This paper investigates the forward discount puzzle in international finance by testing whether survey-based exchange rate forecasts satisfy the Rational Expectation Hypothesis. Drawing on the methodology of Miah, Hassan, and Alam (2004), the study applies unit root tests (ADF and DF-GLS) and restricted cointegration tests to survey data covering the German Mark, GB Pound, and Japanese Yen against the U.S. Dollar from February 1988 to May 1999. The analysis finds that rational expectations hold for short forecast horizons (one and three months) but break down at longer horizons, particularly twelve months. The paper concludes that while a risk premium may partly explain the forward discount bias, failure of rationality at longer horizons cannot be ruled out as a contributing factor.
The paper demonstrates empirical replication as a validation method. Rather than introducing new data or a novel hypothesis, it reconstructs the tests of Miah, Hassan, and Alam (2004) to verify whether their conclusions hold. This approach — common in econometrics — shows how replication studies contribute to scientific reliability by confirming or challenging existing findings using the same dataset and methodology.
The paper follows a conventional quantitative research structure: it opens with a literature-grounded introduction establishing the puzzle, moves through purpose, problem identification, objectives, and hypothesis, then details the statistical methodology (ADF, DF-GLS, cointegration tests) before presenting a dedicated literature review. Findings are reported succinctly by currency pair, and the conclusion ties empirical results back to the two competing theoretical explanations — risk premium versus rationality failure — discussed in the introduction.
The forward discount puzzle concerns the limited ability of the forward discount to predict exchange rate changes. The central conclusion emerging from the literature is that the forward discount is a biased predictor, and two competing explanations have been proposed for this situation. One explanation points to the presence of a time-varying risk premium; the other attributes the bias to the failure of agents to form rational expectations — that is, their inability to use all available information in an efficient manner.
The forward discount puzzle is extensively discussed in the international finance literature, given its considerable practical and theoretical importance. Numerous studies have concentrated on this issue and, in particular, on the causes of the bias. Some authors (Fama, 1984) believe the problem is traceable to the existence of a time-varying risk premium. Others connect it to a learning effect (Lewis, 1989), irrationality (Bilson, 1981), or the "peso problem" (Krasker, 1980).
The term "peso problem" was introduced into the literature by a researcher who focused on the predictability of the Mexican Peso's evolution. The Peso was traded on a large scale on the forward market against the U.S. Dollar during the 1970s, even though it was pegged under a fixed exchange rate regime. The situation arose because a devaluation was widely anticipated — and it indeed took place in 1976.
Testing the rational expectation hypothesis in relation to the estimation of the Mexican Peso during this period is undeniably biased. Accordingly, applying the standard assumption of normality of the distribution — as used in conventional statistical tests — will not yield valid results. This statistical defect may also appear in other circumstances, such as when there is a non-negligible probability (even a quite small one) of a major exchange rate change during the studied period, a speculative bubble, or an important shift in fundamentals, particularly when the sample size is insufficient to correct such faults through the central limit theorem.
The first school of thought, which attributes the bias to a foreign exchange risk premium, begins from the assumption that agents make rational forecasts. Reviewing the available literature in this area, Engel (1996) concluded that the hypothesis asserting no unbiasedness attributable to the predictive ability of the forward rate is false, and that risk premium models have not been able to reasonably explain the high degree to which this proposed solution fails.
Researchers who have grounded their theories in the rationality of agents' expectations have empirically tested the concept using survey data on expected exchange rate changes from various sources. The results point in different directions. Regression techniques show that the degree of rationality among these expectations is not complete. More accurate results were obtained using cointegration tests, which demonstrated that rationality holds for short-term forecasts (one-week, two-week, four-week) but that any forecast extending beyond this horizon is biased, as a literature review by McDonald (2000) evidenced.
Miah, Hassan, and Alam (2004) conducted a research project on the forward discount puzzle, starting from the premise that "a direct test of rational expectation using survey data, which is risk premium free, allows 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 a risk premium."
The rationality of survey data in estimating future exchange rate changes is the central concern of this study. The conclusions provided by the literature, together with the data collection and methodology employed by Miah, Hassan, and Alam (2004), were used to verify independently whether their conclusions are consistent with the actual results of the analysis and with the general trend established by the broader literature.
The authors acknowledge that a large number of studies and tests of the rationality of survey data have been conducted across different periods, using various econometric methods and data sources. Their overall conclusion is that the survey data do not appear to be rational, but the results are not always conclusive because of the limited time periods over which the tests were conducted, which exposed them to the risk of small-sample bias. Time series data also present challenges for traditional econometric methods, which has attracted further methodological criticism.
Another factor influencing this field is government intervention in the foreign exchange market. Although such intervention could prove ineffective if agents form rational forecasts (Dominguez and Frankel, 1993), this is not consistently the case. Studies of this issue typically use no more than five years of data, usually from after 1991. Miah, Hassan, and Alam (2004) used a monthly survey dataset spanning twelve years in order to observe changes in forecasters' performance over time. Their methods include unit root tests and the restricted cointegration test, and their aim is to help practitioners improve their exchange rate estimation techniques.
Replicating the tests and analyzing the conclusions should provide a clearer picture of the accuracy of exchange rate estimation in relation to the rationality of the collected survey data. Starting from the stated hypothesis, the series of tests should either confirm or contradict the initial proposition, thereby facilitating the formulation of a valid scientific conclusion.
The hypothesis of the test is that the collected survey data prove rational. The Rational Expectation Hypothesis holds that if an agent uses all available information when forming an expectation about future exchange rate changes, 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 in the literature as the "test of unbiasedness."
A second test, referred to as the test of orthogonality, may also be applied, though it does not form part of this study. Rationality of expectations implies that forecast errors are uncorrelated with the variables in an agent's information set (e.g., exchange rates, forward rates, money supply, and others).
The data collected by Miah, Hassan, and Alam (2004) were used and their calculations reconstructed. For the survey data to be considered rational, analysis required that the residuals form a white noise process. Serial correlation in the residual series was tested using Q-statistics. The conclusion depended on whether the residual series showed any evidence of serial correlation. No such evidence would confirm the rational expectation hypothesis.
Because the studied forecast periods were finer than the forecast interval used, the residual series had to follow a moving average process. Although the forecast may have been rational, a standard W-test would still have detected serial correlation under these conditions. The actual residuals of the three-month, six-month, and twelve-month forecasts were estimated, and the Q-test was applied to the resulting residual series. These residual series are stationary (cointegrated). The lag lengths chosen for the Q-test were 4, 8, 12, 24, and 36, capturing correlation over both short and long time periods.
The data used in the study were 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, covering the period from February 1988 to May 1999. The survey horizons studied were one, three, six, and twelve months.
The Financial Times' Currency Forecaster is a specialized publication that forecasts the evolution of exchange rates and publishes exchange rate estimates for the currencies of more than 45 countries, drawing on data available from February 1988. The data sample is collected from a group of thirty multinational companies and fifteen forecasting service providers. Forecasts are produced for one-, three-, six-, and twelve-month horizons, all of which were used in this study.
Several statistical methods were employed to determine the rationality of the data. For the first exchange rate — German Mark / U.S. Dollar — the ADF and DF-GLS tests were unable to reject the null hypothesis for the spot rate and one-month-ahead forecasts at the 10% level. However, heterogeneous results were obtained for the other series.
The Augmented Dickey–Fuller (ADF) test was the first method applied. In this test, the statistics do not follow the standard t-distribution. Fuller (1976) and Dickey and Fuller (1981) tabulated the critical values using the test statistics. The test may incorporate either a constant or a constant with a trend; Miah et al. (2004) used both versions.
A controversy exists regarding the appropriate lag length for this test. The choice of lag length was examined in detail by Ng and Perron (1995). Hall's general-to-specific method was found to be more appropriate than alternatives; however, an opposing view — favoring the Bayesian Information Criterion — was expressed by Stock (1994). The Hall method may nonetheless be used, as Stock acknowledged, leaving future researchers free to choose. Miah, Hassan, and Alam used the Bayesian Information Criterion.
The DF-GLS test was proposed by Elliott (1996) as a solution to the size distortion problems of the Augmented Dickey–Fuller test. The DF-GLS is a modified version of the ADF test that uses a detrended series in place of the original series. Detrending was performed using either a linear trend or a constant; the use of a linear trend was preferred in the study under discussion.
A third procedure, the restricted cointegration test, was initially applied by Liu and Maddala (1992) and Osterberg (2000), with further contributions by Granger (1981). This test represents a more direct approach. If the actual exchange rate series is a random walk, its rational forecast should follow a similar evolution, implying that the two series are cointegrated with a coefficient of one and random residuals.
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