Download - On the volatility of exchange rates: Tests of monetary and portfolio balance models of exchange rate determination

On the Volatility of Exchange Rates: Tests of Monetary

and Portfolio Balance Models of

Exchange Rate Determination

By

Daniel Gros

C o n t e n t s : I. Introduction. - II. Methodology. - III. The Flexible Price Monetary Model. - IV. The Role of Sticky Prices. - V. Portfolio Balance Models. - VI. Con- clusions. - Appendix.

I. lntrodnction

T he highly erratic behaviour o f floating exchange rates since the break- down of the fixed exchange rate system has been a puzzle for many observers. Some claim that the degree o f volatility exhibited by ex-

change rates is excessive and thus undesirable; others claim that an efficient foreign exchange market is a better, or more efficient, outlet for many underlying disturbances, rather than markets that might not be able to react as swiftly. Another aspect o f this problem is that there seem to be tranquil and turbulent periods in the foreign exchange markets, that is the degree o f volatility of exchange rates varies over time without corresponding changes in the behaviour of the fundamentals. It is widely claimed that the degree o f this volatility is due to the volatility o f the underlying policies - a claim which has not, as yet been substantiated.

The purpose of this paper is to contribute to the discussion on the volatility o f exchange rates by analyzing a more specific question: is it possible to reject the joint hypothesis that (a) foreign exchange markets are efficient and (b) that the exchange rate is determined by a particular model? This procedure is an application o f the so-called variance bound tests, developed in the finance literature, that examine the issue o f excess volatility of stock prices. The basic idea behind this literature is that any asset price formed in an efficient market is a function o f present and future fundamentals. The volatility o f the asset price itself should thus not exceed the volatility o f the fundamentals. Unfortunately,

Remark: This research was supported by grants from the Thyssen Foundation and Frau Von l.utteroti. The author wishes to thank Peter Borlo and Keller Hannah for excellent research assistance. C. Adams, D. Folkerts-Landau, J. Huss, P. lsard, and S. Ramachandran provided useful comments on an earlier version of this paper.

274 W e l t w i r t s c h a f t l i c h e s A r c h i v

however, there is no general agreement about the fundamentals that ought to determine exchange rates. Therefore, a number of the most widely used exchange rate models are analyzed to determine whether the volatility of exchange rates is larger than the volatility of fundamentals that ought to determine exchange rates. The purpose of this exercise is not to find the model that performs best, but to find out whether these different models yield similar conclusions.

The most widely used exchange rate models in empirical work are all variants of the monetary approach. They can be subsumed in a general specification that implies that the exchange rate is a function of five variables: money supplies, national incomes, interest rate differentials, inflation differentials and relative asset supplies.

The monetary approach has also been integrated with portfolio balance considerations which place the emphasis on differences in asset supplies. Accordingly, the tests performed in this paper are two variants of the monetary approach and one representation of the portfolio balance approaeh.

Assuming that the exchange rate is set in an efficient, forward-lo0king market, the fundamental determinants of exchange rates are the expected, discounted present values of future money supplies, incomes and asset supplies. The test consists in computing the variance of this present value and comparing it to the variance of the actual exchange rate.

However, since exchange rates are widely regarded as non-stationary variables, it is not possible to perform a straightforward test based on the variance of the level of the exchange rate. A solution adopted by a number of researchers [Bini-Smaghi, 1985; Huang, 1981; Wadwani, 1984] has been to use the first difference of the exchange rate, under the assumption that first differences are stationary. However, the results based on first differences have been inconclusive [see Bini-Smaghi, 1985; Wadwani, 1984], and different from the results that are based on levels. This paper, in contrast, uses a methodology that is based on levels but is not subject to the stationary problems because it does not use the variance but calculates a second moment around a different variable whose expectation exists even if the underlying process for exchange rates is non-stationary.

The procedure used for this variance bounds test here is quite different from the usual regression analysis because it asks whether there is enough variability in these fundamentals to justify the observed variability in exchange rates. In contrast, the usual regression analysis minimizes the variance of the difference between the estimated and the actual values. Thus, a good fit usually implies that the variance of the estimated exchange rate model is close to the variance of the actual exchange rate. But such a result, per se, does not answer the question whether exchange rates are too volatile to be compatible with efficient foreign exchange markets.

Gros: The Volatility of Exchange Rates 275

The tests performed in this paper are based on various DM exchange rates, this is in contrast to most empirical work on exchange rates which is usually based on the U.S. dollar. However, one of the results of the paper is that the behaviour of the U.S. dollar (that is the DM/U.S.$ exchange rate) is somehow different (from the other DM exchange rates); this implies that tests that are based on the U.S. dollar might yield similar results for most exchange rates because there is a common U.S. dollar factor. Another advantage of the DM as the base currency is that it allows one to analyze the experience of the EMS. The semi-fixed exchange rates in the EMS represent a useful contrast to the more freely floating currencies like the U.S. dollar or the Japanese yen. Indeed the main result of the test performed in this paper is that for the intra-EMS exchange rates, the variability of the fundamentals can account for the (reduced) variability of the intra-EMS exchange rates. For the other currencies, considered here, the variability of the fundamentals appears much smaller than the variability of the exchange rates. This indicates that the EMS has created an environment in which the variability of the exchange rates has been reduced to the minimum that can be achieved given the variability in the fundamentals.

Section II discusses the general methodology to be followed in dealing with the issue of excess volatility. Section III presents the results of the application of this methodology to the flexible price monetary model. Section IV presents the results for the sticky price, Dornbusch model. Section V analyzes the implications of the portfolio balance model and proposes three different ways to apply the volatility tests of the previous sections to this class of exchange rate models. Section VI contains some concluding remarks.

II. Methodology The view that exchange rates are asset prices can be represented by a

general model in which the (logarithm of the) exchange rate, st, is determined by:

st ---- Xt + /a [Et(st+,) - s,], (1)

where Et(St+l) denotes the expectation of the future exchange rate, st+t, formed and conditional upon information available at time t. Xt denotes the "fundamentals" that, according to the specific model, determine the exchange rate. The parameter # measures the sensitivity of the current exchange rate to its expected rate of change. Assuming that expectations are consistent with the application of ( l ) in all future periods ~ (1) can be solved by forward iteration to yield an expression for the current exchange rate in terms of present and future fundamentals:

That is, expectations are rational (and imposing a suitable boundary condition).


s, = (1 - a) j~0(ay E,(X,+j), (2)

where e~ -- #/(1 + #) < 1. This relationship suggests that the variance of the exchange rate should not

exceed the variance of the discounted sum of future fundamentals . 2 However, if the fundamentals follow a non-stat ionary process the variance,

that is the second momen t a round the mean, o f both sides of(2) does not exist. The technique employed in this paper avoids this non-stat ionary prob lem by comput ing second moments a round a different variable that is independent of the sample mean. This technique was proposed by Mankiw et al. [1985] and was applied by them to reexamine the issue of excess volatility of stock prices.

This technique avoids the use of sample means, or other sample statistics, by defining two additional variables. The first is the perfect foresight or ex-post rational exchange rate, s,*, which is equal to the discounted sum of the actual fundamentals:

s,* = (1 - a) jZ=0(ay X,+j. (3)

The second variable used in the tests of this paper is a so-called "naive forecast" exchange rate, st ~ based on some naive forecast of future fundamentals EN,(X,+j):

s, ~ = (1 - ~)j__:}0(~y EN,(X,+j). (4)

The naive forecast ENt (Xt+j) does not need to be rational, but it is assumed that rational agents have access to this naive forecast. The difference between the perfect forecast exchange rate, s,*, and the naive forecast exchange rate, s, ~ can be written as:

s , * - s , ~ = ( s * - s , ) + ( s , - s , ~ ( 5 )

Squaring both sides of (8) and taking expectations then implies:

E(s,* - s,~ 2 = E(s,* - st) 2 + E(s, - st~ 2 (6)

because the expectation of the cross product , E(s,* - s,) (s, - s, ~ is zero since s,* -

The difference between the actual exchange rate s,, and the perfect foresight exchange rate, s,*, (see equation (3)) is due to an exceptional error which is defined by: s,* = s, + Ut. A rational forecast error, like U,, must be uncorrelated with all information available at time t; and it must therefore also be uncorrelated with s, (i.e., the co-variance (s, U) = 0). This implies that the variance of s,*, denoted by Var (s,*), must exceed the variance of s, since: Var (s,*) = Var (st) + Var (U,), and thus: Var (s,*) >_ Var (s,). In an efficient foreign exchange market, the variance of the perfect foresight exchange rate should exceed the variance of the actual exchange rate if these variances exist.


s, = Ut is uncorrelated with any informat ion available at t ime t or at the beginning of the sample period. The expectation in (6) is thus conditional upon information available at the beginning of the sample period. Equat ion (6) contains the two inequalities that are tested below:

E(st* - s,~ 2 _~ E(st* - s,) 2 (7)

E(st* - st~ 2 ~ E(st - st~ 2. (8)

The intuition behind (7) is that the mean square of the forecast errors is larger if the naive forecast is used instead of the efficient marke t forecast. The intuition behind (8) is that the naive forecast is closer to the marke t forecast (in terms of average squared distances) than to the perfect forecast. The conditional expectations in (7) and (8) exist even if exchange rates follow a non-stat ionary process because they do not rely on a sample mean.

In actual tests, it is necessary to t runcate the infinite series contained in (3) by using terminal values for the nominal exchange rate and the fundamentals . s,* can thus be redefined as:

T- t

st* = (1 - a) j~o(ay Xt+j + a T-'§ ST§ (9)

Since rationality implies st = Et(st*) for all t, this t runcat ion does not affect the inequalities (7) and (8). Moreover , since (9) also includes the actual exchange rate at T + I , (9) and thus (7) and (8) would hold even in the presence of speculative bubbles?

The most impor tant p rob lem in using the inequalities (7) and (8) for a volatility test on exchange rates is that there exist several different models that can be used to specify (1). The models differ not only regarding the fundamentals, X, but also regarding the discount factor, ~. However , by using several o f the most "popular" models it should be possible to obtain results that are robust.

III. The Flexible Price Monetary Model

The models to be used in this paper , all Variants o f the mone ta ry approach , are those most frequently tested in the literature. The general results o f the econometric tests performed so far are summarized in Meese and Rogoff [ 1983; 1985], Boughton [1986] and Isard [1986]. Meese and Rogoff , in part icular, indicate that the in-sample fit o f these models varies widely, depending on the

3 A speculative bubble is defined here as a situation in which the weight of the last term in (12) does not go to zero as T goes to infinity but all other relationships used so far continue to hold.

278 Weltwirtschaftliches Archiv

currency and the period of observation. However , the out-of-sample fit or predictive ability of these models is generally p o o r ?

The starting point for all the models is a conventional money demand function o f the form:

mtd -- k + ~byt 4- pt - oit, (10)

where mt d, y , and pt represent (the natural logarithm) of the quantity o f money demands, income and general price level, th and o represent the income elasticity and interest semi-elasticity o f money demand respectively; it represents the nominal interest rate. Assuming purchasing power parity (PPP), interest parity, and equilibrium on the domestic money market (these three assumptions imply: pt ---- St -Jr- pt*, it - it* = Et(s,+~) - st and m, d = mts = m r )

equation (10) can be rewritten as:

mt = k + ~byt + st + pt* - o[it* + E,(St+l) - st], (11)

where pt* and i,* represent the foreign price level and interest rate respectively. The three assumptions embedded in (11) will be relaxed subsequently. The assumption of continuous PPP is relaxed in the next section that will consider the role of sticky prices in a Dornbusch model. The version of the model that assumes continuous PPP is referred to as the flexible price version o f the monetary model.

Strictly speaking, this flexible price version o f the monetary model does not require PPP to hold in level form. It requires only that PPP holds in an expected sense. PPP holds in an expected sense if the real exchange rate follows a random walk. As documented by a number o f empirical studies [Roll, 1979; Frenkel, 1981; Darby, 1981; Mishkin, 1981, p. 699; Hakkio, 1984] it is difficult to reject the hypothesis that the real exchange rate follows a random walk, the flexible price model can therefore not be rejected out o f hand.

The assumption that desired money balances are always equal to actual balances, is relaxed in the tests that use quarterly data since the form o f the adjustment assumed to govern the money market depends on the time horizon considered. For annual data it is assumed that the money market adjusts fully, for quarterly data it is assumed that actual balances adjust gradually to desired balances. The assumption of uncovered interest parity (including a constant risk premium) ~ will be relaxed in the section that considers portfolio balance

4 This result does not imply, per se, that these models are not able to account for the observed variability of exchange rates. The poor performance of these models might be due to econometric problems which would not affect the results of this paper.

5 The existence of a constant risk premium would not affect the analysis in any way as it would only lead to another constant in the exchange rate equation and would have no effect on the variability measures.


models , where it is assumed, instead, that the risk p remium is a funct ion o f asset stocks.

Equat ion (11) can be rewritten in the general form of (5):

st = [ m t - k - 4,yt - pt* r o'it] + o[E,(St+l) - s,]. (12)

Accord ing to this model , the " fundamenta ls" that determine exchange rates are thus given by Xt ------ m, - k - 4 , y t - p t * + o i t * . The current perfect foresight exchange rate, s,*, can thus be written as:

T-t ~ ) j or T-t+l l _ ( x,+,] + STy,. (13) st* = I + a l + a ( ~ o )

The naive forecast used in this analysis is based on the a s sumpt ion that the fundamenta ls are expected to remain cons tan t forever. This forecast is not as naive as it seems, since for a number o f countr ies money supplies seem to follow a process that is close to a r a n d o m walk. The naive forecast thus implies:

o _ 1 '~ ( ~ (14) st l + o j=0 l + o

A first test of the inequalit ies (10) and (11) thus requires only calcula t ion o f s, ~ and s~* which can then be used to calculate the sample variances o f (s~* - s,) and (s~* - s~~

The figures in Table la repor t the results of a first such test on yearly da ta for various D M exchange rates for the 1973-1984 period. 6 In this test the parameters of a previously es t imated money d e m a n d funct ion for G e r m a n y were used to obtain estimates for 4, and o. The regression results of the money d e m a n d est imate are repor ted in the Appendix; these results show that var ia- t ions in income ( G N P at 1980 prices) and interest rates ( interbank rates) can explain 94 percent of the variance of real money (M 1 divided by the consumer price index) in Germany . The point est imate for 4' is equal to 1.18 and the poin t estimate for o is equal to 1.32. 7

It is apparent that for all of the bilateral D M exchange rates analyzed, at least one o f the inequalities (7) and (8) is always violated. Since violat ion o f only one inequali ty is sufficient to reject the efficient marke t hypothesis, this table implies that the joint hypothesis of an efficient foreign exchange market and the

6 T is equal to 1984 so that the exchange rate at the end of 1985 represents ST+I. In this, as in other tests, the "equilibrium" PPP level was set equal to the average of the sample period.

7 Preliminary sensitivity analysis indicates that changes in the income elasticity of money demand do not influence the results to any appreciable extent. The results are, however, affected by changes in the o, the interest semi-elasticity of money demand because a/(l+a) determines the discount factor used to discount future monetary factors. The point estimate of a = 1.32 gives a discount factor equal to 0.56.

280 Wel twi r t scha f t l i ches Archiv

flexible price m o n e t a r y mode l is i n a d e q u a t e to exp la in the observed var iab i l i ty of exchange r a t e s : This table also seems to suggest tha t the re ject ion o f the m o n e t a r y mode l is s t rongest for the C a n a d i a n a n d U.S. do l la r a n d in genera l is s t ronger for the n o n - E M S currencies like the Swiss f ranc or the British p o u n d than for the EMS currencies. 9

Tab le 1 b con ta ins the results o f a n o t h e r test o f the flexible price vers ion o f the m o n e t a r y model . This test is based on quar te r ly da ta for the f u n d a m e n t a l s f rom Q1 1974 to Q3 1984. Th e basis for this test is a m o n e y d e m a n d func t i on for G e r m a n y that was es t ima ted for the same per iod . l~ In con t r a s t to the test us ing a n n u a l data , however , in this case it is a s s u m e d that , wi th in each quar te r , ac tua l m o n e y ba lances adjus t g r adua l ly towards desired ba lances accord ing to the par t ia l ad jus tmen t process:

m, - mt-i = r '[m, d - m,-~], (15)

where m~ d are desired m o n e y ba lances which d e p e n d o n income a n d interes t rates as specified in (10). The a s s u m p t i o n o f a par t ia l a d j u s t m e n t in m o n e y balances seems a na tu ra l one to m a k e in tests us ing quar te r ly da ta since all m o n e y d e m a n d est imates tha t are based on quar te r ly da t a con ta in lags to a ccoun t for par t ia l ad jus tmen t . However , this pers is tent f ind ing of lagged a d j u s t m e n t has of ten no t been t aken in to a c c o u n t in tests o f the m o n e t a r y mode l o f exchange rate d e t e r m i n a t i o n us ing qua r t e r ly da t a (see for example F ranke l [1979]; Meese, Rogof f [1983]).

The on ly consequence o f this specif icat ion o f the m o n e y marke t equil i - b r i u m is tha t the m o n e t a r y fac tor for qua r t e r ly da t a c o n t a i n s a weighted average o f past a n d current m o n e y ins tead o f jus t cur ren t money . Solving (15)

8 Indeed for all currencies considered here, the sample mean square of the difference between the perfect forecast and the naive forecast exchange rate (st* - s, ~ is much smaller than the sample mean square of the difference between the naive forecast and the actual exchange rate (s, ~ - sd. However, the sample variance of the difference between the perfect forecast and actual exchange rate (s,* - sd is also always much smaller than the variance of the difference between the naive and the actual forecast exchange rate (st ~ - sd. This tends to give some support to the monetary model since it indicates that the market takes future monetary factors into account. Graphs of st, s, ~ and s** for the DM exchange rates used in Table la from 1961 to 1973 show that the fundamentals that determine s, ~ and s,* move very smoothly and that the naive forecast, st ~ is always very close to the perfect forecast, st*. This reflects the fact that money supplies are much more forecastable than exchange rates. The graphs also show that the monetary model is quite successful in tracking the movements of the exchange rates of the EMS members France, Belgium, Italy, and Denmark. The failure of the model in these cases is thus not due to an inability of the model to predict the trend in exchange rates. The graphs are available upon request from the author.

9 The test statistics used in this table (and the following tables as well) are random variables. A precise statistical statement about the "significance" of the results could be made only by taking into account the distribution of the test statistics.

,0 See the second part of the Appendix for the results of the estimate.


Table 1 - Test for Excess Volatility o f Selected Deutsche Mark Exchange Rates: The Flexible Price Monetary Model"

Country b

Belgium Canada Denmark France Italy Japan Netherlands Sweden Switzerland United Kingdom United States


(1) (2) (3) (4) ' t '

- [ ~ , . - ~ ,~162 5 - [ ~ s , . - s , r 5 - [ ~ , - ~ ,~162 s max [(2), (3)] (1)

a. Annual data c

4.04 4.16 6.00 1.49 4.63 19.81 22.89 4.94 6.06 3.38 7.75 1.28 6.58 5.37 8.24 1.25

i 1.21 9.63 17.03 1.52 7.92 13.55 20.05 2.53 2.68 2.60 4.05 1.51 6,81 8.15 11.39 1.67 3,58 9.92 t0,94 3.06 8.86 14.22 19.04 2.15 5.55 17.89 23.10 4.16

b. Quarterly data d

8.63 3.81 9.68 1.12 9.22 18.66 23.70 2.57

13.18 3.04 14.19 1.08 12.61 5.26 12.31 0.98 21.27 7.74 25.53 1.20 13.83 9.70 21.46 1.55 6.72 2.69 7.42 1.10

13.15 7.47 16.15 1.23 6.75 9.55 12.95 1.92

15.23 12.16 21.31 1.40 8.51 16.23 23.20 2.73

' The numbers are equivalent to percentage changes since they represent the standard deviations of logarithms. - b Indicates the currency of the exchange rate vis-A-vis the Deutsche mark. - ' Annual data on fundamentals 1973-1984, end-of-period exchange rate 1985. - * Quarterly data on fundamentals QI 1973-Q4 1984, end-of-period exchange rate Q4 1985.

for m, ~ implies that the exogenous forcing variable becomes:

X, = lint + mt-~ ( F - 1 ) ] / l ' - k - pt* - Syt + oit*. (16)

The formulae for st ~ and s,* remain the same. The results using quarterly data are presented in Table lb. The simple

monetary model is still rejected in 10 out of the 11 cases considered, since, except for France, at least one of the two inequalities (7) and (9) is always violated. It is also apparent from this table that the rejection of the simple monetary model is only marginal for the EMS countries (Belgium, Denmark ,

282 Weltwirtschaft l iches Archiv

and The Netherlands) which operate within the narrow band of the EMS and were members of the snake before the inception of the EMS. However , the strong rejection of the simple mone ta ry model for the D M exchange rate vis-fi-vis the Canadian and U.S. dollars, the Japanese yen, the British pound, and the Swiss franc seems to imply the mone ta ry factors alone are not sufficient to explain the variability of these exchange rates.

IV. The Role o f S t i cky Prices

This section uses a model with sticky prices to check whether the inability of the simple mone ta ry model to explain the exchange rate variability that was found in the preceding section is due to stickiness in nominal prices. The specific model used here is taken f rom Mussa [1985], but it is very similar in spirit to the so-called Dornbusch model.

The only difference between the simple mone ta ry model o f the preceding section and the model used in this section is that it is no longer assumed that PPP holds instantaneously. Instead, it is assumed that the real exchange rate (st + pt* - P0 moves towards its equil ibrium value at a rate equal to (1 - /3) :~

E, (s,+~ + pt+l* - pi l l ) = (1 - / 3 ) (s, + p,* - p,). (17)

The model also contains a money demand function identical to (10). This money demand function can be t ransformed to give an expression containing the real exchange rate; after using the interest pari ty condition this yields:

st (1 + o) = oEt(s,~-,) + [mr - k - ~by, - pt* + air*] + qt. (18)

The expression in the square brackets represent the same, exogenous mone ta ry factor as in the previous section. By using (17), (18) can be iterated forward to yield an expression for the perfect foresight exchange rate: 12

1 + / 3 o ~ O )J Xt+j ] _]_ .~.._o (p t , - pt)" (19) s t * = B o ( l + o ) [ ( 1 + o

This equation shows that the exchange rate depends on an initial condition given by the domestic and the foreign price level and a discounted sum of

~ Prices adjust slowly from PPP according to:

E,(p,,,) - p~ =,8 (S,,p* - p,) + [E, (st§ + p,+fl) - (s, + p,*)].

The second term in this equation allows the domestic price level to rise in line with the foreign price level if the real exchange rate is at its equilibrium level. (The equilibrium level of the real exchange rate has been normalized to zero in this equation.) The parameter/3 indicates how much prices react to the current disequilibrium of the real exchange rate.

z2 See the first part of the Appendix.


present and future fundamentals. The discount factor is the same as in the simple monetary model, however, the discounted sum is multiplied by a factor that is greater than in the simple monetary model.

Compar ing (19) with (13) shows that for a given variance of the discounted sum of the monetary factors, the variance of the perfect foresight exchange rate with sticky prices is greater than the variance of the perfect foresight exchange rate with flexible prices. This is, of course, the result o f the overshooting phenomenon. Neglecting the variance of (pt* - p,) the ratio of the variances of the sticky price exchange rate, denoted by Var (ssp*), to the variance of the flexible price exchange rate, denoted by Var (SFp*) is equal to:

Var(ssp*) 1 + / 3 0 2 Var(srp) -- ( - - - ~ ) > 1. (20)

However , for the volatility tests it is again necessary to t runcate the sum contained in (19). The resulting expression is calculated and repor ted in the Appendix) 3 The naive forecast, st ~ is again based on the assumpt ion that the forcing variable is expected to remain constant forever. This implies:

1 1 + / 3 o s~~ 13o X~ + Bo (P~* - PO. (21)

The tests are again based on the relative variances of(st* - s,~ (st* - st) and (st - s,~ I f markets are efficient and if the sticky price model is an accurate reflection of the way exchange rates and prices are set, the variances o f ( s t * - St)

and (st - st ~ should still obey the inequalities (7) and (8). Table 2a contains the results o f a first test o f volatility using the sticky price

model. It is again based on yearly data for 1973-1984. In this test/3 was set equal to 0.5 and all other parameters and variables are the same as in the test o f the flexible price model.14 By compar ing with the first columns of Table I a and lb it is apparent that the sticky price model predicts a much higher variability of exchange rates because the variance of (s* - s ~ is much higher in the sticky price model.~5 This test clearly rejects the sticky price version of the mone ta ry model for the non-EMS currencies. However , the rejection is less strong than in the flexible price case since the values in the last columns of Table 2a are lower than the values in the last column of Table la; nevertheless it is apparen t that

~3 See equation (A.6) in the first part of the Appendix.

~4,8 = 0.5 implies that in one year prices adjust by one half of the initial difference between the existing price level and the price level that would be obtained if all prices were flexible (i.e., the PPP level).

t5 With/3 = 0.5 and e = 1.3 the magnification factor (see equation (20)) is about 5.8.

284 W e l t w i r t s c h a f t l i c h e s Arch iv

Tab le 2 - Test for Excess Volatility o f Selected Deutsche Mark Exchange Rates: The Sticky Price Monetary Model"

Country b



(1) (2) (3) (4) I I I

- [~s~* - s,~ �9 S - [~s~* - s0-' ] �9 5 - [~s, - s,~ �9 5 Max [(2), (3)] (I)

a. Annual data c

10.11 5.64 11.71 1.16 11.76 21.64 29.77 2.53 15.40 7.86 19.63 1.27 16.88 6.92 17.96 1.06 28.86 12.91 34.92 1.21 18.13 12.22 25.89 1.43 6.82 6.01 lO.l I 1.48

17.36 10.68 22.72 1.31 8.98 12.34 17.19 1.91

22.33 13.19 24.88 1.I 1 12.38 14.37 25.12 2.03

b. Quarterly data d

13.60 4.30 13.83 1.02 14.15 19.41 29.92 2.12 15.40 7.86 19.63 1.27 21.34 6.99 19.51 0.91 35.87 10.18 41.60 1.16 15.57 8.99 21.21 1.36 11.48 4.82 12.42 1.08 20.02 9.05 24.07 1.20

7.13 11.03 14.55 2.04 25.81 11.74 28.67 1.11 10.68 13.85 21.82 2.04

�9 The numbers are equivalent to percentage changes since they represent the standard deviations of logarithms. - b Indicates the currency of the exchange rate vis-:~-vis the Deutsche mark. - ' Annual data on fundamentals 1973-1984, end-of-period exchange rate 1985. - d Quarterly data on fundamentals QI 1973-Q4 1984, end-of-period exchange rate Q4 1985.

the inequal i ty (11) is re jec ted fo r all coun t r i e s (whereas the inequa l i ty (10) is

rejected only in three ou t o f e leven cases). 16

Tab le 2b con ta ins the results o f a n o t h e r test o f the s t icky price mode l , this

test is based on quar te r ly d a t a and uses the s a m e m o n e y d e m a n d es t imates used

in Tab l e lb . In this tes t /3 was set equa l to 0.16 pe rcen t o f the initial d i f fe rence

t6 It seems that the degree to which the inequalities (7) and (8) can be rejected grows with/3, therefore it might be possible to accept (7) and (8) for values of/3 much closer to zero. But for values of/3 below 0.5 the perfect foresight and the naive forecast exchange rates sometimes have unrealistically extreme values.


between the existing price level and the price level (i.e., PPP) that would be obtained if all prices were flexible. The value of/3 = 0.16 was chosen to make Table 2b comparable to Table 2a because it implies that within four quarters (one year) about 50 percent of the disequilibrium is eliminated. 17 Comparing Table 2b with Table lb it seems that the results are very similar, the sticky price version of the monetary model is rejected for all countries, except for France. The rejection is again only marginal for the EMS countries and much stronger for the non-EMS countries. Overall, however, the numbers in the last column of Table 2b are only a little lower than the corresponding numbers in Table lb. This result and the comparison of Table 2a with Table la indicate that the introduction of sticky prices does not improve the performance of the monetary model in terms of its ability to predict the actual degree of exchange rate volatility.

V. Portfolio Balance Models

The two versions of the monetary model used so far, both incorporated the interest parity condition, which implies that the interest rate differential is equal to the expected rate of change of the nominal exchange rate. The preceding analysis and tests are also valid if there exists a constant risk premium, indeed a constant risk premium would just add a constant to the various exchange rate equations and would thus leave the variability measures unaffected. The interest parity condition is usually obtained under the assumption that domestic and foreign bonds are perfect substitutes. In this section this assumption is relaxed, instead it is assumed that domestic and foreign bonds are imperfect substitutes because of exchange risk. The precise form of the risk aversion is not analyzed here; it is simply assumed that investors adjust the proportion of their bond portfolio that go to domestic and foreign bonds respectively as a function of the expected return differential. Is In logarithmic form, this is written as:

b~ - st - f~ = r [i~ - it* - E, (s,, 1 - st)], (22)

where bt represents the logarithm of the stock of bonds denominated in domestic currency and ft the logarithm of the stock of bonds denominated in foreign currency. The parameter r is related to the risk aversion of investors and determines the relationship between the excess return on domestic bonds and the proportion ofdomestic bonds investors wish to hold in their portfolios. It is also assumed that the home country, in this case Germany, is small in relation

~7 Since for quarterly data a = 2.5 this implies that the magnification factor (see equation (20)) is given by about 12.

z8 The microeconomic foundations of this relationship are derived in Frankel [1983; 1985b].

286 W e l t w i r t s c h a f t l i c h e s A r c h l y

to the rest of the world and that domestic residents are the only investors to hold bonds, denominated in domestic currency, thus bt is equal to the stock of domestic bonds. Since investors are only concerned with their net position only outside, that is government bonds enter bt. The only way in which domestic residents can acquire foreign bonds is via a current account surplus, f, is thus equal to the stock of cumulated past current account deficits.

There are two ways to subject the portfolio balance models to a volatility test. The simplest way to obtain an expression for the exchange rate would be to solve (22) for the exchange rate and integrate forward. This yields:

i E, [b,+i - f,§ - r(i,+, i,+,*)] ( 1--T-Ty. (23) S , - l + r

This equation provides a test of the pure portfolio balance model since it uses only the variables that are most important to the portfolio approach: such as interest rate differentials and relative bond supplies. 19

For the actual tests it is again assumed that the naive forecast is based on the expectation that current fundamentals will not change, this implies that the naive forecast exchange rate is given by:

s, ~ = b, - f, - r (i, - i,*). (24)

The perfect forecast exchange rate is again given by a truncated version of the equation that determines the market exchange rate:

1 T-t s

[b,+,- f,+j - r (i,+j - i,+j*)]( l - - ~ r )J s , * - l + r j = 0 (25)

T ) T-t+ 1 + ( 1--47 ST+,.

In contrast to the monetary model, this pure portfolio balance approach implies that the forcing variable contains only relative asset supplies and interest rates. The pure portfolio balance framework can then be tested by selecting values of r and the precise definition of the asset supplies b and f.

For the actual tests it proved difficult to select values for r because regression estimates of r often yield negative values and have almost always large standard errors. However, it is also possible to obtain an estimate of r by using an assumed value for the coefficient of risk aversion and the observed variances of exchange rates in the mean variance optimization approach. In the tests developed in this paper, r was arbitrarily set equal to 30 for all countries since this value represents a mean value found by Frankel [1985], using the mean variance approach for several different currency pairs. The data on asset

)9 Equation (23) is not a complete exchange rate equation in the sense that it does not specify what anchors expectations about present and future interest rates.


supplies was taken from International Financial Statistics and Government Finance Statistics (GFS). It was assumed that the assets that enter (22) refer to the total, privately held, government debt. 2~ Thus, b refers to the debt of the German government held by the private sector (German and foreign residents). 21

Table 3 presents the results of this test of the pure portfolio balance model for the eight currencies for which data on asset supplies were available using yearly data from 1973 to 1983. Recall that the first co lumn of the table shows the root mean squared difference between the naive and the perfect forecast. The values in the first co lumn of Table 3 are very large, indeed more than ten times the numbers in the first co lumn of the preceding tables. This suggests that the methodology applied here is only of limited usefulness in this case, because the naive forecast is too far from the perfect forecast. The reason for this is not that relative bond supplies are extremely volatile, instead the large discrepan- cies between the naive and the perfect forecast are a consequence of the large value o f t . With r--- 30, a change in the interest rate differential of, e.g., 3 percent (at unchanged relative bond supplies) leads to a j ump in the naive forecast

Table 3 - Test for Excess Volatility of Selected Deutsche Mark Exchange Rates: The Pure Portfolio Balance Model"

Country b

Belgium Canada Japan Netherlands Sweden Switzerland United Kingdom United States

(1) (2) (3) (4) I I I

_ [~,~. _ ~ 2 ] . s - [ ~ , * - s,)2] �9 5 - [~s, - ~,~2]. 5 M a x [(2), (3)] (1)

98.26 4.02 96.49 0.98 98.84 35.34 118.87 1.20

124.96 19.18 120.37 0.96 67.37 2.50 68.76 1.02

144.61 10.04 152.79 1.06 122.40 13.93 131.41 1.07 160.91 19.91 176.76 1.10 92.08 32.06 89.01 0.97

�9 The numbers are equivalent to percentage changes since they represent the standard deviations of logarithms. Annual data on fundamentals 1973-1984, end-of-period exchange rate 1985. - b Indicates the currency of the exchange rate vis-:~-vis the Deutsche mark.

20 The data used were taken from GFS, Table 7, which gives outstanding debt by type of debt holder (consolidated central government). Privately held debt was defined as total debt minus debt held by the monetary authorities or other levels of government.

2~ One way to motivate this choice is to assume that all government debt is issued in national currency and that the private sector regards government debt as net wealth. In this case, the bond stocks used here represent the net wealth of the private sector invested in securities with different currency denominations.


exchange rate of more than 100 percent. (The natural logarithms of the exchange rate would jump by 0.9, this corresponds to a jump of 145 percent.) The perfect forecast exchange rate, however, does move only very little because the discount rate used to discount the end-of-the-observation-period exchange rate is very close to one (0.9677 = r/(l + r)), and the observation period is rather short (11 years, for bond supplies only annual data is available). The combination of these two factors implies that even at the beginning of the observation period, the calculation of the perfect foresight exchange rate (see (25)) is dominated by the influence of the discounted end-of-period exchange rate, since the discount factor applied to the end-of-period exchange rate is still close to one, about 0.7 (i.e., 0.9677 raised to the power eleven). In the preceding tests of the monetary model the discount factor was much lower so that the end-of-period exchange rate did not influence the calculation of the perfect foresight exchange rate strongly even up to two years before the end of the observation period.

The large value of r used here, which corresponds to the general finding that assets denominated in different currencies are highly substitutable, thus leads to a very low power of the test. This is borne out in the last column of Table 3, where the values around one indicate that this test is not able to reject the portfolio balance model.

Another test of the portfolio balance model can be obtained by using (22) to solve out for the domestic interest rate and combining the result with the monetary approach and the portfolio balance models. This can be done for both versions of the monetary approach (flexible price and sticky price) considered here.

Equation (22) implies that the domestic interest rate is given by:

1 it = -F- [ b t - f, + ri,* + r E, (st+0 - (I + r) st]. (26)

This equation can be combined with the basic money demand equation in the monetary approach, equation (10), to yield:

o [b, - fi + tit* - Et(st+,) + (1 + r )sO. (27) m, d = k + ~ b y t + p t - u

For the flexible price version of the monetary model it is assumed that purchasing power parity holds at all times, this implies pt = St + p t * , using this condition in (27), assuming money market equilibrium, i.e., mta = mr' = m t and iterating forward, one obtains an expression for the actual exchange rate:

r ~ Et[Xt+j + (bt+j - ft+j)][ ~. + o (1 + r) ]j (28) s t= r + o ( l + r )


To save on notation the exogenous monetary forcing variable is defined as in the preceding sections, that is, Xt -- mt - k - ~yt - p,* + oit*. Equation (28) shows that the incorporation of the portfolio balance approach in the monetary approach leads to two modifications: (i) the fundamentals that determine the exchange rate include 1:elative bond supplies besides money supplies and the factors determining money demand; and (ii) the factor used to discount future fundamentals is also a function of the parameter r which is related to the risk aversion of investors. In general, with r being positive, the discount factor is smaller in this combined model than in the flexible price, pure monetary approach model. This implies that in this combined model future fundamentals are discounted more than in the flexible price, pure monetary approach model.

The flexible price version of the combined portfolio-balance-monetary- approach model leads to the following expression for the naive forecast exchange rate:

r o (b , - f,)]. (29) s, ~ = ~ [ x , + u

And the truncated form of the perfect forecast exchange rate is given by:

T-t OT O r + o ( l r + r ) ~ ( r + d ~ + r ) Y[Xt+j+7 St* (b,+j f,-j)]

O T T-t+ 1 + r + o (1 + r) SX+l. (30)

Table 4a contains the results of the test of the combination of the portfolio balance approach with the flexible price version of the monetary model. These results are very similar to those obtained for the monetary model alone. (This test uses the same values for o and ~b as Table la.) The reason for this outcome lies again in the magnitude of r. With r=30, the elasticity of the naive forecast exchange rate with respect to changes in relative bond supplies is equal to 0.088 (=o/r) . The last column of Table 4a thus suggests, as Table la, that the flexible price version of the monetary model, even in conjunction with the portfolio balance approach is not able to account for the variability of the exchange rates analyzed here. The rejection is again weaker for the EMS currencies (the Belgian franc and the Dutch guilder) than for the non-EMS currencies.

The sticky price version of the monetary model can also be combined with the portfolio balance approach. The only difference to the flexible price model is that in the sticky price version, PPP is no longer assumed to hold, instead the real exchange rate (st + pt* - pt) is assumed to follow Et(St+l + pt+l* - pt+l) = (1 - BXst+p,*-pt)(see equation (17)). Using this adjustment rule of the real exchange rate in (27) yields:

290 W e l t w i r t s c h a f t l i c h e s A r c h l y

s, r + a-(l + r) r j=o

r (31) + q t r + o ( l + Br) "

The naive forecast exchange rate is thus equal to:

[ r + o (1 +/3)] r o s'~ = ~ (1 +/3r) (r + 0) [X, + r (b, - f0] (32)

r + (P'* - P') r + a (1 + /3r ) "

And the perfect forecast exchange rate is equal to:

1 - D D T-, a D .y s t * = ( D - D T-t+' ){ (1 - /3 ) o ~ [ X , + J + r ( b t - f t ) ] ( 1 - - - ~

+ (pt* pt) 1 - D T - t + l -- "3i- ST+I ( )T-t+l}. (33)

1 - D 1 - / 3

Table 4b contains the results of a test of a model that combines the sticky price version of the monetary model with the portfolio balance approach. This test uses the same data (yearly, 1973-83) and parameters as Table 4a. Further- more, to make this table comparable to Table 2b, which contains the results of the sticky price version of the monetary model, the price adjustment parameter,/3, was again set equal to 0.5. The last column in Table 4b indicates that it is still possible to reject this combined model in all of the eight cases for which data is available. It also appears that for most currencies the values of the last columns of Table 2a and of Table 4b are quite similar. Thus, the introduction of portfolio balance considerations does not seem to dramatically improve the power of the monetary model to explain the observed degree of exchange rate volatility.

V I . C o n c l u s i o n s

This paper has examined the question whether it is possible to explain the observed variability of exchange rates in terms of the so-called fundamentals. If money supplies, prices, interest rates, and relative asset supplies are taken to be the fundamentals that ought to determine exchange rates, the results of this paper suggest that the freely floating exchange rates are considerably more volatile than one could justify from the behaviour of the fundamentals.

But the results also suggest that there is a marked difference in this respect between the major freely floating exchange rates, such as the exchange rate of the DM vis-a-vis the U.S. dollar, the yen, and the Swiss franc, and the intra- EMS exchange rates. The variability of the intra-EMS exchange rates can be


Table 4 - Test for Excess Volatility of Selected Deutsche Mark Exchange Rates: The Combined Portfolio Balance/Monetary Model"

Country b



(1) (2) (3) (4) i 2 t Max [(2). (3)1 _ [ ~ . _ o ) 1" 5 - [ ~ s , ' - ~)21" 5 - [ ~ s , - s , ~ 2 �9 5

(1)

a. Flexible price monetary model

4.09 4.19 6.12 1.50 7.47 15,96 19.99 2.68 8.69 10.5 ! 16.86 1.94 2.58 2.56 3.93 1.52 5.86 9.38 12.12 2.07 4.44 9.97 12.01 2.71 8.55 13.78 18.44 2.16

10.51 11.61 19.01 1.81

b. Sticky price monetary model

9.69 5.09 10.76 1.11 14.53 20.72 25.90 1.78 18.67 10.51 16.86 1.94 6.34 5.46 8.95 1.41

14.60 12.84 22.25 1.52 10.73 12.29 19.14 1.78 20.71 12.86 23.14 1.12 21.09 15.00 23.86 1.13

' The numbers are equivalent to percentage changes since they represent the standard deviations of logarithms. Annual data on fundamentals 1973-1984, for the flexible price version and 1973-1983 for the sticky price version, end-of-period exchange rate 1985. - b Indicates the currency of the exchange rate vis-a-vis the Deutsche mark.

explained in terms of the fundamenta ls , whereas this is not the case for the major freely floating exchange rates. This difference in behav iour suggests that the EMS has been successful in reducing the variabi l i ty o f i n t r a - E M S exchange rates to the min imum that is a t ta inable given the differences in policies between the member states. In contrast , the var iabi l i ty of the major freely f loat ing exchange rates cannot be explained in terms of the fundamentals . This does not necessarily imply that markets a lways overreact , but it does suggest that the models of exchange rate de te rmina t ion that are avai lable today cannot explain the observed variabil i ty of exchange rates.


Appendix

1. Derivation of the Expression for st* tbr the Sticky Price Monetary Model

Equation (18) in the text can be iterated one step forward to yield: 2

_ _ O

1 [X, + q, + ~ ( X t + l .9[- q,+,) + l__~oEt(s,+z)]. (A.1)st-- 1 + o 1 + o t

It is apparent that further forward iteration of(A. 1) will lead to two infinite sums; the stable solution then implies that the current exchange rate is given by:

00 O " | o 1 [Z_ ~ ( 1__~o yEt(qt+j)]. 1 [E0 (l___~oYEt(X,+j) ] + (A.2) s , - l + o

However, using (20) in the text, the second infinite sum in this equation can be simplified. Thies yields an expression for the current nominal exchange rate as function of the discounted sum of future monetary factors and the current real exchange rate: 22

l Y - - V | o + 1 qt [~(1 + o "Et(xt+j)] 1 + o (A.3) st-- 1 + o (1-/3) o

1 1 + o

Using the definition of the real exchange rate and taking the realized values of the monetary forcing variables yield an expression for the perfect foresight exchange rate:

(A.4) st* -- 1 +/30 [y~~ ( .---:~)J~ X,+j] + 1 (pt* - pt). /3o(1 + o) -j=0 1 + o - /30

O' ' .~_( a ]T-t+l _ 1 [X'(Xt+j + q,+j) (1---~-~oy] "1--+-~o" ST+I. (A.5) st* 1 + o j=0

This can be transformed into:

[(1 - B)o] T-t+l 1--

T-t O 1 + O 1 [jE=o Xt+j( 1--~o Y] +qt (A.6) st*-- 1 + o 1+o /3

( 0 "}T-t+ I + " l ' i ' - ~ O " ST+, .

22 At this stage, income which is one of the variables determining money demand, is still taken exogenous.


Using the definition of the real exchange rate, this yields an equation that is the finite horizon equivalent to (16) in the text.

1 + o 8 1 (A'7) s t*= + ( ~ o ) x _ , + l { 1 -~o ~0

08 1 + a ( 1 - 8)0 )~_,+,

1-( O T- I ~- 1

+ ( ~ ) S,+, + (,10t * - pt) 1 + o 8 }"

2. Money Demand Estimates for Germany

The two money demand estimates for Germany used in the tests of this paper are based on data from The InternationalFinancialStatisties of the IMF. Line 34, i.e., M 1, was used for money, line 99 a.r., GNP at 1980 prices, was used for income, line 60 b.s., interbank rate, was used for the interest rate and line 64, consumer price index, was used for prices. The dependent variable was real M 1, i.e., the natural logarithm of M 1 divided by the CPI and the two explanatory variables were the natural logarithms of income and the interest rate.

Using yearly data from 1970 to 1984 the result was (standard errors in parentheses):

real M 1 - -7.62 + 1.18 income - 1.32" interest rate (0.61) (0.08) (0.29)

R2=0.94 SEE = 0.03 D.W. = 1.5

In the estimation using quarterly data from Q1 1973 to Q4 1984 the explanatory variables also included a lagged dependent variable to capture the lagged adjustment. The point estimates were little affected by the choice of the correction for seasonality. The results reported here are based on non-seasonal- ly adjusted data for MI but include three seasonal dummies:

real M I = - 1.6 - 0.11 Dummy Q1 - 0.028 Dummy Q2 (0.8) (0.07) (0.006)

0.063 Dummy Q3 + 0.227 income - 0.521 interest rate (0.006) (0.089) (0.087)

+ 0.800 lagged real MI (0.064)

~2= 0.9774 SEE = 0.015 DWH = 0.695

294 Weltwirlschaftliches Archiv

These two regressions were tested for higher order autocorrelation, het- eroskedasticity, normality and structural stability. The tests indicate that it is not possible to reject the hypotheses that there is no autocorrelation, that the errors are homoskedastic and normal and that there is no structural break. The simple money demand functions seem therefore well specified. Details o f the results of the diagnostic tests are available from the author upon request.

References

Bini-Smaghi, Lorenzo, "Have Exchange Rates Varied Too Much with Respect to Market Fundamentals?" Giornale degli Economisti e Annali di Economia, January-- February 1985, pp. 45-54.

Boughton, James M., The Monetary Approach to Exchange Rates." What Now Remains? International Monetary Fund, DM/86/11. Washington, February 1986.

Darby, Michael, Does Purchasing Power Parity Work? Proceedings of the Fifth West Coast Academic/Federal Reserve Economic Research Seminar. Federal Reserve Bank of San Francisco 1981.

Frankel, Jeffrey A., "On the Mark: A Theory of Floating Exchange Rates Based on Real Interest Differentials". The American Economic Review, Vol. 69, 1979, pp. 610-622.

-, "Estimation of Portfolio-Balance Functions that are Mean-Variance Optimizing". European Economic Review, Vol. 23, 1983, pp. 315-327.

-, J.H. Stock [ 1985a], Regression vs. Volatility Tests of the Efficiency of Foreign Exchange Markets. Unpublished paper (January 1985).

- [ 1985b], 171e Implications of Mean- Variance Optimization for Four Questions in lnterna- tionalMacroeconomics. NBER Working Papers, 1617. Cambridge, Mass., May 1985.

Frenkel, Jacob, "The Collapse of Purchasing Power Parity During the 1970's". European Economic Review, Vol. 16, 1981, pp. 145-165.

Hakkio, Craig, "A Re-examination of Purchasing Power Parity: A Multi-Country and Multi-Period Study". Journal of International Economics, Vol. 17, 1984, pp. 265-278.

Huang, Roger D., "The Monetary Approach to Exchange Rate in an Efficient Foreign Exchange Market: Tests Based on Volatility". The Journal of Finance, Vol. 36, 1981, pp. 31--41.

lsard, Peter, Alternative Approaches to the Empirical Modelling of Exchange Rates: Where is the Profession Now? Paper presented at Brookings Institution conference, March 10--I l, 1986.

Mankiw, N. Gregory, David Romer, Matthew D. Shapiro, "An Unbiased Reexamination of Stock Market Volatility". The Journal of Finance, Vol. 40, 1985, pp. 677-689.

Meese, Richard A., Kenneth Rogoff, "Empirical Exchange Rate Models of the Seventies: Do They Fit Out Of Sample?" Journal oflnternationalEconomics, Vol. 16, 1983, pp. 3-24.

-, Was it Real? The Exchange Rate-Interest Differential Relation; 1973-84. Unpublished paper May 1985.


Mishkin, Frederic, "Are Real Interest Rates Equal Across Countries? An Empirical Investigation of International Parity Conditions". Journal of Finance, Vol. 39, ! 984, pp. 1345-1358.

Roll, Richard, "Violations of Purchasing Power Parity and Their Implications for Efficient International Commodity Markets". In: M. Sarnat, G. Szego (Eds.), Inter- national Trade and Finance, Vol. 1. Cambridge 1979.

Wadhwani, Sushil B., Are Exchange Rates "Excessively" Volatile? London School of Economics, Centre for Labour Economics, Discussion Paper 198, July 1984.

Z u s a m m e n fa s s u n g: Zu den Schwankungen von Wechselkursen: Tests von monet/aren und Portfolio-Modellen der Wechselkursbestimmung. - Anhand einer Methodologie, die aus der Literatur des Finanzwesens iibernommen wurde, wird in diesem Aufsatz getestet, ob die beobachteten Schwankungen der Wechselkurse durch die beobachteten Schwankungen der Determinanten erkl~rt werden krnnen. Gem/aB den monet~iren und Portfolio-Modellen sind diese Determinanten: Geldversorgung, Einkommen, Unterschiede in den Inflationsraten und Angebot von Vermrgenstiteln. Die Ergebnisse scheinen unabh~ingig davon zu sein, welches Modell benutzt wird. Sie zeigen, dab die Ver/anderungen der Wechselkurse innerhalb des EWS mit Hilfe von Ver~inderungen der Determinanten erkl/art werden krnnen, dal~ aber die Ver~inderlich- keit anderer Wechselkurse (US$/DM, Yen/DM, sfr/DM) viel grrl3er ist, als aufgrund der Schwankungen der Determinanten zu erwarten w/are.

R 6 s u m 6 : Sur la volatilit6 des taux de change: tests des modules monrtaires et de portefeuille de la drtermination du taux de change. - L'auteur applique une mrthodologie drrivre de la littrrature des finances pour tester si la variabilit~ observre des taux de change peut ~tre expliqure par la variabilit6 des facteurs fondamentaux. Les modules monrtaires et de portefeuille sugg~rent des variables fondamentales suivantes: masse monrtaire, revenu national, diffrrence en inflation et I'offre des valeurs actives. Les rrsultats semblent ~tre indrpendants du module appliqur. Ils indiquent que la variabilit6 des taux de change intra-SME peut ~tre expliqure en terme des variables fondamentales, mais la variabilit6 des autres taux de change (US$/DM, Yen/DM, Swiss Frank/DM) est plus grande qu'on pourrait l'expliquer par des telles variables.

R e s u m e n: Sobre el test de volatilidad de tipos de cambio aplicado a modelos monetarios y de "portfolio balance" de determinacirn del tipo de cambio. - En este trabajo se utiliza una metodologia tomada de la literatura financiera para determinar empiricamente si la variabilidad observada de las tasas de cambio puede explicarse con la variabilidad observada en las variables fundamentales. De acuerdo a los modelos monetarios y de "portfolio balance" las variables fundamentales son: la oferta moneta- ria, el ingreso, la diferencia entre las tasas de inflacirn y la oferta de activos. Los resultados parecen ser independientes del tipo de modelo utilizado. Ellos indican que la variabilidad de los tipos de cambio del Sistema Monetario Europeo puede explicarse en t+rminos de las variables fundamentales, mas la variabilidad de otros tipos de cambio (US$/DM, Yen/DM, Franco Suizo/DM) es m~is alta que la de las variables fundamentales.

Download - On the volatility of exchange rates: Tests of monetary and portfolio balance models of exchange rate determination

Top Related