سیاست های پولی و سوگیری رو به جلو برای بازبینی ارز : شواهد تجربی از نرخ ارز امریکا-انگلیس

Forward exchange rate unbiasedness is rejected for international exchange markets. The two-country monetary model is extended to include an additional forward contract and a numerical solution method is proposed. Simulation exercises suggest that high uncertainty in monetary policy produces greater bias in the estimated slope coefficient in the regression of the change in the logarithm of the spot exchange rate on the forward premium. The model also suggests that the nature of the transmission between monetary shocks might explain the forward bias. Empirical evidence for the US–UK exchange rate according to our theoretical results is provided.

One of the most important issues in international finance refers to the failure of forward exchange rates to forecast the future evolution of spot exchange rates. This is widely known as the unbiasedness puzzle: the estimated slope coefficients in the regression of the change in the logarithm of the spot rate on the forward premium significantly departs from one (see Zhu, 2002, Tauchen, 2001, Baillie and Bollerslev, 2000, Baillie and Ostenberg, 2000 and McCallum, 1994, among many others). More surprisingly, even negative estimates are reported. Such discrepancy from the underlying value in the uncovered interest rate parity implies not only that the forward rate is a biased predictor of the future spot rate, but also that forward rate predicts with the wrong sign. Potential economic explanations of this excess return puzzle are generally divided into three categories: (a) the most popular is that such pattern arises as a consequence of a time-varying risk premia (see Fama (1984)); (b) a second explanation relies on the nature of expectations. When agents have no rational expectations, they do not efficiently use the available information set, and incur systematic forecasting errors over a significant number of time periods ahead (see Froot and Frankel (1989)); and (c) the peso problem, that is, by a rational learning process market participants anticipate a future discrete shift in policy that does not take place within the sample period analyzed (see Lewis (1995)). Engel (1996) reminds us that, under rational expectations: View the MathML sourceplim⁡(βˆ)=1−βr⁢p, Turn MathJax on where View the MathML sourceβr⁢p=Cov⁡(Et⁢(st+l)−st,ft,l−Et⁢(st+l))+Var⁡(ft,l−Et⁢(st+l))Var⁡(ft,l−st), βˆ denotes the OLS estimator of the slope and s and f refers to spot and forward rate, respectively. From the above probability limit it follows that low positive values of βˆ can be explained if the variance of expected forward speculative profit is large enough. Numerous previous studies have considered general equilibrium models related to the Lucas (1982) (see, for example, Hodrick, 1989, Macklem, 1991, Canova and Marrinan, 1993 and Bekaert, 1994), but they do not successfully explain the substantial variability that occurs in the magnitude of predictable excess returns. Standard models of international finance either require unreasonable risk aversion parameters or consumption processes more volatile than in reality. The recent contribution of Moore and Roche (2002) gives substantial additional insights in this respect. In particular, according to the Campbell and Cochrane (1999) framework, these authors consider a cash-in-advance model with habit persistence which account for (i) the low volatility of the forward discount, (ii) the higher volatility of expected forward and (iii) the even higher volatility of the spot return. These authors call this joint pattern as the volatility puzzle. However, their model fails to explain the forward bias because they make the volatility of expected spot returns too high, leading to slope coefficients that significantly exceeds unity. From an econometric point of view, Baillie and Bollerslev (2000) show that the forward premium anomaly might be interpreted as a statistical phenomenon due to high persistency in the forward premium. This fact would explain that the estimated slope coefficient in the regression of the change in the logarithm of the spot rate on the forward premium be lower than unity. According to the UIP-FIGARCH model in Baillie and Bollerslev (2000), higher persistence in the spot rate produces not only higher persistence in the forward premium but also greater volatility of expected forward speculative profit. Hence, the higher persistence in the forward premium, the greater asymptotic bias of the slope estimator. Maynard and Phillips (2001) provide empirical evidence from several exchange markets (Aus$/US$, Can$/US$, FF/US$, DM/US$, Yen/US$ and UK/US$) on the non-stationarity long memory of the forward premium which causes a statistical imbalance in the regression itself. The inability to explain a short stationary variable, like the spot return, using a regressor with a stochastic trend, like the forward premium, leads to reject the null of unbiasedness. However, in a recent work, Maynard (2002) also notes that while the behaviour of both regression estimates and correlations coefficients are highly sensitive to the degree of integration or persistence in the forward premium, the covariance between the spot return and forward premium remains well defined regardless of the degree of integration in the forward premium. This work suggests that persistence probably will not solve the puzzle. In sum, currently there is no conclusive theory in the literature explaining the bias, and it is yet regarded as one of the most important puzzles in international finance. In this paper we use a theoretical general equilibrium model to explain the forward bias for foreign exchange under rational expectations. The model takes the Dutton's model (Dutton (1993)) as a benchmark, which is based on the general equilibrium model developed by Lucas (1982). Our theoretical novelty is that we consider two forward (one and two periods) exchange rates as hedge instruments for spot exchange rate. This is a relevant contribution in several ways: (a) our model allows monetary uncertainty to have a significant role to determine the forward bias for foreign exchange under no stochastic real endowments, (b) it is a more realistic approach to real markets in which different time to maturity can be traded, and (c) this feature enriches the analysis because it would be possible to identify the effect of the time to maturity in the derivative contract on the forward bias.1 Moreover, the persistence of the monetary policy and the potential correlation between monetary shocks of the two countries are explicitly taken into account. Consequently, a broad set of scenarios can be simulated in order to explore for potential explanatory factors of the forward bias. The solution of the model requires to compute expectations of nonlinear expressions. Therefore, numerical solutions are provided. Under the assumption of rational expectations, we provide a solution method that allows us to jointly solve for both prices and positions in one and two-periods ahead forward contracts. This is an interesting extension of Dutton's solution method. The model can reproduce the bias for forward exchange rate to predict the future evolution of spot rate, even when the econometric bias is taken into account, but does not explain negative estimates. This way, our model provides additional insights on a weak version of the puzzle. Theoretical results suggest that the key factor generating high volatility for the risk premium is the persistence (or volatility) of the monetary policy. Under a relative high persistence the estimated slopes dramatically decrease to below one. Moreover, under high persistence, the higher positive correlation of the monetary shocks of the two countries, the higher forward bias. Theoretical results also show that the time to maturity of forward contract is negatively correlated with the size of the slope coefficient in the regression; that is, the estimated slopes corresponding to the long time to maturity contract are relatively lower. The paper reports empirical evidence for the US dollar–British pound. In accordance with the theoretical simulations, a positive linkage between the persistence of the monetary policy and the bias for forward exchange rate arises during different time periods. Interestingly enough, the empirical evidence shows not only a high persistence but also a positive relationship between the forward bias and the correlation between domestic and foreign monetary shocks. The theoretical model also reproduces such pattern. The rest of the paper is organized as follows: Section 2 present the model. In Section 3, simulations of risk premium are presented and theoretical results on the bias of forward premium are provided. Section 4 refers to empirical evidence for the US–UK exchange rate. Finally, Section 5 summarizes and provides concluding remarks.

In this paper, we examine the role of the monetary policy to explain the bias of tests for forward premium in exchange rates. We perform a theoretical analysis by extending the dynamic and stochastic general equilibrium model with goods endowment proposed in Dutton (1993). As to the model, our contribution relies on the introduction of an additional forward contract as a hedge instrument. This is a closer approach to real financial markets. A numerical solution method under rational expectations is also provided. The model explain deviations from the UIP, but it does not account for negative estimated slopes. Our simulation results suggest that a high persistence (or uncertainty) in the domestic monetary policy produces greater volatility in the forward premium. In such case, the estimated slope coefficients show greater departures from one. Moreover, the nature of the transmission between monetary shocks of the two countries is a potential explaining factor for the excess return puzzle. Under a relative high persistence, the estimated slopes dramatically decrease below one when monetary shocks are positively correlated. Finally, we find that the time to maturity of the derivative contract is positively related with the bias of risk premium in forward exchange rates. The UIP condition only holds in the absence of persistence when monetary shocks are uncorrelated or negatively correlated. However, this is an unlikely scenario for most developed economies. Our results are consistent with several recent papers which have shown that the highly persistent behaviour of the forward premium creates a bias in the regression estimates in which the spot return is regressed on the forward premium. The paper provides empirical evidence for the US dollar–British pound exchange rate. In accordance with our theoretical results, a positive relationship between the forward bias and monetary persistence is observed throughout three different subsamples from December 1986 to November 2001. Moreover, a positive relationship between the forward bias and the correlation between monetary shocks arises during the overall sample, where a high persistence in monetary policy is detected. While the focus of this paper is the effect of the monetary policy, a similar analysis can be made by taking into account the presence of both monetary and real shocks. We leave work under such scenarios for further research.