(/u>(_^ - f i r , _ 4) — 0 3 2 h C M ,_ 1 ,.,ш ( - 2 . 2 7 ) (2 .1 6 ) (2 .3 6 ) ( - 2 . 6 1 ) R2 = 0.36 D-W = 2.4 1(0) n = 32 4. DBOP A ér, = -12.74 + 1.1201p, _ , - f p , . j) + 1 .bhgdp, _ 3 - 0.41fgdp, _ 2 - 0.№ (h ir,_ 3 - f i r , . 3) - 0.43 er,_ , МШ (1 .6 2 ) (2 .1 2 ) ( - 3 . 1 9 ) ( - 3 . 3 2 ) ( - 3 . 1 1 ) R 2 = 0.47 D-IV = 2.49 /(0) n = 33 5. DMEPPP1

Ae>, = -1.05 + 0.46 (hm, - f m ,) + 0 .16(/giip, - hgdp,) - 0.52 er,_ ,

Ш (3 .3 9 ) (2 .7 2 ) ( - 3 . 6 4 )

R 2 = 0.46 D - iy = 1.92 /(0) n = 32

6. DMEPPP2

Дег, = 24.14 + 1.11 (hm, - f m ,) - 3 .M igdp,_l + 0.M fgdp, + 0.01 tor, - 0 .0 3 /ir ,_ , - 0 .6 8 e r ,_ ,

(5 .4 6 ) ( - 3 . 3 9 ) (4 .1 4 ) (3 .7 4 ) ( - 2 . 9 B ) ( - 4 . 5 9 ) R 2 = 0.69 D -IV = 1.87 /(0) n = 32 7. MEPPP ér, = -1.98 + 0.81 ( /im, - / m ,) + 0.42(fgdp, - hgdp,) + 0.0006 ( Wr, - f i r , ) M a t ( 1 3 .0 3 ) (1 5 .3 8 ) (2 .9 1 ) R 2 — 0.96 D-W = 1.19 /(0) л = 32

8. MEPPP2 ér, = 23.3 2 + 1.34 (hm, - f m , ) - 2 A l h y d p l_ i + \m f g d p ,+ 0.QI hir, -0 .0 3 /(> ,_ j r-twi (7 .2 4 ) ( - 3 . 3 ) ( 4 .9 0 ) ( 4 .7 4 ) ( - 2 . 9 3 ) R 2 = 0.97 D -W = 1.46 /(0) n = 32 9. MEPPPECM her, = -3.19 +0.21 + 0.2b(fgdp, - hgdp,) +0.04(Air(_ , —f i r , _ ,) +0.23£C M ,_ , f-fttat ( - 1 . B 7 ) (1 .8 4 ) (2 .1 7 1 ) ( - 2 . 4 4 ) R2 = 0.42 D -W = 2 .1 5 /(0) /1 = 31 10. MEPPPER ér, = -1.05 + 0.46( hm, - f m t) + 0A6(fgdp, - hgdp,) + 0.48егг_ , l « U (3 .3 9 ) (2 .7 2 ) (3 .3 1 ) R2 = 0.96 D -W = 1.92 /(0) n = 32 where:

er - log of the nominal exchange rate o f PLN against USD; hp - log o f the Polish producer price index (1995ql = 100); f p - log o f the USA producer price index (1995ql = 100);

hgdp - log of the Polish gross domestic product (1995ql = 100); fg d p - log o f the USA gross domestic product (1995ql = 100);

hm - log of the money supply in Poland (М3) (1995ql = 100); fm - log of the money supply in USA (М3) (1995ql = 100);

hir - W1BOR3M, fir - L1BOR3M.

Fig. A l. Forecasts o f equilibrium nominal exchange rate and empirical value of nominal exchange rate PLN/USD N o te s on F o re ca st in g Nom ina l Eq u ili br iu m

REFERENCES

Lipiński, J. and Sławiński, A. (eds.) (2003), Gospodarka Polski przed wejściem do Unii Europejskiej, Warszawa: PWE.

MacDonald, R. (2000), “Concepts to Calculate Equilibrium Exchange Rates: An Overview”, Economic Research Group of the Deutsche Bank, Deutsche Bundesbank: Discussion Paper, 3, Frankfurt am Main.

Rawdanowicz, L. (2003), The EM U Enlargement and the Choice o f the Euro Conversion Rates: Theoretical and Empirical Issues, CASE: Studies and Analyses, 269, Warsaw.

Rosenberg, M. R. (1996), Currency Forecasting. A Guide to Fundamental and Technical Models o f Exchange Rate Determination, Chicago, London, Singapore: Irwin Professional Publishing. Williamson, J. (1994), Estimating Equilibrium Exchange Rates, Washington, DC: Institute for

International Economics.

Władysław Milo, Magdalena Rutkowska

UWAGI NA TEMAT PROGNOZOWANIA RÓWNOWAGOWEGO KURSU WALUTOWEGO PLN DO USD

(Streszczenie)

Kurs walutowy jest jedną z ważniejszych cen w otwartej gospodarce. Z praktycznych i teoretycznych powodów bardzo użytecznym jest zbadanie jego poziomu równowagowego. Istnieje bardzo wiele teorii wyjaśniających kształtowanie się kursu walutowego. W artykule przedstawiono determinanty kursu walutowego, wynikające zarówno z teorii monetarystycznej, jak i teorii bilansu płatniczego. Następnie, na ich podstawie oraz przyjmując różne definicje równowagi, zbudowano predyktory nominalnego kursu PLN /U SD oraz obliczono jego równo­ wagowe poziomy. Przeprowadzona analiza empiryczna wykazała, że niezależnie od przyjętej definicji stanu równowagi otrzymane trajektorie poziomu kursów równowagi nie różnią się od siebie istotnie oraz są zbliżone do rzeczywistego kształtowania się kursu PLN /U SD w okresie