The Identification of Destabilizing Foreign Exchange Speculation

January 1977

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THE IDENTIFICATION OF DESTABILIZING FOREIGN EXCHANGE SPECULATION

by

Steven W. Kohlhagen

NOTE: International Finance Discussion Papers are preliminary materials circulated to stimulate discussion and critical comment. References in publications to International Finance Discussion Papers (other than an acknowledgment by a writer that

he has had access to unpublished material) should be cleared with the author or authors.

The Identification of Destabilizing Foreign Exchange Speculation

by

Steven W. Kohlhagen*

Ever since Nurkse's (1944) claim that speculation was destabilizing in the 1920s French franc market, theorists and empiricists have endeavored to explain what was meant by such a claim, show how one could identify the phenomenon, and present evidence that proved or disproved its existence in a variety of markets over various sample periods. With the advent of generally floating exchange rates in the 1970s, there has been renewed interest in the subject in both the academic and popular literature.

In this paper, a technique for directly identifying the concept of destabilizing foreign exchange speculation is developed and then it is shown that previous empirical techniques used in the foreign exchange market literature have not provided correct criteria for identifying its existence. In addition, an example of this technique is presented in the form of tests for the existence of destabilizing speculation in the 1973-1975 exchange markets. RL * The research for this paper was completed and the bulk of the paper written while the author was a visiting scholar at the International Finance Division of the Board of Governors of the Federal Reserve System, The views expressed herein are solely those of the author and do not necessarily represent the views of the Federal Reserve System. I am indebted to Bob Aliber for suggesting the topic and (along with Richard Levich) providing the exchange rate data, and to John Bilson, Steve Salant, John Taylor and especially Tom Turner and members of the International Monetary Research Office at the U.S. Treasury and the members of the Federal

Reserve Board's International Finance seminar for helpful comments and suggestions,

The existing literature on destabilizing foreign exchange speculation has in general been concerned with three problems: 1) definition and identification, 2) policy implications, and 3) (belatedly) welfare implications. There are a

‘number of unresolved and important issues that are central to the identification of destabilizing speculation and to the conclusions that should be drawn once it has been

identified. Some of these issues are discussed briefly below,

but a full treatment is beyond the scope of the present paper. The foremost of these issues. is the question of whether "speculation" can be identified at all as a distinct empirical phenomenon. Whereas economists do not hestitate to distinquish conceptually between speculative and nonspeculative motives of demand and supply, the ultimate power of any empirical work on speculation depends on the ability of the test to accurately separate the impact of speculation from the impact of nonspeculative market forces. Any work that claims to identify the existence of destabilizing speculation must first of all have successfully identified the full impact of speculation itself. In the empirical work presented in section 4 below, the weight of the presented evidence depends upon the validity of the interpretation of relative interest rates within a monetarist model as being a correct

proxy for speculative influences on the exchange rate.

At present, the welfare aspects of this issue remain essentially unresolved: Johnson (1976) showed "that destabilizing speculation involves a social loss," while Salant (1976) has demonstrated that profitable speculation necessarily improves welfare even if it is destabilizing.

If destabilizing speculation cannot be shown to be necessarily welfare reducing, then the policy implications of destabilizing speculation are by no means clear.

Merely showing that destabilizing speculation has existed does not imply that the benefits of eliminating it are outweighed by the costs of'doing so (including the use of foreign exchange reserves and manpower, and the resource costs

of possible capital and trade controls). In order to prove

that the existence of destabilizing speculation under a floating regime implies that less flexibility is desirable, it must be shown that not only is it accompanied by a welfare loss, but also that there would be no (or at least less) destabilizing speculation under alternative systems (Johnson (1976)). Put another way, just because central banks recognize the existence of destabilizing speculation, does not necessarily mean that they are able to eliminate it (or that they should eliminate it) by intervening in the foreign exchange markets.

Setting aside these unresolved issues, this paper ad-

dresses the question of how to correctly identify the phenomenon of

destabilizing foreign exchange speculation. Section 2 develops this technique, section 3 shows that previous techniques used in the literature have been neither necessary nor sufficient conditions for identifying destabilizing speculation, and section 4 presents results of an empirical application of

this technique to the French franc-Deutschemark- dollar markets

of the 1970s.

I. Definitions

"Speculation" is defined to be purchases or sales of foreign exchange based on expectations on future prices. This is consistent with the generally accepted concept

of speculation presented in Johnson(1976) ("purchase now

for sale later, or vice versa"), Kemp (1963) ("buying (or refraining from selling) in the expectation of later selling (or refraining from buying) at a higher price"), and Salant (1976) ("“inter-temporal carry-overs").

“"Destabilizing speculation" is defined to be speculation that causes the observed time series of the price to be more volatile than it would have been in the absence of such an activity. This definition is a standard definition and is consistent with that used in almost all of the empirical work on destabilizing foreign exchange speculation.+ As will be shown, this definition is quite distinct from looking at volatility per_ se as a technique for identifying destabiliz-

ing speculation, since it accounts for the variance of the

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exchange rate that is explained by fundamental economic deter- Minants before determining the characteristics of speculation. It is, however, only a special case of the much broader concept that is often used (and so far not yet subjected

to empirical testing) that destabilizing speculation is speculation that causes a price to move away from some mediumterm "equilibrium" level.

The mean-squared deviations of the price series around its mean is used as our measure of stability or volatility as suggested by Farrell, Kemp, Salant, Schimmler, and Telser (for convenience, this measure will be called the variance of the price series, but no probability statements are implied by the use of the term). This measure has a potential defect which turns out to be not relevant to our empirical work: for a price series that is a function of time or otherwise nonstationary, the variance is an inappropriate measure of

stability or volatility.?

For our purposes, a careful destinction is made between what destabilizing speculation is and what different techniques exist that can be used to identify it once it is defined. Examples of techniques that have often been used to identify destabilizing speculation, but that cannot in and of themselves be considered definitions of destabilizing speculation, include:

1) prices that are volatile, 2) evidence that market participants buy

‘ after the price starts rising and sell after it starts falling

(i.e., "bandwagons" or "self-justified" speculation), and 3) “net profits or losses made by speculators as a whole. Such

criteria will be analyzed in detail in section 3.

II. Directly Identifying Destabilizing Foreign Exchange , Speculation

' The hypothesis to be tested then is that the observed exchange rate time series is more volatile than the exchange rate time series that would have occured in the absence of a supply and demand generated purely on the basis of expectations on future exchange rates.? Assume that the process that generates the exchange rate can be represented by the simple (linear) expression:4

x = BW, +d xe + Uy (1) where X is the price of foreign exchange in terms of domestic currency, 8 is a vector of coefficients, W includes all "nonspeculative" variables that determine the current exchange rate, a is a positive scalar coefficient, A x is the variable representing speculative expectations and is equal to the difference between the expected future exchange rate and the current rate (Ax©=x€-x), and u isa normally distributed disturbance term with zero mean. The exchange rate that would exist in the absence of the influence of expectations on the future exchange rate can be represented. to be

(dropping the t subscripts for simplicity): % ; ; ‘aie ,

X = X -aAX© = BWt+u (2)

Speculation will than be destabilizing when:

2 O, > On (3)

where o% is the variance of the time series around its mean,

and stabilizing when

2 2 x < On (4) Since 2 os 2 ‘ Oo, = EB (8 (W-W) (w-W) 'B'} + a One t2a B cov(AX®,W) + o. (5) 2 | _ _ 2

(where W is the mean of W, and (W-W)'and 8' are the transpose of (W-W) and 8 respectively), the condition for the existence

of destabilizing speculation is:

2 2 gg? t2a° v (Axe, W)> 0 7 go - 6, =a Re a B cov(Axe, W) (7) 4

Intuitively, this relationship indicates that if a change in the variables that are fundamental determinants of the exchange rate is associated with a change in the exchange rate and

a change in the expected change in the exchange rate in the same direction, then the impact of expectations is to increase the variance of the exchange rate from what it would have been if expectations were not present in the market. That is, expectations would be destabilizing. Alternatively, if, say, an increase in the interest rate caused an increase in the exchange rate and a reduction in the expected increase (or an increase in the expected decrease) of the exchange rate, then the impact of

(

these expectations would be to reduce the fluctuations in the

exchange rate (as long as this effect was large enough to

offset aro J, A sufficient condition for the existence of AX destabilizing speculation is that expected changes in'the

future exchange rate be orthogonal to the other explanatory

variables of the model.

III. Past Attempts at Identifying Destabilizing Foreign Exchange Speculation

There have been many attempts since Nurkse (1944) to identify the existence of destabilizing foreign exchange speculation, especially in the 1920s French franc market and the 1950s and 1960s Canadian dollar market These techniques can be broken down into roughly two major categories, neither of which contains any criteria that have been shown to be either a necessary or a sufficient condition for identifying destabilizing speculation. In this section, the usefulness. of these criteria as conditions for identifying destabilizing speculation are analyzed in light of conditions (3) and (7) above.

The first category includes those techniques that merely analyze the behavior and time path of the exchange rate without utilizing some notion of the underlying determinants of the rate. Within this category are included those arguments that claim that: 1) a high amplitude of exchange rate fluctuations per se is evidence of destabilizing speculation, and 2) there is destabilizing speculation when the spot rate and

the forward premium move in the same direction. ®

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The issue of increased exchange rate volatility usually has been presented in the following manner: if the exchange

rate is more volatile in period 2 than in period 1 a 2 2 ; : (i.e. oO > o),then speculation is said to be destabilizing 1

X>

in period 2. That is, from (3): 2 2 2 2

fe} - 0 >?0 => 6.- <a >0. Xo

This of course is not true. In fact, all that can. be said, given

. 2 2 ; 2 2 the information 2 > ¢? i - > -3o ion that Ox, ox) , is that Ox, "ye, Oxy x, which implies nothing about whether o, 9? is greater than, . a

2 xX, less than, or equal to zero. Increased variability in the

exchange rate can be evidence of stabilizing speculation, destabilizing speculation, or no speculation at all.

The statement that there is destabilizing speculation when spot rates and forward premia move in the same direction (Aliber (1970, 1973) and Hodgson (1972)) is equivalent to claiming that there is destabilizing speculation if the Cov (X' -X,X)>0 (where x' is the forward exchange rate). Assuming that the forward rate accurately reflects exchange rate expectations, it can be shown from (1) above that the cov (X'-X,X)>0=> 3X

7X) Tyecx) (=0)>0. From (7) it can be seen that a>0 does not imply destabilizing speculation since it does not ensure that 07 Ore + 2aB8 cov (AX®,W)>0. The mere observation that the: forward premium for the ‘expected

‘change in the exchange rate) moves in the same direction as the

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exchange rate cannot identify the existence of destabilizing speculation, since this analysis includes no information about the net effect of the endogenous components of expectations on the variability of the exchange rate ( 208 cov (AX®, W)).

| The second major category includes those techniques that utilize some knowledge of the relationship between the exchange rate and some set of fundamental economic variables (e.g., the components of W).

The first technique of this sort claims that exchange rate "bandwagons" are evidence of destabilizing speculation. This argument is usually made in one of two ways. The first is a special case of the excessive variability argument discussed above,and claims simply that exchange rates that move in excessively large swings or "bandwagons" are evidence of destabilizing speculation. As was shown above, excessive movements of the exchange rate per se imply nothing at all about the net effect of the endogenous components of expectations on the variability of

the exchange rate, and thus nothing at all about the nature of

speculation. //

A second type of "bandwagon" argument is often represented by expressing the expected future exchange rate as an increasing

function of the current rate®:

x© = 6,2 + 62 X ; (8)

where Z is a matrix of other variables that are used to

form expectations (perhaps even coincident with W), 6, and

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6; are a scalar and a vector of coefficients repectively, and bandwagons are implied by 56,>0.

Substituting from (8) into (1) and solving for X yields:

x Totes) *ratres) *Tati=s2) | ”

Assuming for simplicity that w and 2Z are each conm-

posed of only’ one variable, we find that’ ;

2 o. - Oo, = i _2 xX ¥ “1-afl-62)

. a [{ad,) o, + 2Ba6é; cov (W,Z)

#(a (82 («(2-62)+2)-(24a) )) (Bo + 02)] (10) If there are no bandwagons . (6, is negative) the behavior of OF - oa, will be less volatile then if there are, and as ad, approaches unity, oF - On approaches positive or negative ‘infinite. If 6,. is positive and thus there are bandwagons, speculation is more likely to be destabilizing, but the sign of 6, implies nothing in general about whether speculation

10 The reason it does not

is stabilizing or destabilizing. is that the sign of 6, gives. no information on the net effect of the relationships among the other fundamental variables (2Baé6, cov (W,Z) on the variability of the exchange rate. A second technique within this category has been to identify

as periods of destabilizing speculation those periods where the exchange rate "overreacts" to changes in certain fundamental variables such as prices or interest rates (Aliber (1970), Artus (1976), Kohlhagen (1975a, 1975b), Price and Wood (1974), Thomas (1973a,

1973b) , and Williamson (1973)). There have heen two approaches

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to identifying this phenomenon empirically. The first has

been to show that the regression coefficient of the exchange rate as a function of the fundamental variable is greater than unity. That is, separating out some fundamental variable, say p, our true model of the foreign exchange market can be represented by x=B"W* 4 yp + aAx©® +u, (11)

where #* and Ware the remaining coefficients and variables

after removing y and p. The hypothesis is that /Y/ >1 implies

destabilizing speculation. Using (11) to solve for of =o e and substituting for oF from (5), yields OF 9, =a." O° gf 28* a cov (x, we) + 2ya cov (p,Ax®), (12) x x

which is by no means necessarily positive when /y/>l. Alternatively, it has often been claimed that an exchange rate with a higher volatility (oF) than the fundamental vari- . . waa . 11 . able ( oS) implies destabilizing speculation. That is, _ «2 = 2252 5 ‘ 2 7 ome %p >0 => o se 0. Using (11) to solve for oF {and

2

thus Oy

“O5) 4 subtracting (12), ana rearranging yields: 2_~2 = 2_~2 _ e252 2_ o2 _ * k 13 (0% on) (0-04) ~ BOL -( y?-1)0", -2.8*7 cov (w*,p) (13) It is clear, that whereas ora, is more likely to occur during x periods of destabilizing speculation, it by no means guarantees that the period is necessarily characterized by destabilizing

speculation.

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The third criterion in this category has been implicit in much of the literature and explicit in Aliber (1975, p.375). It is claimed that destabilizing speculation exists when the expected exchange rate itself is affected by the fundamental variable in such a way as to reinforce capital flows. That is, if the expected future exchange rate is: Xxe€= xe* + Yp, (14) where x“ is the portion of the expected exchange rate that is independent of the fundamental variable p, speculation is destabilizing if y ( from (11)) and ¥ have the same Sign (i.e., y¥>0).

Substituting into (11) for X© from (14,

and then solving for o* and of (=0? yields x x x-aAx 2 g2 = a ¥--y (24a) t+a¥?) o2 -—(2+a) (R207 +07) + Ox ~% Giza | y (2¥-y (2+a) ) oy -( (Boo toy

aoye* + 28* (¥- Y (2+a)) cov (wWw*,p) + 28" cov (w* ,xe*)

+ 2 (y +a¥) cov (p,x®*) ] (15) This expression is not necessarily positive if y¥>0, since this condition provides no information about the relationships among the variables other than p.

In summary, analyses of exchange rate behavior that are partial equilibrium in nature in that they examine the relationship between expectations and the exchange rate through only a subset (or none) of their fundamental economic determinants, cannot identify the nature of speculation. Studies that show that the exchange rate is volatile or is more volatile than should be justified by some incomplete set of independent variables have not shown that the net effect of all specula-

tive forces is destabilizing. To correctly characterize

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speculation as... stabilizing or destabilizing, empirical work | must identify the "true" model determining the dependent price variable and then show that the net effect of all speculative forces has been to increase the volatility of the price from what’ it would have been in the absence of speculation. Iv. A Direct Empirical Test For Destabilizing Speculation

In this section, a test is presented for the presence of destabilizing’ speculation in three foreign exchange markets during the 1973-1975 float. This test is meant to be illustrative of the technique presented in section 2 and is subject to all of the qualifications outlined in the introduction to this paper. Essentially, in order to accept this test as actually identifying destabilizing speculation, the reader must accept the following assumptions: a) speculative demands and supplies can be empirically distinguished from other sources of demand and supply, b) the model of exchange rate determination presented in this section is the "true" model, and c) the variable representing exchange rate expectations in this model fully measures the impact of speculation in the market. 12

Our "true" model of the foreign exchange market is the empirical Monetary model of the foreign exchange rate developed and tested by Bilson (1976) and Frenkel (1976). Basically, this model advances the notion that the exchange rate is the relative price of two currencies. Demand and supply equilibrium in two money markets is specified and both Purchasing

Power Parity and Interest Rate Parity conditions are invoked

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to specify a monetarist model of the determination of the foreign exchange rate. Reproducing this model, it is assumed that the demand for real money balances can be represented

in the familiar form:

dad: a : =" = 23) e 7? (16)

where mM? is the nominal demand for money, P is the price level, Y is nominal income, i is the interest rate, Qo and Oy (the income elasticity of the demand for money) are expected to be positive, and a, negative (where the interest elasticity of the demand for’ money equals agi).

Taking logs of (16) yields:

in mM? = a, +a, ln (¥/P)+ a,i + In P (17)

and similarly for the "foreign" country:

a,i* + in px _ (18)

where (*) denotes foreign, and %, and a, are assumed the same

kK ok bape pa in md =O, +a, ln; Y*/P* +

for both countries.

If Purchasing Power Parity and Interest Rate Parity

hold then: in X =I1n P-ln P*, and (19)

i* - i = X-X . (20)

Subtracting (18) from (17) and substituting from (19) and (20) then yields: (

In X =a' + ay ln: Y*/P* + a, 'x-x"\ + a3 in wa — x \ Md" }, (21)

y /P x | ros gt. Pa = where A, = a, < 0, and a3= l.

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This final form then states that the exchange rate is a function of relative money supplies and demands, where relative demand factors are represented by relative real income (transactions demand) and relative nominal interest rates or, equivalently, expected changes in the exchange rate as represented by the forward premium or discount (demand based purely on expectations of future values of currencies, i.e., speculation). This interpretation of the model depends upon a particular point of view about the role of interest rates.

In this model the interest rate is viewed as a price of "futures" money, so that relative interest rates (and thus forward premia) represent the relative price of two future monies. A relatively high interest rate is then indicative of an expected depreciation in the value of that currency. The full impact of expectations in the market for currencies is then reflected

in relative interest rates and the interest elasticity (i.e. elasticity of expectations) for the demand for money .+3

Equation (21) is a specific form of (1), where the elements

of W are the constant, relative nominal money supplies, and relative real incomes, and where speculative expectations are represented by the forward premium or discount. The exchange

rate that would have existed in the absence of speculation is

~ ~op (X-X") | /, Nar) 30 then: X = Xe 7 —~x = at ye /pe\T1/ yd a3 (22) \ ¥/P

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Table 1 presents the 2SLS estimates of (21) for three currency markets for March 1973 - December 1975, where the forward premium is treated as an endogenous explanatory variable with levels and changes of the exogenous variables used as instruments in the first stage of the estimation, and, since exchange rates were floating over the sample period, the relative money supply variable is treated as exogenous.

For each of the markets 14

the important coefficients had the correct sign and were significant while the standard error of the estimate was from 3 to 5%. The only truly perverse coefficient was the relative money supply coefficient in the French franc - U.S. dollar market, which is significantly different from unity. It is not clear whether or not this provides an explanation for the relatively smaller coefficient on the expectations variable in this case. The income elasticity of the demand for money (a) is surprisingly volatile, ranging from 0.261 in the Deutschemark-French franc case to 1.367 (but not significantly greater than unity) in the Deutschemark-U.S. dollar case. The interest elasticity of the demand for money (a,) is only about 0.4 for the Frenchfranc-U.S. dollar case, but about 0.75 for the two German cases.

Figures 1-3 present graphs of the observed exchange rate

series (X), and the exchange rate time series that would have % occurred in the absence of speculation (X from (22)) as

estimated from the regression results presented in Table 1.

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Table 2 presents the variance of each observed exchange rate and each derived exchange rate that would have occured

in the absence of speculation and indicates. that specu-

lation has been destabilizing in each French franc market and stabilizing in the Deutschemark-U.S. dollar market. That is,

as a result of foreign exchange speculation during the 1973-1975 floating exchange rate regime, the variance of the French

franc has been 238 higher against the Deutschemark and 46% higher against the U.S. dollar than it would have been had

there been no speculation. In contrast, the variance of the Deutschemark against the U.S. dollar has been 19% less than

if there had been no speculation, implying that speculation

has been stabilizing in this case.?°

If the three assumptions at the beginning of this section are accepted, evidence has been found that there was destabilizing speculation in the first three years of the 1970s floating exchange rate regime. During this period there were many instabilities and large exogenous shocks, and one might be cautious about projecting from the experience of these early years of the float. In addition, during this period economic agents were only just beginning to learn to live with the float, so that, allowing for some "learning by doing", future speculation might well be structurally dif-

ferent from that in this period.

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V. Summary and Conclusions

In this paper, it has been shown that the criteria that have been developed in the foreign exchange market literature are neither necessary nor sufficient conditions for identifying destabilizing speculation. A technique was then presented for directly testing for the presence of destabilizing speculation. Using a monetary model of the foreign exchange rate, evidence was presented that is consistent with the presence of destabilizing speculation in the 1973-1975 French franc- Deutschemark and French franc-U.S. dollar markets, and stabi-

lizing speculation in the Deutschemark-U.s. dollar markets.

Acceptance of the conclusions of this illustrative test is contingent upon acceptance of the fact that speculation is an empirically identifiable phenomenon, that the monetary model of the exchange rate is the "true" model, and that the forward premium fully reflects the impact of speculation in the market. Alternative models and empirical specifications

are potentially fruitful areas for future research on this

subject.

The presence of destabilizing speculation however does not imply that either more central bank exchange market intervention or fixed exchange rates are necessarily desirable.

As discussed earlier, the welfare theory of the economic costs of higher exchange rate volatility induced by destabilizing speculation are simply not very well developed. It is by no

means Glear that the benefits of Central Banx action to

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reduce or limit fluctuations outweigh the costs associated with doing so. Similarly, it is not clear that during periods of volatile financial markets, any other exchange rate system other than floating is possible without overly restrictive

capital and trade controls. In addition, since there was Significant Central Bank intervention during the period analyzed, a.complete interpretation of these results cannot exclude the possibility that the observed presence of destabilizing speculation was because of Central Bank intervention

rather than despite it.

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Variance of Observed Spot Rate and Calculated Spot Rate in the Absence of Speculation

Deutschemarks * 02686 02187 00499 French francs oe

French francs 2.52767 . 1.73141 . 79626 U.S, dollar

Deutschemarks -73351 . .90193 -.16842 U.S. dollar :

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Footnotes

It is explicitly used in Farrell (1966), Friedman (1953),

Johnson (1976), Kemp (1963), Salant (1976), Schimmler (1973), Stern (1973), Telser (1959), and Yeager (1976), and implicit in Nurkse (1944). The other definition that has been used in

this literature, but that is not used in this paper, is

speculation within the context of a simultaneous equations model that causes the system to be mathematically unstable

(e.g., Stein and Tower (1967)).

The general problems of a non-finite variance arising from non-stationarity do. not arise in our empirical work, since the sample period is short (less than three years of monthly data) and, as a result of the unique set of events that occurred, is treated as though it were the whole population (e.g., the oil crisis, unusually high and widely dispersed inflation rates, and the unfamiliarity of many economic agents with floating exchange rates). In addition, no exchange rate time series that is a function of time

has been used as the dependent variable in our empirical work (i.e., all exchange rates were estimated as linear functions of the constant and time, and all exchange rates that had a significant coefficient on the time variable at at

least the .9 level were eliminated from consideration in our empirical work).

This test is based on implicit suggestions made in a

somewhat different context by both Kemp (1963 189 and Salant (1976, P. 3). ° VP

As is shown in section 4, the functional form of (1) may

see Kohlhagen (1976) for a survey of the literature on foreign exchange speculation.

This has been referred to as a "speculative period" in the sense of Stein, from his characterization of "speculative" and "normal" periods (Stein(1962)).

Our analysis implies nothing about the efficient markets literature in which the presence of significant bandwagons is used as evidence of market inefficiencies, - Bandwagons have been used in the literature variously as evidence

of destabilizing speculation, too little stabilizing speculation, poorly:behaved speculation, and inefficient markets. For a discussion of this literature and a list of references see Chapter 2 of Willett (1977). Only the fact that bandwagons are not evidence of destabilizing

speculation is shown in the present paper.

10.

ll.

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For the use of this type of evidence, see Arndt (1968), Artus (1976), Black (1972), Eastman (1958), Kohlhagen (1975a,b), Myhrmann (1976), Nurkse (1944), Poole (1967).

If W and Z are composed of more than one explanatory

variable, the results are more complex due to the multiple variance terms and the covariance terms within Z, but they are not substantively different: _

0 2:-02 =E{ fod, \(2-8) (2-2)'/ ad, "} +_ 28081 -, cov (W,2) * ratiz8e) Tra(i62) a (1-82)

+ (a(S, (4 (2-62)+2) = (24a))) - (870? + 02) uo! I4+a(1-62) “ where Z is the mean of Z, and (Z-%)" and / a6, ' are the

transpose of (2~Z) and/ a6, -- respectively. ae (Ta (I=8,)

In the special and somewhat unrealistic case where Z is coincident with W and W is composed of only one funda- _ mental explanatory variable, the existence of bandwagons does imply that destabilizing speculation exists.

In both the economic and popular literature, it is often asserted that a major problem with floating exchange rate regimes (as evidenced by the experience in the 1920s and 1970s) is that they are characterized by periods of destabilizing speculation as reflected

. in the high volatility of exchange rates relative to prices and interest rates.

12.

13.

14,

15.

-28-

If the first assumption cannot be accepted, destablizing speculation can never be identified. If one or both of the latter assumptions is unacceptable then the test suggested in section 2 could more profitably be applied to a different model than the one used here.

The interest rate therefore will not adjust to choke off an excess demand or supply of money in this interpretation. Full adjustment must come from price and possibly income changes.

These three markets were chosen because consistent data were available and the exchange rate time series during the sample period were not functions of time.

~ Since X and X are not independent time series we cannot use a simple F-test to see if their variances are significantly different. In addition (for the reasons given in footnote 2), since our sample variance is unlikely to be an unbiased sample of a larger population, even more sophisticated tests (e.g. using the Wishart distribution presented in Anderson (1962)) will not necessarily yield meaningful tests of significance in this case.

Bibliography

Aliber, Robert Z., 1970, "Speculation in the Flexible Exchange Re-visited," Kyklos, (Fasc .2), pp. 303-314.

, 1973, “Speculation in the Flexible Exchange Re-revisited: Reply," Kyklos, pp. 619-620.

, 1975,"Monetary Interdependence Under Floating Exchange Rates, "Journal of Finance, May, pp. 365-376.

Anderson, T.W., 1962, An Introduction to Multivariate Statistical Analysis, John Wiley and Sons, Inc., New York.

Arndt, Sven W., 1968, "International Short Term Capital Movements: A Distributed Lag Model of Speculation in Foreign Exchange," Econometrica, January, pp. 59-70.

Artus, Jacques P., 1976, "Exchange Rate Stability and Managed Floating: The German Experience," IMF Staff Papers, July, pp. 312-333.

Bilson, John F.O., 1976, "A Monetary Approach to the Exchange Rate," unpublished doctoral dissertation, Department of Economics, University of Chicago.

Black, Stanley W., 1972, "International Monetary Markets and Flexible Exchange Rates," Board of Governors of the Federal Reserve System, Staff Economic Studies, No. 70.

Eastman, Harry C., 1958, "Aspects of Speculation in the Canadian Market for Foreign Exchange," Canadian Journal of Economics, August.

Farrell, M.K., 1966, "Profitable Speculation," Economica, 33, pp. 183-193.

Frenkel, Jacob A., 1976, "A Monetary Approach to the Exchange Rate: Doctrinal Aspects and Empirical Evidence," Scandinavian Journal of Economics, vol. 78, no. 2.

Friedman, Milton, 1953, Essays in Positive Economics, University of Chicago Press, Chicago.

Hodgson, John A., 1972, "An Analysis of Floating Exchange Rates: The Dollar-Sterling Rate, 1919-1925," Southern Economic Journal, October, pp. 249-257.

Johnson, Harry G., 1976, "Destabilizing Speculation: A General Equilibrium Approach, "Journal of Political Economy, vol. 84, No. 11, pp. 101-108.

Kemp, Murray C., 1963, "Speculation, Profitability, and Price Stability," Review of Economics and Statistics, 45, pp. 185- 189.

-30- Bibliography (con't)

Kohlhagen,Steven W., 1975a, "Exchange Rate Expectations and

International Capital Flows," Research Program in Finance, Working Paper No. 30, University of California, Berkeley, February.

, 1975b, "'Rational' and 'Endogenous' Exchange Rate Expectations and Speculative Capital Flows in Germany," paper presented at a joint session of the American Economic Association and the Econometric Society, December 28, 1975, Dallas Texas.

, 1976, "The Foreign Exchange Markets - Models, Tests, and Empirical Evidence," paper presented at a U.S. Treasury conference, February 26, 1976, Washington, D.C.

Myhrman, Johan, 1976, "Experiences of Flexible Exchange Rates in Earlier Periods: Theories, Evidence and a New View," Scandinavian Journal of Economics, vol. 78, No. 2.

Nurkse, Ragnar, 1944, International Currency Experience, League of Nations.

Poole, William, 1967, "The Stability of the Canadian Flexible Exchange Rate, 1950-1962," Canadian Journal of Economics and Political Science, pp. 205-217.

Price, Lionell D.0O., and Geoffrey E. Wood, 1974, "Another Case of Profitable Destabilizing Speculation," Journal of International Economics, May, pp. 217-220.

Salant, Stephen, 1976, "Profitable Speculation, Price Stability and Welfare," mimeo, International Finance Division, Board of Governors of the Federal Reserve System, March.

Schimmler, J., 1973 , "Speculation, Profitability, and Price- Stability-A Formal Approach," Review of Economics and Statistics, February, pp. 110-114.

Stein, Jerome L., 1962, "The Nature and Efficiency of the Foreign Exchange Market," International Finance Section, Princeton University, Princeton, New Jersey.

, and Edward Tower, 1967, "The Short-Run Stability of the Foreign Exchange Market," Review of Economics and Statistics, May, pp. 173-185.

Stern, Robert, 1973, Balance of Payments, Aldine Press.

--31- Bibliography (con't)

Telser, L.A., 1959, "A Theory of Speculation Relating Profitability and Stability, "Review of Economics and Statistics, XLI, No. 3, pp. 295-301.

Thomas, Lloyd, B., 1973a, Behavior of Flexible: Exchange Rates: Additional Tests From the Post World War I Episode," Southern Economic Journal, October, pp.

167-182.

, 1973b, "Speculation in the Flexible Exchange Revisited = Another View, "Kyklos (Fasc. 1), pp. 143-149.

Willett, Thomas D., 1977, Floating Exchange Rates and International Monetary Reform, American Enterprise Institute.

Williamson, John, 1973, "Another Case of Profitable Destabilizing Speculation," Journal.:-.of International. Economics, February, pp. 77-83.. °

Yeager, Leland B., 1976, International Monetary Relations: Theory, History, and Policy, Harper and Row, New York.