Semi-rational expectations and exchange-rate dynamics

/owna/

aj International Money and Finance (1984), 3, 51-66

Semi-Rational Expectations and Exchange-Rate Dynamics DAVID BIGMAN* Department of Agrictrltural Economics, The Hebrew UrGersit_ of Jerusalem, Jerusalem, Israel

The Rational Expectations Hypothesis (REH) asserts that, on average, the economic agents are accurate in predicting future economic developments. The paper demonstrates, however, that in a world of costly information, individual rationality may result in consistent and persistent forecasting biases. A distinction is drawn between perfect foresight or efficient with the REH-and myopic perfect forecasting-which is consistent foresight-which is the profit maximizing, and thus the rational one from an individualistic point of view, even though the latter may result in persistently biased forecasting. These concepts are illustrated in a model of exchange rate dynamics which introduces myopic or ‘semi’ rationality into Dornbusch’s familiar model.

Despite recent criticism, the rational expectations hypothesis (REH) is still a fundamental building block in most macro and micro-economic models that consider a stochastic environment. The attractive features of the REH are well known: it removes the ad hoc nature of previous extrapolation rules for expectations formation and offers a formulation that fits the tradition of neoclassical economic theory and springs from its underlying premise of individual rationality.’ Indeed, for utility and profit maximizing individuals, operating in a world of perfect and costless information and pure competition, the only utility and profit maximizing forecasts are the rational ones. The REH, as defined by Muth (1961), avoids the potential contradiction to this premise existing in other expectation formulations which may imply that traders are consistently wrong in their forecasts. Nevertheless, the REH has its critics. Arrow wryly remarked that this hypothesis requires the economic agents to be ‘superior statisticians, capable of analysing the future general equilibrium of the economy’ (1978, p.10). In Hayek’s view, the assumption that people’s knowledge corresponds with the objective facts of the

* I am grateful to Hanna Lifson for helpful comments and to Itzhak Weksler for his meticulous research assistance. I would like also to thank the two anonymous referees and the editor of this Journal for helpful comments. The research was supported in part by a grant from the United States-Israel (Binational) Agricultural Research and Development Fund (BARD). 0261-5606/84/01/0051-16$03.00

0 1984 Butterworth

& Co (Pubhshers)

Ltd

52

Semi- Rational Expectations

and Exchange-

Rate Dynamics

situation, systematically leaves out what is the economists’ main task to explain. Lucas (1976), Barro (1980), Friedman (1979), Howitt (1981), Grossman and Stiglitz (1980), Grossman (1981), Flood and Hodrick (1982), and Frydman (1982), among others, examined economies in which the information is costly, asymmetrically distributed among individuals or gradually acquired through learning by doing. One conclusion emerging from these analyses has been summarized by Friedman (1979, p. 40) as follows: ‘The information availability assumption of the rational expectations hypothesis places such models in a long-run equilibrium context in which their classical properties-including the neutralitv of monetary policy-are not surprising’. The main argument in this paper is that the applications of the REH in macroeconomic models assume a much larger information set than that actually relevant for the formation of efficient or profit-maximizing forecasts. In general, these models assume freely available and equally distributed information about all contemporenous economy-wide data, leading to predictions of events indefinitely into the future that will indeed be realized (except perhaps for purely random errors) and thus toperfectforesight. When, however, information costs are reckoned with and weighted against the present value of the gains expected from improving the forecasts, individuals are likely to focus only on that information actually relevant and sufficiently beneficial for forming forecasts of the variables in question, while ignoring other segments of the model. This, in turn, may give rise to inconsistencies between the ‘full-information’ rational forecasts-as conventionally defined-and the partial-information ‘semi-rational’ forecasts-as defined in this paper.* Nevertheless the ‘semi-rational’ forecasts are shown to still be efficient in the sense that the relevant predictions are realized, thereby leading to m_lropic perfect foresight. The paper demonstrates these principles in a model of exchange-rate dynamics. In Section I the conceptual issues associated with rational and ‘semi-rational’ expectations are discussed. Section II examines the behavior of exchange rates under rational expectations. Section III extends the model to examine exchange rate behavior under semi-rational expectations. The paper demonstrates that an efficient learning process need not remove possible discrepancies between the two to persistent biases in their predictions. These expectational forms, leading conclusions are demonstrated both analytically and in diagrams which summarize the results of simulation experiments with the models. I. The Conceptual

Framework

The main arguments of this paper can be summarized as follows: in a world of costly information, even efficient learning of, and perfect competition among profit and utility maximizing individuals need not eliminate persistent biases that may exist in their forecasts, and these biases are likely to be larger the longer-term are the forecasts. An important source of these biases is possible discrepancies between stock and flow equilibrium-that coincide, in turn, with discrepancies between short- and long-run equilibria. It has long been established that clearing conditions corresponding to stock equilibrium may differ from those corresponding to flow equilibrium; Foley (1975) and later Turnovsky and Burmeister (1977) have proved that the two types of equilibrium conditions will be consistent with each other if and only if the economic agents have perfect foresight.

53

DAVID BIGMAN

According

to the

REH,

individual

agents

would

have

perfect

foresight

b!

making efficient use of all the available information, and obtaining complete knowledge of the economic structure. Having this knowledge, and barring any new and unexpected

developments,

informed

individuals

would be able to forecast

the

pertinent economic variables, and their forecasts would be realized-except, perhaps, for purely random errors. Any consistent bias in their predictions should, according to this hypothesis, indicate either that information was not efficiently processed or that it was not equally distributed. In a more realistic world of costly information and time consuming learning, such biases are, however, by no means forecasts require far more information

impossible. Thus, for instance long-term than short-term ones and knowledge of

segments of the economic model and variables which are not relevant for short-term forecasting. In terms of the above-mentioned concepts, short-term forecasting requires knowledge of the short-run (stock) equilibrium conditions whereas long-term forecasting requires, on top of it, also knowledge of the long-run (flow) equilibrium conditions. At each stage in the learning process rational, profit maximizing individuals weigh the gains expected from having more information and improving their forecasts against the costs of acquiring this information. If the additional costs involved exceed the present value of the expected gains, then agents will be perfectly rational in choosing not to expand the scope of their learning, even though their forecasts may, as a result, be biased. Nevertheless, efficient learning of the variables and structures which determine the short-run equilibrium would still enable them to perfectly forecast the pertinent economic variables over the short-run. In other words, they would have myopic perfect foresight. To characterize the difference between myopic and long-term perfect foresight we examine a continuous time, deterministic model. Efficient forecasting leading to perfect foresight would be manifested in this model when the rate of change of the pertinent economic variable at time r forecasted by individuals at an earlier period t(t < z) is equal to the actual rate of change in this variable at time Z. Myopic perfect foresight is manifested when the accurate forecasting is for the immediate future only. For a variable X, myopic perfect foresight would be manifested when EQ,)

=

=P -_x ‘x”; ’

pl$

i

I

x1+/>-x/ = X, = Lim ___ h-Cl+ h 1 1 where a dot over a the logarithm; &+,,‘P q(Xr) denotes the time t. Perfect foresight

variable denotes the time differential; lower case letters denote denotes the logarithm of X expected at time t for time t+h, and rate of change of variable X at time Z, (subjectively) expected at over the entire future

Ep,)

=

,:$ L

is manifested

{‘““;GYj

= Lim /J-.0+

=

Xr+h--X7 {

h

when for all T> t,

= DzT 1

54

Semi- Rationai Expectations

and Exchange-

Rate Dynamics

In other words, when the rate of change forecasted at time t for any time period in the future T, would be equal to the actual rate of change actually realized at time r.3 A heuristic illustration of the foregoing argument is given in Figure 1 where a block diagram is drawn describing the dynamics of a typical macroeconomic model.4 In very general terms, the model describes two types of markets: financial asset markets and goods markets. Equilibrium conditions in the asset markets are typically stock-equilibrium conditions, whereas in the goods markets these are flow-equilibrium conditions. Indeed, reaction of traders in financial markets is much more rapid than that in the goods markets and the former are cleared much faster than the latter markets. Equilibrium conditions in the asset markets thus characterize the short-run equilibrium whereas those in the goods market characterize the long-run equilibrium.

Ex ter ,nal

Shot ks FIGURE 1.

The financial magnitudes, denoted by the vector Z,+, (e.g., interest rate, exchange rate) are determined in the financial markets and the most important variable affecting their level is assumed to be the price level (and the exchange rate) expected are formed on the basis at time t for time (t+ l), denoted by ,e+,. Price expectations of various signals, the most important of which are the actual prices existing at time t, denoted by the vector P,, the level of unemployment (and other ‘real’ signals such as the trade balance) denoted by the vector U,, and external shocks up to that period of time (mostly, due to policy changes). The formation of expectations is denoted by the block Zin Figure 1, which stands for ‘Interpetation’. Both relative prices and the level of unemployment are determined in the goods market on the basis of the prevailing supply and demand conditions. The above is, for instance, a typical structure of exchange-rate models which take the monetary approach.’ The exchange rate is determined in the asset market in which price and exchange-rate expectations play a pivotal role. The exchange rate affects, in turn, imports and exports, and the resulting consequences for the trade balance are important factors in the formation of new exchange-rate predictions. Let F, and FG denote the ‘transfer functions’ in the financial assets market and the goods market and let FI denote the expectations formation, i.e., the transfer function of block I. These functions have the following general form:

55

DAVID BICMAN

Z I+1 = F&e+,) J?,,

= F,(P,,U,,

(Pl, 24) =

FG(Z,,

...)

2-t-1,

. . * >

From this structure we can deduce the reduced form equation or the transfer function of the entire system which, in the absence of new shocks, would have the form,

Feedback (Z,+I) = FA (,F,+,)

= F,(F/ (Pi,

ut>>

= F.4 . FI . FG (Input

(Z,, ZI-l, . . . ))

Obviously, in specific models, the lag structure and the functional relationships can be more complex. Even in this simple model, however, the distinction between myopic and long-term perfect foresight is vividly demonstrated: for short-term forecasts of the pertinent financial variables, individuals must focus only on that segment of the model in which Z ,+, is determined. The information required includes P, and U, and the (known) policy rules. The transfer function of this segment is given by

Z,+l = F, . Fi (f’t,

ut, . . . >

Hence, for an accurate prediction of Z ,+I agents must learn the structure and estimate the parameters of F.4 and F, only. If their interest is in short-term forecasts only they have no incentive to spend resources on learning also the structure of Fc. If, as a consequence, their perception of FG is incorrect, their forecast tP,+, may be consistently different from the realization P,+i (even though, it should be emphasized again, their forecast of Z ,+, will still be accurate). As a result, if they were to make forecasts at time t of Z,+,:i>2, their forecasts may be consistently biased due to the bias existing in their estimation of P,,,. This bias represents the profit opportunities existing in speculations with longer maturities. For such longer-term maturities, agents would have to expand the scope of their learning to include also the structure of FG (as well as the structure-if any-of the external shocks). The costs involved in this learning would have to be traded-off against the present value of the gains expected from improving the prediction. On average, these gains are proportional to the bias existing in the forecasts of the Z7’s for 5 > t, which result from their misperception of FG. If information costs are non-negligible it is not at all certain that this extra learning is indeed economically desirable. Nevertheless, developments in the ‘real’ part of the economy, i.e., in the goods markets have direct effect on the monetary part, even in the short-run. This effect, however, is mostly the result of the informative value of demand and supply conditions, the rate of unemployment, the balance of trade, etc. for traders. Seeking signals of future price and exchange-rate trends, traders are often assumed to anchor their expectations on these ‘fundamentals’, which ultimately determine prices and the exchange rate in the long-run .6 In the short-run, though, the determining factor is not the ‘fundamentals’ themselves but the collective opinion about them. If the collective opinion perceives certain developments in the ‘real’ economy as leading to changes in specific monetary variables then, regardless of whether this is true or not, the cumulative response of traders to any expected

56

Semi- Rational Expectations

and Exchange- Rate Dynamics

change is likely to bring about the actual change. For an individual trader in the foreign exchange market, to correctly predict the exchange rate he must know the response of the other traders to ‘news’ about the balance of payments rather than the endogeneous forces working in the economy as an effect of a trade surplus or deficit and their eventual influence on the exchange rate. Traders must therefore devote their intelligence to anticipate what the average opinion expects the average opinion to be-as Keynes’ argument goes-and speculators must speculate on the view of the other speculators.’

II. Exchange-Rate Perhaps the most familiar expectations is Dornbusch’s

Dynamics with Rational Expectations example of an exchange-rate model with now classical model (1976). As a benchmark

rational for the

analysis that follows we summarize in this section the main building blocks of this model. The first block specifies the equilibrium condition in the domestic money market: (1)

m-p

= $y-i,r

where ZV,p andy are the logarithms of the domestic money supply, price level and real output; r is the domestic (nominal) interest rate; C#Iand i, are the parameters of the model, specifying the corresponding elasticities. Henceforth m is assumed to be exogenous andy to be fixed. The second block embodies the assumption of efficient international asset markets which, in the absence of capital controls, eliminates any consistent opportunities for profits through arbitrage, thus leading to the interest rate parity condition (2)

r = r*+x

where r* is the foreign interest rate and x= (e“P-e) is the expected rate of exchange depreciation, e“p and e being the logarithms of the expected and the actual exchange rate, respectively (measured in units of domestic currency per unit of foreign currency). The third building block specifies the subjective expectations formation by traders, assumed to be adaptive of the form, (3)

Pp = &+

(1 - e>e

where F is the logarithm of the long-run equilibrium describes the price adjustment mechanism in the goods (4)

rate. The market,

fourth

block

P = z[V+8(e-_P)+0r]

The domestic rate of inflation is thus proportional to excess demand, given by the expression in the brackets, and it varies negatively with the interest rate (and income) and positively with the relative price (e-p). The equilibrium exchange rate is attained where x=0 andp=O. Inserting these conditions in equations (1) through (4) determines the equilibrium levels of the endogenous variables f, e and p. Taking total differentials of these equations and setting dr* and dy equal to zero implies (5)

dF = dp = dm

Hence, a lq/, increase in the domestic monev supply will cause a 19:) rise in the equilibrium price level and a 1 O; depreciation’of the equilibrium exchange rate, i.e., purchasing power parity (PPP) holds in the long-run. The preceding system of

57

DAVID BIGMAN

equations can be solved for the actual and the anticipated rate, leading to the following reduced form equation

i=

(6)

values

of the exchange

-a(e-a)

where

The motion is generated by a monetary shock; m is thus a step function having zero value up to r=O, at which time the shock occurs, and m(O) thereafter. The instantaneous response to this exogenous shock is a jump of the exchange rate by an amount de

(O+) dm

which overshoots its equilibrium level. For the expectations specified in equation (3) to be correct and accurately predict the actual path of the exchange rate, the changes forecasted by traders must be equal to the actual changes depicted by the model (except, perhaps, for random errors): (9)

E(e’) = (ecxP-e) = -0(e-4

where ,?3 denotes the subjective expectations operator. A subjective expectations coefficient consistent with the model must therefore satisfy: 8=a; i.e., 8 must satisfy the quadratic equation (10)

1ea-e@16+xa)-7?6

= 0

Gray and Turnovsky (1979a) established the transversality conditions under which the solution is stable. They also proved that stability requires that perfect foresight in the sense of equation (9) exists only for t>O but not for t=O. The behaviour of the exchange rate system following a once-and-for-all change in the money supply can now be traced. After an initial overshooting caused by the external monetary shock, the exchange rate is expected to gradually adjust to its long-run level. This gradual adjustment, it should be noted, does not result from slow learning. Instead it represents a correct learning of the structure of the economy and knowledge of structural frictions (specified by the relevant elasticities) which allow only gradual adjustments of the goods and the money markets. It should also be noted that with this knowledge of the structure of the economy, individual agents have in fact perfect foresight over the entire future path of the exchange rate. The dynamic behavior of the exchange rate following a monetary shock is illustrated by the solid and the dotted lines in Figure 2 for alternative representative values of the parameters (the solid line corresponds to a larger value of 0): as an effect of the increase in the money supply, the exchange rate will instantaneously rise to a level higher than that toward which it will eventually converge. Following this one-time overshooting, the rate will decline gradually and monotonically toward its new long-run equilibrium level. Neihans (1977) added a trade balance building block to the monetary model and analyzed exchange-rate dynamics with stock/flow interaction. The basic features of

58

Semi-Rafional Expectations

and Exchange-Rate

Exchange

Rate

D_ymnic.r

Effect

16 l4 -\ L..

\ . -\ . ~‘--.-----..-___.....................

32 6 rl0

U

‘.

$8 0

--

---

I““‘/

c---

:: a-

W

0.

0

11

11

4

“‘1

8

I”’

1’1

12

16

Time

(months)

20

24

28

FIGURE2. his model are, however, essentially similar to those of Dornbusch’s as we shall see shortly. Accounting for the stock/flow interaction in Neihan’s framework leads to the conclusion that any accumulation of foreign assets during the transition to a new equilibrium must subsequently be followed before the new equilibrium is reached. Only

by a decumulation of these assets that way will there be no net

accumulation of foreign assets over the entire adjustment process. Assuming the Marshall-Lerner conditions to be satisfied (either instantaneously or with some lag), the initial overshooting will thus lead to trade surplus accumulation. In Neihan’s model, the country can decumulate having a trade dejcit later on. But a necessary condition for that the currency. The dynamic path of the exchange rate under this be the one described by the broken line in Figure 2. III.

Exchange-Rate

and foreign assets these assets only by is an appreciation of constraint will thus

Dynamics with Semi-Rational Expectations

The model developed in this section is similar in most parts to the Dornbusch model. One distinction is that now we do not assume that the long-run equilibrium exchange rate is known. Instead this rate is inferred from the state of the balance of payments. Accordingly, exchange-rate expectations are determined on the basis of the (known) trade statistics, rather than the (unknown) long-run equilibrium exchange rate. Specifically, the following relationship is assumed by the individual traders between the expected exchange rate and the trade balance-denoted by B.

(11)

In other

words:

a trade surplus

if B>O

then eCXP
if B
then eCXP>e

if B=O

then eexp=f

raises expectations

for an exchange

appreciation

59

DAVID BIGMAN

while a trade deficit raises expectations for an exchange depreciation. The long-run equilibrium rate is that rate at which the current account is balanced. In a dynamic model a simple functional representation of this relationship is given by, 6’ = yb+w(e-4

(12)

Thus although implicitly expectations are formed on the basis of (the unknown) (e-e?, explicitly th ey are formed on the basis of the (known) balance of payments figures (h+yb), which stand as a proxy for the unknown (e-4. that the relationship specified in equation (12), which Suppose, however, individual agents assume to be true, is in fact incorrect and the true relationship is given by (13)

I; = yb+o(e--e‘)-[(e’--m)

only an illustration, indicates that, contrary to Equation (13), which is obviously what the individual agents assume, in the short-run the Marshall-Lerner conditions are not satisfied and thej-curve effect is exhibited. A devaluation will thus lead to a ‘perverse’ response of the current account and a temporary deficit; only after some time will the economy adjust to the new terms of trade, and a surplus will emerge. The gap between the individuals’ perception, specified in equation (12), and the true functional relationship, specified in equation (13), raises two types of questions: first, are there endogenous forces in the economy that will bring the rational, profit and utility maximizing individuals to realize their mistaken perception? Second, if there are no such forces and the bias thus persists, what would be its consequences? To answer the first question we retain the assumption that implicitly exchange-rate expectations are formed adaptively, as in equation (3). Combining that equation with equation (12) allows the specification of agents’ expectations in terms of the balance of payments statistics, (14)

E(eJ

= PP-e

= -$

(E;+yb)

If, however, the true functional form of the trade account is given by equation (13), the implicit relationship between the expected change in the exchange rate and the long-run equilibrium rate is obtained by inserting equation (13) into equation (14), yielding (15)

E’(eJ = -z

[w(e-g-t(i-M)]

and not by -&e-e7 as agents incorrectly assume. To simplify the notation we normalize r* andp* to be zero (i.e., we specify r andp The long-run equilibrium in terms of deviations from r* and p*, respectively). exchange rate is given by the long-run PPP rate, 6=p. Following a one time monetary shock equal to tll, the domestic price level would rise so that eventually p=,. Combining equations (1) and (2) together with the long-run relationships thus implies (16)

p = dflx

and (17)

p = m+I&

Semi- Rational Ex-pectations

60

Equations following

(4) and (15) relationships

thus

lead,

and Exchange-

after

some

Rate D_pnamics

algebraic

manipulations,

to the

and

Combining derivatives

equations

(17),

(1 S),

and

thus leads to the following ,4e’+Cf=

(20)

(19)

and

functional

solving

for

e and

its time

form:

D+F(e-_+Gm

where

D = n*r,~ F = n[6(1 +le)-de] G = ; From

equation

(20)

+qhLa)-(l+/Le)

it can also be established de(O+) p= dm

l_

that 0

ey(u - a) - 2ew

Hence the initial reaction of the exchange rate to a monetary shock may be either an depending on the specific values of the overshooting or an undershooting, parameters. In the simulation analysis below it is demonstrated, however, that even if the exchange rate does not initially overshoot its equilibrium level, it later periods.
(21)

Ci-(F+,40)

will do so in back to its the rate of to the actual and (20) to

(e-e-, = D+Gm

The solution of this equation yields the dynamic path of the exchange rate. Along this path all instantaneous expectations are realized, i.e., at any time t (except for t=O) e(i)=i(t+). Nevertheless, predictions made at time t for later periods will not be realized, since e(f) #?(f+); the reason being the bias in the prediction of the trade balance, i.e., e(b) Z&t+).

61

DAVID BIGMAN

Still, if the predictions relevant for agents are short-term only, this bias will not cause them any losses, and they should not spend resources on obtaining the information in order to improve their balance of payments predictions. If, on the other hand, longer-term forecasts are also relevant, they will compare the present value of the gains expected from reducing the estimation bias with the information costs involved in order to determine the desirability of further learning. If information costs make further learning undesirable, the bias may persist. This, however, cannot be taken to indicate that the market is inefficient, nor that traders are irrational. For an individual trader to correctly forecast next period’s exchange rate he must learn the (incorrect) functional relationship in equation (13) if the others believe it to be true, rather than the (correct) one in equation (12). A block diagram describing the functional form of all the transfer functions in the model (written in their Laplace transform) and the details of the stock-flow interaction, is given in Figure 7 in the appendix. We can now turn to examine the second question, namely, the consequences of a persistent bias in the individuals’ perception. This is done via simulation analysis of the dynamic path of the exchange rate in this model for representative values of the parameters. In general the parameter space which satisfies the stability condition can be divided into two subspaces: one in which the dynamic path is monotonic and the other in which it is oscillatory. Figure 3 describes a typical path which is both stable and monotonic. A number of differences between this path and the one obtained with the Dornbusch model should be noted. First, in the present model the exchange rate need not instantaneously overshoot its new equilibrium level (the level 10 in Figure 3 which corresponds to a monetary shock of lOoi,). Following the initial shock, it rises, however, gradually above its new equilibrium level, reaching its peak only 7 to 8 months after the shock. The rate then gradually declines, converging to its long-run level, though at a pace considerably slower than that in

Exchange

Rate Effect

W 2

8-

rz p6 0

4-

5 r W

20

I 0

L

10

1

I

90

1

I

I

I

30 40 Time (months) FIGURE 3.

I

I

50

I

I 60

62

Semi- Rational Expectations

and Exchange-

Trade Balance

Rate Dynamics

Effect I

-2

I 0

i

I

I

80

I

40

Time

I 60

I

I 80

I

(months!

FIGURE4. the Dornbusch model. Figure 4 describes the dynamic path of the trade balance which corresponds to the exchange-rate path described in Figure 3. It shows that as a result of the J-curve effect, a trade deficit will be revealed immediately after the devaluation. Following this ‘perverse’ response, a trade surplus later emerges; but, after a period of about 18 months, the surplus gradually declines and eventually vanishes. It is possible also to envisage what effect Neihans’s approach would have within this framework. The constraint of zero net accumulation of foreign assets is represented by the constraint

(22)

ji

B, dt

=

0

0

As a consequence, the surplus revealed during most of the overshooting period will have to be balanced by a deficit of an almost equal amount later on. This can happen only if the exchange rate will later decline below its long-run equilibrium level (i.e., appreciates). The actual undershooting will, however, be even larger than that needed to offset the previous surplus due to the inertia in the stock/flow adjustment, and will lead to a net trade deficit. This, in turn, will force the rate to rise again in order to eliminate the deficit and a new overshooting will occur. Under these circumstances the system may continue to oscillate for a very long period of time. Figure 5 describes a typical path of the exchange rate which is still stable but no longer monotonic. It should be emphasized again that this path is also the one exact4 forecasted by the traders in the exchange market (except, possibly, for a random error) and in each and every minute following the shock the exchange rate forecasted for the next period will indeed be the one realized in financial markets in the next period. Agents thus suffer no losses even though they no longer have perfect foresight over the entire dynamic path. A number of things should be noted

63

DAVID BIGMAN

Exchange I

I

I

I

I 40

I

Rate Effect

I

I

I

I

80 Time

I

I

I

I

I

I

I 160

1

120

(months)

FIGURE 5.

in regard to this path. First, the extent of overshooting here is much larger than in the path described in Figure 2. The reason is the difference in the level of 8 between the two simulation experiments, each associated with a different parameter level in the solution subspace. In the present simulation 8 is much smaller than in the previous one, and this means much smaller elasticities and thus more rigid structure and slower adjustments in the goods market but much higher response in the asset market to any interest rate disparity. Second, the exchange rate converges to its long-run level at a much slower pace and the pace becomes slower the smaller is 8. Third, the overshooting and undershooting of the exchange rate also produce oscillatory movements of the trade balance which can be seen in Figure 6. IV. Concluding

Remarks

A fundamental conclusion of the neoclassical theory is that competition among rational though self-centered individuals will bring the economy at large to a state which is collectively most desirable. 1n.a stationary framework this is manifested in that the competitive equilibrium is Pareto-optimal. In growth models this is manifested in that the competitive dynamic path dominates, in terms of efficiency, all other feasible paths. The REH extends this conclusion to a stochastic world. The premise underlying this hypothesis is that rational, profit and utility maximizing individuals, use all currently available information--assumed to be known to everyone-to form optimal forecasts. The structure of the economic process which will ultimately generate the actual outcomes in question is thus known to all consumers and producers, and their forecasts will differ from the eventual outcome only by purely random errors. The paper draws a distinction between knowledge involving a// contemporeneous, economy wide data and the structure of the entire economic process, and knowledge involving certain segments of the economic structure which are

64

Semi- Rational Expectations

Trade 40

I

I

and Exchange-

Balance

I

I

Rate QpnamicJ

Effect

I

I

I

I

I

----___ -5

I 0

I 40

I

I 80

Time

I

I 120

I

I 160

I _

(months)

FIGURE 6.

relevant for the forecasts in question. The former is associated with long-term forecasts and leads to perfect foresight of the entire dynamic path of the pertinent economic variables while the latter is associated with short-term forecasts and leads to myopic perfect foresight. The former is thus characteristic of collective rationality in that it yields the most efficient dynamic path for the economy at large, while the latter is characteristic of individual rationality, which must reckon with costly information and time-consuming learning. Nonetheless, individual, or ‘semi-rational’ expectations are still efficient-as this term is statistically defined in the literature, since expectations are still realized. The dynamic path generated under ‘semi-rational’ expectations can, however, be substantially different from the one generated under ‘fully’-rational expectations. The main conclusion emerging from this analysis is that in a stochastic world individual rationality may not bring the economy as a whole to the most desirable dynamic path-contrary to the outcome in a deterministic world-and individual rationality need not be consistent with collective rationality. Following the herd is, in most cases, individually very rational, no matter whether the herd is heading in the desirable direction. By assuming an individual cognitive process which is concerned with all segments of the economic model irrespective of the information costs on the one hand, and the contribution of each bit of information to improving the forecasts, the REH avoided any such inconsistency. Allowing for these considerations is likely to result in potentially significant and persistent biases.

65

DAVID BIGMAN

Appendix -----w-7 7 -TRADE BALANCE e a

I 1 1

_ o-sk

I I

4

V+S

I

I L

---

J

---

l----e

EXOGENOUS

SHOCKS

e -oASSET ” MARKET1 -F

P

I---------

I

J

L -------; I -51

‘1

I I -l

~FxPECT~T~O~%~O;;M~TION~

FIGURE 7.

Notes this point. See also Colander and Guthrie (1980). 1. Ando (1978) and Kantor (1979) have emphasized analyzed what they have termed 2. Darby (1976) and Feige and Pearce (1976) have previously economically rational expectations under conditions of costly acquisition and processing of information. Darby assumes that given costs are associated with acquiring any series while Feige and Pearce assume variable amounts of information. Since neither formal solution to the optimal use of information is applied here, it is appropriate to refer to the expectations examined as semi-rational. and Burmeister (1977) define ‘perfect myopic foresight’ in a way which is similar to the 3. Turnovsky first of the above two definitions. Their subsequent analysis leads, however, to perfect foresight-in correspondance to the reconddefinition-and there is no room in their analysis for any inconsistency between the two. 4. See, for instance, Barro (1976), Lucas (1973). (1976, 1980). Kouri (1976, 1980). and Mussa (1976). 5. See, for instance, Dornbusch 6. Kouri and de Macedo (1978) and Rodriguez (1980) made this point in reference to the effect of the trade balance on exchange-rate expectations. See also Flood and Hodrick (198’2), Frenkel (1981). 7. Keynes (1921, 1936). See also Begg (1982).

References ANDO, A., ‘On a Theoretical and Empirical Basis of Macroeconometric Models’, Pennsylvania, unpublished, 1978. ARROW, K.J., ‘The Future and the Present in Economic Life’, Econ. Znq., April 1978, BARRO, R.J., ‘Rational Expectations and the Role of Monetary Policy’,j. Monet. Econ., 2: l-32. BEGG, D.K.H., ‘Rational Expectations, Wage Rigidity and Involuntary Unemployment: Theory’, Oxford Econ. Papers, March 1982, 34: 23-47. COLANDER, D.C. AND R.S. GUTHRIE, ‘Great Expectations: What the Dickens Expectations” Mean?‘, J. Post Kgmesian Em., Winter 198@81, 3: 219-234.

University

of

16: 157-169. January 1976, A Particular do

“Rational

66

Semi- Rational Expectations

and Exchange- Rate Dyamics

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