QUASI

PURCHASING

STRUCTURAL

CHANGE

PESO/US DOLLAR

REAL

POWER I N T H E

PARITY: M E X I C A N

EXCHANGE

RATE

A n t o n i o E. Noriega* Lorena Universidad

Medina de

Guanajuato

Resumen: Analizamos si el tipo de cambio real peso/dolar se revierte a un valor de equilibrio de largo plazo, y si este valor es único. Utilizamos un m é t o d o para verificar estacionariedad que permite un número desconocido de cambios estructurales en el nivel de la serie. A l utilizar datos anuales (1925-1994), nuestros resultados proveen evidencia en favor de l a cuasi paridad del poder adquisitivo. E n particular, encontramos que el tipo de cambio real peso/dolar ha fluctuado estacionariamente alrededor de un nivel de largo plazo durante 70 años, perturbado por una serie de eventos, d o m é s t i c o s y externos, durante o alrededor de 1981.

Abstract: T h i s paper analyzes whether the real exchange-rate of the Mexican peso/US dollar revert to a long-run equilibrium value, and whether this value is unique.

We use a method for testing stationarity, that

allows for an unknown number of structural breaks in the level of the series. Using a long span of annual data covering the period 1925-1994, our results provide evidence favoring long-run Quasi-Purchasing Power Parity. In particular, we find that the real peso/dollar exchange rate has fluctuated stationarily around a 70 year long-run level, perturbed by a series of events, both domestic and external, in or around 1981

JEL

Classifications: Ci 2, Ci 3, Ci 5, C22, F31

Fecha de recepción:

29 V 2002

Fecha de aceptación:

21 X 2002

* Departamento de Econometria, Escuela de Economia, Universidad de G u a najuato, noriegam@quijote. ugto. mx.

227

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E S T U D I O S ECONÓMICOS

1. I n t r o d u c t i o n

T h e issue of w h e t h e r real exchange rates, R E R , revert to a l o n g - r u n e q u i l i b r i u m value has been a w i d e l y researched area i n i n t e r n a t i o n a l finance d u r i n g t h e last decade. M e a n reversion i n t h i s c o n t e x t i m p l i e s t h a t relative prices -valued i n a c o m m o n currency- t e n d t o converge over l o n g spans o f d a t a , thus s u p p o r t i n g the d o c t r i n e of P u r c h a s i n g Power P a r i t y , P P P ) . T h i s p a r i t y d o c t r i n e is c e n t r a l t o m a n y t h e o r e t ical models o f exchange r a t e d e t e r m i n a t i o n . I t is c o m m o n practice i n t h e l i t e r a t u r e t o a p p l y u n i t r o o t tests to investigate w h e t h e r t h e R E R reverts t o its ( e q u i l i b r i u m ) l o n g - r u n mean. F o l l o w i n g t h e i n f l u e n t i a l paper o f P e r r o n (1989), t h e r e are a n u m b e r of studies s h o w i n g t h e relevance o f a l l o w i n g mean shifts i n m o d e l l i n g the l o n g - r u n behavior o f R E R s . See, for instance, C o r b a e a n d O u l i a r i s (1991), P e r r o n a n d Vogelsang (1992), Culver a n d P a p e l l (1995), and B a u m , B a r k o u l a s , and Caglayan (1999). I n t h i s l i t e r ature, the n u m b e r o f s t r u c t u r a l breaks allowed i n t h e d e t e r m i n i s t i c t r e n d f u n c t i o n is fixed a priory, based m a i n l y o n v i s u a l i n s p e c t i o n o f the d a t a . For m a n y o f the real exchange rates series analyzed i n t h e above papers, i t is n o t unambiguous how m a n y significant s t r u c t u r a l breaks have occurred w i t h i n the sample. H e g w o o d a n d P a p e l l (1998) argue t h a t rejection o f a u n i t r o o t i n real exchange r a t e d a t a o n l y i m plies t h a t P P P holds i n t h e absence of s t r u c t u r a l breaks. T h i s means t h a t P P P requires reversion t o a constant mean. I n t h e i r e m p i r i c a l i n v e s t i g a t i o n ( w h i c h includes several long annual periods o f real exchange rates), t h e y use a t w o step procedure. A f t e r t h e y establish t h a t t h e R E R s are s t a t i o n a r y using A u g m e n t e d D i c k e y - F u l l e r , A D F , tests, t h e y a p p l y a sequential test for s t r u c t u r a l breaks, developed b y B a i a n d P e r r o n (1998a), t o find t h a t there are indeed m u l t i p l e s t r u c t u r a l breaks i n most o f t h e R E R s a n a l y z e d . These findings led t h e m to conclude t h a t t h e series revert t o an occasionally changing m e a n , a n d called t h i s p h e n o m e n o n Q u a s i - P P P . I n t h i s paper, we test t h e s t a t i o n a r i t y of the M e x i c a n p e s o / U S d o l l a r R E R a l l o w i n g for an u n k n o w n (endogenously d e t e r m i n e d ) n u m ber o f s t r u c t u r a l breaks i n t h e level o f the series. A l t h o u g h t h e app l i c a t i o n o f a ' s t a n d a r d ' A D F test w o u l d indicate r e j e c t i o n o f a u n i t 1

2

It is difficult to expect P P P to be valid in the short-run, due to trade barriers, transaction costs, foreign exchange market interventions, etc. These factors affect the basic assumption of perfect intercountry commodity arbitrage. 2

T h i s implies, however, that none of the identified breaks were sufficiently

strong so as to induce unit root behaviour in the series.

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229

r o o t , as i n the case of t h e series analyzed by H e g w o o d and P a p e l l (1998), there is s t r o n g evidence of a m a j o r change i n t h e l o n g - r u n behaviour o f the M e x i c o R E R , s t a r t i n g a r o u n d t h e b e g i n n i n g o f the 1980s. T h i s has n o t been t a k e n i n t o account i n previous studies concerning t h e p e s o / d o l l a r R E R . Mexico's i n t e r n a l a n d e x t e r n a l economic e n v i r o n m e n t was p a r t i c u l a r l y i n t e r e s t i n g d u r i n g those years. I n 1979, t h e government adopted a m o d e l based on o i l exports, f o l l o w i n g the o i l field discoveries o f 1978 a n d t h e 150% increase i n o i l prices t h e foll o w i n g year. However, this oil-based strategy ended w i t h a decrease i n o i l prices i n 1981, leaving the c o u n t r y w i t h an enormous e x t e r n a l debt, w h i c h h a d been c o n t r a c t e d t o develop the o i l i n d u s t r y . A s docu m e n t e d i n Aspe (1993), the chronology o f t h e financial crises begins w i t h the worsening o f M e x i c o ' s terms o f t r a d e a r o u n d the m i d d l e of 1981, m a i n l y as a result of t h e decline i n o i l prices. T h e n , i n 1982 increases i n i n t e r n a t i o n a l interest rates accelerated c a p i t a l outflows. T h e macroeconomic adjustment of 1982 i m p l i e d a 500% n o m i n a l dev a l u a t i o n o f the peso (from 25 t o 150 pesos per d o l l a r ) , w h i l e the i n f l a t i o n rate rose f r o m 29% t o nearly 100%. B y 1982 t h e R E R h a d depreciated 272% w i t h respect t o the previous year. W e u t i l i z e a l o n g span o f d a t a for t h e peso/US dollar R E R , cove r i n g t h e p e r i o d 1925-1994. T h e evidence on t h e s t a t i o n a r i t y of t h e R E R between M e x i c o a n d t h e US is m i x e d t h u s far. Avalos and H e r n á n d e z (1995), do n o t find evidence against a u n i t r o o t over the p e r i o d 1961-1994 using b o t h annual and q u a r t e r l y data. I n M e j i a and G o n z á l e z (1996), t h e u n i t r o o t hypothesis is m a r g i n a l l y rejected usi n g an A u g m e n t e d Dickey-Fuller test and annual d a t a over the longer p e r i o d 1940-1994; s i m i l a r conclusions are reached i n G a l i n d o (1995). I n these papers there is no allowance for s t r u c t u r a l breaks i n the data. O u r results i n d i c a t e t h a t the peso/US dollar R E R is b e t t e r modeled as a stochastically s t a t i o n a r y AR process a r o u n d a l o n g - r u n level p e r t u r b e d by a single s t r u c t u r a l break, i n 1981. A l o n g t h e lines of H e g w o o d and P a p e l l (1998), t h i s implies t h a t Quasi-PPP holds. 3

T h e n e x t section presents the econometric methodology, based on t h e procedures and methods i n B a i (1997b), B a i and P e r r o n (1998a, 1998b), a n d Noriega and R a m í r e z - Z a m o r a (1999). Section 3 presents The data source is Alzati (1997), who constructs a series of RERs for the period 1895-1994. He argues, however, that some data points along the period (1910-1920) could be extremely distorted by effects of the Mexican Revolution. In 1925 the central bank (Bank of Mexico) was established, and with it the generation of official statistics. We chose 1994 as the final year due to the potential break occurring in 1995 (following the peso devaluation in late 1994), leaving very little data points afterwards to identify it.

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E S T U D I O S ECONÓMICOS

and discusses results for the M e x i c o / U S R E R . F i n a l l y , section 4 s u m marizes final comments.

2. E c o n o m e t r i c M e t h o d o l o g y T h e procedure for t e s t i n g for the presence o f a u n i t r o o t w i t h a n u n k n o w n n u m b e r o f s t r u c t u r a l breaks i n the d e t e r m i n i s t i c t r e n d funct i o n , based o n the U n i t R o o t Rejection S t o p p i n g Rule, URR-SR, w o r k s as follows (for details see Noriega a n d R a m í r e z - Z a m o r a , 1999). D e n o t i n g b y Yt t h e l o g a r i t h m of the observed real exchange r a t e series, we first estimate (by OLS) t h e following M e a n S t a t i o n a r y MS a n d Difference Stationary, DS models, respectively:

m AY

t

k

= fi + ^OiDUit

+ aYt-i

+ ] T a Ar _¿ + e ¿

i=l

AY

£

u

(1)

i=l

t

k = ^a AYt-i i=l i

+ eu

(2)

for ¿ = 1,2, . . . T , where T is the sample size, et is an iid process, a n d DUu is a d u m m y variable a l l o w i n g changes i n the mean's level, t h a t is, DUu = 1(¿ > T b J , where l ( - ) is the i n d i c a t o r f u n c t i o n a n d is the u n k n o w n date of the i break. I n the MS m o d e l (1), Quasi-PPP holds whenever — 2 < a < 0, i n w h i c h case Y fluctuates s t a t i o n a r i l y a r o u n d a d e t e r m i n i s t i c level / i , (possibly) p e r t u r b e d by m level shifts. U n d e r the DS specification (2), a = 0 (the n u l l hypothesis), a n d t h e real exchange r a t e behaves like a r a n d o m w a l k , i m p l y i n g t h a t PPP does n o t h o l d . I n d e t e r m i n i n g the autoregressive order k for each m o d e l , we use the k — m a x c r i t e r i o n , as i n Noriega a n d R a m í r e z Z a m o r a (1999) a n d P e r r o n (1997). I n order t o d i s c r i m i n a t e between these t w o models, we simulate the d i s t r i b u t i o n o f the t-statistic for the n u l l hypothesis of a u n i t r o o t (a = 0 i n ( 1 ) ) , called f , under t h e hypotheses t h a t the t r u e models are the MS m o d e l (1) a n d the DS m o d e l (2), b o t h estimated from the d a t a . W e call these e m p i r i c a l densities / M s ( r ) , (m = 0 , 1 , 2 , . . . ) and Jds(t), respectively. t h

t

4

m

We use 10,000 replications for each model. A similar approach is used by Kuo and Mikkola (1999), who use bootstraped critical values, based on stationary and non-stationary ARIMA models fitted to the US/UK real exchange rate series. However, they do not consider the case of structural breaks in the trend function.

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231

For d e t e r m i n i n g t h e l o c a t i o n o f breaks, t h e c r i t e r i o n we use chooses, a m o n g a l l possible c o m b i n a t i o n s o f m break dates, t h e one w h i c h yields t h e smallest residual s u m o f squares (called m i n RSS) f r o m ( 1 ) . T h i s is done for a l l values o f k < /cmax. A s i n B a i a n d P e r r o n (1998b), we u t i l i z e a d y n a m i c p r o g r a m m i n g a l g o r i t h m t o o b t a i n g l o b a l m i n i m i z e r s o f the RSS. N o t e t h a t t h i s c r i t e r i o n implies simultaneous d e t e r m i n a t i o n o f m breaks v i a a g l o b a l search. 5

I n order t o d e t e r m i n e t h e n u m b e r o f breaks, we equip the above procedure w i t h t h e URR-SR, w h i c h indicates t h e t e r m i n a t i o n o f t h e search. U n d e r t h e URR-SR, we proceed sequentially: after we estimate e q u a t i o n (1) w i t h m = 0, t h e relevance o f b o t h t h e n u l l (a u n i t r o o t ) a n d a l t e r n a t i v e (a, MS m o d e l w i t h m = 0) hypotheses are analyzed i n t e r m s o f t h e p o s i t i o n where t h e sample estimate o f t h e ^-statistic for t e s t i n g a u n i t r o o t (fsample) lies relative t o t h e e m p i r i c a l densities o f f under t h e e s t i m a t e d MS m o d e l (1) a n d DS m o d e l ( 2 ) . I f as a result i t is concluded t h a t t h e n u l l hypothesis can n o t be rejected, or t h a t i t is n o t possible t o d i s c r i m i n a t e between hypotheses, t h e n we allow t h e procedure t o search a n d locate one s t r u c t u r a l break i n t h e level of t h e series, a n d t h e relevance of b o t h t h e n u l l o f a u n i t r o o t a n d t h e a l t e r n a t i v e o f a M S m o d e l w i t h a single s t r u c t u r a l break is analyzed. T h i s process continues u n t i l t h e n u l l hypothesis is rejected a n d t h e a l t e r n a t i v e hypothesis most s u p p o r t e d b y t h e d a t a is found. A f t e r t h e search finishes, we suggest a n a l y z i n g t h e results from a l l o w i n g one a d d i t i o n a l break. T h a t is, c o m p a r i n g t h e relevance o f b o t h t h e n u l l a n d a l t e r n a t i v e hypotheses under t w o different t r e n d specifications. As can be seen, t h i s is a sequential procedure w h i c h g l o b a l l y searches for an increasing n u m b e r of s t r u c t u r a l b r e a k s . 6

3. R e s u l t s a n d D i s c u s s i o n We first present results o b t a i n e d from t h e a p p l i c a t i o n o f the URR-SR. This results are t h e n c o m p a r e d t o those o b t a i n e d f r o m t h e a p p l i c a t i o n With thanks to Pierre Perron for providing us with his GAUSS code, which was adapted for this study. 6

Some authors have used versions of this rule in empirical applications (for :he case of models allowing for up to two breaks in the trend function): Clemente, Vlontanes and Reyes (1998), Ohara (1999), Mehl (2000), Aggarwal, Montanes and Ponz (2000). Arestis and Biefang-Frisancho Mariscal (1999) conclude that "...unit root tests that do not account sufficiently for the presence of structural breaks ire misspecified and suggest excessive persistence" (p. 155).

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E S T U D I O S ECONÓMICOS

of t h e Parameter Constancy S t o p p i n g R u l e ( P C - S R , based o n B a i , 1997b), T h e e m p i r i c a l results are presented i n table 1. T h e first c o l u m n indicates t h e n u m b e r of breaks allowed i n the t r e n d f u n c t i o n u n d e r the a l t e r n a t i v e hypothesis, m. C o l u m n 2 reports t h e value o f t h e e s t i m a t e d value o f k ( s t a r t i n g f r o m an upper value of A; m a x = 10). C o l u m n 3 reports t h e estimated break dates under t h e m i n RSS c r i t e r i o n . C o l u m n s 4-6 r e p o r t , respectively, the A k a i k e I n f o r m a t i o n C r i t e r i o n , A I C , t h e sample estimate o f t h e ^-statistic for t e s t i n g a u n i t r o o t (^sample), and t h e s t a n d a r d error o f regression. T h e last t w o c o l u m n s r e p o r t the rejection p r o b a b i l i t i e s of difference s t a t i o n a r y and m e a n s t a t i o n a r y models for t h e real exchange rate data, using exact c r i t i c a l values based on t h e M o n t e C a r l o d i s t r i b u t i o n s of the D i c k e y - F u l l e r t y p e t—statistic. These values i n d i c a t e the p o s i t i o n where t h e sample estimate of t h e ^-statistic for t e s t i n g a u n i t r o o t (jsampie) lies r e l a t i v e t o those d i s t r i b u t i o n s . T o draw exact inference on the u n i t r o o t hypothesis t h r o u g h r i , we calculate, under each density, the p r o b a b i l i t y massjbo t h e left of rumple, denoted P r [ f < T i | fos(r)}, and P r [ f < r ample | / M 5 ( T ) ] , respectively. s a r r i p

e

s a r n p

e

s

F r o m the r e p o r t e d p r o b a b i l i t i e s based on r mpie — —3.78 ( w i t h m = 0 ) , we can conclude t h a t i t is very u n l i k e l y t h a t t h i s e s t i m a t e d value of the ^-statistic for t e s t i n g a u n i t r o o t i n t h e R E R c o u l d have been generated by a DS m o d e l . O n the other h a n d , the p r o b a b i l i t y associated w i t h t h e MS m o d e l (69.5%) indicates t h a t t h i s specificat i o n is m u c h more plausible. sa

T h e d i s p r o p o r t i o n a t e changes observed i n t h e n o m i n a l exchange rate, and the relative price indices i n the early 80s, led us t o a p p l y t h e procedure for t e s t i n g t h e n u l l of a u n i t r o o t against t h e a l t e r n a t i v e of s t a t i o n a r y fluctuations a r o u n d a level p e r t u r b e d by one s t r u c t u r a l break. A s r e p o r t e d i n the second row of table 1, the m i n RSS c r i t e r i o n selects 1981 as t h e break date, w i t h k = 5. T h e c o r r e s p o n d i n g ts t a t i s t i c for t e s t i n g a u n i t r o o t ( f / ) is -6.43, a n d t h e p -values i n t h e last t w o columns show a clear rejection of the DS m o d e l i n favor of the MS m o d e l w i t h a single s t r u c t u r a l break i n t h e level of t h e series. I n fact, t h e p r o b a b i l i t y under t h e MS m o d e l w i t h one s t r u c t u r a l break lies nearly i n t h e m i d d l e of the e m p i r i c a l d i s t r i b u t i o n (0.48), suggesting t h a t t h i s specification is even more plausible t h a n t h e MS one w i t h o u t a s t r u c t u r a l break. A d d i t i o n a l l y , b o t h the A I C a n d t h e s t a n d a r d error of the regression indicate a b e t t e r f i t for t h e m o d e l a l l o w i n g for a single s t r u c t u r a l b r e a k . s a m p

e

7

It should be noted, however, that this break was not strong enough to induce

QUASI P U R C H A S I N G P O W E R P A R I T Y

233

Table 2 reports results o f t h e a p p l i c a t i o n of the parameter constancy s t o p p i n g r u l e . Over t h e entire sample (1925-1994) a significant break is identified i n 1981 for t h e peso/US dollar R E R . U p o n d i v i d i n g t h e sample i n t o t w o subsamples separated by t h i s break, no a d d i t i o n a l significant breaks are found by the procedure. T h e t a b l e also shows a n o t - v e r y - t i g h t 95% confidence i n t e r v a l for t h e break date. Note t h a t t h e break date is t h e same as the one o b t a i n e d under t h e u n i t r o o t r e j e c t i o n ' s t o p p i n g rule. Hence, f r o m t h e results o f a p p l y i n g t h e URR-SR, we can conclude :hat t h e peso/US dollar R E R is b e t t e r modeled as a stochastically stationary A R process a r o u n d a l o n g - r u n level p e r t u r b e d by a single j t r u c t u r a l break, i m p l y i n g t h a t Quasi-PPP holds. Since we are able t o •eject t h e u n i t r o o t hypothesis for o u r data, the r e s t r i c t i v e d y n a m i c i t r u c t u r e o f t h e a d j u s t m e n t process r e l a t i n g n o m i n a l exchange rates tnd r e l a t i v e price indices i m p l i e d i n u n i t r o o t tests, as discussed i n 5teigerwald (1996), is n o t b i n d i n g i n our case. T h e e s t i m a t e d break late under t h i s procedure, 1981, is confirmed using the p a r a m e t e r :onstancy s t o p p i n g rule. 8

L

Conclusions

^his paper has shown t h a t the M e x i c a n peso/US dollar real exchangeate does revert t o a l o n g - r u n e q u i l i b r i u m value. O u r results show, owever, t h a t t h i s value u n d e r w e n t an u p w a r d level shift d u r i n g 1981. Lccording t o some authors, t h i s date coincides w i t h t h e w o r s e n i n g of Mexico's t e r m s o f t r a d e , m a i n l y as a result of the decline i n o i l prices, 'he macroeconomic adjustment of 1982 i m p l i e d a 500% n o m i n a l dea l u a t i o n o f the peso, w h i c h t r a n s l a t e d i n t o a 272% d e p r e c i a t i o n of tie real exchange rate, w i t h respect t o the previous year. O u r results rovide evidence favoring l o n g - r u n Quasi-Purchasing Power P a r i t y , nd i m p l y t h a t i t is possible t o separate a s t a t i o n a r y cycle for t h e ?al exchange rate f r o m a l o n g - r u n d e t e r m i n i s t i c level. I n p a r t i c u l a r , le peso/US dollar R E R has fluctuated s t a t i o n a r i l y a r o u n d a 70 year lit root behaviour in the data. In table 2, the trimming parameter, 7T, is selected such that k + 3 < Tb < — 3, that is, 7T X T = 3, where T represents either the sample size, or the size a subsample (see Andrews, 1993). For example, for the full sample of the real :change rate in the table, 1925-1994, we have 70 observations, and 7T X 70 = 3 lplies 7T = 0.043. Tests were also carried out for the case 7T X T = 6. We )tained the same qualitative results. 8

1

s

s

s

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E S T U D I O S ECONÓMICOS

l o n g - r u n level, p e r t u r b e d by a series o f events, b o t h domestic e x t e r n a l , i n or a r o u n d 1981.

and

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