International Short-Term Financing and Investment 251

(1 + e_y ⁾ > (1 + L ) 291

(1+f ) 300

(1+f ) 302

International Long-Term Financing, Capital Structure and the Cost of Capital 284

D = Z D, 283

E = Z 283

k = Z 289

International Long-Term Portfolio Investment 296

Rj,t = b 0,j + b 1, jR m,t + b 2,j$t + e j,t (11.40) 311

dL 319

dm ₁ -¹'—-¹'-²'"² --v-^"³ '-³ (1149) 319

+ 2ct(S 1, S ₄)w 4 +1 1 = 0 319

= 2w3 s ² (S3 ) + 2s(S 1 , S3 )w 1 + 2s(S2 , S3 )w2 320

+ 2s(S 3 , S₄ )w 4 +2 1 = 0 = 2w4 s ² (S4 ) + 2s(S 1 , S4 )w 1 + 2s(S 2 , S4 )w2 + 2s(S 3 , S4 )w 4 + 2 2 = 0 320

= w 1 + W2 + w 3 -1 = 0 320

w' = [w 1 w 2 w 3 w 4 2 1 2 2] and 331

Foreign Direct Investment 344

i 341

References 341

i 361

Index 363

E(St+ 1 ) = X bⁱSt-i 0 < b < 1 (8.4)

i=0

where E(S t+1 ) is the expected change in the exchange rate during the period extending between t and t + 1, such that the expectation is made at time t (the present). In general, we define extrapolative expectations to imply positive dependence of period-to-period changes in the exchange rate, such that a rise in the exchange rate is expected to be followed by another rise and vice versa. Equation (8.1) says that the expected change in the exchange rate is a positive fraction of the current change. Equation (8.2) tells us that the expected change in the exchange rate is a weighted average of the current change and the previous period's change, such that the higher the value of the parameter q the greater the weight assigned to the previous period's change. Equation (8.3) simply postulates that the expected change in the exchange rate is an «-period moving average of previous actual changes. Finally, equation (8.4) says that the expected exchange rate is a geometrically declining distributed lag of previous actual changes. The difference between (8.3) and (8.4) is that (8.3) assigns the same weight to all of the actual changes, whereas (8.4) assigns greater weights to the most recent changes.

Pilbeam (1995a) suggests a simple representation of the extrapolative expec­tations hypothesis, based on the notion that a rise in the exchange rate is followed by another rise and vice versa. Formally, extrapolative expectations are represented by

^E(^St+1) > _if ^St > ₍₈₅₎ E(S t+ ¹) < 0J ^if S ^t< 0j ⁽⁸.⁵⁾

When traders base their decisions on extrapolative expectations, a buy signal is given by St > 0, whereas a sell signal is given by S_t < 0. This representation only indicates the direction, not the magnitude, of the expected change.

Regressive expectations

There are two versions of the regressive expectation formation mechanism, which are given by

E(S _t+ i) = aS _t^,

(8.6) (8.7)

a < 0 0 < 2 < 1

St-1

E(S _t+ i) = - 2

Equation (8.6) tells us that the expected change in the exchange rate is a nega­tive fraction of the current change, implying that a rise in the exchange rate is expected to be followed by a fall and vice versa. Equation (8.7) says that the exchange rate tends to converge on a long-run equilibrium value, St. If the current level of the exchange rate is above (below) the long-run equilibrium

value, then the exchange rate is expected to fall (rise) by a fraction of the gap between the two rates. This is the specification popularised by Dornbusch (1976) since he first introduced it as an element of the sticky-price monetary model of exchange rate determination. Notice that the right-hand side of equation (8.7) is the percentage deviation of the actual exchange rate from its long-run equilibrium value. Several methods can be used to estimate the long­run equilibrium value of the exchange rate, one of which is PPP.

Some economists (for example, Takagi, 1991) take equations (8.1) and (8.6) to represent extrapolative expectations such that equation (8.1) represents desta­bilising (or bandwagon) expectations, whereas equation (8.6) represents stabi­lising expectations. The two concepts correspond to the concepts of stabilising and destabilising speculation, which we came across in Chapter 7. Furthermore, if d or a is equal to zero, then we have static expectations, whereas if d > 1, then we have explosive expectations (extremely strong destabilising expectations). We prefer to distinguish between extrapolative and regressive expectations on the basis of whether a rise in the exchange rate is followed by a rise or a fall. This is why equation (8.6) in our view represents one version of regressive expecta­tions. It is interesting to note that Takagi (1991, p. 171) uses the term "extrapolative" for "the obvious reason that the expected currency movement for the next period is given by the past currency movement for the most recent period", implying that only equations (8.1) and (8.6) represent extrapolative expectations. However, he then argues that extrapolative expectations imply that the expected change in the exchange rate is a weighted average of the changes in the current and last period as represented by equation (8.2). If this is the case, then there is no reason why extrapolative expectations cannot be represented by an n-period simple moving average or by an exponentially weighted moving average as in (8.3) and (8.4) respectively.

According to Pilbeam (1995a), regressive expectations are the opposite of extrapolative expectations, in the sense that the exchange rate is expected to rise if it falls in the current period, and vice versa. Formally, this representa­tion can be written as

if

(8.8)

which again shows the expected direction of the change only. If this is the underlying expectation formation mechanism, then a buy signal is given by S_t < 0, whereas a sell signal is given by S_t > 0.

Although regressive expectations are the opposite of extrapolative expecta­tions, both mechanisms (as in (8.6) and (8.1) respectively) can be represented on the same diagram, as shown in Figure 8.1. This is the normal four-quadrant diagram, with two lines passing through the origin defining the conditions representing the two mechanisms. The line with the positive slope (d > 0) represents extrapolative expectations. Any point on the extrapolative

FIGURE 8.1 Extrapolative and regressive expectations.

expectations line implies that the expectation has been fulfilled (that is, accu­rate prediction). Otherwise, points falling off the line in the first and third quadrants indicate either overestimation or underestimation of the percentage change in the exchange rate. The same descriptions are valid for regressive expectations (points falling in the second and fourth quadrants).

Adaptive expectations

Adaptive expectations can be shown to be rather similar to one version of extrapolative expectations, which can be demonstrated very easily as follows. The adaptive expectations mechanism can be written as

Et (St+ 1 ) - Et- 1(S t ) = k[St - Et- 1(St)], 0 < k < 1 (8.9)

(8.10)

where E_t- 1(S t )is the percentage change of the exchange rate at t as expected at time t - 1. Since the specification of adaptive expectations requires expectation formation at more than one point in time, the expectations operator appears in equation (8.9), and some equations that follow, with a time subscript. Equa­tion (8.9) can be rewritten as

^Et ^{( S}t+ 1 ⁾ = ^kSt + ^{(1 - k)E}t- 1^(S t )

By applying the lag operator to equation (8.10) period by period, while at the same time multiplying by (1 -k) ^j, where j is the number of periods involved in the lag process, we obtain

(1 -k)Et- 1(St) = k(1 -k)St + (1 -k)² Et-2 (St-1 ) (8.11)

(1 -k)² Et-2 (St-1 ) = k(1 -k)² S t-1 + (1 -k)³ Et-3 St-2 (8.12)

and so on. By substituting the resulting equations into (8.10) and combining the terms, we obtain

¥

Et (S t+1) = k[S t+1 + (1 - k)S t + (1 - k)² S t-1 +...] = k X (1 - k)^j S t-j +1 (8.13)

j=0

which resembles the GDL model represented by equation (8.4).

According to Pilbeam (1995a), adaptive expectations mean that if the exchange rate rises in at least two of the latest three periods then it should be expected to rise in the coming period. Formally, adaptive expectations have the following representation

^{E( S}t+1 ⁾ > ⁰1 _if ^St-i > ⁰1 ₍₈₁₄₎

E( St+1) < 0j St-i < 0] ^ ^;

for at least two values of i = 0,1, 2.

Rational expectations

The rational expectations hypothesis postulates that the expected value of the change in the exchange rate is equal to the actual change plus a random error term that may be positive or negative. The underlying idea is that the trader collects and processes all available information and that she does not make systematic errors, which is possible under the previous expectation formation mechanisms. This point is illustrated with the help of Figure 8.2, which is based on hypothetical data generated from equations (8.1), (8.2) and (8.10) under four behavioural patterns of the percentage change in the exchange rate (rising, falling, constant and fluctuating). As we can see, the expectation error is system­atic in all four cases, in the sense that it is always positive. The expected value is consistently below what the actual value turns out to be, although this is not necessarily the case.

As a result, the trader converges on the "correct" underlying model in the long run, forming accurate expectations on average. Hence, the process is specified as

E( St+1 ) = St+1 + X t+1 (8.15)

where X t+1 is white noise, which is totally random.

It is arguable that the rational expectations hypothesis does not presuppose any particular expectation formation mechanism. The hypothesis stipulates

(a) Extrapolative expectations (rising exchange rate)

Actual Expected • Error

(b) Regressive expectations (falling exchange rate)

Actual Expected • Error

FIGURE 8.2 Systematic expectation errors (continued opposite).

that regardless of how forecasts are generated, rationality of agents combined with the discipline of the market should eliminate persistent errors and force all participants to make efficient use of available information. Although Takagi (1991) considers rational expectations, he does not regard it as an expectation formation mechanism like extrapolative, adaptive and regressive expectations. Likewise, MacDonald (2000, p. 73) considers the rationality of survey expectations to be of interest in terms of explaining the poor predictive power of the forward rate. However, he refers to the kind of expectation process by asking whether financial market expectations are adaptive, extrapolative or regressive.

There are problems with the rational expectations hypothesis. For example, Ito (1990) argues that to the extent that individuals are not likely to possess private information, the presence of individual effects may reflect the failure of the hypothesis. Davidson (1982) argues against the rational expectations hypothesis by saying that it is a poor guide to real-world economic behaviour,

because it assumes that market participants passively forecast events rather than cause them.