An Empirical Examination of the Post Keynesian View of Forward Exchange Rates

8/12/2019 An Empirical Examination of the Post Keynesian View of Forward Exchange Rates

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Introduction

One of the issues on which there is a rift between neoclassical and Post Keynesian

economists is the ability of the monetary authorities to control interest rates in an open

economy. The neoclassical or mainstream view is that it is impossible to control or

determine the level of interest rates, given the effect of openness and capital flows in the

era of globalisation. In other words, the mone tary authorities cannot set real interest

rates that are different from those ruling the rest of the world (Lavoie, 2000, p 168). By

contrast, the Post Keynesian view, as put forward by Lavoie (2000, p 163), is that even

in an open economy with financial mobility, central banks retain the ability to set interest

rates of their choice, within a wide spectrum.

The mainstream neoclassical view is based on the real interest parity (RIP) condition,

stipulating that real interest rates must be equated across countries. As Smithin (2002, p

224) puts it, RIP implies that there is no possibility for any independent control over the

real rate of interest for any individual jurisdiction. Hence, according to Smithin,

interest rates in the small open economy must conform to interest rates established in

world markets or possibly by the world central bank. If the real interest rate is

determined in the world economy, exogenously according to RIP, the nominal interest

rate can only be influenced by controlling the inflation rate. If the inflation rate is beyond

the control of the monetary authorities, then the nominal interest rate cannot be

influenced, since it will be determined as the difference between the exogenous real

interest rate and the domestic inflation rate (which is also determined exogenously by the

world money supply, according to the monetarist theory of inflation). The question that


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arises here concerns the empirical validity of RIP, for if RIP is not valid then this pillar of

the mainstream argument collapses.

RIP is the most stringent of the four international parity conditions, which also include

covered interest parity (CIP), uncovered interest parity (UIP) and purchasing power

parity (PPP).1It is more stringent because the other three conditions need to be satisfied

for RIP to be satisfied. The empirical evidence shows significant deviations from PPP

and UIP but not from CIP. Let us for the purpose of this paper concentrate on UIP, which

is obtained by combining CIP and unbiased efficiency. This means that the empirical

validity of UIP, and hence RIP, requires the empirical validity of the unbiased efficiency

hypotheses stipulating that the forward rate is an unbiased and efficient predictor of the

spot rate prevailing in the future (on the maturity of the underlying forward contract). The

Post Keynesian view, as put forward by Lavoie (2000), is that the forward rate is not a

good predictor of the spot rate. If this view is sound then RIP is not empirically valid,

which casts doubt on the mainstream proposition that the monetary authorities cannot

control interest rates.

The objective of this paper is to demonstrate that the unbiased efficiency hypothesis does

not hold. It is argued that unbiased efficiency is not substantiated by theoretical

plausibility nor is it supported by empirical evidence. It will be specifically shown that

the spot and forward exchange rates are related by a contemporaneous relationship (CIP)

1For a comprehensive treatment of the parity conditions, see Moosa and Bhatti (1997).


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rather than a lagged relationship (unbiased efficiency), which necessarily means that the

forward rate cannot be used to forecast the spot rate on an ex ante basis.

The Model

The real interest rate differential can be written as follows:

)()( * 1*

1

*

++ = tttttt iirr (1)

where ris the real interest rate, iis the nominal interest rate, is the subsequent inflation

rate and an asterisk denotes the corresponding foreign (as opposed to domestic) variable.

Obviously, RIP will be violated if 0* tt rr . The right hand side of equation (1) can be

manipulated by adding and subtracting the percentage change in the exchange rate, 1+ ts ,

and rearranging to obtain

)()( 11*

11

**

++++ ++= tttttttt ssiirr (2)

which shows that deviations from RIP (as represented by the real interest differential) is

equal the deviations from UIP (represented by the uncovered interest differential) and

deviations from PPP. Equation (2) can be modified further by adding and subtracting the

forward spread,f, and rearranging to obtain

)()()( 11*

11

**

++++ +++= tttttttttt ssffiirr (3)

in which case deviations from UIP are split into deviations from CIP (covered interest

differential) and unbiased efficiency (the forward rate forecasting error). If there are no

deviations from CIP and unbiased efficiency then we have

*

ttt iif = (4)

1+= tt sf (5)


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which are CIP and unbiased efficiency respectively (written in percentage terms). Since

there is no empirical evidence supporting the hypothesis that the exchange rate moves by

a rate that is equal to (or even related to) the interest rate differential, equations (4) and

(5) cannot be mutually consistent, and one of them must be invalid. Our task here to find

out which of these two relationships is invalid. Before we take this matter further, we will

rewrite equations (4) and (5) in levels using exact formulas as follows

+

+=

*1

1

t

t

tti

iSF (6)

1+=

tt

SF (7)

where Sand F are the spot and forward exchange rates respectively. For the purpose of

empirical testing we need to write equations (6) and (7) in stochastic forms as

ttt vFS ++= (8)

ttt uFS ++= 1 (9)

where 0= , )1/()1( *tt ii ++= , 0= and 1= . Note that is a measure of the

interest rate differential, such that 1= if *tt ii = .2 Equation (8) is a legitimate

modification of equation (6) once we take into account transaction costs and

measurement errors. While equation (8), which represents CIP, tells us that the

relationship between the spot and forward exchange rates is contemporaneous, equation

(9), which represents unbiased efficiency, tells us that it is lagged.

2Equations (8) and (9) can be alternatively written as the stochastic versions of (4) and (5), which would

give )( *ttt

iif += and1++= tt sf respectively. The empirical work can be done on the basis of

these specifications if there is concern about nonstationarity and unit roots, but this is not a problem with

the estimation procedure used in this paper. Either way, the results will not be affected qualitatively.


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The Post Keynesian or cambistview on this issue can be found in Smithin (1994) based

on the argument of Coulobis and Prissert (1974). The argument is that while CIP holds

always perfectly by definition, the forward exchange rate is not an expectation variable

but rather the result of a simple arithmetic operation (Lavoie, 2000, p 172). Therefore,

equation (8) should fit very well with the coefficient restrictions satisfied, because it

represents the simple arithmetic operation. Conversely, equation (9) would produce

poor results, including the violation of coefficient restrictions because it represents a

hypothesis that lacks theoretical plausibility. Smithin (2002, p 220) explains the Post

Keynesian view with reference to equation (9) by suggesting that Post Keynesian

authors presumably do not want to suggest that the discrepancy between the forward

exchange rate and the expected future spot rate is tightly determined by any kind of

statistical/probabilistic process. Moreover, Smithin argues that the failure of unbiased

efficiency can be explained in theoretical terms.

The prime objective of this paper is to find out which of these two relationships is

empirically valid, as judged by the goodness of fit and diagnostics of the estimated

models. But before we proceed to empirical testing we will discuss the theoretical

foundations of CIP and unbiased efficiency, hence following Smithins argument that

some theoretical explanation can be suggested for the failure of unbiased efficiency.

Some Theoretical Considerations: Unbiased Efficiency

The rationale for the unbiased efficiency hypothesis, postulating that the forward rate is

an unbiased and efficient forecaster of the spot rate, can be illustrated as follows. If a


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speculator believes that the one-period forward exchange rate will be lower than the spot

rate prevailing at time t+1, it will be profitable to buy (the foreign currency) forward and

sell spot when the forward contract matures at t+1. Let 1+tS be the spot rate prevailing at

time t+1 where tis the present time, and tF be the forward rate agreed upon at time tfor

delivery at time t+1. If the speculator is correct, he or she will make profit, m, amounting

to the difference between the selling rate and the buying rate. Hence

ttt FSm = ++ 11 (10)

If this speculator acts on the basis of public information, then there is no reason why

other speculators do not do the same thing to obtain the same profit as the first speculator

(hence, the assumption of rational expectations). If this happens, the resulting increase in

the demand for forward contracts will raise the forward rate and reduce profit until the

latter disappears. At time t, when the decision to speculate is taken, 1+tS is not known,

which means that the speculator has to act on the basis of his or her expectation with

respect to the spot exchange rate. Hence, the speculator buys forward at time tand sells

spot at time t+1 if the expected value of the spot exchange rate is higher than the forward

rate, that is if ttt FSE >+ )( 1 , whereEis the expectation operator. Speculation comes to

an end when

ttt FSE =+ )( 1 (11)

or if profit is expected to be zero, that is

0)( 1 =+tt mE (12)

The term representing speculative profit, 1+tm , is also the forecasting error when the

forward exchange rate is used as a forecaster of the spot rate. Thus, the idea is that


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changes in the forces of supply and demand resulting from the activity of speculators

keep the forecasting error (speculative profit) at zero, making the forward rate (on

average) equal to the spot rate prevailing on the maturity date of the forward contract.

On the surface, this line of reasoning sounds fine, but the problem is that the empirical

evidence for the unbiased efficiency hypothesis is rather weak (see, for example, Lewis,

1995; Engel, 1996; Wang and Jones, 2002; Zhu, 2002). In general, it is agreed now that

unbiased efficiency does not hold, and this failure is typically attributed to the presence

of a (time-varying) risk premium and/or the irrationality of expectations. The presence of

the risk premium is represented by the violation of the restriction 0= in equation (9),

which will be tested later. For the time being, we will discuss the other pillar of unbiased

efficiency, that of rational expectations.

It has been conclusively established that the idea of rational expectations in the foreign

exchange market is bizarre, to say the least. To start with, the rational expectations

hypothesis precludes heterogeneity in favour of some representative agent hypothesis.

But the literature disputes the validity of this hypothesis, rejecting it in favour of

heterogeneity on the grounds that the former is inconsistent with observed trading

behaviour and the existence of speculative markets. Indeed, it is arguable that there is no

incentive to trade if all market participants are identical with respect to information,

endowments and trading strategies (Frechette and Weaver, 2001). Brock and Hommes

(1997), Cartapanis (1996), and Dufey and Kazemi (1991) have demonstrated that

persistence of heterogeneity can result in boom and bust behaviour under incomplete


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information. Furthermore, Harrison and Kreps (1978), Varian (1985), De Long et al.

(1990), Harris and Raviv (1993), and Wang (1998) have shown that heterogeneity can

lead to market behaviour that is similar to what is observed empirically.

In response to concerns about the representative agent hypothesis, financial economists

started to model the behaviour of traders in speculative markets in terms of heterogeneity.

Chavas (1999) views market participants to fall in three categories in terms of how they

form expectations: nave, quasi-rational and rational. Weaver and Zhang (1999) allowed

for a continuum of heterogeneity in expectations and explained the implications of the

extent of heterogeneity for price level and volatility in speculative markets. Frechette and

Weaver (2001) classify market participants by the direction of bias in their expectations,

their bullish or bearish sentiment, rather than by how they form expectations. The

message that comes out of this research is loud and clear: homogeneity is conducive to

the emergence of one-sided markets, whereas heterogeneity is more consistent with

behaviour in speculative markets characterised by active trading and volatility.

There is indeed little evidence for rational expectations in the foreign exchange market,

which is the conclusion of studies based on both survey data and the demand for money

approach. 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 rational expectations hypothesis. Davidson (1982) argues against the rational

expectations hypothesis by asserting that it is a poor guide to real world economic

behaviour because it assumes that market participants passively forecast events rather


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than cause them. Both Harvey (1999) and Moosa (1999) find no evidence for rational

expectations in the foreign exchange market based on survey data and estimates of the

demand for money function respectively. Moosa (2002) finds strong empirical support

for the Post Keynesian hypothesis on expectation formation in the foreign exchange

market, hence rejecting rational expectations.

Some Theoretical Considerations: Covered Interest Parity

Apart from the presence of the risk premium and the irrationality of expectations some

other explanations have been put forward for the failure of the unbiased efficiency

hypothesis. These explanations include covered interest parity, the peso problem, central

bank intervention, transaction costs, political risk, foreign exchange risk, purchasing

power risk, interest rate risk, differences in real interest and exchange rates, and the effect

of news (see Moosa, 2000, for details). Out of these, the least emphasised but the most

plausible explanation is that of covered interest parity, which reflects the Post Keynesian

view. This is because this condition implies that the spot and forward rates are related

contemporaneously, which necessarily means that the lagged model represented by

equation (9) is misspecified.3

The Post Keynesian view stipulates that the forward rate is determined by the CIP

(deterministic) equation (6), which Lavoie calls an arithmetic operation. This equation

can be derived either as an arbitrage condition or a hedging condition. Lavoie (2000, 175)

3The idea here is that the forward rate (and hence the forward spread) does not reflect exchange rate

expectations but rather the interest rate differential. It is this inconsistency between CIP and unbiasedness

that can be used to explain the failure of unbiased efficiency.


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seems to suggest that it is more appropriately derived and defined as a hedging condition.

This is at least my interpretation of the following quotations:

An obvious implication of the cambist view of forward exchange market is that

covered interest arbitrage has no impact whatsoever on flows of funds or foreignreserves.. When covered arbitrageurs decide to sell spot and buy forward

(domestic currency), commercial banks take the buy forward order of theircustomers and are the counterpart to it. To cover themselves, banks buydomestic currency on the spot market. (Lavoie, 2000, p 175).

The forward exchange rate is set by bank dealers at a rate that will allow banks tocover their costs, and the markup is given by the interest cost differential.(Lavoie, 2000, p 174).

However, it can be demonstrated that the deterministic CIP equation (6) can be derived

either as an arbitrage or a hedging condition. In the presence of bid-offer spreads,

however, the hedging condition is more plausible, which supports Lavoies view. We will

now illustrate this proposition by deriving CIP as an arbitrage and a hedging condition,

starting with the case of no bid-offer spreads.

Consider covered arbitrage by going short on the domestic currency and long on the

foreign currency while covering the long position forward. By borrowing (one unit of)

the domestic currency at the domestic interest rate, i, converting the borrowed funds at

the current spot rate, S, and investing the funds at the foreign interest rate, *i , the

arbitrager obtains )1)(/1( *iS + units of the foreign currency. The domestic currency

value of the proceeds when they are converted at the forward rate is )1)(/( *iSF + . Hence

arbitrage profit is


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)1()1( * iiS

Fm ++= (13)

CIP is the no-arbitrage condition obtained when 0=m , which gives

)1()1( * iiS

F +=+ (14)

It is obvious that by manipulating equation (14) we obtain equation (6). The same result

is obtained by conducting arbitrage in the opposite direction (see Moosa, 2003a, 2003b).

Now, we derive equation (6) as a hedging condition. Consider a bank that grants a

customer a forward contract whereby the bank would provide K units of the foreign

currency some time in the future. To cover its short (forward) position on the foreign

currency, the bank borrows an amount equal to )1/( *iKS + domestic currency units. This

amount is converted into the foreign currency at the spot exchange rate, which in turn is

invested at *i to obtain Kunits of the foreign currency on maturity. When the domestic

currency loan becomes due, the bank has to pay )1/()1(

*

iiKS ++ . Thus, the implicit

forward rate is given by

+

+=

++=

*

*

1

1)1/()1(

i

iS

K

iiKSF (15)

which again gives the CIP equation (6). The same result is obtained when we consider a

bank granting a forward contract to buy the foreign currency (see Moosa, 2003a, 2003b).

When the bid-offer spreads in interest and exchange rates are allowed for, the arbitrage

condition seems to break down, whereas the hedging condition still works. Consider

arbitrage first, repeating the same operation described earlier. In this case the domestic


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currency value of the proceeds is )1)(/( *bab iSF + , where the subscripts aand bdenote

the offer and bid rates respectively. Thus, arbitrage profit would be

)1()1(*

aba

b

iiS

F

m ++= (16)

The problem here is that the no-arbitrate condition can no longer defined as 0=m , but

rather as 0>m , in which case the equivalent of equation (6) cannot be derived. It is easy

to demonstrate that if we work on the assumption 0=m , we obtain the bizarre result that

ab FF > (Moosa 2003b).

This problem does not arise when we derive the equivalent of equation (6) as a hedging

condition. In this case the value of the domestic currency loan is )1/()1( *baa iiKS ++ ,

which gives

+

+=

*1

1

b

a

aai

iSF (17)

Likewise, it can be shown that

+

+=

*1

1

a

b

bbi

iSF (18)

in which case ba FF > . This proves Lovies view that the CIP condition is more

appropriately defined as a hedging rather than an arbitrage condition. Furthermore,

viewing CIP as a hedging condition may be more appropriate than viewing it as an

arbitrage relationship because the latter requires perfect capital mobility, whereas the

former does not need this requirement. CIP, it is suggested, holds at all times, regardless


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of the efficiency of capital markets, and whether or not there is perfect capital mobility

(Lavoie, 2002, p 238).

Irrespective of how it is derived, the CIP equation whereby the forward rate is determined

tells us that the spot-forward relationship is contemporaneous, not lagged as the unbiased

efficiency hypothesis suggests. Now, we turn to the empirical results to show that the

lagged relationship is misspecified.

Data and Empirical Results

The empirical results presented in this study are based on quarterly data covering the

period 1980:1-2000:4 on six exchange rates involving the following currencies: U.S.

dollar (USD), Canadian dollar (CAD), Japanese yen (JPY), and British pound (GBP).

The data were obtained from the OECDsMain Economic Indicators. We start with some

informal examination of the behaviour of spot and exchange rates.

Figure 1 shows the relationship between the spot and (lagged) forward exchange rates

involving the four currencies. The observed behaviour of the two rates obviously

supports the contemporaneous rather than the lagged relationship. We can see that the

lagged forward rate reverses direction after the spot rate, which means that the former is a

follower, not a predictor, of the latter. This behaviour shows that the two rates are

determined jointly and that they are related by a contemporaneous relationship, which is

CIP. Given the behaviour exhibited by the spot and forward rates, the forward rate must

be a very bad forecaster berceuse it consistently misses the turning points in the spot rate.


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In fact, the forward rate fails to predict turning points consistently, and this is why we

have errors of directions ranging between 59 per cent of total observations in the case of

the JPY/USD rate and 33.7 per cent in the case of the GBP/USD rate. In practical

financial decision making (such as hedging and speculation) forecasting the direction of

change may be more important than forecasting the magnitude of change. By definition,

if the spot and forward rates are contemporaneously related, then the forward rate cannot

be used to forecast the spot rate on an ex ante basis, which is what matters in practice.

Now, we present the results of estimating CIP and the unbiased efficiency model as

represented by equations (8) and (9). In order to allow for time variation in the

coefficients over time, the two equations are written in a TVP framework as follows:

ttttt vFS ++= (19)

ttttt uFS ++= 1 (20)

The terms t and t represent (time-varying) stochastic trends, which may represent the

variables not appearing explicitly on the right hand side of the equations (missing

variables, if any). According to the deterministic versions of these equations, there are no

missing variables. In equation (20), however, t may be taken to represent a time-

varying risk premium. These trends are specified in such a way as to allow for

possibilities ranging from I(0) to I(2) variables, without having to worry about unit root

testing, as the data will speak for itself.4The estimation method is maximum likelihood

4With respect to equation (19), for example,

t is specified as

tttt ++= 11 , where ttt += 1 ,

),0(~2 NIDt and ),0(~

2 NIDt . Whether the underlying time series is I(0), I(1) or I(2) depends on


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coupled with the recursive routine of the Kalman filter. This requires writing the two

equations in state space form (see, for example, Cuthbertson et al, 1992; Harvey, 1989;

Koopman et al, 1995).

The results of estimating equations (19) and (20) in a TVP framework are presented in

Table 1, which reports the estimated coefficients of the final state vector (with the t

statistics in parentheses) as well as some diagnostics and goodness of fit measures. Q is

the Ljung-Box test statistic for serial correlation, which is distributed as )8(2 .His a test

statistic for heteroscedasticity, distributed as F(27,27). The AICand BICare respectively

Akaikes Information Criterion and the Schawrtz Bayesian Information Criterion.

The results tell us that equation (19), which represents CIP, fits very well and passes the

diagnostic tests for serial correlation and heteroscedasticity in all cases. The coefficients

have the anticipated values, as 0=t and 0>t . In contrast, equation (20), which

represents unbiased efficiency, fails to pass the diagnostic test for serial correlation in two

cases, and it is inferior to equation (19) in terms of the BICand AIC. More importantly,

the coefficient restrictions 0=t and 1=t are rejected consistently. Moreover, the

restriction 0=t cannot be rejected in four out of six cases, implying no connection

between the spot and lagged forward rates. The rejection of the restriction 0=t is

interpreted in the literature to indicate the presence of a risk premium, to which the

failure of unbiased efficiency is attributed. In fact this result is taken to be a salvation for

the variances2 and

2 . Since exchange rates typically follow a random walk with little or no drift, it is

likely the case that 0=t

.


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deviations from CIP, and hence it may or may not be statistically significant. 5 It is

important to point out at this juncture that this result is not inconsistent with Smithins

(2002) argument about t . The presence of this term is theoretically plausible on the

grounds suggested by Smithin or what is suggested in this paper. However, the

importance of this term is a purely empirical matter. It remains the case here that the

results tell us that the relationship is indeed contemporaneous rather than lagged.

Further Empirical Results

In this section further results are presented to demonstrate that the relationship between

the spot and forward rates is contemporaneous rather than lagged. The results are

obtained from non-nested model selection tests and measures of forecasting accuracy. For

the purpose of conducting non-nested model selection tests, let 1M be the

contemporaneous model and 2M the lagged model. These two models are non-nested in

the sense that the explanatory variables of one model are not linear combinations of the

explanatory variables of the other. By applying non-nested model selection tests, we can

tell whether or not 1M is preferred to 2M , and hence whether tF or 1tF is the

appropriate explanatory variable. For this purpose, six model selection tests are used:Nis

the Cox (1961, 1962) test as formulated in Pesaran (1974); NT is the adjusted Cox test

formulated by Godfrey and Pesaran (1983); Wis the Wald-type test proposed by Godfrey

and Pesaran (1983); J is the Davidson-MacKinnon (1981) test; JA is the Fisher-McAleer

5Apart from transaction costs, these factors include political risk, tax differentials, liquidity differences,

capital controls, capital market imperfections and speculation. Moosa (2003b) presents a model showing

how speculation could lead to deviations from CIP and hence the significance oft

. This model is based

on a similar argument to that presented by Lavoie (2002) on the role of speculation in the forward market.


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(1981) test; andENis the encompassing test proposed, inter alia, by Mizon and Richard

(1986). All of the test statistics have t distribution except the EN test, which has an F

distribution with (1,104) degrees of freedom. In testing 1M against 2M , a significant test

statistic implies the rejection of 1M in favour of 2M and vice versa. The results, which

are presented in Table 3, show that all tests lead to consistent results: 1M cannot be

rejected against 2M , but 2M is always rejected against 1M . Hence, 1M is the preferred

model, implying the superiority of the contemporaneous relationship.

Now, we compare the (ex post out-of-sample) forecasting power of the lagged and

contemporaneous models represented by equations (19) and (20) respectively. The

purpose of this exercise is to demonstrate that the contemporaneous model is more

powerful in forecasting the spot exchange rate out of sample, hence enhancing the results

showing that the lagged model is not correctly specified.

For this purpose the two models are estimated over the period up to 1996:4, then the

estimated models are used to forecast the spot exchange rate over the period 1997:1-

2000:4. Table 4 reports the mean square error (MSE) and the root mean square error

(RMSE) of the contemporaneous and lagged models. The results show that the

contemporaneous model has a lower MSE and RMSE than the lagged model. This is also

shown in Figure 2, which plots the forecasting errors of the two models

To find out if the difference in the forecasting power of the two models is statistically

significant, we use the Ashley, Granger and Schmalensee (1980) AGS test for the


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difference of the RMSEs of two models. The AGS test requires the estimation of the

linear regression

ttt uXXD ++= )(10 (22)

where ttt wwD 21 = , ttt wwX 21 += , Xis the mean of X, tw1 is the out-of-sample error

at time tof the model with the higher RMSE (the lagged model) and tw2 is the out-of-

sample error at time tof the model with the lower RMSE (the contemporaneous model).

If the sample mean of the forecast errors is negative, the forecast error series must be

multiplied by 1 before running the regression.

The estimates of the intercept term ( 0 ) and the slope ( 1 ) are used to test the statistical

difference between the RMSEs of the contemporaneous and lagged models. If the

estimates of 0 and 1 are both positive, then a Wald test of the joint hypothesis

0: 100 ==H is appropriate. However, if one of the estimates is negative and

statistically significant then the test is inconclusive. But if the estimate is negative and

statistically insignificant the test remains conclusive, in which case significance is

determined by the upper-tail of the t-test on the positive coefficient estimate.

The results of the AGS test are presented in Table 5. Since all of the coefficients are

positive a Wald test for the joint coefficient restriction 010

== is used. It is obvious

that the null hypothesis (that the RMSE of the contemporaneous model is not

significantly different from that of the lagged model) is decisively rejected in all cases.

Thus, we can firmly state the conclusion that the contemporaneous model is superior to


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the lagged model, which is inferior because it is misspecified.

It is noteworthy that, by its very nature, the contemporaneous model cannot be used for

ex ante forecasting. Hence, the forward rate cannot be used as a forecaster of the spot

rate. Indeed if one suggests that the forward rate can be used as a forecaster of the spot

rate, one can also argue that the spot rate is a forecaster of the forward rate. The validity

of the contemporaneous model tells us that the two rates are determined jointly by other

(the same) factors, and so they can only be predicted jointly.

Conclusions

The results presented in this paper, on the basis of an extensive set of empirical tests,

explain what Ethier (1988, p 516) calls the neoclassical puzzle that day-to-day

movements in forward rates tend to be accompanied by almost identical day-to-day

movements in current (not future) spot rates. The explanation, which is supported by the

empirical results presented here, is that the spot-forward relationship is contemporaneous,

as represented by covered interest parity, rather than lagged, as represented by the

unbiased efficiency hypothesis. It was demonstrated explicitly and comprehensively that

the forward rate cannot be used to forecast the spot rate because the two rates are

determined jointly and contemporaneously. The failure of unbiased efficiency can be

rationalised theoretically on several grounds, most notably the failure of the ill-fated

rational expectations hypothesis. While the initial empirical results show that the failure

of unbiased effect can be attributed to the presence of the risk premium, or whatever it

may be called, other results show that what appears to be a risk premium is a stochastic

trend reflecting missing variables or, in the case of a correctly specified model, such


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factors as transaction costs. As far as CIP is concerned, this paper puts forward the

argument that this condition is more appropriately perceived and derived as a hedging

rather than an arbitrage condition, which is consistent with the argument put forward by

Lavoie (2000). However, what is important for the main objective of this paper is not

how CIP is derived but rather that it represents the correct specification of the spot-

forward relationship.

The finding that the spot rate is related to the contemporaneous rather than the lagged

forward rate implies the failure of the unbiased efficiency hypothesis. Given that this is a

necessary condition for RIP to hold, this finding implies the empirical failure of RIP,

irrespective of the validity of PPP (which is another necessary condition). If this is the

case then the Post Keynesian view that the monetary authorities can control domestic

interest rates is valid, or at least that the opposite mainstream view is invalid.


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Table 1: Estimation Results (Equations 19 and 20)

CAD/USD GBP/USD JPY/USD CAD/GBP JPY/GBP JPY/CAD

Eq (19)

t 0.027 0.006 1.341 0.040 10.051 1.009

(1.52) (0.87) (1.45) (1.39) (1.14) (1.45)t 0.982 0.992 1.003 0.981 0.952 1.002

(8.31) (103.48) (122.84) (79.05) (48.12) (110.94)2R 0.99 0.99 0.99 0.99 0.99 0.99

DW 1.92 1.83 1.90 1.86 1.87 2.00Q 4.17 0.04 11.44 6.99 9.07 12.94

H 1.19 0.16 0.01 0.24 0.03 0.06AIC -11.19 -11.13 -0.48 -8.38 2.23 -0.76BIC -11.10 -11.09 -0.40 -8.30 2.33 -0.67

Eq (20)

t 1.473 0.554 102.13 1.915 134.91 57.30

(9.02) (7.55) (8.93) (8.12) (8.21) (7.08)

t 0.018 0.171 0.119 0.146 0.233 0.258

(0.17) (1.57) (1.11) (1.37) (2.23) (2.48)2R 0.94 0.81 0.96 0.78 0.97 0.96

DW 1.93 1.99 1.99 1.98 1.97 2.05

Q 8.60 18.17 7.87 17.64 4.79 4.43H 0.98 0.29 0.28 0.51 0.31 0.21

AIC -7.10 -6.76 4.73 -4.25 5.57 4.27BIC -7.01 -6.68 4.82 -4.17 5.65 4.36


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Table 2: Estimation Results (Equation 21)


Eq (19)

t 0.045 -0.001 2.885 -0.001 9.450 1.918

(1.18) (0.15) (1.61) (-0.003) (1.29) (1.23)t 0.990 0.971 1.006 0.966 0.949 1.004

(70.46) (84.60) (124.9) (73.20) (46.43) (111.7)

t -0.020 0.030 -0.018 0.033 0.009 -0.015

(-1.43) (1.76) (-1.38) (1.55) (0.43) (-1.76)2R 0.99 0.99 0.99 0.99 0.99 0.99

DW 1.86 1.88 1.96 1.61 1.86 2.02

Q 2.26 6.59 11.47 6.53 8.77 11.22H 1.40 0.16 0.02 0.27 0.03 0.06

AIC -11.18 -11.25 -0.52 -8.44 2.26 -0.77

BIC -11.07 -11.13 -0.40 -8.32 2.38 -0.65


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Table 3: Non-Nested Model Selection Tests(M1: Contemporaneous , M2: Lagged)


M1vs M2N 1.04 -1.06 1.84 -1.24 -0.87 1.13

NT 1.04 -1.03 1.80 -1.21 -0.86 1.09W 1.05 -1.14 1.16 -1.04 -0.84 1.20J -1.05 1.02 -1.38 1.18 0.84 -1.39

JA -1.05 1.02 -1.38 1.18 0.84 -1.39EN 1.11 1.12 1.19 1.14 0.70 1.54

M2vs M1N -43.63 -49.98 -49.61 -42.23 -33.12 -49.43

NT -43.20 -49.46 -49.02 -41.61 -32.81 -48.83W -10.28 -10.80 -9.32 -10.16 -9.01 -9.27J 57.92 72.81 100.52 52.12 37.17 96.43

JA 57.92 72.81 100.52 52.12 37.17 96.43EN 3354.61 5301.30 10104.90 2716.15 1382.0 9299.71


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Table 4: Indicators of Forecasting PowerCAD/USD GBP/USD JPY/USD CAD/GBP JPY/GBP JPY/CAD

MSE ( 310 )Contemporaneous 0.0233 0.0037 14.437 0.0899 78.930 85.921

Lagged 0.816 0.375 69274.7 7.399 170.4 30860.9

RMSEContemporaneous 0.005 0.002 0.120 0.009 0.888 0.293

Lagged 0.028 0.019 8.32 0.086 13.054 5.555


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Table 5: Results of the AGS Test

Coefficient CAD/USD GBP/USD JPY/USD CAD/GBP JPY/ GBP JPY/CAD

0 0.008 0.005 0.028 0.006 1.338 0.465

(3.25) (4.98) (0.69) (1.12) (4.35) (3.08)

1 1.005 0.958 1.022 0.985 0.901 0.972

(10.44) (18.56) (208.34) (16.79) (39.96) (36.14)2 ( )010 == 119.6 369.6 42408.0 283.3 1615.8 1315.8

An Empirical Examination of the Post Keynesian View of Forward Exchange Rates

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