nonlinearities in real exchange rate determination: do african exchange rates follow a random walk?

17
This article was downloaded by: [Stony Brook University] On: 20 December 2014, At: 14:16 Publisher: Routledge Informa Ltd Registered in England and Wales Registered Number: 1072954 Registered office: Mortimer House, 37-41 Mortimer Street, London W1T 3JH, UK Applied Economics Publication details, including instructions for authors and subscription information: http://www.tandfonline.com/loi/raec20 Nonlinearities in real exchange rate determination: do African exchange rates follow a random walk? Juan Carlos Cuestas a & Estefanía Mourelle b a Nottingham Business School, Division of Economics, Nottingham Trent University , Burton Street, NG1 4BU, Nottingham, UK b Universidade da Coruña , A Coruña, Spain Published online: 22 Oct 2008. To cite this article: Juan Carlos Cuestas & Estefanía Mourelle (2011) Nonlinearities in real exchange rate determination: do African exchange rates follow a random walk?, Applied Economics, 43:2, 243-258, DOI: 10.1080/00036840802467065 To link to this article: http://dx.doi.org/10.1080/00036840802467065 PLEASE SCROLL DOWN FOR ARTICLE Taylor & Francis makes every effort to ensure the accuracy of all the information (the “Content”) contained in the publications on our platform. However, Taylor & Francis, our agents, and our licensors make no representations or warranties whatsoever as to the accuracy, completeness, or suitability for any purpose of the Content. Any opinions and views expressed in this publication are the opinions and views of the authors, and are not the views of or endorsed by Taylor & Francis. The accuracy of the Content should not be relied upon and should be independently verified with primary sources of information. Taylor and Francis shall not be liable for any losses, actions, claims, proceedings, demands, costs, expenses, damages, and other liabilities whatsoever or howsoever caused arising directly or indirectly in connection with, in relation to or arising out of the use of the Content. This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any form to anyone is expressly forbidden. Terms & Conditions of access and use can be found at http:// www.tandfonline.com/page/terms-and-conditions

Upload: estefania

Post on 15-Apr-2017

213 views

Category:

Documents


0 download

TRANSCRIPT

Page 1: Nonlinearities in real exchange rate determination: do African exchange rates follow a random walk?

This article was downloaded by: [Stony Brook University]On: 20 December 2014, At: 14:16Publisher: RoutledgeInforma Ltd Registered in England and Wales Registered Number: 1072954 Registered office: Mortimer House,37-41 Mortimer Street, London W1T 3JH, UK

Applied EconomicsPublication details, including instructions for authors and subscription information:http://www.tandfonline.com/loi/raec20

Nonlinearities in real exchange rate determination: doAfrican exchange rates follow a random walk?Juan Carlos Cuestas a & Estefanía Mourelle ba Nottingham Business School, Division of Economics, Nottingham Trent University , BurtonStreet, NG1 4BU, Nottingham, UKb Universidade da Coruña , A Coruña, SpainPublished online: 22 Oct 2008.

To cite this article: Juan Carlos Cuestas & Estefanía Mourelle (2011) Nonlinearities in real exchange rate determination: doAfrican exchange rates follow a random walk?, Applied Economics, 43:2, 243-258, DOI: 10.1080/00036840802467065

To link to this article: http://dx.doi.org/10.1080/00036840802467065

PLEASE SCROLL DOWN FOR ARTICLE

Taylor & Francis makes every effort to ensure the accuracy of all the information (the “Content”) containedin the publications on our platform. However, Taylor & Francis, our agents, and our licensors make norepresentations or warranties whatsoever as to the accuracy, completeness, or suitability for any purpose of theContent. Any opinions and views expressed in this publication are the opinions and views of the authors, andare not the views of or endorsed by Taylor & Francis. The accuracy of the Content should not be relied upon andshould be independently verified with primary sources of information. Taylor and Francis shall not be liable forany losses, actions, claims, proceedings, demands, costs, expenses, damages, and other liabilities whatsoeveror howsoever caused arising directly or indirectly in connection with, in relation to or arising out of the use ofthe Content.

This article may be used for research, teaching, and private study purposes. Any substantial or systematicreproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in anyform to anyone is expressly forbidden. Terms & Conditions of access and use can be found at http://www.tandfonline.com/page/terms-and-conditions

Page 2: Nonlinearities in real exchange rate determination: do African exchange rates follow a random walk?

Applied Economics, 2011, 43, 243–258

Nonlinearities in real exchange rate

determination: do African exchange

rates follow a random walk?

Juan Carlos Cuestasa,* and Estefanıa Mourelleb

aNottingham Business School, Division of Economics,

Nottingham Trent University, Burton Street, NG1 4BU, Nottingham, UKbUniversidade da Coruna, A Coruna, Spain

In this article, we aim at modelling the long-run behaviour of the Real

Effective Exchange Rates (REER) for a pool of African countries. Not

much attention has been paid to this group of countries, in particular, to

the existence of nonlinearities in the long-run path of such a variable.

Controlling for two sources of nonlinearities, i.e. asymmetric adjustment to

equilibrium and nonlinear deterministic trends allows us to gain some

insight about the behaviour of the African REER. We find that these

sources of nonlinearities help us to explain the apparent unit root

behaviour found applying linear unit root tests for most of the countries.

I. Introduction

Real Exchange Rate (RER) modelling has become

a very popular topic within international economics

during the last decades. Its understanding has several

implications not only from the theoretical, but also

from the applied point of view. From the theoretical

point of view, many macroeconomic models

assume a constant equilibrium real exchange rate.

Moreover, the real exchange rate can be used as

a means to asses the overvaluation or undervaluation

of currencies and, therefore, it is a tool for exchange

rate policy making. In addition, real exchange rate

misalignment can be understood as a measure of

economic integration (in the real markets) among

countries (Wei and Parsley, 1995). Finally, as Faria

and Leon-Ledesma (2003, 2005) point out, the real

exchange rate has an impact on long-run relative

growth rates and unemployment. This adds another

feature to exchange rate modelling: it can be used as

a means of promoting growth, in particular, in

developing countries.

During the last decades, several authors have tried

to contribute to the literature on the issue of whether

monetary models of exchange determination are

able to explain observed exchange rates movements.

However, the results of the empirical applications

have not been that successful (see Taylor, 2006,

for a recent literature review).Recent contributions to this literature claim that

the failure of the former empirical literature lies on

the fact of not taking into account the possibility of

nonlinearities in the long-run path of the real

exchange rates. There are several reasons for assum-

ing a nonlinear behaviour in this variable. First, as

Dumas (1992), Taylor and Peel (2000), Taylor et al.

(2001), Kilian and Taylor (2003) point out, the

existence of trade barriers, transport costs and

exchange rate intervention, may prevent the eco-

nomic agents from getting a profit from arbitrage.

This implies that the real exchange rate might behave

as a unit root process within a threshold, but as

a stationary variable outside the threshold, yielding

to an asymmetric speed of adjustment towards the

*Corresponding author. E-mail: [email protected]

Applied Economics ISSN 0003–6846 print/ISSN 1466–4283 online � 2011 Taylor & Francis 243http://www.informaworld.com

DOI: 10.1080/00036840802467065

Dow

nloa

ded

by [

Ston

y B

rook

Uni

vers

ity]

at 1

4:16

20

Dec

embe

r 20

14

Page 3: Nonlinearities in real exchange rate determination: do African exchange rates follow a random walk?

equilibrium, i.e. the exchange rate tends to revertfaster to the equilibrium, the more misaligned itbecomes after a shock.

Furthermore, Taylor (2004) and Reitz and Taylor(2008) evidence nonlinearities in real and nominalexchange rate movements through the effect ofofficial exchange rate intervention operations orannouncements ‘oral intervention’, since the inter-vention is more likely to occur and be effective, thegreater the degree of misalignment is. The coordinat-ing role of the authorities’ intervention or the‘coordination channel’ is then displayed, i.e. giventheir coordinating influence on informed traders,they raise the confidence of the latter and lead to thestabilization of the exchange rates (see also Taylor,1995; Sarno and Taylor, 2001).

In addition, nonlinearities may affect the realexchange rate in the form of structural changes.Devaluations/revaluations of the nominal exchangerates, as well as other exogenous events that canaffect the exchange rates with permanent effects,might generate a broken time trend.

These sources of nonlinearities might affect thepower of the unit root tests (see Kapetanios, Shin andSnell (KSS) 2003; Bierens, 1997, among others) and,therefore, traditional (linear) unit root tests may bebiased towards the nonrejection of the unit roothypothesis. In economic terms this implies thatthese unit root tests may incorrectly conclude thatthere is no evidence of stationary behaviour in thereal exchange rate, rejecting, thus, the PurchasingPower Parity (PPP) hypothesis.

In this article, we aim at contributing on theanalysis of the empirical fulfilment of PPP in a groupof African countries, in order to gain some insightabout the long-run behaviour of their real exchangerates. As Kargbo (2006) pin points, African countrieshave performed a number of economic reforms(Section III), mainly focused on exchange ratesadjustment in order to improve their competitivenessand economic growth, based on the assumption thatPPP holds. Hence, the empirical analysis of PPPbecomes the corner stone for the success of thesepolicies and neglecting these reforms and its effects onthe real exchange rate may yield to wrongconclusions.

In order to test for the order of integration of theAfrican real exchange rates, we apply three groups ofunit root tests. The first are the Ng and Perron (2001)(linear) unit root tests that are modified version ofexisting unit root tests in order to obtain tests withbetter properties in terms of size and power. Second,we account for the possibility of asymmetric speed

of mean reversion by means of the KSS (2003) unitroot test. For those stationary real exchange rates,we also estimate an Exponential Smooth TransitionAutoregressive (ESTAR) model so as to understandthe equilibrium values of the variable. Finally, forthose countries where we cannot reject the nullhypothesis of unit root, we apply the Bierens (1997)unit root tests that takes the possibility of nonlineartrend stationary under the alternative.

The remainder of this article is organized asfollows. Section II summarizes the PPP theory andthe recent contributions on the PPP analysis forAfrican countries, applying nonlinear techniques.Section III describes the data. In Section IV, wedescribe the methodology applied in this empiricalresearch and the results. Finally, the last sectionsummarizes the main contributions.

II. The PPP Hypothesis

The PPP hypothesis, in its strict form (or so-calledabsolute PPP) contends that the nominal exchangerate1 (st) between two countries should be equal to theprice ratio between the countries. This means that thereal exchange rate, defined as

et ¼stptp�t

ð1Þ

should be equal to one, where p�t and pt are,respectively, the foreign and domestic price indices.However, rejection of the absolute version of PPPdoes not necessarily imply that prices in commoncurrency are only explained by idiosyncratic factors;prices may still react with proportional instead ofidentical deterministic components. In this case it issaid that is the relative version of PPP the one thatholds, i.e. the real exchange rate is equal to a constantdifferent from one.

It is well known that PPP only holds in the longrun, which implies that the real exchange rate has tobe an I(0) process, thus, testing for unit roots inreal exchange rates became a popular way to test forPPP empirically (see Huizinga, 1987; Meese andRogoff, 1988; Mark, 1990; Ardeni and Lubian, 1991;Chowdhury and Sdogati, 1993, among the morerelevant contributions), although the results areambiguous.

However, as mentioned in the previous section,the traditional unit root tests might not be able todistinguish between a unit root and a stationaryprocess when the autoregressive parameter is near

1Units of foreign currency for a unit of domestic currency.

244 J. C. Cuestas and E. Mourelle

Dow

nloa

ded

by [

Ston

y B

rook

Uni

vers

ity]

at 1

4:16

20

Dec

embe

r 20

14

Page 4: Nonlinearities in real exchange rate determination: do African exchange rates follow a random walk?

unity and the data generating process followsa nonlinear path. For these reasons, another strandof the literature apply univariate techniques that

takes into account asymmetric adjustment towardsthe equilibrium (Michael et al., 1997; Obstfeld andTaylor, 1997; Taylor and Peel, 2000; Baum et al.,2001; Taylor et al., 2001) and structural changes andnonlinear trends (Papell, 2002; Sollis, 2005; Camareroet al., 2006, 2008; Christopoulos and Leon-Ledesma,2007; Cuestas, 2009; Cushman, 2008, among others),finding more favourable results towards the statio-narity of real exchange rates.

Although the evidence is pretty abundant forindustrialized countries, the empirical literature for

African countries is quite scarce. As Kargbo (2006)summarizes, there are number of authors who haveapplied multivariate techniques, within the linearframework, finding fairly mixed results for this groupof countries. Nevertheless, more recently some otherauthors (Anoruo et al., 2006; Bahmani-Oskooee andGelan, 2006) have started to apply unit root testscontrolling for nonlinearities, when testing for theorder of integration of the real exchange rates for

African countries. Whereas Anoruo et al. (2006)apply the KSS’ (2003) unit root test to the realexchange rate versus the US dollar for a sample of13 African countries, finding evidence of nonlinearmean reversion for only four of them; Bahmani-Oskooee and Gelan (2006) apply the same unit roottest for a pool of 21 Real Effective Exchange Rates(REER), obtaining evidence of asymmetric meanreversion for eight of them.

Although in both papers the authors consider thecase of a linear trend, it is not considered the case of

a nonlinear trend, as a proxy of structural changes.Hence, in this article we aim at complementingBahmani-Oskooee and Gelan (2006) first usinga Modified Information Criterion (Ng and Perron,2001) to obtain the lag length in the auxiliaryregression of the KSS’ (2003) nonlinear unit roottest, estimating a nonlinear ESTAR model for theexchange rates and, finally, allowing for the possibi-lity of nonlinear trend stationary real exchange rates

under the alternative hypothesis.

III. The Data

The data used for this empirical application areREER for a pool of African countries, i.e. Burkina

Faso, Burundi, Cameroon, Ivory Coast, Egypt,Ethiopia, Gabon, Ghana, Kenya, Madagascar,

Mauritius, Morocco, Niger, Nigeria, Rwanda,Senegal, Seychelles, Sierra Leone, South Africa,Tanzania and Togo. The data for REER have beenobtained from Bahmani-Oskooee and Gelan (2007).These authors compute the nominal and Effectiveexchange rates for several African countries asa weighted average of indexes of real bilateralexchange rates of all trading partners, i.e.

REERj ¼X20i¼1

!ijð pjsij=piÞtð pjsij=piÞ2003

� 100

� �ð2Þ

where !ij is the imports share of partner i withcountry j;2 sij is the nominal bilateral exchange ratedefined as number of units of country i’s per unit ofj’s currency; pi is country i price level; and pj iscountry j price level.

We have displayed the series of REER in Fig. 1.From these graphs we can highlight several features;first, for some of the countries there is clear down-ward pattern, implying a general depreciation of thecurrencies in real terms. Second, it is pretty obviousthat these countries’ REER have suffered from anumber of structural changes. For instance, the sharpfall in the REER of Burkina Faso, Ivory Coast,Niger, Senegal and Togo in 1994 was caused bya devaluation of their currencies by the Central Bankof West African countries against the French Frank.Likewise, the Central Bank of Central African Statesdevaluated the currencies of Cameroon and Gabon atthe end of 1993 that were pegged with the FrenchFrank. For the case of Egypt, in 1990 the presidentMubarak devaluated the currency against the USdollar. In the case of Ghana, there is a significantappreciation of the national currency during 1982–1984. This was due to an economic and politicalturmoil that raised inflation and the nationalcurrency was overvalued. The currency returned toits normal levels after the devaluation of 1984 whenan economic recovery programme was set.

All these interventions and structural changesmight have generated a nonlinear behaviour in thelong-run paths of these countries’ REER.

IV. Unit Root Testing and NonlinearModelling

Unit root testing

In order to test for the order of integration of theREER in this group of countries, in this section weapply two different types of unit root tests.

2 For major trading partners, see Bahmani-Oskooee and Gelan (2007) and Table 1.

Nonlinearities in real exchange rate determination 245

Dow

nloa

ded

by [

Ston

y B

rook

Uni

vers

ity]

at 1

4:16

20

Dec

embe

r 20

14

Page 5: Nonlinearities in real exchange rate determination: do African exchange rates follow a random walk?

The first are the Ng and Perron (2001) unit roottests. Following these authors, traditional unit roottests might suffer from two main problems. First,they might suffer from power problems when theautoregressive parameter is close to 1 and, second,when the errors of a Moving Average process areclose to �1, it is necessary to have a high laglength in order to avoid size problems. However, theAkaike Information Criterion (AIC) and BayesianInformation Criterion (BIC) tend to select a loworder of the lag length. In order to overcome theseissues, Ng and Perron (2001) propose a ModifiedInformation Criterion (MIC) that controls for thesample size. Additionally, the authors proposea method to avoid the power problem associated tothe aforementioned traditional unit root tests.Combining these two approaches, Ng and Perron(2001) obtained the following unit root tests: MZ�and MZt that are the modified versions of the Phillips(1987) and Phillips and Perron (1988) Z� and Zt tests;the MSB that is related to the Bhargava (1986) R1

test; and, finally, the MPT test that is a modifiedversion of the Elliot et al. (1996) Point Optimal Test.

Moreoever, the presence of the aforementioned

nonlinearities in the REER has implications for the

power of the technique and, therefore, traditional

(linear) unit root tests tend to accept a false unit

root null hypothesis (see KSS, 2003, among others).

Thus, nonlinearities can be present in REER in

the form of different behaviour of the variable

depending on its values, i.e. the variable behaves as

a nonstationary process when it is within a band, but

is stationary when it is outside the band. As stated by

Dumas (1994) and Michael et al. (1997), among

others, it is sensible to assume that the shift between

regimes is smooth rather than sudden, due to time

aggregation and individuals’ behaviour.In order to account for this source of nonlinearity,

we apply the KSS (2003) unit root test. KSS propose

a unit root test that takes into account the possibility

of smooth transitions between regimes. Thus, the null

hypothesis of unit root is tested against the alter-

native of globally stationary nonlinear process, i.e.

qt ¼ �qt�1 þ �qt�1ð1� expf��q2t�1gÞ þ �t ð3Þ

Table 1. Ng–Perron and KSS unit root test results

Country MZa MZt MSB MPT tNL tNLD

Burkina Faso 0.786 0.773 0.983 64.943 �1.893 �0.907Burundi 0.871 1.276 1.464 138.026 �4.122** �3.542**Cameroon �6.521 �1.771 0.271 3.878 �0.892 �1.914Ivory Coast �6.297 �1.756 0.278 3.950 �0.839 �2.281Egypt �6.632 �1.655 0.249 4.259 �2.230* �3.949**Ethiopia �5.797* �1.591 0.274* 4.570 �2.257** �4.571**Gabon �9.905** �2.161** 0.218** 2.727** �1.531 �2.926**Ghana �16.190** �2.843** 0.175** 1.518** �8.131** �8.687**Kenya �2.051 �0.808 0.394 10.135 �0.550 �2.559Madagascar �2.549 �0.897 0.351 8.628 �1.246 �2.384Mauritius �1.670 �0.759 0.454 12.279 �1.238 �2.469Morocco 0.736 0.649 0.881 53.002 �1.889 �1.043Niger �0.764 �0.379 0.496 16.409 �1.311 �1.925Nigeria �7.337* �1.892* 0.257* 3.425* �1.645 �1.628Rwanda �2.510 �1.090 0.434 9.610 �0.980 �1.056Senegal �3.511 �1.167 0.332 6.971 �1.013 �1.524Seychelles �1.321 �0.729 0.552 16.293 �0.513 �1.916Sierra Leone �8.399** �2.038** 0.242* 2.958** �2.359** �3.216**South Africa �2.738 �1.050 0.383 8.558 �1.229 �2.316Tanzania �7.849* �1.931* 0.246* 3.3115 �3.670** �5.665**Togo �0.375 �0.210 0.560 20.684 �1.314 �1.600

Notes: The order of lag to compute the tests has been chosen using the MAIC suggested by Ng and Perron (2001).The Ng–Perron tests include an intercept, whereas the KSS test has been applied to the raw data, tNL say, and to thedemeaned data, tNLD say.The symbols * and ** mean rejection of the null hypothesis of unit root at the 10 and 5% levels, respectively.The critical values for the Ng–Perron tests have been taken from Ng and Perron (2001), whereas those for the KSS have beenobtained by Monte Carlo simulations with 50 000 replications.

MZa MZt MSB MPT tNL tNLD

5% �8.100 �1.980 0.233 3.170 �2.196 �2.92510% �5.700 �1.620 0.275 4.450 �1.906 �2.633

246 J. C. Cuestas and E. Mourelle

Dow

nloa

ded

by [

Ston

y B

rook

Uni

vers

ity]

at 1

4:16

20

Dec

embe

r 20

14

Page 6: Nonlinearities in real exchange rate determination: do African exchange rates follow a random walk?

where �t� i.i.d. (0, �2). Note that KSS assume thatthe transition function is an ESTAR one. AnESTAR function is appropriate to model REERmovements since this type of function assume thatthe shocks have a symmetric effect over thevariable, regardless the sign of the shock (Taylorand Peel, 2000). It is a common practice to

reparameterize Equation 3 as

�qt ¼ �qt�1 þ �qt�1ð1� expf��q2t�1gÞ þ �t ð4Þ

in order to test for unit roots. KSS impose

�¼ 0, which is equivalent to saying that the variable

is an I(1) process in the central regime. In order to

test the null hypothesis H0: �¼ 0 against H1: �40

1971 1974 1977 1980 1983 1986 1989 1992 1995 1998 2001 200480

100

120

140

160

180

200

(a) Burkina Faso

1971 1974 1977 1980 1983 1986 1989 1992 1995 1998 2001 20040

250

500

750

1000

(b) Burundi

1971 1974 1977 1980 1983 1986 1989 1992 1995 1998 2001 200470

80

90

100

110

120

130

140

150

160

(c) Cameroon

1971 1974 1977 1980 1983 1986 1989 1992 1995 1998 2001 200460

70

80

90

100

110

120

130

140

(d) Ivory Coast

1971 1974 1977 1980 1983 1986 1989 1992 1995 1998 2001 200450

100

150

200

250

300

350

400

(e) Egypt

1971 1974 1977 1980 1983 1986 1989 1992 1995 1998 2001 200450

100

150

200

250

300

350

(f) Ethiopia

Fig. 1. Real exchange rates

Nonlinearities in real exchange rate determination 247

Dow

nloa

ded

by [

Ston

y B

rook

Uni

vers

ity]

at 1

4:16

20

Dec

embe

r 20

14

Page 7: Nonlinearities in real exchange rate determination: do African exchange rates follow a random walk?

outside the threshold,3 KSS (2003) propose a Taylor

approximation of the ESTAR model since, in

practice, the coefficient � cannot be identified under

H0. Thus, under the null, the model becomes

�qt ¼ q3t�1 þ t ð5Þ

where t is an error term. Now, it is possible to

apply a t-statistic to test whether qt is an I(1) process,

H0: ¼ 0, or is an I(0) process, H1: 50.The results of these unit root tests are reported in

Table 2. The first feature is that the results of

applying both types of tests are pretty similar,

1971 1974 1977 1980 1983 1986 1989 1992 1995 1998 2001 200460

80

100

120

140

160

180

(g) Gabon

1971 1974 1977 1980 1983 1986 1989 1992 1995 1998 2001 20040

1000

2000

3000

4000

5000

(h) Ghana

1971 1974 1977 1980 1983 1986 1989 1992 1995 1998 2001 200450

60

70

80

90

100

110

120

(i) Kenya

1971 1974 1977 1980 1983 1986 1989 1992 1995 1998 2001 200450

75

100

125

150

175

200

(j) Madagascar

1971 1974 1977 1980 1983 1986 1989 1992 1995 1998 2001 200480

85

90

95

100

105

110

115

120

(k) Mauritius

1971 1974 1977 1980 1983 1986 1989 1992 1995 1998 2001 200480

90

100

110

120

130

140

150

(l) Morocco

Fig. 1. Continued

3Note that the process is globally stationary provided that �25�50.

248 J. C. Cuestas and E. Mourelle

Dow

nloa

ded

by [

Ston

y B

rook

Uni

vers

ity]

at 1

4:16

20

Dec

embe

r 20

14

Page 8: Nonlinearities in real exchange rate determination: do African exchange rates follow a random walk?

i.e. for Ethiopia, Gabon, Ghana, Sierra Leone and

Tanzania, it is not possible to reject the null

hypothesis of unit root at the 5% significance

level. In addition, with the KSS test we find that

the REER of Burundi and Egypt is also stationary.

Finally, with the Ng–Perron test, it is possible to

reject the null hypothesis, but only at the 10%

significance level. In summary, we find that the

REER of these countries is stationary with drift in

eight up to 21 countries.4

1971 1974 1977 1980 1983 1986 1989 1992 1995 1998 2001 200480

100

120

140

160

180

200

220

240

(m) Niger

1971 1974 1977 1980 1983 1986 1989 1992 1995 1998 2001 20040

100

200

300

400

500

600

700

(n) Nigeria

1971 1974 1977 1980 1983 1986 1989 1992 1995 1998 2001 200475

100

125

150

175

200

225

250

(o) Rwanda

1971 1974 1977 1980 1983 1986 1989 1992 1995 1998 2001 200460

80

100

120

140

160

180

(p) Senegal

1971 1974 1977 1980 1983 1986 1989 1992 1995 1998 2001 200450

60

70

80

90

100

110

120

130

(q) Seychelles

1971 1974 1977 1980 1983 1986 1989 1992 1995 1998 2001 200450

100

150

200

250

300

350

(r) Sierra Leone

Fig. 1. Continued

4Note that our results are similar to those obtained by Bhamani-Oskooee and Gelan (2006), although we have used theModified AIC (MAIC) in order to select the lag length of the auxiliary Augmented Dickey–Fuller (ADF) regression.

Nonlinearities in real exchange rate determination 249

Dow

nloa

ded

by [

Ston

y B

rook

Uni

vers

ity]

at 1

4:16

20

Dec

embe

r 20

14

Page 9: Nonlinearities in real exchange rate determination: do African exchange rates follow a random walk?

For these eight countries we estimate nonlinear

models in order to gain some insight about their long-

run behaviour (see next section).

Estimated models

Foundations. Smooth Transition (ST) models are

members of the family of state-dependent

models; these are a local linearization of the general

nonlinear specification. The data generating process

is a linear one that switches between a certain

number of regimes according to some rule; the

regime is characterized as a continuous function of

a predetermined variable, so that interactions

between variables are permitted, as well as inter-

mediate states between the extreme regimes.This article focuses on STs over other usual

specifications because, among other reasons: their

flexibility enables the description of a wide range of

nonlinear behaviours; there exists a modelling cycle;

once the state is given, the model is locally linear and

easy to interpret; and standard nonlinear estimation

techniques can be used. See Granger and Terasvirta(1993), Terasvirta (1994, 1998) and van Dijk et al.(2002), for a deeper insight on STs.

The Smooth Transition Autoregression (STAR) isthe basic univariate version of the ST model;

1971 1974 1977 1980 1983 1986 1989 1992 1995 1998 2001 200460

80

100

120

140

160

(s) South Africa

1971 1974 1977 1980 1983 1986 1989 1992 1995 1998 2001 20040

100

200

300

400

500

600

(t) Tanzania

1971 1974 1977 1980 1983 1986 1989 1992 1995 1998 2001 200460

80

100

120

140

160

180

(u) Togo

Fig. 1. Continued

Table 2. Bierens (1997) unit root tests

Country m p t(m) A(m) F(m)

Burkina Faso 2 0 0.0166 0.0130 0.9736Cameroon – – I(1) I(1) I(1)Ivory Coast – – I(1) I(1) I(1)Kenya 4 0 0.0162 0.0138 0.9610Madagascar – – I(1) I(1) I(1)Mauritius 9 2 0.0376 0.0354 0.9234Morocco 5 1 0.0010 0.0004 0.9994Niger 2 0 0.0094 0.0204 0.9904Rwanda – – I(1) I(1) I(1)Senegal 20 0 0.9614 0.9558 I(1)Seychelles 17 0 0.0328 0.0608 0.9000South Africa – – I(1) I(1) I(1)Togo 2 0 0.0050 0.0026 0.9926

Note: The values in the table are p-values.

250 J. C. Cuestas and E. Mourelle

Dow

nloa

ded

by [

Ston

y B

rook

Uni

vers

ity]

at 1

4:16

20

Dec

embe

r 20

14

Page 10: Nonlinearities in real exchange rate determination: do African exchange rates follow a random walk?

all predetermined variables are lags of the dependent

variable and regimes are endogenously determined.

Suppose yt is a stationary, ergodic process, the STAR

model of order p is given by

yt ¼ �0 þXpi¼1

�iyt�i þ Fð yt�dÞ �0 þXpi¼1

�iyt�i

" #þ ut

ð6Þ

where F( yt�d) is a transition function customarily

bounded between 0 and 1 that makes the STAR

coefficients vary between �i and �iþ �i (i¼ 1, . . . , p),

respectively; d is the transition lag; and ut is an error

process, ut�N i.i.d. (0, �2). The transition variable,

yt�d, and the associated value of F( yt�d) determine

the regime at each t. In its basic version, the regime-

switching STAR model considers two extreme

regimes, corresponding to F¼ 0 and F¼ 1; the

transition from one regime to the other is smooth

over time, involving that parameters in (6) gradually

change with the state variable.The STAR model links two linear components

by means of F( yt�d), so that the formulation for this

function comes out a key issue when investigating

nonlinearities. Two specifications are the most

commonly used. First, the logistic function, which

has the form:

Fð yt�dÞ ¼1

1þ exp½��ð yt�d � cÞ�ð7Þ

and the resulting model is the Logistic STAR

(LSTAR). This function usually represents the odd

case in the literature, meaning that F(�1)¼ 0 and

F(1)¼ 1. The slope parameter �(�40) determines

the smoothness of the transition; the higher it is, the

more rapid the change from one extreme regime to

the other. The location parameter c indicates the

threshold between the two regimes; here, F(c)¼ 0.5,

so that regimes are associated with low and high

values of yt�d relative to c.Second, the exponential function

Fð yt�dÞ ¼ 1� exp ��ð yt�d � cÞ2� �

ð8Þ

is the habitual one in the case of an even transition

and provides the ESTAR model. This specification

implies F(c)¼ 0 and F(�1)¼ 1 for some finite c,

defining the inner and the outer regime, respectively.LSTAR and ESTAR models describe quite differ-

ent types of behaviour. In the logistic model the

extreme regimes are associated with yt�d values far

above or below c, where dynamics may be different;

the ESTAR model suggests rather similar dynamics

in the extreme regimes, related to low and high yt�d

absolute values, while it can be different in thetransition period.

As it was anticipated in section ‘Unit root testing’,the exponential specification comes out the mostsuitable one for describing the evolution of realexchange rates; the appeal of this function lies inallowing a symmetric adjustment of the variable fordeviations below and above the equilibrium value.The location parameter would reflect the equilibriumreal exchange rate and the dynamics of the variablewould change according to the proximity/distance tothe equilibrium state; in the last case, there would notbe differences between highly overvaluated or highlyundervalued exchange rates.

Going now into the modelling cycle for STARmodels, it has traditionally been based on reprodu-cing Box and Jenkins (1970) iterative methodology;search for specification, estimation and evaluationof the model. There is a well-established STARmodelling procedure in the literature (Granger andTerasvirta, 1993; Terasvirta, 1994). Nonetheless, themost recent investigations do not follow this strategyin a strict manner. Ocal and Osborn (2000), van Dijket al. (2002) and Sensier et al. (2002), among others,argue that it is possible to develop valid nonlinearformulations that improve the fit of the linear ones bymeans of an extensive search of STAR models; anypossible inadequacy of the models will be unveiledat the validation stage.

We define several combinations of p and d, tryingfor different values of � and using a value close to thesample mean of the transition variable for c; thelag order p ranges from 1 to 8 (eighth-order dynamicsseem to be general enough for quarterly data) and thetransition lag d varies from 1 to p. STAR models areestimated by nonlinear least squares; following therecommendations of Terasvirta (1994), the argumentof the exponential transition function is scaled bydividing it by the variance of the dependent variable.Where parameter convergence is reached, modelsare subject to further refinement. First, nonsignificantcoefficients are excluded to conserve degrees offreedom; then, we simplify this first set of estimationsthrough cross-parameter restrictions in order toincrease efficiency. We take 1.6 as the limit t-valuefor these coefficients since the variables arestationary.

The properties of the finally proposed models areevaluated using several misspecification tests. Weconsider the test of no Autoregressive ConditionalHeteroskedasticity (ARCH) with four lags and thetest of Business Cycle Heteroskedasticity (BCH)posed by Ocal and Osborn (2000). Particular atten-tion is also paid to significant estimated coefficients,the features of the transition functions and the results

Nonlinearities in real exchange rate determination 251

Dow

nloa

ded

by [

Ston

y B

rook

Uni

vers

ity]

at 1

4:16

20

Dec

embe

r 20

14

Page 11: Nonlinearities in real exchange rate determination: do African exchange rates follow a random walk?

of the following diagnostic statistics: the residual SE

(s), the adjusted determination coefficient ð �R2Þ and

the variance ratio of the residuals from the nonlinear

model and the best linear specification ðs2=s2LÞ.

Empirical results. As a starting point, we determine

the linear models that would describe the behaviour

of the exchange rates in the eight countries where

we find that the REER is stationary around a drift.

An ordinary least squares estimation is carried out,

where the proper number of lags is selected using

the AIC. These models are not reported for space

reasons, but they are available from authors upon

request.The next step involves estimation and specification

of the STAR models for all countries following

the aforementioned extensive search strategy. A large

number of STAR models are generated, although

parameter convergence is not attained in some of

them.5 The final selected models are reported in

Table 3, along with several descriptive statistics and

diagnostic tests. These specifications reflect how high

absolute values for the lagged exchange rate generate

nonlinear effects on the variable at present time.

Linearity tests against the estimated ESTAR models

prove evidence of nonlinearities for all countries;

Table 4 displays the p-values of the F-tests

(5% significance level).The dependence of the exchange rates on their own

recent history is moderate for some countries. The

transition from one regime to the other is rather fast

in the majority of the countries; in particular,

Burundi and Sierra Leone models behave like thresh-

old ones, as they display sharp switches. The values

of the location parameter are reasonably close to the

sample means of the exchange rates for four out

of the six countries; for the remaining two, Gabon

and Nigeria, almost all the observations lie to the

right of c, making the transition a logistic one in

practice (Fig. 2). The latter would mean the pretty

absence of a devaluation regime in both countries,

which is confirmed by Fig. 1(g)–(r). The reason for

this behaviour may be found in that Gabon and

Nigeria are leading oil exporters; this brings about a

surplus in their current account balances, causing

appreciation in the currencies.The evaluation stage does not unveil signs of

misspecification in the models, so the proposed

ESTARs are adequate. According to the variance

ratio, the estimated nonlinear models explain 7–24%

of the residual variance of the best linear autoregres-

sion in all six countries.The evaluation of the estimated nonlinear specifi-

cations is completed with the analysis of their localdynamic properties, which will allow us to character-

ize the variables better. The necessary information is

obtained from the roots of the characteristic poly-

nomials associated to the models; in this article, we

compute the roots for the two extreme values of thetransition function, F¼ 0 and F¼ 1. To save space,

Table 5 only displays the dominant root, i.e. the root

with the highest modulus that is determining the

long-run behaviour of the series within each regime.Table 5 reveals, on the one hand, that the estimated

ESTAR models are stable in the inner and in the

outer regime for three out of the six countries, i.e.

Ethiopia, Gabon and Nigeria, especially in Gabon,

which might have to do with being the only countrywith fixed (strict) exchange rates. On the other hand,

Burundi, Egypt and Sierra Leone have globally

stationary although locally unstable models. This

second group of countries shows explosive roots in

the inner regime, involving that exchange rates passthis regime rapidly on their way up or down; the

outer regime is a stable one, so that once the variable

undergoes an overvaluation or an undervaluation, it

will tend to remain there unless an exogenous shock

occurred.The asymmetry between the extreme regimes is

particularly severe in Egypt and Sierra Leone. Both

countries are characterized by the following pattern

of two opposite forces; on one hand, they have a well-

recognized and high-added value main export pro-duct (oil and derivatives in Egypt, diamonds in Sierra

Leone) but, on the other hand, they are great

importers (Egypt is a major food importers on

worldwide scale and Sierra Leone highly demandshydrocarbons and food). The dynamics of these two

opposite forces are expected to determine the evolu-

tion of the exchange rates in both countries, as they

are not fixed (rigid) ones.Lastly, in Burundi the transition between the

extreme regimes is nearly abrupt and, moreover, the

unstable inner regime contains few observations.

As a result, the currency almost always suffers from

a greater or lesser overvaluation/undervaluation in

this agricultural economy whose foreign tradedepends on imports and on a vulnerable exporting

balance caused by food products with volatile prices

in international markets.

5 For Tanzania and Ghana, it is not possible to obtain adequate specifications with endogenous transition that explain theirrespective behaviours; convergence problems in the estimation, as well as not very satisfactory results of the latter, are themain justifications.

252 J. C. Cuestas and E. Mourelle

Dow

nloa

ded

by [

Ston

y B

rook

Uni

vers

ity]

at 1

4:16

20

Dec

embe

r 20

14

Page 12: Nonlinearities in real exchange rate determination: do African exchange rates follow a random walk?

V. Allowing for Deterministic Trends

In this section, we relax the assumption that theREER is stationary around a drift under thealternative hypothesis and we allow for the possibi-lity of nonlinear deterministic trends. It is wellknown within the literature that misspecification ofthe deterministic components might bias the resultsof the unit root tests towards the acceptance of thenull hypothesis of unit root (Perron and Phillips,1987; West, 1988; Bierens, 1997). As it was

Table 3. Estimated ESTAR models for real exchange rates

BURUNDI

et ¼ 2369:69ð873:88Þ

þ 1:80ð0:26Þ

et�1 � 0:39ð0:13Þ

et�2 þ 0:19et�3ð0:08Þ

� 5:84et�6ð2:13Þ

þ 0:45ð0:29Þ

et�7

þ �2367:55ð873:85Þ

� 0:62ð0:25Þ

et�1 þ 5:84ð2:13Þ

et�6 � 0:45ð0:29Þ

et�7

� �1� exp � 160:11

ð68:97Þ�2:12ðet�6 � 489:26

ð2:89ÞÞ2

� � �þ at

s¼ 18.97; �R2 ¼ 0:99; s2=s2L ¼ 0:84; ARCH¼ 0.54 (0.71); BCH¼ 0.02 (0.88)

EGYPT

et ¼ �26:32ð31:08Þ

þ 1:24ð0:10Þ

et�1 þ 0:73et�4ð0:20Þ

� 0:87ð0:18Þ

et�5 þ 46:71ð30:49Þ

� 0:58ð0:15Þ

et�1 þ 0:27ð0:12Þ

et�2 � 0:79ð0:21Þ

et�4 þ 0:87ð0:18Þ

et�5

� �

� 1� exp � 1:56ð0:95Þ�0:0003ðet�3 � 254:04

ð9:95ÞÞ2

� � �þ at

s¼ 17.62; �R2 ¼ 0:91; s2=s2L ¼ 0:76; ARCH¼ 0.72 (0.58); BCH¼ 0.005 (0.94)

ETHIOPIA

et ¼ 34:63ð74:93Þ

þ 1:56ð0:25Þ

et�1 � 1:09ð0:46Þ

et�2 þ 0:92ð0:53Þ

et�3 � 0:53ð0:48Þ

et�4 þ � 11:93ð77:34Þ

� 0:89ð0:26Þ

et�1 þ 1:09ð0:46Þ

et�2 � 0:920:53

et�3 þ 0:64ð0:49Þ

et�4

� �

� 1� exp � 1:11ð0:57Þ�0:0003ðet�4 � 220:26

ð15:64ÞÞ2

� � �þ at

s¼ 16.73; �R2 ¼ 0:91; s2=s2L ¼ 0:79; ARCH¼ 0.89 (0.47); BCH¼ 0.97 (0.33)

GABON

et ¼ 114:78ð62:82Þ

� 0:40ð0:81Þ

et�1 þ � 79:66ð59:64Þ

þ 1:67ð0:71Þ

et�1 � 0:54ð0:17Þ

et�2

� �1� exp �0:42

ð0:37Þ�0:0022ðet�1 � 62:12

ð14:96ÞÞ2

� � �þ at

s¼ 7.64; �R2 ¼ 0:86; s2=s2L ¼ 0:93; ARCH¼ 0.06 (0.99); BCH¼ 1.62 (0.20)

NIGERIA

et ¼ 7:33ð22:28Þ

þ 0:93ð0:23Þ

et�1 þ 6:07ð21:34Þ

þ 0:96ð0:25Þ

et�1 � 0:95ð0:14Þ

et�2

� �1� exp �2:67

ð4:46Þ�0:00005ðet�1 � 85:29

ð39:65ÞÞ2

� � �þ at

s¼ 27.68; �R2 ¼ 0:96; s2=s2L ¼ 0:81; ARCH¼ 0.01 (0.99); BCH¼ 2.01 (0.16)

SIERRA LEONE

et ¼ � 172:52ð76:34Þ

þ 0:76ð0:06Þ

et�1 þ 1:06ð0:40Þ

et�2 � 0:90ð0:52Þ

et�3 þ 0:54ð0:40Þ

et�4 þ 0:83ð0:34Þ

et�7

þ 200:70ð76:80Þ

� 1:06ð0:40Þ

et�2 þ 0:90ð0:52Þ

et�3 � 0:71ð0:42Þ

et�4 þ 0:33ð0:12Þ

et�5 þ 0:30ð0:11Þ

et�6 � 1:26ð0:36Þ

et�7

� �

� 1� exp � 19:07ð7:28Þ�0:0004ðet�6 � 134:43

ð1:51ÞÞ2

� � �þ at

s¼ 25.43; �R2 ¼ 0:73; s2=s2L ¼ 0:76; ARCH¼ 2.20 (0.07); BCH¼ 1.38 (0.24)

Notes: et denotes the real exchange rate. Values under regression coefficients are SEs of the estimates. Numbers in parenthesesafter values of ARCH and BCH are p-values.

Table 4. Linearity tests against estimatedESTAR models

Country (lag order) p-value

Burundi ( p¼ 7) 0.00003

Egypt ( p¼ 5) 0.000002

Ethiopia ( p¼ 4) 0.00001

Gabon ( p¼ 2) 0.0363

Nigeria ( p¼ 2) 0.00001

Sierra Leone ( p¼ 7) 0.0001

Nonlinearities in real exchange rate determination 253

Dow

nloa

ded

by [

Ston

y B

rook

Uni

vers

ity]

at 1

4:16

20

Dec

embe

r 20

14

Page 13: Nonlinearities in real exchange rate determination: do African exchange rates follow a random walk?

mentioned earlier, nonlinearities can be present inthe form of structural changes and, therefore, thesenonlinearities affect the deterministic components.Many authors have applied unit root tests withstructural changes in order to test for PPP, findingin general more favourable results towards PPPempirical fulfillment. However, a broken time trendcan be understood as a particular case fora nonlinear trend. Thus, even unit root tests withstructural changes may suffer from power problems(Bierens, 1997).

Bierens (1997) proposes some tests which take intoaccount the possibility of stationarity arounda nonlinear deterministic trend under the alternativehypothesis. This author generalizes the ADF aux-iliary regression to incorporate Chebishev polyno-mials to approximate the nonlinear deterministictrend. Following Bierens (1997), the reason forusing Chebishev polynomials instead of regular timepolynomials (Park and Choi, 1988; Ouliaris et al.,

1989) to approximate the nonlinear deterministic

trend is that the former create less power distortions.

Thus, the auxiliary regression becomes

�qt ¼ �qt�1 þXpj¼1

�j�qt�j þ �TPðmÞt,n þ "t ð9Þ

where PðmÞt,n are the Chebishev polynomials and m is

the order of the polynomials, such that P0,t through

Pm,t, where P0,t equals 1, P1,t is equivalent to a linear

trend, and P2,t through Pm,t are cosine functions.

In order to test for the order of integration of the

variables, Bierens (1997) proposes several tests. In

this article we apply the t-test over the coefficient �,tðmÞ. Moreover, this can be tested by means of the

AðmÞ ¼ ½ðn�Þ=ðj1�Pp

i¼1 �ijÞ� test. The last one is an

F-test, FðmÞ, for the joint hypothesis that � and the

last m components of the parameter vector � in

model (9) are zero under the null. The conclusions

from these tests are different under the alternative

1.00

0.75

0.50

0.25Tran

sitio

n fu

nctio

n

0.00

1.00

0.75

0.50

0.25Tran

sitio

n fu

nctio

n

0.00

1.00

0.75

0.50

0.25Tran

sitio

n fu

nctio

n

0.00

1.00

0.75

0.50

0.25Tran

sitio

n fu

nctio

n

0.00

Tran

sitio

n fu

nctio

n

0.0

0.2

0.4

0.6

0.8

1.0Tr

ansi

tion

func

tion

0.0

0.2

0.4

0.6

0.8

1.0

0

80

0 100 200 300 400 500 600 700 50 100 150 200 250 300 350

120 160 200 240 280 320 380 60 80 100 120 140 160 180

250 500e (t–6)

e (t–4)

e (t–1)

e (t–3)

e (t–1)

e (t–6)

750 1000 50 100 150 200 250 300 350 400

Burundi Egypt

Ethiopia Gabon

Nigeria Sierra Leone

Fig. 2. Estimated transition functions

254 J. C. Cuestas and E. Mourelle

Dow

nloa

ded

by [

Ston

y B

rook

Uni

vers

ity]

at 1

4:16

20

Dec

embe

r 20

14

Page 14: Nonlinearities in real exchange rate determination: do African exchange rates follow a random walk?

hypothesis depending upon the side of the rejection.Whereas with the AðmÞ and t-test’s right-side rejectionimplies stationarity around a nonlinear trend, left-side rejection does not allow us to distinguish betweenmean stationarity, linear trend stationary and non-linear trend stationarity. With the F-test it is notpossible to distinguish between those alternatives(Table 6).

A number of authors have applied Bierens’ (1997)approach in order to test for the order of integrationof the RER (Sollis, 2005; Assaf, 2006; Camareroet al., 2008; Cuestas, 2009; Cuestas and Regis, 2008;Cushman, 2008) finding that in general it is possibleto reject the null hypothesis once nonlinear determin-istic trends are accounted for.

In Table 2, we present the results of the Bierens(1997) tests. Following this author, these tests sufferfrom important size distortions (Bierens, 1997), there-fore the critical values have been obtained by MonteCarlo experiment based on 5000 replications ofa Gaussian AR( p) process for �qt. The parametersand error variances are equal to the estimated AR( p)null model, where the order p of the ADF auxiliaryregression has been obtained by the AIC and the initialvalues have been taken from the actual series. Notethat we have only performed the Bierens’ tests forthose countries which we could not reject thenull hypothesis with the Ng–Perron and KSS tests.The results show that in eight of the remaining13 countries, we can reject the null hypothesis of unitroot. Additionally, it is worth highlighting that in allcases, except for Senegal, we obtain left-side rejectionwhichmeans that the series could be stationary arounda drift, linear or nonlinear trend. For Senegal theresults point to nonlinear trend stationarity process.

This is not surprising since the order to the Chebishevpolynomial necessary to reject the null hypothesis ispretty high.6 Figure 3 displays the nonlinear trendsadjustment for these eight countries. Since a higherorder of m implies a higher degree of nonlinearity, forsome countries such as Senegal of Seychelles, it isnecessary to use a high order for m in order toapproximate structural changes.

This implies that for these eight countries the stricthypothesis of PPP needs to be relaxed in order toaccount for structural changes, finding thus,a nonconstant or time varying equilibrium realexchange rate.

In parallel to this analysis of nonlinearities in realexchange rate adjustment, Lothian and Taylor (2000)and Lothian and Taylor (2008) evidence the so-calledHarrod–Balassa–Samuelson effect for certain realexchange rates, that is, the dependence of theequilibrium real exchange rate on productivitydifferentials; the first empirical work considersnonlinear time trends proxying for this effect. Thesefindings justify our interest in allowing for realshocks in the African countries and, as a futureresearch, we intend to consider the effect of realshocks to the equilibrium real exchange in this groupof countries.

VI. Conclusions

Aimed at contributing to the literature on PPP inAfrica, in this article we have applied several unit roottests that account for different forms of nonlinea-rities, i.e. asymmetric speed of adjustment andnonlinear deterministic trends. In the former, statio-narity is found in eight up to 13 countries andESTAR models can adequately capture the behaviourof the real exchange rates for some of these countries;in fact, modelling the nonlinearity in the data explains7–24% of the residual variance of the best linearautoregression. In most of the countries, the

Table 5. Local dynamics: dominant roots in each regime

CountryRegime(value of F ) Root Modulus

Burundi Inner (F¼ 0) 1.5796� 0.4820i 1.65Outer (F¼ 1) 0.9745 0.97

Egypt Inner (F¼ 0) 1.2636 1.26Outer (F¼ 1) 0.8919 0.89

Ethiopia Inner (F¼ 0) 0.8889� 0.2481i 0.92Outer (F¼ 1) 0.8570 0.86

Gabon Inner (F¼ 0) �0.3996 0.40Outer (F¼ 1) 0.6352� 0.3674i 0.73

Nigeria Inner (F¼ 0) 0.9352 0.93Outer (F¼ 1) 0.9470� 0.2354i 0.97

Sierra Leone Inner (F¼ 0) 1.3833 1.38Outer (F¼ 1) 0.4383� 0.8342i 0.94

Table 6. Alternative hypotheses

Test Left-side-rejection Right-side-rejection

tðmÞ MS, LTS or NLTS NLTS

AðmÞ MS, LTS or NLTS NLTSFðmÞ – MS, LTS or NLTS

Note: MS¼mean stationarity, LTS¼ linear trend statio-narity, NLTS¼ nonlinear trend stationarity.

6As Bierens (1997) claims, there is not a unique way to choose the order of m. Since we know that the ADF test tends to over-accept the null hypothesis, we have selected the order of m that yields more evidence against the alternative hypothesis.

Nonlinearities in real exchange rate determination 255

Dow

nloa

ded

by [

Ston

y B

rook

Uni

vers

ity]

at 1

4:16

20

Dec

embe

r 20

14

Page 15: Nonlinearities in real exchange rate determination: do African exchange rates follow a random walk?

transition from the equilibrium location to theovervaluation/undervaluation stage takes place quitefast, which strengthens the nonlinearity hypotheses;in addition, the threshold value between both regimesis generally in the neighbourhood of the variable’ssample mean. Furthermore, half of the countriesevidence explosive roots in the inner regime, invol-ving that real exchange rates pass rapidly this stage toreach the outer regime. The intrinsic features of eacheconomy may underlie this behaviour.

Further, the evidence in favour of the alternativehypothesis of stationarity increases when allowingfor nonlinear deterministic trends, approximated

by means of Chebishev polynomials. This impliesthat the real exchange rate tends to revert toa time-dependent equilibrium value. This feature isimportant since structural changes might drive usto wrong conclusions when testing for PPP, inparticular, for developing countries.

Acknowledgements

J. C. Cuestas gratefully acknowledges the financialsupport from the CICYT and FEDER projectSEJ2005-01163 and the Bancaja project P1.1B2005-03.

Solid line: BFADotted line: Nonlinear time trend in BFA [OLS model]

Solid line: MAUDotted line: Nonlinear time trend in MAU [OLS model]

Solid line: MORDotted line: Nonlinear time trend in MOR [OLS model]

Solid line: KENDotted line: Nonlinear time trend in KEN [OLS model]

BFA minus nonlinear trend

MAU minus nonlinear trend MOR minus nonlinear trend

KEN minus nonlinear trend

(The nonlinear trend includes the intercept) (The nonlinear trend includes the intercept)1971.1 2004.3

(The nonlinear trend includes the intercept)1971.1 2004.3

(The nonlinear trend includes the intercept)1971.1 2004.3

1971.1 2004.3

−20.833

−12.7422

12.7422

82.17

146.0654

0

20.833

55.82

118.

0

−33.4863

−10.9793

10.9793

82.02

121.2208

0

33.4863

82.26

189.16

0

Solid line: NIGDotted line: Nonlinear time trend in NIG [OLS model]

Solid line: SENDotted line: Nonlinear time trend in SEN [OLS model]

Solid line: SEYDotted line: Nonlinear time trend in SEY [OLS model]

Solid line: TOGDotted line: Nonlinear time trend in TOG [OLS model]

NIG minus nonlinear trend

SEY minus nonlinear trend

SEN minus nonlinear trend

1971.1 2004.3

−40.4377

−10.4106

10.4106

55.04

123.5

0

40.4377

81.09

231.98

0

(The nonlinear trend includes the intercept)

1971.1 2004.3

−28.3206

−29.1556

29.1556

73.53

167.53

0

28.3206

77.47

176.38

0

(The nonlinear trend includes the intercept)

1971.1 2004.3

(The nonlinear trend includes the intercept)

1971.1 2004.3

(The nonlinear trend includes the intercept)

Fig. 3. Nonlinear trends

256 J. C. Cuestas and E. Mourelle

Dow

nloa

ded

by [

Ston

y B

rook

Uni

vers

ity]

at 1

4:16

20

Dec

embe

r 20

14

Page 16: Nonlinearities in real exchange rate determination: do African exchange rates follow a random walk?

The authors gratefully acknowledge an anonymousreferee for his/her helpful comments. J. C. Cuestasis a member of the INTECO research group. Theusual disclaimer applies.

References

Anoruo, E., Liew, V. K.-S. and Elike, U. (2006) Nonlinearreal exchange rate behavior: are the African currenciesexceptional?, International Research Journal of Financeand Economics, 1, 98–111.

Ardeni, P. G. and Lubian, D. (1991) Is there a trendreversion in purchasing power parity?, EuropeanEconomic Review, 35, 1035–55.

Assaf, A. (2006) Nonlinear trend stationarity in realexchange rates: evidence from nonlinear ADF tests,Annals of Economics and Finance, 2, 283–94.

Bahmani-Oskooee, M. and Gelan, A. (2006) Testing thePPP in the nonlinear STAR framework: evidence fromAfrica, Economics Bulletin, 6, 1–15.

Bahmani-Oskooee, M. and Gelan, A. (2007) Real andnominal effective exchange rates for African countries,Applied Economics, 39, 961–79.

Baum, C., Caglayan, M. and Barkoulas, J. T. (2001)Nonlinear adjustment to purchasing power parity inthe post-Bretton Woods era, Journal of InternationalMoney and Finance, 20, 379–99.

Bhargava, A. (1986) On the theory of testing for unit rootsin observed time series, Review of Economics Studies,53, 369–84.

Bierens, H. J. (1997) Testing the unit root with drifthypothesis against nonlinear trend stationarity, withan application to the US price level and interest rate,Journal of Econometrics, 81, 29–64.

Box, G. E. P. and Jenkins, G. M. (1970) Time SeriesAnalysis, Forecasting and Control, Holden-Day,San Francisco.

Camarero, M., Cuestas, J. C. and Ordonez, J. (2006) PPPversus the EU in the Mediterranean countries, AppliedFinancial Economics, 16, 157–67.

Camarero, M., Cuestas, J. C. and Ordonez, J. (2008)Nonlinear trend stationarity of real exchangerates: the case of the Mediterranean countries,International Journal of Banking, Accounting andFinance, 1, 30–46.

Chowdhury, A. R. and Sdogati, F. (1993) Purchasingpower parity in the major EMS countries: the role ofprice and exchange rate adjustment, Journal ofMacroeconomics, 15, 25–45.

Christopoulos, D. and Leon-Ledesma, M. A. (2007) Post-Bretton Woods real exchange rates: mean revertingwith breaks and nonlinear adjustment, mimeo.

Cuestas, J. C. (2009) Purchasing power parity in Centraland Eastern European countries: an analysis of unitroots and nonlinearities, Applied Economics Letters,16, 87–94.

Cuestas, J. C. and Regis, P. J. (2008) Testing for PPP inAustralia: evidence from unit root tests against non-linear trend stationarity alternatives, EconomicsBulletin, 3, 1–8.

Cushman, D. (2008) Real exchange rates may havenonlinear trends, International Journal of Finance andEconomics, 13, 158–73.

Dumas, B. (1992) Dynamic equilibrium and the realexchange rate in a spatially separated world, Reviewof Financial Studies, 5, 153–80.

Dumas, B. (1994) Partial equilibrium versus general equili-brium models of the international capital market,in The Handbook of International Macroeconomics,Chap. 10 (Ed.) F. van der Ploeg, Blackwell, Oxford,pp. 301–47.

Elliot, G., Rothenberg, T. J. and Stock, J. H. (1996)Efficient tests for an autoregressive unit root,Econometrica, 64, 813–36.

Faria, J. R. and Leon-Ledesma, M. A. (2003) Testing theBalassa–Samuelson effect: implications for growth andthe PPP, Journal of Macroeconomics, 25, 241–53.

Faria, J. R. and Leon-Ledesma, M. A. (2005) Realexchange rate and employment performance in anopen economy, Research in Economics, 59, 67–80.

Granger, C. W. J. and Terasvirta, T. (1993) ModellingNonlinear Economic Relationships, Oxford UniversityPress, Oxford.

Huizinga, J. (1987) An empirical investigation of the long-run behavior of real exchange rates, Carnegie-Rochester, Conference Series on Public Policy, 27,149–214.

Kapetanios, G., Shin, Y. and Snell, A. (2003) Testing fora unit root in the nonlinear STAR framework, Journalof Econometrics, 112, 359–79.

Kargbo, J. M. (2006) Purchasing power parity and realexchange rate behaviour in Africa, Applied FinancialEconomics, 16, 169–83.

Kilian, L. and Taylor, M. P. (2003) Why is it so difficultto beat the random walk forecast of exchange rates?,Journal of International Economics, 60, 85–107.

Lothian, J. R. and Taylor, M. P. (2000) Purchasing powerparity over two centuries: strengthening the case forreal exchange rate stability, Journal of InternationalMoney and Finance, 19, 759–64.

Lothian, J. R. and Taylor, M. P. (2008) Real exchange ratesover the past two centuries: how important is theHarrod-Balassa-Samuelson effect?, CRIF SeminarSeries No. 26, Frank J. Petrilli Center for Researchin International Finance (CRIF).

Mark, N. (1990) Real and nominal exchange rates in thelong run: an empirical investigation, Journal ofInternational Economics, 28, 115–36.

Meese, R. A. and Rogoff, K. (1988) Was it real? The realexchange rate-interest differential relation over themodern floating-rate period, Journal of Finance, 43,933–48.

Michael, P., Nobay, A. and Peel, D. (1997) Transactioncosts and nonlinear adjustment in real exchangerates: an empirical investigation, Journal of PoliticalEconomy, 105, 862–79.

Ng, S. and Perron, P. (2001) Lag selection and theconstruction of unit root tests with good size andpower, Econometrica, 69, 1519–54.

Obstfeld, M. and Taylor, M. P. (1997) Nonlinear aspectsof goods-market arbitrage and adjustment: Hekscher’scommodity point revisited, Journal of the Japanese andInternational Economics, 11, 441–79.

Ocal, N. and Osborn, D. R. (2000) Business cycle non-linearities in UK consumption and production, Journalof Applied Econometrics, 15, 27–43.

Ouliaris, S., Park, J. Y. and Phillips, P. C. B. (1989) Testingfor a unit root in the presence of a maintained trend,

Nonlinearities in real exchange rate determination 257

Dow

nloa

ded

by [

Ston

y B

rook

Uni

vers

ity]

at 1

4:16

20

Dec

embe

r 20

14

Page 17: Nonlinearities in real exchange rate determination: do African exchange rates follow a random walk?

in Advances in Econometrics and Modelling, Chap. 1(Ed.) B. Raj, Kluwer, Amsterdam, pp. 6–28.

Papell, D. (2002) The great appreciation, the greatdepreciation, and the purchasing power parity hypoth-esis, Journal of International Economics, 57, 51–82.

Park, J. and Choi, B. (1988) A new approach to testingfor a unit root, CAE Working Paper No. 88–23,Cornell University.

Perron, P. and Phillips, P. C. B. (1987) Does GNP havea unit root? A reevaluation, Economics Letters, 23,139–45.

Phillips, P. C. B. (1987) Time series regression with a unitroot, Econometrica, 55, 311–40.

Phillips, P. C. B. and Perron, P. (1988) Testing for a unitroot in time series regression, Biometrica, 75, 335–46.

Reitz, S. and Taylor, M. P. (2008) The co-ordinationchannel of foreign exchange intervention: a nonlinearmicrostructural analysis, European Economic Review,52, 55–76.

Sarno, L. and Taylor, M. P. (2001) Official intervention inthe foreign exchange market: is it effective and if sohow does it work?, Journal of Economic Literature,Papers and Proceedings, 39, 839–68.

Sensier, M., Ocal, N. and Osborn, D. R. (2002) Asymmetricinterest rate effects for the UK real economy, OxfordBulletin of Economics and Statistics, 64, 315–39.

Sollis, R. (2005) Evidence on purchasing power parity fromunivariate models: the case of smooth transitiontrend-stationarity, Journal of Applied Econometrics,20, 79–98.

Taylor, M. P. (1995) Exchange rate behaviour underalternative exchange rate regimes, in UnderstandingInterdependence: The Macroeconomics of the Open

Economy (Ed.) P. B. Kenen, Princeton UniversityPress, Princeton, pp. 34–81.

Taylor, M. P. (2004) Is official exchange rate interventioneffective?, Economica, 71, 1–2.

Taylor, M. P. (2006) Real exchange rates and purchasingpower parity: mean-reversion in economic thought,Applied Financial Economics, 16, 1–7.

Taylor, M. P. and Peel, D. A. (2000) Nonlinearadjustment, long-run equilibrium and exchange ratefundamentals, Journal of International Money andFinance, 19, 33–53.

Taylor, M. P., Peel, D. A. and Sarno, L. (2001) Nonlinearmean-reversion in real exchange rates: towardsa solution to the purchasing power parity puzzles,International Economic Review, 42, 1015–42.

Terasvirta, T. (1994) Specification, estimation, and evalua-tion of smooth transition autoregressive models,Journal of the American Statistical Association, 89,208–18.

Terasvirta, T. (1998) Modeling economic relationshipswith smooth transition regressions, in Handbook ofApplied Economic Statistics (Eds) A. Ullah andD. E. A. Giles, Marcel Dekker, New York, pp. 507–52.

van Dijk, D., Terasvirta, T. and Franses, P. H. (2002)Smooth transition autoregressive models – a surveyof recent developments, Econometric Reviews, 21,1–47.

Wei, S.-J. and Parsley, D. C. (1995) Purchasing powerdisparity during the float rate period: exchange ratevolatility, trade barriers and other culprits, WorkingPaper No. 5032, NBER.

West, K. D. (1988) Asymptotic normality when regressorshave a unit root, Econometrica, 56, 1397–418.

258 J. C. Cuestas and E. Mourelle

Dow

nloa

ded

by [

Ston

y B

rook

Uni

vers

ity]

at 1

4:16

20

Dec

embe

r 20

14