Exchange rate determination mechanisms and models

¶ … forward discount in predicting exchange rate modifications. The conclusion of the literature review is that the forward discount is a biased predictor and that are two possible explanations for this situation. One cause would be the presence of a time varying risk premium, and the other the failure of agents to make rational expectations (the inability to use all available information in an efficient manner).

The forward discount puzzle (as a predictor of exchange rate modifications) is a very discussed puzzle in the international finance literature, since its importance is quite high. As a result, numerous studies have concentrated on this issue, i.e. On the causes on the bias. Some authors (Fama, 1984), believe that this problem is traceable to the existence of a time-varying risk premium. Others connect it to learning effect (Lewis, 1989) or irrationality (Bilson, 1981) the "peso problem" (Krasker, 1980),

The "peso problem term" was introduced into the literature by a researcher who concentrated his attention on the predictibility of the Mexican Peso's evolution, which was traded on large scale on the forward market against thE U.S. Dollar in the 1970's, although it was on a fixed exchange rate. The cause of that situation was that a devaluation was expected - and it indeed took place in 1976.

Testing the rational expectation hypothesis in realtion to the estimation of the Mexican Peso in this time frame is biased beyond doubt. Therefore, applying the standard assumption of normality of the distribution, currently used in statistic tests, will not yeald any valid results. This statistical defect may also be observed in other circumstances, such as the probability (even quite small) of a major modification of the exchange rate in the studied period, a speculative bubble or an important change in fundamentals, especially iF the sample size is not sufficient in order to correct such faults (by applying the central limit theorem).

The first opinion, which attributes the bias to a foreign exchange risk premium, starts from the assumption that agents make rational forecasts. Analyzing the available literature in this area, Engel (1996) arrived to the conclusion that the hypothesis according to which there is no unbiasedness to be attributed to the ability of prediction of the forward rate is false and that the model of the risk premiums haven't been able to reasonably explain the high degree of failure of this solution.

The researchers who have based their theories on the rationality of agents' expectations have empirically tested the concept by using survey data regarding expected exchange rate modifications from various sources. The results are not going in the same direction. The regression technique shows that the degree of rationality among these expectations is not 100%. A more accurate result was obtained by using a cointegration test, which proved that rationality exists for short-term forecasts (one-week, two-week, four-week) but any forecast for a period exceeding this horizon is biased, as a literature review conducted by McDonald in 2000 has evidenced.

Miah, Hassan and Alam have conducted in 2004 a research project on the forward discount puzzle, by starting from the idea that "A direct test of rational expectation using survey data, which is risk premium free, allow us to see whether there is a bias in the expectation formation process by agents. If expectations are found to be rational, then the forward discount bias could be due to the presence of risk premium."

2. PURPOSE

The rationality of survey data in estimating future exchange rate modification is the object of the current study. I have used the conclusions which the literature provides and the collection of data and methodology available to Miah, Hassan and Alam (2004) to check for myself whether their conclusions are consistent with the actual results of the analysis and with the general trend set by the literature.

3. PROBLEM IDENTIFICATION

The authors admit that there has been a myriad of studies and tests of the rationality of survey data in different periods, using various econometric methods and data sources. The conclusion they draw is that the survey data does not appear to be rational, but the results are not always conclusive because of the limited time periods in which the tests were made, which exposed them to the risk of small sample bias. Time series studies are also an inappropriate working material for traditional econometric methods, which has provided extra criticism.

Another factor that makes its influence felt in this field is that of government intervention in the foreign exchange market. Although this intervention could prove ineffective, should the agents make rational forecasts (Dominguez and Frankel,1993), this is not often the case. Normally, studies of the issue do not use more than five years of data, usually after 1991. Miah, Hassan and Alam (2004) have used a monthly data survey stretched on twelve years, in order to observe the modifications of forecasters perfomance over time. Their methods include unit root tests and the restricted cointegration test, and their purpose is to help practitioners improve their exchange rate estimation techniques.

4. OBJECTIVES

Reconducting the tests and analyzing the conclusions should provide a clearer picture of the accuracy of estimation of exchange rate modification, in relation to the rationality of the collected survey data. Starting from the hypothesis, the series of tests should either confirm or contradict the initial statement, therefore facilitating the arrival to a valid scientific conclusion.

5. HYPOTHESIS

The hypothesis of the test is that the collected survey data prove rational. The Rational Expectation Hypothesis refers to the fact that, should an agent use all available information when forming an expectation on future exchange rate modifications, the estimated rate will be an unbiased predictor of the actual spot rate. The equations used in this case show that any difference between the actual rate and the expected rate will be nothing more than a random error (a situation commonly referred to by the literature as the "the test of unbiasedness."

Another test, referred to as the test of orthogonality, may also be applied, although not making the object of this study. Rationality of expectations leads to uncorrelation of the forecast errors with the variables in an information set (e.g. exchange and forward rates, money supply and others.

6. METHODOLOGY have used the data collected by Miah, Hassan and Alam (2004) and remade their calculations.Analysis and testing of the survey data collected required, in order for the date to be rational, that the residual be a white noise process. The serial corellation is the residual series was tested using Q-statistics. The conclusion to which the researchers could have arrived at depended on whether the residual series showed any trace of serial correlation or not. No evidence of such a fact pointer to the fact the rational expectation hypothesis was correct.

The studied forecast periods were finer than the forecast used, which lead to the conclusion that the residual series had to follow a moving average process. Although the forecast may have been rational, a W-test would have showed a serial correlation. The actual residuals of the 3-month, 6-month and 12-month forecast were estimated and then the Q-test was applied on the residual series obtained from this estimation. The residuals series are stationary (cointegrated). The lag lentghts chosem for the Q-test were 4, 8, 12, 24 and 36 and signify the correlation after both short and long time periods.

The data used by the study was collected from the Financial Times' Currency Forecaster for the German Mark / U.S. Dollar, GB Pound / U.S. Dollar and Japanese Yen / U.S. Dollar exchange rates, during the February 1988 - May 1999 period. The studied survey horizons were one, three, six and twelve months.

The Financial Times' Currency Forecaster is a specialized in forecasting the evolution of excahnge rate modfication and which publishes exchange rates estimations for the monetary units of more than 45 countries, based on data available from February 1988. The data sample is collected from a group of thirty multinational companies and fifteen forecasting service providers. The time horizons for which forecasts are performed are one, three, six and twelve months, all which were used in the study.

This particular study used various statistical methods in order to determine the rationality of the data. For the first exchange rate - German Mark / U.S. Dollar, the ADF and DFGLS tests weren't able to reject the null for the spot rate and one-month ahead forecasts at the 10% level. However, heterogenous results have been obtained for the other series.

Several tests were applied on the data: the Augumented Dickey Fuller test; in this case, the statistics do not have the normal t distribution. Fuller's study from 1986 and the joint study of Fuller and Dickey from 1981 tabulated the critical values using the test statistics. The test may use a either a constant or a constant and a trend. Miah et all. (2004) used both versions.

There is also a controversy regarding the appropriate lag for this test. The choice of leg length was thoroughly examined by Ng and Perron in 1995. Hall's general to specific method was found to be more adequate than others. However, an opposite view, in favor of the Baysian Information Criterion was expressed by Stock (1994). Nontheless, the Hall method may also be used, as suggested by Stock, who left future researchers with the liberty of choice. Miah, Hassan and Alam used the Baysian Information Criterion.

The second test, known as the DF-GLS was proposed by Elliot (1996) as a solution to the size distorsion problems of the Augumented Dickey Fuller test. Actually, the DF-GLS is a modified version of the ADF test, which uses a detrended series instead of the original series (Detrending was perfomed using either a liniar trend or a constant. The use of a liniar trend was preffered in the above mentioned study.

A third test, the restricted cointegration test, was initially applied by Liu and Mdalla (1992) and Osterberg (2000), with further contributions by Granger (1981). This test represents a moe direct approach. If the actual rate of excahnge rate modifications is random, than its rational forecast should have a similar evoultion, which means that the two series are cointegrated with a factor of one and random residuals.

7. LITERATURE REVIEW

Literature reviews in this area have been previously conducted by various researchers, such as McDonald (2000), Maddala (1994) and Takagi (1991), who provide a comprehensive image of the concept of rationality of exchange rate expectations.

The review made by Takagi in 1991 concludes that there are three characteristics of the survey data regarding expectations of exchange rates. The first one is that the dispersion of expectations increases along with the forecast horizion. The second refers to the fact that the expected exchange rate changes are not very successful in actually resembling the real exchange-rate modifications, which leads to the conclusion that there is a great deal of uncertainty in this particular point. In the third place, it would seem that long-term expectations and short-term expectation have totally different trends, which is named a "twist" by the literature.

The unbiasedness hypothesis was tested by Dominguez (1986), Ito (1990), Chinn and Frankel (1994), based on various data sources, which resulted in very different results. Dominguez preferred to use data collected from Money Market Services; the results indicated that the unbiasedness hypothesis is not substantiated, at least within a horizon ranging from one week to three months. Approximately the same result were obtained by Cavaglia (1993), who used the EMS exchange rates published by Business International Corporation; the time horizon ranged from three months to a year.

Beng and Siong (1993) have conducted the most comprehensive study by observing the evolution of the Singapore currency against the U.S. Dollar for the 1984-1991 for all forecast horizons. The data used by Chinn and Frankel (1994) was provided by the Financial Times' Currency Forecaster (CDF) for February 1888 - February 1991 period; the result was that bias exists on a large scale in the available survey data. Another researcher, Ito (1990) benefited form the data collected by the Japanese Center for International Finance during the 1985-1987 period. Although for shorter horizions (one, three months) the unbiasedness was not evident, for longer periods of time it became unacceptable.

Conitegration tests were another method used by researchers to establish the degree of bias in expectation of foreign exchange moficiations. One of the most recent studies, conducted by Miah in 2003 arrived to approximately the same conclusions as the ones before it. Liu and Midala (1992) tested the Rational Expectation Hypothesis by using the same data as Dominguez, in 1986, which lead them to the conclusion that one-week forecast were unbiased, a fact which was not true for longer time intervals. Kim (1997) used survey data collected from Australia to establish whether the one-week and four-week forecast were rational. Osterberg (2000) made use of the Money Market Services data, which made him conclude that the one-week-ahead and four-week-ahead forecasts were rational.

8. FINDINGS AND RESULTS

The ADF test couldn't reject the null at 1% for the six-month-ahead horizion and at 5% for the other two time intervals. The DF-GLS test showed contradictory results for the six-months horizon, so the conclusion was that six-month-ahead forecast are nonstationary. As a general rule, it would seem that the German Mark / U.S. Dollar exchange rate date were nonstationary.

A similar conclusion was arrived at for the GB Pound / U.S. Dollar and Japanese Yen / Us Dollar exchange rates. In the case of the latter, there was not even a trend to be noticed.

9.CONCLUSIONS AND RECOMMENDATIONS

The rational expectation hypothesis relating to the foreign exchange market modifications was analyzed and tested using various statistical methods using survey data which included three very important exchange rates: German Mark / U.S. Dollar, GB Pound / U.S. Dollar and Japanese Yen / U.S. Dollar. Econometric methods and their inappropriateness for evaluating time series was overcome by using the most modern discoveries in this field. Therefore, the examination of the relationship between the estimated exchange rates and the real exchange rates was possible with regard to a long-term horizon.

Overlapping forecasting causes the serial correlation problem, which was corrected by estimating the forecast errors as a moving average process.

One of the conclusions of the study is that the expectations of spot exchange rates at various horizons and the actual rates have unit roots. All exchange rates showed stationary forecast errors for the one-month and three-month ahead estimations, and the GB Pound / U.S. Dollar proved also stationary for the six-month ahead estimation, which was consistent with the results of the unit root tests.

Therefore, the rational expectation hypothesis is correct for one-month ahead estimations for all tested currencies, the three-month ahead forecasts are valid for the German Mark / U.S. Dollar and the GB Pound / U.S. Dollar. The only situation in which the six-month-ahead forecast proved right is that of the GB Pound / U.S. Dollar exchange rate.

However, twelve-month expectations were not rational even for the GB Pound / U.S. Dollar rate, which triggered the researchers to say that further insight might be provided by a much longer data ser. Another finding of the study was that there is a direct relation between the dispersion of expectations and the length of the time horizons.

The literature also speaks about other implications of the rational expectations hyphothesis, beside the unbiasedness of the survey data. such as the concept of orthogonality of forecast errors regarding the available information at the time of the forecast. The test of orthogonality, although not making the object of this study, was covered by Dominguez (1986), Frankel and Froot (1989), Ito (1990), Sobichewski (1994), MacDonald and Torrance (1989), Cavaglia, (1993), and Beng and Siong (1993), who arrived to the conclusion that exchange rate expectations are not supported by all the available information.

The conclusion of the study is that it is not the inability of the rational expectation hypothesis to present an adequate solution to the forward discount problem; the puzzle may be attributed to the existence of a risk premium. However, this conclusion is only applicable to those cases were the time-horizons satisfied the rational expectation hypothesis (three-months-ahead or six-moths ahead, at most; for the Japanese Yen / U.S. Dollar test, that is also an excessive conclusion). Failure of the rationality hypothesis could be a cause of the incapacity to correctly estimate the future modifications of exchange rates, along with the existence of the risk premium.

10. REFERENCES

Beng, G.W. And W.K. Siong. (1993) Exchange Rate Expectations and Risk Premium in the Singapore/U.S. Dollar Exchange Rate: Evidence from Survey Data Applied Financial Economics, 3(4), pp. 365-73.