Is there a relationship between real exchange rate movements and the output cycle?

Transcription

1 Loughborough Universiy Insiuional Reposiory Is here a relaionship beween real exchange rae movemens and he oupu cycle This iem was submied o Loughborough Universiy's Insiuional Reposiory by he/an auhor. Addiional Informaion: This paper forms par of he ESRC funded projec (Award No. L ) Business Cycle Volailiy and Economic Growh: A Comparaive Time Series Sudy, which iself is par of he Undersanding he Evolving Macroeconomy Research programme. Meadaa Record: hps://dspace.lboro.ac.uk/2134/725 Publisher: c Loughborough Universiy Please cie he published version.

2 This iem was submied o Loughborough s Insiuional Reposiory by he auhor and is made available under he following Creaive Commons Licence condiions. For he full ex of his licence, please go o: hp://creaivecommons.org/licenses/by-nc-nd/2.5/

3 Deparmen of Economics Business Cycle Volailiy and Economic Growh Research Paper No. 01/2 IS THERE A RELATIONSHIP BETWEEN REAL EXCHANGE RATE MOVEMENTS AND THE OUTPUT CYCLE Terence C. Mills and Eric Penecos June 2001 This paper forms par of he ESRC funded projec (Award No. L ) Business Cycle Volailiy and Economic Growh: A Comparaive Time Series Sudy, which iself is par of he Undersanding he Evolving Macroeconomy Research programme.

4 1 Inroducion The Neo-classical heory of exchange rae deerminaion, wih a sock view of capial movemens, has he equilibrium exchange rae dependen on purchasing power pariy (PPP); ha is, he bilaeral nominal exchange rae is deermined by he raio of domesic o foreign price levels. Thus he real exchange rae is prediced o be consan. This predicion, however, is largely rejeced by he daa (see, for example Rogoff, 1996). Less resricive models of he equilibrium exchange rae, such as he radiional Mundell-Fleming model (Mundell, 1963) or generalised porfolio balance (Branson and Buier, 1983), assume ha oupu is no fixed a he level of full employmen, and posulae ha he curren accoun balance deermines he equilibrium exchange rae. In oher words, he real exchange rae, raher han assumed o be consan, is relaed o he relaive oupu levels. The empirical implicaion of his hypohesis is ha he real exchange rae should be co-inegraed wih he relaive levels of domesic and foreign oupu. This hypohesis is, however, rejeced by he daa in his paper, jus as he PPP relaionship has been empirically rejeced. This resul nowihsanding, he real exchange rae does shown a long, cyclical paern, no dissimilar o a business cycle paern. Cyclical oupu paerns could ranslae ino real exchange rae cycles, since he inernaional ransmission of he business cycle radiionally akes place hrough he rade balance (see, for example, Williamson and Milner, 1991). This cycle, however, is no apparen from eiher monhly or quarerly daa because, as noed by Baxer (1994) in a differen conex, he frequency is oo high. A lower frequencies, however, a cyclical relaionship may emerge beween oupu and he real exchange rae. If confirmed, his analysis also explains why PPP is rejeced in he shor o medium erm, since i implies ha he real exchange rae, raher han remain consan as suggesed by PPP, in fac flucuaes over he business cycle. This paper examines his relaionship for he U.S. and U.K. over he floaing exchange rae period from 1973 o Secion 2 posis a simple model of he relaionship beween U.S. and U.K. oupu and he real dollar-serling exchange rae. Secion 3 considers he derending of ime series and models he cyclical componens of he series o reveal he relaionship beween he real exchange rae and he wo oupu cycles. Secion 4 offers a brief conclusion. 2 The Basic Equilibrium Model Wih a sock-view of inernaional capial flows and a freely floaing nominal exchange rae regime, in equilibrium he curren accoun of he balance of paymens 1

5 mus be in balance. This exernal balance condiion, expressed in erms of he home counry, is: Q, Y M Q Y X, (1) X Q Y Q Y 0, X 0, M 0, M 0 where home expors, X, are idenical o foreign impors and home impors, M, are idenical o foreign expors. Q is he real exchange rae, measured as he foreign currency price of domesic currency, Y is domesic oupu, Y is foreign oupu, and he respecive parial derivaives are given below (1) 1. According o (1), domesic expors depend inversely on he real exchange rae, such ha as Q rises domesic expors become more expensive in foreign markes and he demand for hem falls. Conversely, a rise in Q is expeced o lead o an increase in domesic impors. An upurn in he foreign economy will lead o Y rising above rend, raising he demand for home expors. Similarly, a rise in Y will raise he domesic demand for foreign impors Equaion (1) is more general han he usual PPP equilibrium since we do no assume ha domesic and foreign goods are perfec subsiues such ha X Q M Q. Equaion (1) also permis price adjusmen o be slow, and hence oupu prices o be sicky, which is again an appealing feaure consisen wih New Keynesian ype research sraegies. If prices are sicky in he shor run, he real exchange rae may change, alering relaive prices and hence he demand for naional oupu. Suppose, for example, here is an increase in foreign demand for home oupu. If he exchange rae does no appreciae o offse he effec of he higher demand hen oupu will rise. Thus, in he shor run, over which prices are sicky, here may sill be an inernaional ransmission of he business cycle despie he floaing exchange rae policy. The need o mainain his equilibrium implies ha here is a relaionship beween he business cycle and he real exchange rae. To examine his poenial relaionship (1) can be assumed o be log-linear, where in equaion (2) lower case leers denoe he logs of heir upper case counerpars: q x q m y m q y x q x y m q y (2) 2

6 This says ha he real exchange rae is direcly relaed o foreign income and inversely relaed o domesic income. There are wo resricions ha can be esed on his simple quasi-reduced form model of exernal balance. Firs, if PPP is o hold hen x q mq and (2) would collapse o q 0, implying a consan real exchange x m y rae. Second, if here is symmery beween he wo economies such ha y, hen (2) reduces o q [ m y ( xq mq )]( y y). Alernaively, he relaive sizes of he wo economies could lead o asymmeric income effecs on he real exchange rae. Thus, if he foreign economy is larger han he domesic hen a foreign boom could be associaed wih an appreciaion of he real foreign currency price of domesic currency. Since all variables in (2) are sricly endogenous, his model is bes esed wihin a hree-equaion VAR framework using he cyclical componens of domesic and foreign oupu and he real exchange rae. This will also allow disequilibrium dynamics ino he srucure, which may be empirically imporan given he apparen empirical evidence in suppor of J-curves. 3 Empirical Implemenaion of he Model In his secion we consruc he cyclical componens of he variables in (2) and hence analyse he cyclical relaionship beween U.K. and U.S. oupu and he real dollarserling exchange rae. The daa period is he floaing rae regime from 1973 o 1999, wih quarerly observaions being used. The oupu series are logarihms of real GDP for boh counries and are denoed y and y. The (logarihm of he) real exchange rae is formally defined as: q s p p (3) where s is he logarihm of he nominal exchange rae and p and p are he logarihms of he respecive consumer price indices. The oupu series are shown in Figure 1, and he real exchange rae is shown in Figure 2. These series display familiar properies. The wo oupu series boh conain prominen rends and shorrun movemens abou hese rends, alhough for he U.S. such cyclical flucuaions have been much aenuaed in he las decade. The real exchange rae, on he oher hand, conains no rend bu is characerised by long swings, paricularly up o All hree series hus have he characerisics of inegraed processes conaining a 1 We assume in his secion ha he Marshall-Lerner condiion holds such ha Q X X Q Q M M Q 1 0, alhough his is sricly an empirical quesion and does no in any way affec our resuls. 3

7 single uni roo, alhough he real exchange rae does no conain a drif. Sandard Dickey-Fuller ess confirm his supposiion. As Baxer (1994) and Baxer and King (1999) poin ou, relaionships beween business cycle componens are ofen difficul o deec when convenional rend removal echniques, such as linear de-rending or firs differencing, are employed. Sochasic rends associaed wih he presence of a uni roo canno be removed by linear de-rending, and his is a major drawback since permanen (rend) componens will remain in he cyclical componen obained as he residual from he fied rend (shor-run noise will also be included in his residual). Alhough firs differencing will remove uni roo componens, his filer has several drawbacks. I alers iming relaionships beween variables by inducing a subsanial phase shif and i involves a dramaic re-weighing of frequencies high frequency (noise) componens are emphasised a he expense of down-weighing lower frequencies: in paricular, much of he cyclic variaion is removed. A popular choice of business-cycle filer is ha proposed by Hodrick and Presco (1997). This filer has some desirable properies. I will remove uni roo rend componens, i has no phase shif and, for an appropriae choice of is smoohing parameer, i closely approximaes he opimal filer ha isolaes only componens having business-cycle frequencies, defined o be hose having periods beween 6 and 32 quarers. An arguably beer choice is he band-pass filer proposed by Baxer and King (1999), which avoids he disorions associaed wih he Hodrick-Presco filer ha are caused by rapidly changing weighs a he ends of he sample, which resul in subsanial disorions of hese cyclical observaions. Pedersen (2001), for example, recommends he use of his filer in siuaions such as hose found here. For he quarerly ime series x, he band-pass filer ha passes componens having periodiciies beween 6 and 32 quarers is defined as x k 12 a k 12 k x k, a k a k, k 12 k 12 a k 0 a a a , a , a , a , a4.1012, a , a , a , , a , a , a , This filer is employed here o exrac he cyclical componens from he wo oupu series and real exchange raes, all of which conain single uni roos, alhough he 4

8 laer does no conain a drif: as we have poined ou above, i displays long swings raher han any rend. Our firs empirical modelling exercise, however, is o invesigae he relaionships beween he observed series. The presence of uni roos in he hree series opens he possibiliy ha he series are coinegraed, as implied by he equilibrium exchange rae models menioned in he inroducion, in which case hey can be modelled using a VECM framework. If hey are no coinegraed, hen a VAR in firs differences is appropriae. In fac, here appears o be no compelling evidence of coinegraion. For example, a likelihood raio es of he null of no coinegraing vecors agains he alernaive of here being one, wih a rend in he daa bu no in he coinegraing vecor, yields a es saisic of compared o a 5% criical value of We hus considered a VAR(2) in he differences, y, q, a y and second order being chosen by a sequenial hypohesis esing procedure. This seing is consisen wih he lag order used in he es for coinegraion repored above and is general enough o ensure ha he residuals from he esimaed VAR passed diagnosic ess for residual auocorrelaion, ec.. An implicaion of his framework is ha we are de-rending via firs differencing o use oupu growh raes and real exchange rae appreciaion. The impulse responses for his ordering of he variables are shown in Figure 3. (The correlaions beween he hree residual series are 0.15, and 0.07, respecively, so ha he impulse responses are virually unaffeced by alernaive orhogonalisaions.) When compared o heir wo sandard error bounds, only he response of y o an innovaion in y looks o be a all significan, which is no surprising, bu here does no appear o be any relaionship beween oupu growhs and real exchange rae appreciaion. 5

9 If he relaionship beween oupu and he real exchange rae is a cyclical one, hen using firs differences will remove mos of hese componens, so ha i is hardly surprising ha lile can be gleaned from Figure 3. Figure 4 presens pair-wise plos of he band-pass filered cyclical componens y, y and q, from which i can be seen ha lead-lag relaionships cerainly appear o be presen. Figure 5 presens he impulse responses from fiing a VAR(4) and using he above ordering. This lag order was again seleced o ensure ha all residual diagnosic checks were saisfied. I is clear ha here are imporan cyclical relaionships presen. Innovaions o y and y influence q wih approximaely seven and 13 quarer delays before he maximum response is fel. Innovaions o q, on he oher hand, have a much more mued effec on y and y. y responds o an innovaion in y wih a delay of around seven quarers, wih lile evidence of feedback. This is consisen wih he being a small counry relaive o he. The paern of causaliy would hus appear o run from o, wih a delay of seven quarers, and hence o q, wih a delay of anoher seven quarers. There is hen a weak feedback effec from q o y ha peaks afer a furher 12 quarers, and an even more mued effec on y y y afer anoher six quarers. This paern suggess ha over a hree-year ime horizon he exchange rae is driven by he relaive oupu cycle, which is consisen wih exchange rae heory and ha he subsequen feedback from he exchange rae o oupu is relaively weak. This weak feedback effec suggess ha any overvaluaion of serling akes approximaely hree years o affec oupu, bu even hen he effec is relaively small. 4 Conclusions This paper has demonsraed ha here is no long-run empirical relaionship beween he real dollar-serling exchange rae and relaive oupus, as may be expeced from a neo-keynesian approach o he equilibrium exchange rae. On he oher hand, i demonsraes a cyclical relaionship beween he real exchange rae and relaive oupus, where he direcion of causaliy is from oupus o he exchange rae, wih only weak feedback effecs. Thus he medium run relaionship is beween he cyclical componens of real oupus and he real exchange rae series and no he rends. This empirical resul may also be aken as supporive of he neo-keynesian, sicky-price model of he equilibrium exchange rae, if he benchmark is aken o be he business cycle and no he rend growh in oupus, while also explaining he rejecion of he neo-classical PPP hypohesis. References 6

10 Baxer, M. (1994), Real exchange raes and real ineres differenials. Have we missed he business-cycle relaionship Journal of Moneary Economics, 33, Baxer, M. and King, R.G. (1999), Measuring business cycles: Approximae bandpass filers for economic ime series, Review of Economics and Saisics, 81, Branson, W.H. and Buier, W. (1983), Moneary and fiscal policy wih flexible exchange raes, in J.S. Bhandri and B.H. Punam (eds), Economic Inerdependence and Flexible Exchange Raes, Cambridge Mass: MIT Press. Hodrick, R.J. and Presco, E.C. (1997), Pos-war U.S. business cycles: An empirical invesigaion, Journal of Money, Credi and Banking, 29, Mundell, R.A. (1963), Capial mobiliy and sabilisaion policy under fixed and flexible exchange raes, Canadian Journal of Economics and Poliical Science, 27, Pedersen, T.M. (2001), The Hodrick-Presco filer, he Sluzky effec, and he disorionary effec of filers, Journal of Economic Dynamics and Conrol, 25, Rogoff, K. (1996), The purchasing power pariy puzzle, Journal of Economic Lieraure, 34, Williamson, J. and Milner, C.R. (1991), The World Economy, London: Harveser- Wheasheaf. 7

11 12.2 U.S U.K Figure 1. U.K. and U.S. oupu Figure 2. Real exchange rae 8

12 Response o One S.D. Innovaions ± 2 S.E Response of D(Q) o D(Y) 0.06 Response of D(Q) o D(Y) Response of D(Y) o D(Q) Response of D(Y) o D(Y) Response of D(Y) o D(Q) Response of D(Y) o D(Y) Figure 3. Impulse responses from he VAR(2) of y (denoed D(Y)), (D(Y)) and q (D(Q)), surrounded by wo sandard error bounds. y 9

13 3 2 Oupu Cycle Real Dollar Cycle Real dollar cycle Oupu Cycle oupu cycle oupu cycle Figure 4. Cyclical componens, y, y and q. 10

14 Response o One S.D. Innovaions ± 2 S.E. Response of real dollar cycle o oupu cycle 0.03 Response of real dollar cycle o oupu cycle Response of oupu cycle o real dollar cycle Response of oupu cycle o oupu cycle Response of oupu cycle o real dollar cycle Response of oupu cycle o oupu cycle Figure 5. Impulse responses from he VAR(4) of wo sandard error bounds. y, y and q, surrounded by 11