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The monetary approach to analysing floating exchange rate behaviour in developing countries: Evidence from sub-Saharan African countries, 1986–1992
JOURNAL OF ELSEVIER
Journal of DevelopmentEconomics Vol. 52 (1997) 463-481
Development ECONOMICS
The monetary approach to analysing floating exchange rate behaviour in developing countries: Evidence from sub-Saharan African countries, 1986-1992 M.O. Odedokun Economics and Management Department, Unicersi~ of Dundee, Dundee, UK
Abstract
The study tests the monetary approach to floating exchange rate analysis with monthly data for five sub-Saharan African countries over the 1986-1992 period. The results are in strong support of the approach. JEL classification: F31 Keywords: Floating exchange rate; Monetaryapproach
1. Introduction
The relevance or irrelevace of the monetary approach to floating exchange rate determination has far-reaching implications for the conduct of monetary and exchange rate policies. For instance, while the orthodox view (e.g. based on the prediction of the popular Mundel-Fleming model) is that an increase in domestic real income and interest rate should respectively depreciate and appreciate domestic currency, the monetary approach predicts the reverse. Thus, many empirical tests have been conducted for verifying this approach, based on data for industrial countries. An earlier comprehensive survey of such studies can be found in Frenkel and Mussa (1985), Levich (1985), Isard (1988) and MacDonald (1988), while the most current survey is provided by MacDonald 0304-3878/97/$17.00 © 1997 Elsevier Science B.V. All rights reserved. PII S0304-3878(96)00442-7
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and Taylor (1992). As shown by these surveys, the whole idea of the monetary approach is an unsettled issue at the empirical level. When it comes to developing economies, very few such studies can be spotted and the only ones that have come to our notice are those reported by Fry (1976) for Afghanistan; Edwards (1983) for Peru during the 1950s; and Lyons (1992), also for Peru during the 1950s. While the first two studies come out in support of the approach, the last one contradicts it, This limited number of studies for developing countries might partly be due to the small number of countries that have had floating exchange rate experience--in addition to the usual reason of non-availability of data. But due to recent developments in domestic economies and in the international financial scene, a large number of developing countries have started to experiment with this exchange rate system. It is in the light of this that the study reported here examines the recent experience of those sub-Saharan African countries that have had the experience for some time. Five countries' experiences during the 1986 to 1991/92 period are analysed. The countries are Gambia, Ghana, Nigeria, South Africa and Zaire. The remaining discussion is organised into four sections. Recent exchange rate experiences of the five countries studied are described in Section 2. The theoretical framework and methodology are described in Section 3, while the empirical results are presented and evaluated in Section 4. The summary and concluding remarks are in the last section. There are also appendices on co-integration tests and the data employed in the study.
2. Background issues We shall briefly describe the exchange rate practices in and experiences of the five countries included in the study, by way of providing appropriate background information. As mentioned earlier, the five countries are Gambia, Ghana, Nigeria, South Africa and Zaire. These, according to available information, constitute all African countries that have had floating exchange rate experiences for a c o n s e c u tive period of not less than two years up to the end of 1991--the only exception being Guinea, for which we do not have requisite data. 1 However, this is not to say that the system is not popular in sub-Saharan Africa. In fact it has recently started to be widely practised outside the CFA monetary zone. ~ For example, going by the classification of countries according to exchange rate systems as contained in the IMF's I n t e r n a t i o n a l F i n a n c i a l Statistics (IFS), Sierra Leone
1For the purpose of this discussion, we do not reckon what the IMF classifies as a managedfloating exchange rate systemto be an actual floating exchangerate system. 2The CFA monetary zone comprises 14 sub-Saharan countries having a commoncurrency that is pegged and freely convertibleto the French franc.
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changed from a fixed exchange rate system (pegged to SDR) in 1985 to an independent floating arrangement, then back to a fixed system (pegged to US$) in 1988, and "finally" back to independent floating in 1990. Somalia, too, temporarily adopted this independent floating arrangement in 1987; Uganda, in 1985; and Zambia, in 1985 and 1986. Concerning the five countries being studied, Gambia's currency (dalasi) was being pegged to the pound sterling prior to May 1986 when it adopted an independent floating system. Similarly, Ghana adopted an independently floating rate system in October 1986, in place of a fixed rate arrangement (pegged to US$) for determining its cedi. In Nigeria, a form of managed floating arrangement was being used to determine the value of the naira prior to September 1986 when the independent floating system started. While these three countries (former members of the defunct West African Currency Board) started floating arrangements within an interval of few months during 1986, the same is not applicable to the remaining two countries whose experiences date to earlier years. In fact, South Africa started with the system for determining the value of the rand as far back as 1979, while Zaire commenced it in November 1984 in place of a managed floating arrangement that was being used to determine the value of the zaire. All the five countries continue--up to 1992, at least--with the independent floating system. In these countries, the typical institutional arrangement for implementing the independent floating system is to remove the erstwhile controls on currency conversion. Also, in addition to banking concerns, private non-banking institutions are being given licenses and free hands to buy and sell foreign currencies. In a way, the exchange rates are left to the market forces of demand and supply to determine, subject to few controls by the state as in many other modern practices of floating exchange rate arrangement--even in industrial countries. These five countries experienced diverse inflation rates during the period. Zaire experienced the highest rates, these being 46.8%, 90.4%, 82.7%, 104.1%, 81.3% and 550.0% for the years 1986 to 1991 respectively (based on the consumer price index). This is followed by Ghana, with annual inflation rates of 24.6%, 39.8%, 31.4%, 25.2%, 37.3% and 17.2% for the years 1986 to 1991 respectively. The annual figures for the remaining three countries over the six years are as follows: 56.6%, 23.5%, 11.7%, 8.3%, 6.2% and 4.1% for Gambia; 5.3%, 10.3%, 38.3%, 51.0%, 7.1% and 13.0% for Nigeria; and 18.6%, 16.1%, 12.8%, 14.7%, 14.3% and 15.2% for South Africa.
3. Theoretical framework and methodology 3. I. The m o n e t a r y model
Earlier formulations of the monetary approach to floating exchange rate analysis are contained in the writings of Frenkel (1976), Mussa (1976) and Kouri
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(1976), among others. There are alternative variants of the monetary model, notable among which are the f l e x i b l e - p r i c e and s t i c k y - p r i c e versions, both of which are described in detail by MacDonald and Taylor (1992). A basic difference between the two is that the flexible-price version is based on the assumption of continous fulfilment of the purchasing power parity (PPP) condition, while the sticky-price variant (e.g. as developed by Dornbusch, 1976), in a way, constitutes a refinement of its flexible-price counterpart. This extension enables short-term deviation from the PPP condition to be accommodated. Below, we present a description of the flexible-price model and its extension to sticky-price formulation, as in Edwards (1983) and Lyons (1992). The approach starts from the the premise of a stable domestic and foreign money demand function of the form: mt --Pt = k + oty t - fir t + v t
(la)
mtdf _ p f = k f + a f y f t _ flfrft + v f
(lb)
and
where m d is domestic nominal money demand, in logarithms; p is domestic price level, in logarithms; y is a domestic scale variable (usually, income level) in logarithms; r is opportunity cost of holding money, usually interest rate; k is a constant term; a is income (or any other scale) elasticity of money demand; /3 is interest (or any other opportunity cost) quasi-elasticity of money demand; v is an error term; and the superscript " f " indicates that the notation applies to foreign, as opposed to domestic, economy. Also, c~, a f,/3,/3 f > 0. By assuming non-fulfilment of the PPP condition in the short run, the relationship between the domestic price, the foreign price and the nominal exchange rate can be described as follows: d = s t - Pt + P] = 6 d , _ j + ~,
(2)
where s is the logarithm of nominal exchange rate, defined as the domestic currency price of foreign currency; d is the logarithim of deviation from PPP or real exchange rate; is a random term; and 6 is a coefficient of d, an inverse indicator of the speed at which the deviation from PPP would be removed. Eq. (2), in effect, expresses the current real exchange rate as a function of its preceding value. The coefficient 6 should be zero if PPP always holds and one if there is no tendency for the condition to hold, even in the long run. By equating
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money supply m s (in logarithms) to money demand m d as the condition for money market equilibrium, we can solve for the price level p. By repeating the same for the foreign economy, we can solve for the foreign price level p f . Substituting for p and pf in Eq. (2) would yield the following relationship: St = t~ + m t
f
-- m t -- o l y t + otfy~ ' + f i r t - [ ~ f r f + t ~ d t _ l + i~t
(3)
where m = m s = m d and m f = Fn sf = mdf; qb is a constant term; /z is a random or error term; and other notations are as described earlier. Thus, the elasticities of nominal exchange rate depreciation with respect to domestic and foreign money stock are predicted to be 1 and - 1 respectively. Similarly, the elasticities with respect to domestic and foreign incomes are the same (but opposite in sign) as the domestic and foreign income elasticities of demand for money, in the same manner as the quasi-elasticities with respect to interest rates are absolutely equal (but opposite in sign) in the money demand and nominal exchange rate functions. The economic explanations for the predicted effects of m, y and r are as follows. An increase in domestic money stock prompts domestic economic agents to get rid of it by spending on goods and services, which, in turn, drives prices up and--through the PPP mechanism--depreciates the nominal exchange rate. On the other hand, an increase in domestic real income, by increasing money demand, reduces excess money supply in the domestic money market and, hence, the price level. This would then operate via the PPP channel to appreciate the nominal exchange rate. An increase in domestic interest rate leads to nominal exchange rate depreciation by increasing (or creating) domestic excess money supply. As pointed out earlier, these predicted effects of income and interest rates are contrary to the received notions, especially as predicted by the popular Mundel-Fleming framework. It is the presence of the lagged value of real exchange rate term d t.~ in the above equation that distinguishes it from the orthodox flexible-price formulation. This difference is due to the fact that short-run deviation from the PPP is permited to exist, as shown in Eq. (2). The long-run money demand functions in Eq. (la) and Eq. (lb) can be substituted for by short-run ones. This would be accomplished through the usual partial adjustment model thus: (m,--Pt)--(mt
1--Pt-1)=O[(md--pt)--(mt-I--Pt-l)]
(4a)
and (m~-Pft)-(mft-,-Pft-,)=of[(mt
df
pf) - (m~ I - Pf- l )l
(4b)
where 0 and 0 f are the domestic and foreign adjustment coefficients respectively --inversely related to the speed of adjustment of desired to actual money balances.
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By substituting Eq. (4a) into Eq. (la), and Eq. (4b) into Eq. (lb) before deriving the reduced-form exchange rate equation, we shall arrive at the following Eq. (5), instead of the earlier Eq. (3): S t = ~9 + m t - - r a f t -
{0o~/[1 -- (1 -- O L ) ] } y t
+{Ofotf/[1 --(1 -- OfL)]}yft + {013/[1 - ( 1 - OL)]}r t -{of~f/[1-(1-OfL)]}rft
+6d,-1 +~'t
(5)
where L is the lag operator, e is the error term, and ~b is the constant term. The reduced-form Eq. (5) differs from Eq. (3) only due to inclusion of lagged values of real incomes and interest rates as additional regressors. It is this Eq. (5) that was estimated by Edwards (1983) and Lyons (1992). As pointed out by Edwards, it is the inclusion of the lagged values of incomes and interest rates--together with the presence of the d t_ l term--in Eq. (5) that make it a short-run model and distinguishes it from the simple versions of the monetary approach. In practice, estimates of the parameters of Eq. (3) and Eq. (5) are generally found difficult or even impossible to derive with reasonable precision due to intractable intercorrelations between m and m f, y and yf, and r and r f. This has led to the common "device" of imposing the restrictions: 0 = Of, a = ~f and /3 = fl f. Imposition of these restrictions would convert Eq. (3) and Eq. (5) to Eq. (3a) and Eq. (5a) respectively:
st=qb+(mt-m~)-ot(yt-yf)+fl(rt-rf)+tdt_l+l, S t : qb + ( m t -- m ~ ) --
Zt
(3a)
{ 0 a / [ 1 - (1 - 0 t ) ] }{ Y t - Yf}
+ {013/[1 - (1 - OL)] }{rt - r f} + 6dr_ 1 + ~t
(5a)
where the notations are as defined earlier. In many studies of advanced economies, further modifications are made to the above by substituting expected rate of devaluation for the domestic-foreign interest rate differential r t - r f in the above equation. This is due to an assumption that an uncovered interest parity condition always holds. However, in the setting of economies without international financial centres, this assumption would have little or no economic logic in its support.
3.2. Present model and method of estimation The above equations constitute the econometric model estimated in the present study. Specifically, we report the estimates of Eq. (3), Eq. (3a) and Eq. (5a). In estimating Eq. (5a), the current and past four values of income and opportunity cost variables are included in the lag specification. This leads to the issue of the right variables to include as the opportunity cost of holding money in the domestic economy. In virtually all studies, the interest rate is treated as the opportunity cost
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for holding money in advanced countries and we too subscribe to this view. However, studies have shown--starting from initial evidence made available by Ojo (1974) and Wong (1977)--that the expected inflation rate is often a better candidate than the interest rate for the opportunity cost in the money demand function in the setting of developing countries. Thus, the expected inflation rate is chosen as the main opportunity cost proxy in the domestic money demand function in this study. 3 But we also support this with the interest rate in some estimates so that, in such estimates, r t in Eq. (3) becomes a vector of two elements --expected domestic inflation and interest rates--in the same manner that the r t - r [ term in Eq. (3a) and Eq. (5a) turns into a vector of expected domestic inflation rate and domestic-foreign interest rate differential. Given the alternative forms of equations estimated as just discussed, it would be unwieldy to report these estimates separately for each country. Thus, the leading equation estimates in the study are derived by pooling the time-series data across the five countries. Another reason for pooling the data is the fact that some explanatory variables (like the interpolated domestic income figures) may not show sufficient variations within a period of 5 to 6 years to allow the estimates to adequately capture the actual effects, whereas the relatively substantial cross-country variations in such regressors would more likely make these effects discernable. All the same, we still support the pooled-data estimates with time-series estimates for a variant of the aforementioned specifications--and, as will be seen in the next section, no material differences are found to exist between these time-series estimates and the pooled-data estimates. In deriving the pooled time-series/crosscountry estimates, we employ the fixed-effect technique of panel data estimates--which caters for inter-country differences in the autonomous nominal exchange rates by permitting the intercepts to differ across the countries. As pointed out in the MacDonald and Taylor (1992) survey, a criticism sometimes levied against monetary model estimation is the possibility of non-exogeneity of domestic and foreign money stocks, m t and mft, in the nominal exchange rate s t equations for industrial countries in the sense that monetary target setting may be dependent on nominal exchange rate. Thus, we experiment by employing one-period lagged values of domestic and foreign money stocks in the place of the contemporaneous values, but as this makes no material difference to the estimates we report only one or two such equations. Finally, all the panel data estimates are derived by the A R 1 G L S technique of correcting for serial correlation that uses country-specific serial correlation coefficients to transform the data. Also, for countries where serial correlation is detected in the time-series estimates, the A R 1 G L S method is adopted to correct this.
3 A n o t h e r reason for m a k i n g the expected inflation rate the main opportunity cost is due to the tact that n o m i n a l interest rate data are not adequately available for some of the countries and are not available at all for Zaire.
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3.3. (Expectational) P P P and co-integration issues
There is the issue raised by Lyons (1992) in connection with his analysis of Peruvian floating exchange rate behaviour to the effect that a particular version of PPP, which he called the "expectational" PPP model, performs better than the monetary model. There is also a related issue of whether the orthodox PPP condition would be applicable to the data used in the present study. We shall now address these issues. It should be recalled that the monetary model is based on the assumption that PPP holds, at least in the long run. Lyons (1992, p. 105) advanced some reasons why PPP should hold in developing countries and supported this with estimates of an expectational PPP model with Peruvian data. 4 This model consists of expressing the nominal exchange rate as a function of expected domestic and foreign price levels, in addition to the lagged value of real exchange rate, thus: St =
k o + Ap~
+
Afpt f + g2d t_ 1 -~
Ut
(6)
where pe is the expected domestic price level in logarithms; s is logarithm of nominal exchange rate as defined earlier; d is real exchange rate as defined earlier; u is a random error term; k 0 is a constant term; A and /2 are parameters; and the " f " subscript denotes the foreign variable/parameter as before. For the expectational PPP proposition to hold, the coefficients of the domestic and foreign prices--A and Af--have to be 1 and - 1 respectively. The inclusion of the lagged value of real exchange rate, d t _ 1, is for the same reason of probable short-run deviation from the PPP condition. In this study, we also experiment with the above model, using the pooled or panel data. We proxy the expected domestic and foreign prices by their respective one-period lagged values. (More sophisticated techniques of generating expected price levels, e.g. by using a larger information set, do not produce materially different results.) Because the specifications produce robust results, we report them in the next section. The associated issue is whether the exchange rate and prices are, in fact, co-integrated. If they are not, there are two possible consequences. First, the PPP condition would not likely be satisfied, even in the long run, whereas the monetary model hinges on the fulfilment of this condition. Second, since exchange rate and prices are not likely to be stationary or integrated of degree zero, the chances of the estimates reflecting just a spurious relationship among the variables would be
4 However, the author did not provide any formal theoretical basis for this model.
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high (Granger and Newbold, 1974). 5 Therefore, we conducted an augumented Dickey-Fuller co-integration test, using quarterly data for the 1980-1991 period for each country, and we found that the data suggest the existence of co-integrat i o n - e x c e p t for Zairean data. The result and a brief description of the augumented Dickey-Fuller test are provided in Appendix A. 3.4. The data
Monthly data are employed in estimating the equations. The methods of measuring the variables and the specific sources of the data are spelt out in Appendix B. We wish to point out here that all the data are from IMF sources and that the nominal exchange rate, the real exchange rate and the foreign price level are multilateral and effective ones. This means that the nominal exchange rate is the trade-weighted average of bilateral nominal exchange rates in the same way that the foreign price is the trade-weighted average of price levels in trading-partner countries. The real exchange rate is calculated from the nominal effective rate, the domestic price level, and trade-weighted foreign prices. (Interestingly, each of the five countries conducted over 90% of its foreign trade with the industrial countries of Western Europe, USA, Canada and Japan whose currencies are convertible and whose economies are open. This supports the choice of trade weights in computing exchange rates and foreign price levels, instead of merely choosing a particular country--like, say, the U S A - - a s the benchmark country.) The period covered for each country in the study is as indicated in Table 2, in the next section.
4. Empirical results The estimates of the monetary and expectational PPP equations with the panel or pooled data for all the five countries are as reported in Table 1, while the time-series estimates for individual countries are those presented in Table 2. Further explanatory notes are provided at the foot of each table. The estimates of Tables 1 and 2 display high adjusted R 2 values, evidence of the high explanatory power of the models. Also, the Durbin-Watson statistic values are close enough to 2.0, particularly in Table 1, that an absence of serial correlation of residuals is suggested. As predicted by the monetary approach, the coefficients of domestic money stock are positive and statistically significant in those equations where it features in Table 1, with values not far from 1, which is the ideal value predicted by the theory. But the coefficients of foreign money stock have perverse positive values
5 But if the variablesare co-integrated,there need not be a spurious relationship even if they are not stationary in the level form. However, the estimated standard errors are wrong (though the estimates are consistent).
1
1 -- mft_ l
m~
2lint[
intft
X(it -
f,f)
Y~*f
f, - f/
int t
y[
Yt --
X,(y,- y[)
Y t - Yf
Yt
mft-
mft
mt_
m t --
mt- l
mt
- 1.13 (-2.3)
-5.51 (-9.8) 2.887 (13.9)
- 0.24 (-1.1)
0.530 (2.5)
0.917 (57.5)
Table 1 Pooled-data estimates
- 1.33 (-2.9)
-2.50 (-5.1)
- 1.39 (-7.3)
0.316 (1.6)
0.835 (60.1)
- 1.57 (-3.4)
-2.87 (-5.6)
0.481 (2.3) - 1.40 (-7.1)
0.843 (57.9)
1.393 (6.9)
1.99 ( - 10.0)
0.736 (59.6)
1.164 (6.6)
1.82 ( - 10.4)
0.673 (65.7)
-5.44 ( - 10.9)
(-2.35) ( - 14.2)
0.754 (71.1)
-3.13 (-6.9)
-2.30 ( - 13.0)
0.736 (70.1)
2.07
2 . 4 6
( - 5.6)
-
( - 12.9)
-
0.690 (74.0)
-3.32 ( - 7.4)
-2.18 ( - 12.5)
0.764 (85.9)
I 4~
4:.
6,a
.~ -.a
1
0,983 1.88 293
0.286 (4.4)
1.41 (9.3)
0.987 1.99 311
0.359 (5.8)
1.60 (11.2)
0.987 2.02 308
0.425 (6.7)
2.24 (15.9)
0.978 1.89 297
0.300 (4.2)
2.22 (13.6)
0987 1.76 287
4.59 (23.6)
0.984 •.99 315
0.387 (5.8)
2.55 (17.2)
0.985 1.92 315
0.339 (5.2)
2.01 (13.5)
0.990 1.76 309
4.15 (21.6)
0.985 1.80 317
2.03 (13.7)
0.994 1.63 308
-0.954 (-40.7)
1.108 (168.8)
0.994 1.85 308
-1.076 (-43.9)
1.071 (154.9)
0.877 (21.2)
0.995 2.01 311
- 0.945 ( - 44.8)
0.774 (20.9) 0,997 (174.0)
- 1.019 (-40.2) 0,995 2.10 304
1.045 (123.1)
0.821 (21.6)
Notes: (i) The dependent variable is the log of index of effective nominal exchange rate, domestic currency price of foreign currency so that its upward movement represents domestic currency depreciation. (ii) The figures in parentheses below the parameter estimates are t-values. At 5% and 1% levels of significance (two-tailed test), a parameter estimate is statistically different from zero if the t-value is absolutely up to 2.0 and 2.6 respectively. (iii) D W and N are the Durbin-Watson statistic and the total number of observations respectively. The variables are as lollows: m is nominal money stock (in logarithms); 3' is index of real income proxied by GDP (in logarithms); y* f is index of real income proxied by industrial production (in logarithms); d is index of real effective exchange rate (also in logarithms), with upward movement representing depreciation of domestic currency in real terms: p is index of domestic price (in logarithms): inf e is expected inflation rate; and int is nominal interest rate. ~ indicates that the affected coefficient is derived as the sum of the coefficients of the current and past three values (past two values in the case of p and pf) of the variable in the lag specification. Finally, the " £ ' superscript denotes a foreign variable. (iv) Estimates including domestic interest rate int are for only tour countries, with Zaire being excluded.
Adjusted R 2 DW N
-Ypf
P~ I
p[
X,pt
Pt- 1
Pr
dt
X inf7
inJ)~
.~
~"
"~
~
.~ .~
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Table 2 Time-series estimates
Constant m t - m~ Yt -- Yf ft - ft f
Gambia
Ghana
Nigeria
S. Africa
Zaire
4.097 (9.7) 0.008 (0.2) - 1.54 (-5.9) 0.487 (2.1)
0.852 (1.0) 0.224 (3.0) 1.31 (1.5) 0.391 (1.5)
8.021 (16.3) 0.803 (7.2) - 4.23 (-3.0) 1.777 (2.2)
3.176 (6.3) 0.361 (5.3) - 2.90 (-6.6) 0.464 (1.7)
8.986 (15.0) 0.769 (8.3) - 5.27 ( - 1.1)
int ft
0.233 (0.4) dt- 1 0.137 (1.6) Adjusted R 2 0.926 DW 1.82 p 0.661 (6.3) Q 16.0 Period 1986:7-1992:1 N 66 inf e
- 1.899 ( - 5.5) 1.092 (8.6) 0.960 1.33
0.129 (0.2)
0.965 1.45 0.745 (8.6) 53.2 24.1 1986:10-1991:9 1986:10-1991:3 60 53
- 2.434 (-0.5) 0.685 (7.4) 0.932 1.72
- 6.920 ( - 1.9) 0.200 (0.9)
0.995 1.76 0.958 (16.0) 22.4 23.3 1986:1-1991:6 1986:1-1992:1 66 73
Notes:
(i) The dependent variable is the effective nominal exchange rate (in logarithms), whose upward movement represents depreciation of domestic currency in nominal terms. (ii) The figures in parentheses below the parameter estimates are t-values. At 5% and 1% levels of significance (two-tailed test), a parameter estimate is statistically different from zero if its t-value is absolutely up to 2.0 and 2.6 respectively. (iii) D W , Q and N are the Durbin-Watson statistic, the Ljung-Box Q-statistic, and the number of monthly observations respectively. Estimates with p-values are the ones derived after correcting for serial correlation of residuals through the A R 1 GLS technique. (iv) The variables are as follows: m is log of money stock, y is log of real output index, int is interest rate, inf e is expected inflation rate, and d is effective real exchange rate (in logarithms) whose upward movement represents depreciation of domestic currency in real terms. An " f " superscript indicates a foreign varaible.
- - w h i c h a r e h a r d l y s t a t i s t i c a l l y s i g n i f i c a n t , h o w e v e r - - i n t h e t h r e e e q u a t i o n s , this b e i n g a r e f l e c t i o n o f t h e l i k e l y p r o b l e m o f m u l t i c o l l i n e a r i t y b e i n g e n c o u n t e r e d in m o s t p r e v i o u s s t u d i e s as p o i n t e d o u t in S e c t i o n 2. 6 I n T a b l e 1, t h e c o e f f i c i e n t s o f
6 Another reason that could account for these perverse coefficient values is that what is employed as the proxy for foreign money stock might be inappropriate. As pointed out in Appendix B, the proxy is the index of money stock for all industrial countries combined instead of the trade-weighted index of money stock of the trading partners which non-availability of requisite data does not permit us to employ.
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domestic-foreign money stock differential have the expected and statistically significant positive values that average about 0.75, a number that is not far from the predicted value of unity--especially when compared with the findings reported in previous studies even for advanced economies. 7 The coefficients of this money stock differential are also positive in all the time-series estimates of Table 2, although the values are not as high. In the equations in Table 1 where domestic and foreign incomes are separately included, the coefficients of domestic income have expected negative values that are statistically very significant in two of the three. But foreign income coefficients have perverse negative values, the explanation again being the practical difficulty of separately deriving the estimates due to multicollinearity problems. In the remaining equations, we have a domestic-foreign income differential instead and the coefficients of this variable are negative and statistically very significant - - w i t h the average value being just a little above - 2 . 0 in absolute terms. This compares with - 2 . 9 reported by Edwards (1983) for Peru and the average (long-run) income elasticities of money demand of about 2.0 for developing countries, e.g. Edwards (1981) and Fry (1978). 8 The corresponding coefficients in time-series estimates are also similar, except that the coefficient in the equation for Ghana has a positive s i g n - - w h i c h is statistically insignificant anyway. The coefficient of domestic interest rate is positive and very significant in the Table 1 results, again as predicted by the monetary approach. Also, the coefficients of foreign interest rate are very significantly negative, in line with the prediction, in all the estimates reported in Table 1. As a result, the coefficients of the domestic-foreign interest rate differential are found with positive and and very significant values. These performances of domestic and foreign interest rates are also duplicated, without any exception, in the time-series estimates reported in Table 2, Thus, although evidence in the early 1970s (e.g. see Ojo, 1974) suggests the non-importance of interest rates in money demand functions in sub-Saharan Africa due to the evolving nature of financial systems and pegging of interest rates well below market equilibrium, this may no longer apply. This is because the financial development that has taken place during the past two decades or so,
7 Although these coefficients of the money stock differential (which average about 0.75) and the three coefficientsof the domestic money stock (which are 0.92, 0.84 and 0.84) marginally miss passing the formal statistical test of being equal to unity at the conventional significance levels, they are still among the closest figures to unity when compared with other similar studies for developing countries and even many of the empirical studies that came out in support of the monetary approach in industrial countries. The robustness of these findings becomes more apparent when the low quality of data for typical sub-Saharan African countries is taken into account. 8 It should be recollected that the coefficient of income in the exchange rate equation is predicted to be equal but opposite in sign to that of income elasticity of money demand, i.e. the coefficient of income in the (logarithmic) money demand equation.
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coupled with deregulation of interest rates that typically accompanies adoption of a deregulated or floating exchange rate system with effect from around the mid-1980s, might now have reversed this situation and hence account for the present finding. The expected inflation rates have the expected positive and statistically significant coefficients in the Table 1 results, thus butressing the view that expected inflation rate is (another) opportunity cost for holding money. However, the coefficients are found with negative values in the Table 2 time-series results for Ghana and South Africa and also with statistically insignificant positive values in the equations for the remaining three countries. This may be due to intercorrelation with interest rates. Given the consistently and significantly positive values in Table 1, however, there is sufficient evidence in support of the prediction that expected inflation depreciates the nominal exchange rate. The lagged value of the real exchange rate also has positive and statistically significant coefficients in the Table 1 results, with the average value being about 0.35--which is less than 1.0 as expected so that the short-run deviation from the PPP condition will tend to be removed over time. 9 The Table 2 results are practically the same, except that the coefficient is around 1.0 (precisely, 1.092) for Ghana. The independence of the coefficients of other regressors on the inclusion of the lagged real exchange rate as an additional regressor can be seen in those Table 1 equation estimates where it is excluded. This suggests that the flexible monetary approach equation that does not require inclusion of this as a regressor fits the data equally well. Concerning the lagged specification, it can be observed from Table 1 that the sum of the coefficients of the current and past three values of the regressors (and their t-values too) do not differ from the results obtained by including only the contemporaneous values as regressors. The only exception is the expected inflation rate. l0 Thus, with the exception of the expected inflation rate, there appear to be quick responses of the nominal exchange rate to the regressors tested for. Finally, we come to the issue of the expectational PPP model and its relevance. As shown by the last four equation estimates of Table 1, the results of estimating this version of PPP equations are robust. The values of the coefficients of domestic and foreign prices are practically 1.0 and - 1 . 0 respectively, in line with the prediction. However, this is not found to be dependent on the lagged value of real
9 This average of 0.35 means that only about 35% of the deviations from PPP should remain after one month and 12% after two months. This is a faster rate of adjustment than that reported by most other authors. However, going by the results of the expectational model as presented in the last four equations of Table l, a much slower rate of adjustment is implied as the coefficients of the lagged real exchange rate now average about 0.8, suggesting that not more than 20% from PPP would be removed within one month, not more than 36% within two months, and not more than 50% within three months. 10 In fact, our experiment with greater lag specifications shows that the sum of coefficients of this variable (and the t-values) continues to increase for up to seven past values.
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exchange rate being included as an additional regressor or the inclusion of expected (proxied by one-period lagged value) in place of actual price levels as the PPP regressors. In other words, the results are in fact a validation of the orthodox, as opposed to expectational, PPP condition.
5. Summary and conclusion The study is an attempt to confront the monetary approach to floating exchange rate analysis with data from five sub-Saharan African countries, viz. Gambia, Ghana, Nigeria, South Africa and Zaire. Monthly data over the 1986-1992 period are employed. In addition to estimating regression equations for both the flexibleprice and sticky-price variants of the monetary model, we also present the estimates of the expectational version of the PPP equation. The highlights of our findings from the tests are as follows: (a) The domestic-foreign money stock ratio depreciates the nominal exchange rate, with the elasticities in the exchange rate equation being about unity as predicted by the monetary approach. (b) The domestic-foreign real income ratio appreciates the nominal exchange rate, with the elasticities being about 2.0 in the equations. Thus, as predicted by the monetary approach, an increase in domestic income has the effect of appreciating the value of domestic currency. (c) An increase in the domestic interest rate is found to depreciate the nominal exchange rate, with the reverse being the case for a foreign interest rate. Again, this is perfectly in agreement with the prediction of the monetary approach. (d) The expected inflation rate in the domestic economy has the same effect of depreciating the nominal exchange rate as interest rate, both being opportunity costs of holding money in developing countries. This also supports the monetary approach. (e) There is some evidence that there might be some short-run deviation from the PPP condition but there is strong evidence that the condition holds, at least in the long run. Particularly, the elasticities of domestic and foreign prices in the nominal exchange rate equations are found to be 1.0 and - 1 . 0 respectively, implying that a given percentage increase in domestic (foreign) prices is associated with the same percentage depreciation (appreciation) of domestic currency. On the whole, the available evidence from the study strongly supports the monetary approach and also the validity of the PPP condition.
Acknowledgements The financial support and facilities provided by the Department of Economics and Management, University of Dundee, Dundee, Scotland for carrying out this
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study is acknowledged. So also are the comments on the paper and other forms of academic assistance provided by Ian Marsh of the same Department. The comments made by the two anonymous referees also served to enhance the quality of the article. All errors and omissions, however, exclusively belong to the author.
Appendix A. Results of the augumented Dickey-Fuller tests The augumented Dickey-Fuller test for co-integration of variables (which is discussed here in connection with the PPP test) is conventionally conducted as described b e l o w - - f o r details, see Engle and Granger (1987). First, estimate the following equations:
(a.1)
A x t = ol 0 -~- / 3 x t _ 1 q- ~ o l i x t _ i ~- Et
and A 2 x t = "17"o~ 6 A x t - 1
~- ~ ' w i A 2 x t - i
~- ~t
(A.2)
where a i, fl, 6, and zri are parameters; and e are random error terms; x is a variable in level (logarithm) form; and d and A 2 indicate the first- and second-difference of x respectively. The above equations are to be estimated by replacing x with each of the following variables: nominal exchange rate (s); domestic price (p); foreign price (pf); and the residuals obtained by regressing s on p and pf or by regressing p on s and pf or both separately. The residuals correspond to estimates of real exchange rate values. For the PPP condition to be fulfilled, each of s, p and pf should be integrated of order one and this would be so if the values of the fl estimates in Eq. (A.1) were statistically insignificant in a situation when the values of the 6 estimates in Eq. (A.2) are significant. Special t-value statistical tables, as provided by Engle and Yoo (1987), exist for this significance test. The condition stated in the preceding paragraph can be regarded as the necessary one. The sufficient condition still requires the residuals or real exchange rate estimates to be integrated of order zero and this would be fulfilled if the estimates of the fl value in Eq. (A. 1) were statistically significantly different from zero. Following the procedure just described, we conducted the test with quarterly data over 1980(I)-1991(II) for each of the countries and the results are as presented below in respect of the estimates of the /3 and ~ values.
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values Nominal exchange rate Domestic price Foreign price Residuals ~ 6 values Nominal exchange rate Domestic price Foreign price Residuals "
Gambia
Ghana
Nigeria
S. Africa
Zaire
- 1.25 - 0.57 0.86 - 3.56
- 1.14 - 2.65 0.29 - 3.70
- 0.22 - 0.25 0.92 - 3.30
- 2.77 1.89 - 1.74 - 3.09
- 2.05 2.20 2.92 - 1.78
- 4.26 - 3.25 -3.28 - 6.53
-
- 3.75 - 3.31 -2.97 - 3.78
- 5.43 - 7.44 -5.08 - 7.25
- 1.98 - 0.70 -5.16 - 3.55
4.53 4.17 10.33 4.20
Notes: a The residuals are the ones obtained by regressing domestic price level on nominal exchange rate and foreign price level. (i) Either one or two lagged values of the dependent variable is included in estimating Eq. (A. 1) and Eq. (A.2). (ii) At 5% and 1% significance levels, the critical values for the significance (Dickey-Fuller) t - t e s t - - a s extracted from Engle and Yoo ( 1 9 8 7 ) - - a r e - 2 . 9 7 and - 3.58 respectively. As can be seen from the above results, it is only in Zaire that the PPP condition is not satisfied. For other countries, each of the nominal exchange rate, the domestic price level, and the foreign price level are integrated of order 1 and all three are co-integrated since the residuals are integrated of order zero.
Appendix B. Data sources and variable measurements Data on effective nominal exchange rate, domestic price index, foreign price index, and effective real exchange rate for Gambia, Ghana, Nigeria and Zaire are from an unpublished IMF source. 1l The nominal exchange rate is the tradeweighted average of bilateral exchange rates vis-h-vis trading-partners' currencies. Similarly, foreign price is the trade-weighted average of trading-partners' price indices. The real exchange rate is calculated from the domestic price level (which is the consumer price index), the nominal effective exchange rate, and the foreign price level in the usual way. For South Africa (because data are not available for the country in the unpublished IMF source), industrial countries' average consumer price level is taken to represent the average foreign price level and the SDR price of South Africa's rand is taken to represent the effective nominal exchange
H These figures on the nominal effective exchange rate and trade-weighted average prices could as well have been computed from the bilateral exchange rate and foreign consumer price level data contained in the monthly issues of the IMF's IFS, when used in conjuctionwith the monthlyissues of the IMF's Direction of Trade Statistics, where trade-weight figures can be found. But this alternative would require more calculationsand might produce less timely data.
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rate. All the data for South Africa are from the relevant monthly issues of the I M F ' s IFS. In all cases, the data are in indices, normalised to 100 for the month of September 1986. Real income is the real G D P interpolated from annual data. The interpolation utilises the assumption that the monthly real G D P growth rate is the same throughout the 12 months in a year so that the annual growth rate converted to the monthly equivalent is used to compound the index of the real G D P - - w i t h the base month being September 1 9 8 6 - - f o r previous and subsequent months covered for each country. The annual G D P growth rate data for the countries are from the W o r l d Bank and U N D P (1992), while the corresponding averages for the industrial group of countries are from the I F S Yearbook (1991). The monthly data on the index of industrial production of the industrial group of countries are from the same source as money stock that we discuss below. M o n e y stock is the end-of-month value of narrow money (M1), just as the nominal interest rate. Both are sourced from relevant monthly issues of the IFS. This is so for individual countries and the industrial group of countries. The foreign real income (GDP or industrial production) and money stock are the average values for industrial countries. In the case of the foreign interest rate, this is represented by the London Inter-Bank Offer Rate (LIBOR) on six-month US dollar deposits. The expected foreign inflation rate is autoregressively generated as the fitted values from regressing the current on the past four values, while the expected domestic inflation rate is the fitted value obtained by regressing the current inflation rate on its past four values and the past four values of each of monetary growth and rate of nominal exchange rate depreciation. This is done with time-series data for individual countries before pooling the data across the countries.
References
Dombusch, R., 1976, Expectations and exchange rate dynamics, Journal of Political Economy 84, 1161-1176. Edwards. S., 1981, Aspects of economics of exchange rates, PhD Dissertation, University of Chicago. Edwards, S., 1983, Floating exchange rates in less developed countries: A monetary analysis of Peruvian experience, Journal of Money, Credit and Banking 15, 73-81. Engle, R. and C. Granger, 1987, Co-integration and error correction: Representation, estimation and testing, Econometrica 55, 251-276. Engle, R, and B.S. Yoo, 1987, Forecasting and testing cointegrating systems, Journal of Econometrics 55, 143-159. Frenkel, J.A., 1976, A monetary approach to exchange rate: Doctrinal aspects and empirical evidence, Scandinavian Journal of Economics 78, 200-224. Frenkel, J.A. and M.L. Mussa, 1985, Asset markets, exchange rates, and the balance of payments, in: R.B. Jones and P.B. Kenen, eds., Handbook of international economics, Vol. 2 (North-Holland, Amsterdam).
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Fry, M.J., 1976, A monetary approach to Afghanistan's flexible exchange rate, Journal of Money, Credit and Banking 8, 219-225. Fry, M.J., 1978, Money and capital or financial deepening in economic development?, Journal of Money, Credit and Banking 10, 464-475. Granger, C. and P. Newbold, 1974, Spurious regression in econometrics, Journal of Econometrics 2. 111-120.
Kouri, P.K., 1976, The exchange rate and the balance of payments in the long run: A monetary approach, Scandinavian Journal of Economics 78, 280-304. Levich, R.M., 1985, Empirical studies of exchange rate: Price behaviour, rate determination, and market efficiency, in: R.B. Jones and P.B. Kenen, eds., Handbook of international economics, Vol. 2 (North-Holland, Amsterdam). Lyons, R.K., 1992, Floating exchange rates in Peru, 1950-54, Journal of Development Economics 38, 99-118. MacDonald, R., 1988, Floating exchange rates: Theories and evidence (Allen and Unwin, London). MacDonald, R. and M.P. Taylor, 1992, Exchange rate economics: A survey, IMF Staff Papers 39, 1-57.
Mussa, M.L., 1976, The exchange rate, the balance of payments, and monetary and fiscal policy under a regime of controlled floating, Scandinavian Journal of Economics 78, 229-248. Ojo, O., 1974, The demand for money: Evidence from an underdeveloped money market, Nigeria Journal of Economic and Social Studies 16. Wong, C., 1977, Demand for money in developing countries: Some theoretical and empirical results, Journal of Monetary Economics 3, 59-86. World Bank and United Nations Development Program, UNDP, 1992, African Development Indicators, The World Bank, Washington, DC.
Journal of DevelopmentEconomics Vol. 52 (1997) 463-481
Development ECONOMICS
The monetary approach to analysing floating exchange rate behaviour in developing countries: Evidence from sub-Saharan African countries, 1986-1992 M.O. Odedokun Economics and Management Department, Unicersi~ of Dundee, Dundee, UK
Abstract
The study tests the monetary approach to floating exchange rate analysis with monthly data for five sub-Saharan African countries over the 1986-1992 period. The results are in strong support of the approach. JEL classification: F31 Keywords: Floating exchange rate; Monetaryapproach
1. Introduction
The relevance or irrelevace of the monetary approach to floating exchange rate determination has far-reaching implications for the conduct of monetary and exchange rate policies. For instance, while the orthodox view (e.g. based on the prediction of the popular Mundel-Fleming model) is that an increase in domestic real income and interest rate should respectively depreciate and appreciate domestic currency, the monetary approach predicts the reverse. Thus, many empirical tests have been conducted for verifying this approach, based on data for industrial countries. An earlier comprehensive survey of such studies can be found in Frenkel and Mussa (1985), Levich (1985), Isard (1988) and MacDonald (1988), while the most current survey is provided by MacDonald 0304-3878/97/$17.00 © 1997 Elsevier Science B.V. All rights reserved. PII S0304-3878(96)00442-7
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and Taylor (1992). As shown by these surveys, the whole idea of the monetary approach is an unsettled issue at the empirical level. When it comes to developing economies, very few such studies can be spotted and the only ones that have come to our notice are those reported by Fry (1976) for Afghanistan; Edwards (1983) for Peru during the 1950s; and Lyons (1992), also for Peru during the 1950s. While the first two studies come out in support of the approach, the last one contradicts it, This limited number of studies for developing countries might partly be due to the small number of countries that have had floating exchange rate experience--in addition to the usual reason of non-availability of data. But due to recent developments in domestic economies and in the international financial scene, a large number of developing countries have started to experiment with this exchange rate system. It is in the light of this that the study reported here examines the recent experience of those sub-Saharan African countries that have had the experience for some time. Five countries' experiences during the 1986 to 1991/92 period are analysed. The countries are Gambia, Ghana, Nigeria, South Africa and Zaire. The remaining discussion is organised into four sections. Recent exchange rate experiences of the five countries studied are described in Section 2. The theoretical framework and methodology are described in Section 3, while the empirical results are presented and evaluated in Section 4. The summary and concluding remarks are in the last section. There are also appendices on co-integration tests and the data employed in the study.
2. Background issues We shall briefly describe the exchange rate practices in and experiences of the five countries included in the study, by way of providing appropriate background information. As mentioned earlier, the five countries are Gambia, Ghana, Nigeria, South Africa and Zaire. These, according to available information, constitute all African countries that have had floating exchange rate experiences for a c o n s e c u tive period of not less than two years up to the end of 1991--the only exception being Guinea, for which we do not have requisite data. 1 However, this is not to say that the system is not popular in sub-Saharan Africa. In fact it has recently started to be widely practised outside the CFA monetary zone. ~ For example, going by the classification of countries according to exchange rate systems as contained in the IMF's I n t e r n a t i o n a l F i n a n c i a l Statistics (IFS), Sierra Leone
1For the purpose of this discussion, we do not reckon what the IMF classifies as a managedfloating exchange rate systemto be an actual floating exchangerate system. 2The CFA monetary zone comprises 14 sub-Saharan countries having a commoncurrency that is pegged and freely convertibleto the French franc.
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changed from a fixed exchange rate system (pegged to SDR) in 1985 to an independent floating arrangement, then back to a fixed system (pegged to US$) in 1988, and "finally" back to independent floating in 1990. Somalia, too, temporarily adopted this independent floating arrangement in 1987; Uganda, in 1985; and Zambia, in 1985 and 1986. Concerning the five countries being studied, Gambia's currency (dalasi) was being pegged to the pound sterling prior to May 1986 when it adopted an independent floating system. Similarly, Ghana adopted an independently floating rate system in October 1986, in place of a fixed rate arrangement (pegged to US$) for determining its cedi. In Nigeria, a form of managed floating arrangement was being used to determine the value of the naira prior to September 1986 when the independent floating system started. While these three countries (former members of the defunct West African Currency Board) started floating arrangements within an interval of few months during 1986, the same is not applicable to the remaining two countries whose experiences date to earlier years. In fact, South Africa started with the system for determining the value of the rand as far back as 1979, while Zaire commenced it in November 1984 in place of a managed floating arrangement that was being used to determine the value of the zaire. All the five countries continue--up to 1992, at least--with the independent floating system. In these countries, the typical institutional arrangement for implementing the independent floating system is to remove the erstwhile controls on currency conversion. Also, in addition to banking concerns, private non-banking institutions are being given licenses and free hands to buy and sell foreign currencies. In a way, the exchange rates are left to the market forces of demand and supply to determine, subject to few controls by the state as in many other modern practices of floating exchange rate arrangement--even in industrial countries. These five countries experienced diverse inflation rates during the period. Zaire experienced the highest rates, these being 46.8%, 90.4%, 82.7%, 104.1%, 81.3% and 550.0% for the years 1986 to 1991 respectively (based on the consumer price index). This is followed by Ghana, with annual inflation rates of 24.6%, 39.8%, 31.4%, 25.2%, 37.3% and 17.2% for the years 1986 to 1991 respectively. The annual figures for the remaining three countries over the six years are as follows: 56.6%, 23.5%, 11.7%, 8.3%, 6.2% and 4.1% for Gambia; 5.3%, 10.3%, 38.3%, 51.0%, 7.1% and 13.0% for Nigeria; and 18.6%, 16.1%, 12.8%, 14.7%, 14.3% and 15.2% for South Africa.
3. Theoretical framework and methodology 3. I. The m o n e t a r y model
Earlier formulations of the monetary approach to floating exchange rate analysis are contained in the writings of Frenkel (1976), Mussa (1976) and Kouri
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(1976), among others. There are alternative variants of the monetary model, notable among which are the f l e x i b l e - p r i c e and s t i c k y - p r i c e versions, both of which are described in detail by MacDonald and Taylor (1992). A basic difference between the two is that the flexible-price version is based on the assumption of continous fulfilment of the purchasing power parity (PPP) condition, while the sticky-price variant (e.g. as developed by Dornbusch, 1976), in a way, constitutes a refinement of its flexible-price counterpart. This extension enables short-term deviation from the PPP condition to be accommodated. Below, we present a description of the flexible-price model and its extension to sticky-price formulation, as in Edwards (1983) and Lyons (1992). The approach starts from the the premise of a stable domestic and foreign money demand function of the form: mt --Pt = k + oty t - fir t + v t
(la)
mtdf _ p f = k f + a f y f t _ flfrft + v f
(lb)
and
where m d is domestic nominal money demand, in logarithms; p is domestic price level, in logarithms; y is a domestic scale variable (usually, income level) in logarithms; r is opportunity cost of holding money, usually interest rate; k is a constant term; a is income (or any other scale) elasticity of money demand; /3 is interest (or any other opportunity cost) quasi-elasticity of money demand; v is an error term; and the superscript " f " indicates that the notation applies to foreign, as opposed to domestic, economy. Also, c~, a f,/3,/3 f > 0. By assuming non-fulfilment of the PPP condition in the short run, the relationship between the domestic price, the foreign price and the nominal exchange rate can be described as follows: d = s t - Pt + P] = 6 d , _ j + ~,
(2)
where s is the logarithm of nominal exchange rate, defined as the domestic currency price of foreign currency; d is the logarithim of deviation from PPP or real exchange rate; is a random term; and 6 is a coefficient of d, an inverse indicator of the speed at which the deviation from PPP would be removed. Eq. (2), in effect, expresses the current real exchange rate as a function of its preceding value. The coefficient 6 should be zero if PPP always holds and one if there is no tendency for the condition to hold, even in the long run. By equating
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467
money supply m s (in logarithms) to money demand m d as the condition for money market equilibrium, we can solve for the price level p. By repeating the same for the foreign economy, we can solve for the foreign price level p f . Substituting for p and pf in Eq. (2) would yield the following relationship: St = t~ + m t
f
-- m t -- o l y t + otfy~ ' + f i r t - [ ~ f r f + t ~ d t _ l + i~t
(3)
where m = m s = m d and m f = Fn sf = mdf; qb is a constant term; /z is a random or error term; and other notations are as described earlier. Thus, the elasticities of nominal exchange rate depreciation with respect to domestic and foreign money stock are predicted to be 1 and - 1 respectively. Similarly, the elasticities with respect to domestic and foreign incomes are the same (but opposite in sign) as the domestic and foreign income elasticities of demand for money, in the same manner as the quasi-elasticities with respect to interest rates are absolutely equal (but opposite in sign) in the money demand and nominal exchange rate functions. The economic explanations for the predicted effects of m, y and r are as follows. An increase in domestic money stock prompts domestic economic agents to get rid of it by spending on goods and services, which, in turn, drives prices up and--through the PPP mechanism--depreciates the nominal exchange rate. On the other hand, an increase in domestic real income, by increasing money demand, reduces excess money supply in the domestic money market and, hence, the price level. This would then operate via the PPP channel to appreciate the nominal exchange rate. An increase in domestic interest rate leads to nominal exchange rate depreciation by increasing (or creating) domestic excess money supply. As pointed out earlier, these predicted effects of income and interest rates are contrary to the received notions, especially as predicted by the popular Mundel-Fleming framework. It is the presence of the lagged value of real exchange rate term d t.~ in the above equation that distinguishes it from the orthodox flexible-price formulation. This difference is due to the fact that short-run deviation from the PPP is permited to exist, as shown in Eq. (2). The long-run money demand functions in Eq. (la) and Eq. (lb) can be substituted for by short-run ones. This would be accomplished through the usual partial adjustment model thus: (m,--Pt)--(mt
1--Pt-1)=O[(md--pt)--(mt-I--Pt-l)]
(4a)
and (m~-Pft)-(mft-,-Pft-,)=of[(mt
df
pf) - (m~ I - Pf- l )l
(4b)
where 0 and 0 f are the domestic and foreign adjustment coefficients respectively --inversely related to the speed of adjustment of desired to actual money balances.
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By substituting Eq. (4a) into Eq. (la), and Eq. (4b) into Eq. (lb) before deriving the reduced-form exchange rate equation, we shall arrive at the following Eq. (5), instead of the earlier Eq. (3): S t = ~9 + m t - - r a f t -
{0o~/[1 -- (1 -- O L ) ] } y t
+{Ofotf/[1 --(1 -- OfL)]}yft + {013/[1 - ( 1 - OL)]}r t -{of~f/[1-(1-OfL)]}rft
+6d,-1 +~'t
(5)
where L is the lag operator, e is the error term, and ~b is the constant term. The reduced-form Eq. (5) differs from Eq. (3) only due to inclusion of lagged values of real incomes and interest rates as additional regressors. It is this Eq. (5) that was estimated by Edwards (1983) and Lyons (1992). As pointed out by Edwards, it is the inclusion of the lagged values of incomes and interest rates--together with the presence of the d t_ l term--in Eq. (5) that make it a short-run model and distinguishes it from the simple versions of the monetary approach. In practice, estimates of the parameters of Eq. (3) and Eq. (5) are generally found difficult or even impossible to derive with reasonable precision due to intractable intercorrelations between m and m f, y and yf, and r and r f. This has led to the common "device" of imposing the restrictions: 0 = Of, a = ~f and /3 = fl f. Imposition of these restrictions would convert Eq. (3) and Eq. (5) to Eq. (3a) and Eq. (5a) respectively:
st=qb+(mt-m~)-ot(yt-yf)+fl(rt-rf)+tdt_l+l, S t : qb + ( m t -- m ~ ) --
Zt
(3a)
{ 0 a / [ 1 - (1 - 0 t ) ] }{ Y t - Yf}
+ {013/[1 - (1 - OL)] }{rt - r f} + 6dr_ 1 + ~t
(5a)
where the notations are as defined earlier. In many studies of advanced economies, further modifications are made to the above by substituting expected rate of devaluation for the domestic-foreign interest rate differential r t - r f in the above equation. This is due to an assumption that an uncovered interest parity condition always holds. However, in the setting of economies without international financial centres, this assumption would have little or no economic logic in its support.
3.2. Present model and method of estimation The above equations constitute the econometric model estimated in the present study. Specifically, we report the estimates of Eq. (3), Eq. (3a) and Eq. (5a). In estimating Eq. (5a), the current and past four values of income and opportunity cost variables are included in the lag specification. This leads to the issue of the right variables to include as the opportunity cost of holding money in the domestic economy. In virtually all studies, the interest rate is treated as the opportunity cost
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for holding money in advanced countries and we too subscribe to this view. However, studies have shown--starting from initial evidence made available by Ojo (1974) and Wong (1977)--that the expected inflation rate is often a better candidate than the interest rate for the opportunity cost in the money demand function in the setting of developing countries. Thus, the expected inflation rate is chosen as the main opportunity cost proxy in the domestic money demand function in this study. 3 But we also support this with the interest rate in some estimates so that, in such estimates, r t in Eq. (3) becomes a vector of two elements --expected domestic inflation and interest rates--in the same manner that the r t - r [ term in Eq. (3a) and Eq. (5a) turns into a vector of expected domestic inflation rate and domestic-foreign interest rate differential. Given the alternative forms of equations estimated as just discussed, it would be unwieldy to report these estimates separately for each country. Thus, the leading equation estimates in the study are derived by pooling the time-series data across the five countries. Another reason for pooling the data is the fact that some explanatory variables (like the interpolated domestic income figures) may not show sufficient variations within a period of 5 to 6 years to allow the estimates to adequately capture the actual effects, whereas the relatively substantial cross-country variations in such regressors would more likely make these effects discernable. All the same, we still support the pooled-data estimates with time-series estimates for a variant of the aforementioned specifications--and, as will be seen in the next section, no material differences are found to exist between these time-series estimates and the pooled-data estimates. In deriving the pooled time-series/crosscountry estimates, we employ the fixed-effect technique of panel data estimates--which caters for inter-country differences in the autonomous nominal exchange rates by permitting the intercepts to differ across the countries. As pointed out in the MacDonald and Taylor (1992) survey, a criticism sometimes levied against monetary model estimation is the possibility of non-exogeneity of domestic and foreign money stocks, m t and mft, in the nominal exchange rate s t equations for industrial countries in the sense that monetary target setting may be dependent on nominal exchange rate. Thus, we experiment by employing one-period lagged values of domestic and foreign money stocks in the place of the contemporaneous values, but as this makes no material difference to the estimates we report only one or two such equations. Finally, all the panel data estimates are derived by the A R 1 G L S technique of correcting for serial correlation that uses country-specific serial correlation coefficients to transform the data. Also, for countries where serial correlation is detected in the time-series estimates, the A R 1 G L S method is adopted to correct this.
3 A n o t h e r reason for m a k i n g the expected inflation rate the main opportunity cost is due to the tact that n o m i n a l interest rate data are not adequately available for some of the countries and are not available at all for Zaire.
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3.3. (Expectational) P P P and co-integration issues
There is the issue raised by Lyons (1992) in connection with his analysis of Peruvian floating exchange rate behaviour to the effect that a particular version of PPP, which he called the "expectational" PPP model, performs better than the monetary model. There is also a related issue of whether the orthodox PPP condition would be applicable to the data used in the present study. We shall now address these issues. It should be recalled that the monetary model is based on the assumption that PPP holds, at least in the long run. Lyons (1992, p. 105) advanced some reasons why PPP should hold in developing countries and supported this with estimates of an expectational PPP model with Peruvian data. 4 This model consists of expressing the nominal exchange rate as a function of expected domestic and foreign price levels, in addition to the lagged value of real exchange rate, thus: St =
k o + Ap~
+
Afpt f + g2d t_ 1 -~
Ut
(6)
where pe is the expected domestic price level in logarithms; s is logarithm of nominal exchange rate as defined earlier; d is real exchange rate as defined earlier; u is a random error term; k 0 is a constant term; A and /2 are parameters; and the " f " subscript denotes the foreign variable/parameter as before. For the expectational PPP proposition to hold, the coefficients of the domestic and foreign prices--A and Af--have to be 1 and - 1 respectively. The inclusion of the lagged value of real exchange rate, d t _ 1, is for the same reason of probable short-run deviation from the PPP condition. In this study, we also experiment with the above model, using the pooled or panel data. We proxy the expected domestic and foreign prices by their respective one-period lagged values. (More sophisticated techniques of generating expected price levels, e.g. by using a larger information set, do not produce materially different results.) Because the specifications produce robust results, we report them in the next section. The associated issue is whether the exchange rate and prices are, in fact, co-integrated. If they are not, there are two possible consequences. First, the PPP condition would not likely be satisfied, even in the long run, whereas the monetary model hinges on the fulfilment of this condition. Second, since exchange rate and prices are not likely to be stationary or integrated of degree zero, the chances of the estimates reflecting just a spurious relationship among the variables would be
4 However, the author did not provide any formal theoretical basis for this model.
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high (Granger and Newbold, 1974). 5 Therefore, we conducted an augumented Dickey-Fuller co-integration test, using quarterly data for the 1980-1991 period for each country, and we found that the data suggest the existence of co-integrat i o n - e x c e p t for Zairean data. The result and a brief description of the augumented Dickey-Fuller test are provided in Appendix A. 3.4. The data
Monthly data are employed in estimating the equations. The methods of measuring the variables and the specific sources of the data are spelt out in Appendix B. We wish to point out here that all the data are from IMF sources and that the nominal exchange rate, the real exchange rate and the foreign price level are multilateral and effective ones. This means that the nominal exchange rate is the trade-weighted average of bilateral nominal exchange rates in the same way that the foreign price is the trade-weighted average of price levels in trading-partner countries. The real exchange rate is calculated from the nominal effective rate, the domestic price level, and trade-weighted foreign prices. (Interestingly, each of the five countries conducted over 90% of its foreign trade with the industrial countries of Western Europe, USA, Canada and Japan whose currencies are convertible and whose economies are open. This supports the choice of trade weights in computing exchange rates and foreign price levels, instead of merely choosing a particular country--like, say, the U S A - - a s the benchmark country.) The period covered for each country in the study is as indicated in Table 2, in the next section.
4. Empirical results The estimates of the monetary and expectational PPP equations with the panel or pooled data for all the five countries are as reported in Table 1, while the time-series estimates for individual countries are those presented in Table 2. Further explanatory notes are provided at the foot of each table. The estimates of Tables 1 and 2 display high adjusted R 2 values, evidence of the high explanatory power of the models. Also, the Durbin-Watson statistic values are close enough to 2.0, particularly in Table 1, that an absence of serial correlation of residuals is suggested. As predicted by the monetary approach, the coefficients of domestic money stock are positive and statistically significant in those equations where it features in Table 1, with values not far from 1, which is the ideal value predicted by the theory. But the coefficients of foreign money stock have perverse positive values
5 But if the variablesare co-integrated,there need not be a spurious relationship even if they are not stationary in the level form. However, the estimated standard errors are wrong (though the estimates are consistent).
1
1 -- mft_ l
m~
2lint[
intft
X(it -
f,f)
Y~*f
f, - f/
int t
y[
Yt --
X,(y,- y[)
Y t - Yf
Yt
mft-
mft
mt_
m t --
mt- l
mt
- 1.13 (-2.3)
-5.51 (-9.8) 2.887 (13.9)
- 0.24 (-1.1)
0.530 (2.5)
0.917 (57.5)
Table 1 Pooled-data estimates
- 1.33 (-2.9)
-2.50 (-5.1)
- 1.39 (-7.3)
0.316 (1.6)
0.835 (60.1)
- 1.57 (-3.4)
-2.87 (-5.6)
0.481 (2.3) - 1.40 (-7.1)
0.843 (57.9)
1.393 (6.9)
1.99 ( - 10.0)
0.736 (59.6)
1.164 (6.6)
1.82 ( - 10.4)
0.673 (65.7)
-5.44 ( - 10.9)
(-2.35) ( - 14.2)
0.754 (71.1)
-3.13 (-6.9)
-2.30 ( - 13.0)
0.736 (70.1)
2.07
2 . 4 6
( - 5.6)
-
( - 12.9)
-
0.690 (74.0)
-3.32 ( - 7.4)
-2.18 ( - 12.5)
0.764 (85.9)
I 4~
4:.
6,a
.~ -.a
1
0,983 1.88 293
0.286 (4.4)
1.41 (9.3)
0.987 1.99 311
0.359 (5.8)
1.60 (11.2)
0.987 2.02 308
0.425 (6.7)
2.24 (15.9)
0.978 1.89 297
0.300 (4.2)
2.22 (13.6)
0987 1.76 287
4.59 (23.6)
0.984 •.99 315
0.387 (5.8)
2.55 (17.2)
0.985 1.92 315
0.339 (5.2)
2.01 (13.5)
0.990 1.76 309
4.15 (21.6)
0.985 1.80 317
2.03 (13.7)
0.994 1.63 308
-0.954 (-40.7)
1.108 (168.8)
0.994 1.85 308
-1.076 (-43.9)
1.071 (154.9)
0.877 (21.2)
0.995 2.01 311
- 0.945 ( - 44.8)
0.774 (20.9) 0,997 (174.0)
- 1.019 (-40.2) 0,995 2.10 304
1.045 (123.1)
0.821 (21.6)
Notes: (i) The dependent variable is the log of index of effective nominal exchange rate, domestic currency price of foreign currency so that its upward movement represents domestic currency depreciation. (ii) The figures in parentheses below the parameter estimates are t-values. At 5% and 1% levels of significance (two-tailed test), a parameter estimate is statistically different from zero if the t-value is absolutely up to 2.0 and 2.6 respectively. (iii) D W and N are the Durbin-Watson statistic and the total number of observations respectively. The variables are as lollows: m is nominal money stock (in logarithms); 3' is index of real income proxied by GDP (in logarithms); y* f is index of real income proxied by industrial production (in logarithms); d is index of real effective exchange rate (also in logarithms), with upward movement representing depreciation of domestic currency in real terms: p is index of domestic price (in logarithms): inf e is expected inflation rate; and int is nominal interest rate. ~ indicates that the affected coefficient is derived as the sum of the coefficients of the current and past three values (past two values in the case of p and pf) of the variable in the lag specification. Finally, the " £ ' superscript denotes a foreign variable. (iv) Estimates including domestic interest rate int are for only tour countries, with Zaire being excluded.
Adjusted R 2 DW N
-Ypf
P~ I
p[
X,pt
Pt- 1
Pr
dt
X inf7
inJ)~
.~
~"
"~
~
.~ .~
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M.O. Odedokun / Journal o f Development Economics 52 (1997) 4 6 3 - 4 8 1
Table 2 Time-series estimates
Constant m t - m~ Yt -- Yf ft - ft f
Gambia
Ghana
Nigeria
S. Africa
Zaire
4.097 (9.7) 0.008 (0.2) - 1.54 (-5.9) 0.487 (2.1)
0.852 (1.0) 0.224 (3.0) 1.31 (1.5) 0.391 (1.5)
8.021 (16.3) 0.803 (7.2) - 4.23 (-3.0) 1.777 (2.2)
3.176 (6.3) 0.361 (5.3) - 2.90 (-6.6) 0.464 (1.7)
8.986 (15.0) 0.769 (8.3) - 5.27 ( - 1.1)
int ft
0.233 (0.4) dt- 1 0.137 (1.6) Adjusted R 2 0.926 DW 1.82 p 0.661 (6.3) Q 16.0 Period 1986:7-1992:1 N 66 inf e
- 1.899 ( - 5.5) 1.092 (8.6) 0.960 1.33
0.129 (0.2)
0.965 1.45 0.745 (8.6) 53.2 24.1 1986:10-1991:9 1986:10-1991:3 60 53
- 2.434 (-0.5) 0.685 (7.4) 0.932 1.72
- 6.920 ( - 1.9) 0.200 (0.9)
0.995 1.76 0.958 (16.0) 22.4 23.3 1986:1-1991:6 1986:1-1992:1 66 73
Notes:
(i) The dependent variable is the effective nominal exchange rate (in logarithms), whose upward movement represents depreciation of domestic currency in nominal terms. (ii) The figures in parentheses below the parameter estimates are t-values. At 5% and 1% levels of significance (two-tailed test), a parameter estimate is statistically different from zero if its t-value is absolutely up to 2.0 and 2.6 respectively. (iii) D W , Q and N are the Durbin-Watson statistic, the Ljung-Box Q-statistic, and the number of monthly observations respectively. Estimates with p-values are the ones derived after correcting for serial correlation of residuals through the A R 1 GLS technique. (iv) The variables are as follows: m is log of money stock, y is log of real output index, int is interest rate, inf e is expected inflation rate, and d is effective real exchange rate (in logarithms) whose upward movement represents depreciation of domestic currency in real terms. An " f " superscript indicates a foreign varaible.
- - w h i c h a r e h a r d l y s t a t i s t i c a l l y s i g n i f i c a n t , h o w e v e r - - i n t h e t h r e e e q u a t i o n s , this b e i n g a r e f l e c t i o n o f t h e l i k e l y p r o b l e m o f m u l t i c o l l i n e a r i t y b e i n g e n c o u n t e r e d in m o s t p r e v i o u s s t u d i e s as p o i n t e d o u t in S e c t i o n 2. 6 I n T a b l e 1, t h e c o e f f i c i e n t s o f
6 Another reason that could account for these perverse coefficient values is that what is employed as the proxy for foreign money stock might be inappropriate. As pointed out in Appendix B, the proxy is the index of money stock for all industrial countries combined instead of the trade-weighted index of money stock of the trading partners which non-availability of requisite data does not permit us to employ.
M.O. Odedokun / Journal of DeL'elopment Economics 52 (1997) 463-481
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domestic-foreign money stock differential have the expected and statistically significant positive values that average about 0.75, a number that is not far from the predicted value of unity--especially when compared with the findings reported in previous studies even for advanced economies. 7 The coefficients of this money stock differential are also positive in all the time-series estimates of Table 2, although the values are not as high. In the equations in Table 1 where domestic and foreign incomes are separately included, the coefficients of domestic income have expected negative values that are statistically very significant in two of the three. But foreign income coefficients have perverse negative values, the explanation again being the practical difficulty of separately deriving the estimates due to multicollinearity problems. In the remaining equations, we have a domestic-foreign income differential instead and the coefficients of this variable are negative and statistically very significant - - w i t h the average value being just a little above - 2 . 0 in absolute terms. This compares with - 2 . 9 reported by Edwards (1983) for Peru and the average (long-run) income elasticities of money demand of about 2.0 for developing countries, e.g. Edwards (1981) and Fry (1978). 8 The corresponding coefficients in time-series estimates are also similar, except that the coefficient in the equation for Ghana has a positive s i g n - - w h i c h is statistically insignificant anyway. The coefficient of domestic interest rate is positive and very significant in the Table 1 results, again as predicted by the monetary approach. Also, the coefficients of foreign interest rate are very significantly negative, in line with the prediction, in all the estimates reported in Table 1. As a result, the coefficients of the domestic-foreign interest rate differential are found with positive and and very significant values. These performances of domestic and foreign interest rates are also duplicated, without any exception, in the time-series estimates reported in Table 2, Thus, although evidence in the early 1970s (e.g. see Ojo, 1974) suggests the non-importance of interest rates in money demand functions in sub-Saharan Africa due to the evolving nature of financial systems and pegging of interest rates well below market equilibrium, this may no longer apply. This is because the financial development that has taken place during the past two decades or so,
7 Although these coefficients of the money stock differential (which average about 0.75) and the three coefficientsof the domestic money stock (which are 0.92, 0.84 and 0.84) marginally miss passing the formal statistical test of being equal to unity at the conventional significance levels, they are still among the closest figures to unity when compared with other similar studies for developing countries and even many of the empirical studies that came out in support of the monetary approach in industrial countries. The robustness of these findings becomes more apparent when the low quality of data for typical sub-Saharan African countries is taken into account. 8 It should be recollected that the coefficient of income in the exchange rate equation is predicted to be equal but opposite in sign to that of income elasticity of money demand, i.e. the coefficient of income in the (logarithmic) money demand equation.
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coupled with deregulation of interest rates that typically accompanies adoption of a deregulated or floating exchange rate system with effect from around the mid-1980s, might now have reversed this situation and hence account for the present finding. The expected inflation rates have the expected positive and statistically significant coefficients in the Table 1 results, thus butressing the view that expected inflation rate is (another) opportunity cost for holding money. However, the coefficients are found with negative values in the Table 2 time-series results for Ghana and South Africa and also with statistically insignificant positive values in the equations for the remaining three countries. This may be due to intercorrelation with interest rates. Given the consistently and significantly positive values in Table 1, however, there is sufficient evidence in support of the prediction that expected inflation depreciates the nominal exchange rate. The lagged value of the real exchange rate also has positive and statistically significant coefficients in the Table 1 results, with the average value being about 0.35--which is less than 1.0 as expected so that the short-run deviation from the PPP condition will tend to be removed over time. 9 The Table 2 results are practically the same, except that the coefficient is around 1.0 (precisely, 1.092) for Ghana. The independence of the coefficients of other regressors on the inclusion of the lagged real exchange rate as an additional regressor can be seen in those Table 1 equation estimates where it is excluded. This suggests that the flexible monetary approach equation that does not require inclusion of this as a regressor fits the data equally well. Concerning the lagged specification, it can be observed from Table 1 that the sum of the coefficients of the current and past three values of the regressors (and their t-values too) do not differ from the results obtained by including only the contemporaneous values as regressors. The only exception is the expected inflation rate. l0 Thus, with the exception of the expected inflation rate, there appear to be quick responses of the nominal exchange rate to the regressors tested for. Finally, we come to the issue of the expectational PPP model and its relevance. As shown by the last four equation estimates of Table 1, the results of estimating this version of PPP equations are robust. The values of the coefficients of domestic and foreign prices are practically 1.0 and - 1 . 0 respectively, in line with the prediction. However, this is not found to be dependent on the lagged value of real
9 This average of 0.35 means that only about 35% of the deviations from PPP should remain after one month and 12% after two months. This is a faster rate of adjustment than that reported by most other authors. However, going by the results of the expectational model as presented in the last four equations of Table l, a much slower rate of adjustment is implied as the coefficients of the lagged real exchange rate now average about 0.8, suggesting that not more than 20% from PPP would be removed within one month, not more than 36% within two months, and not more than 50% within three months. 10 In fact, our experiment with greater lag specifications shows that the sum of coefficients of this variable (and the t-values) continues to increase for up to seven past values.
M.O. Odedokun / Journal of Development Economics 52 (1997) 463-481
477
exchange rate being included as an additional regressor or the inclusion of expected (proxied by one-period lagged value) in place of actual price levels as the PPP regressors. In other words, the results are in fact a validation of the orthodox, as opposed to expectational, PPP condition.
5. Summary and conclusion The study is an attempt to confront the monetary approach to floating exchange rate analysis with data from five sub-Saharan African countries, viz. Gambia, Ghana, Nigeria, South Africa and Zaire. Monthly data over the 1986-1992 period are employed. In addition to estimating regression equations for both the flexibleprice and sticky-price variants of the monetary model, we also present the estimates of the expectational version of the PPP equation. The highlights of our findings from the tests are as follows: (a) The domestic-foreign money stock ratio depreciates the nominal exchange rate, with the elasticities in the exchange rate equation being about unity as predicted by the monetary approach. (b) The domestic-foreign real income ratio appreciates the nominal exchange rate, with the elasticities being about 2.0 in the equations. Thus, as predicted by the monetary approach, an increase in domestic income has the effect of appreciating the value of domestic currency. (c) An increase in the domestic interest rate is found to depreciate the nominal exchange rate, with the reverse being the case for a foreign interest rate. Again, this is perfectly in agreement with the prediction of the monetary approach. (d) The expected inflation rate in the domestic economy has the same effect of depreciating the nominal exchange rate as interest rate, both being opportunity costs of holding money in developing countries. This also supports the monetary approach. (e) There is some evidence that there might be some short-run deviation from the PPP condition but there is strong evidence that the condition holds, at least in the long run. Particularly, the elasticities of domestic and foreign prices in the nominal exchange rate equations are found to be 1.0 and - 1 . 0 respectively, implying that a given percentage increase in domestic (foreign) prices is associated with the same percentage depreciation (appreciation) of domestic currency. On the whole, the available evidence from the study strongly supports the monetary approach and also the validity of the PPP condition.
Acknowledgements The financial support and facilities provided by the Department of Economics and Management, University of Dundee, Dundee, Scotland for carrying out this
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M.O. Odedokun / Journal of Development Economics 52 (1997) 463-481
study is acknowledged. So also are the comments on the paper and other forms of academic assistance provided by Ian Marsh of the same Department. The comments made by the two anonymous referees also served to enhance the quality of the article. All errors and omissions, however, exclusively belong to the author.
Appendix A. Results of the augumented Dickey-Fuller tests The augumented Dickey-Fuller test for co-integration of variables (which is discussed here in connection with the PPP test) is conventionally conducted as described b e l o w - - f o r details, see Engle and Granger (1987). First, estimate the following equations:
(a.1)
A x t = ol 0 -~- / 3 x t _ 1 q- ~ o l i x t _ i ~- Et
and A 2 x t = "17"o~ 6 A x t - 1
~- ~ ' w i A 2 x t - i
~- ~t
(A.2)
where a i, fl, 6, and zri are parameters; and e are random error terms; x is a variable in level (logarithm) form; and d and A 2 indicate the first- and second-difference of x respectively. The above equations are to be estimated by replacing x with each of the following variables: nominal exchange rate (s); domestic price (p); foreign price (pf); and the residuals obtained by regressing s on p and pf or by regressing p on s and pf or both separately. The residuals correspond to estimates of real exchange rate values. For the PPP condition to be fulfilled, each of s, p and pf should be integrated of order one and this would be so if the values of the fl estimates in Eq. (A.1) were statistically insignificant in a situation when the values of the 6 estimates in Eq. (A.2) are significant. Special t-value statistical tables, as provided by Engle and Yoo (1987), exist for this significance test. The condition stated in the preceding paragraph can be regarded as the necessary one. The sufficient condition still requires the residuals or real exchange rate estimates to be integrated of order zero and this would be fulfilled if the estimates of the fl value in Eq. (A. 1) were statistically significantly different from zero. Following the procedure just described, we conducted the test with quarterly data over 1980(I)-1991(II) for each of the countries and the results are as presented below in respect of the estimates of the /3 and ~ values.
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M.O. Odedokun / Journal of Development Economics 52 (1997) 463-481
values Nominal exchange rate Domestic price Foreign price Residuals ~ 6 values Nominal exchange rate Domestic price Foreign price Residuals "
Gambia
Ghana
Nigeria
S. Africa
Zaire
- 1.25 - 0.57 0.86 - 3.56
- 1.14 - 2.65 0.29 - 3.70
- 0.22 - 0.25 0.92 - 3.30
- 2.77 1.89 - 1.74 - 3.09
- 2.05 2.20 2.92 - 1.78
- 4.26 - 3.25 -3.28 - 6.53
-
- 3.75 - 3.31 -2.97 - 3.78
- 5.43 - 7.44 -5.08 - 7.25
- 1.98 - 0.70 -5.16 - 3.55
4.53 4.17 10.33 4.20
Notes: a The residuals are the ones obtained by regressing domestic price level on nominal exchange rate and foreign price level. (i) Either one or two lagged values of the dependent variable is included in estimating Eq. (A. 1) and Eq. (A.2). (ii) At 5% and 1% significance levels, the critical values for the significance (Dickey-Fuller) t - t e s t - - a s extracted from Engle and Yoo ( 1 9 8 7 ) - - a r e - 2 . 9 7 and - 3.58 respectively. As can be seen from the above results, it is only in Zaire that the PPP condition is not satisfied. For other countries, each of the nominal exchange rate, the domestic price level, and the foreign price level are integrated of order 1 and all three are co-integrated since the residuals are integrated of order zero.
Appendix B. Data sources and variable measurements Data on effective nominal exchange rate, domestic price index, foreign price index, and effective real exchange rate for Gambia, Ghana, Nigeria and Zaire are from an unpublished IMF source. 1l The nominal exchange rate is the tradeweighted average of bilateral exchange rates vis-h-vis trading-partners' currencies. Similarly, foreign price is the trade-weighted average of trading-partners' price indices. The real exchange rate is calculated from the domestic price level (which is the consumer price index), the nominal effective exchange rate, and the foreign price level in the usual way. For South Africa (because data are not available for the country in the unpublished IMF source), industrial countries' average consumer price level is taken to represent the average foreign price level and the SDR price of South Africa's rand is taken to represent the effective nominal exchange
H These figures on the nominal effective exchange rate and trade-weighted average prices could as well have been computed from the bilateral exchange rate and foreign consumer price level data contained in the monthly issues of the IMF's IFS, when used in conjuctionwith the monthlyissues of the IMF's Direction of Trade Statistics, where trade-weight figures can be found. But this alternative would require more calculationsand might produce less timely data.
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M.O. Odedokun / Journal of Development Economics 52 (1997) 463-481
rate. All the data for South Africa are from the relevant monthly issues of the I M F ' s IFS. In all cases, the data are in indices, normalised to 100 for the month of September 1986. Real income is the real G D P interpolated from annual data. The interpolation utilises the assumption that the monthly real G D P growth rate is the same throughout the 12 months in a year so that the annual growth rate converted to the monthly equivalent is used to compound the index of the real G D P - - w i t h the base month being September 1 9 8 6 - - f o r previous and subsequent months covered for each country. The annual G D P growth rate data for the countries are from the W o r l d Bank and U N D P (1992), while the corresponding averages for the industrial group of countries are from the I F S Yearbook (1991). The monthly data on the index of industrial production of the industrial group of countries are from the same source as money stock that we discuss below. M o n e y stock is the end-of-month value of narrow money (M1), just as the nominal interest rate. Both are sourced from relevant monthly issues of the IFS. This is so for individual countries and the industrial group of countries. The foreign real income (GDP or industrial production) and money stock are the average values for industrial countries. In the case of the foreign interest rate, this is represented by the London Inter-Bank Offer Rate (LIBOR) on six-month US dollar deposits. The expected foreign inflation rate is autoregressively generated as the fitted values from regressing the current on the past four values, while the expected domestic inflation rate is the fitted value obtained by regressing the current inflation rate on its past four values and the past four values of each of monetary growth and rate of nominal exchange rate depreciation. This is done with time-series data for individual countries before pooling the data across the countries.
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