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Previous articleNext article FreeTaylor Rule Exchange Rate Forecasting during the Financial CrisisTanya Molodtsova and David H. PapellTanya MolodtsovaEmory University Search for more articles by this author and David H. PapellUniversity of Houston Search for more articles by this author PDFPDF PLUSFull Text Add to favoritesDownload CitationTrack CitationsPermissionsReprints Share onFacebookTwitterLinked InRedditEmailQR Code SectionsMoreI. IntroductionThe past few years have seen a resurgence of academic interest in out-of-sample exchange rate predictability. Gourinchas and Rey (2007, using an external balance model); Engel, Mark, and West (2008, using monetary, Purchasing Power Parity [PPP], and Taylor rule models); and Molodtsova and Papell (2009, using a variety of Taylor rule models) all report successful results for their models vis-à-vis the random walk null. There has even been the first revisionist response. Rogoff and Stavrakeva (2008) criticize the three abovementioned papers for their reliance on the Clark and West (2006) statistic, arguing that it is not a minimum mean squared forecast error statistic.An important problem with these papers is that none of them use real-time data that was available to market participants.1 Unless real-time data is used, the "forecasts" incorporate information that was not available to market participants, and the results cannot be interpreted as successful out-of-sample forecasting. Faust, Rogers, and Wright (2003) initiated research on out-of-sample exchange rate forecasting with real-time data. Molodtsova, Nikolsko-Rzhevskyy, and Papell (2008) use real-time data to estimate Taylor rules for Germany and the United States and forecast the Deutsche mark/dollar exchange rate out-of-sample for 1989:Q1 to 1998:Q4. Molodtsova, Nikolsko-Rzhevskyy, and Papell (2011), henceforth MNP (2011), use real-time data to show that inflation and either the output gap or unemployment, variables which normally enter central banks' Taylor rules, can provide evidence of out-of-sample predictability for the US dollar/euro exchange rate from 1999 to 2007. Adrian, Etula, and Shin (2011) show that the growth of US dollar-denominated banking sector liabilities forecasts appreciations of the US dollar from 1997 to 2007, but their results break down in 2008 and 2009.Molodtsova and Papell (2009) conduct out-of-sample exchange rate forecasting with Taylor rule fundamentals, using the variables, including inflation rates and output gaps, that normally comprise Taylor rules. Engel, Mark, and West (2008) propose an alternative methodology for Taylor rule out-of-sample exchange rate forecasting. Using a Taylor rule with prespecified coefficients for the inflation differential, output gap differential, and real exchange rate, they construct the interest rate differential implied by the policy rule and use the resultant differential for exchange rate forecasting. We use a single equation version of their model, which we call the Taylor rule differentials model.2 Since there is no evidence that either the Fed or the European Central Bank (ECB) targets the exchange rate, we do not include the real exchange rate in the forecasting regression for either model.3Out-of-sample exchange rate forecasting with Taylor rule fundamentals received blogosphere, as well as academic, notice in 2008. On July 28 and September 9, Menzie Chinn posted on Econbrowser a discussion of in-sample estimates of one of the specifications used in an early version of MNP (2011).4 On August 17, he posted an article by Michael Rosenberg of Bloomberg, who discussed Taylor rule fundamentals as a foreign currency trading strategy. By December 22, however, optimism had turned to pessimism. Once interest rates hit the zero lower bound, they cannot be lowered further. With zero or near-zero interest rates for Japan and the United States, and predicted near-zero rates for the United Kingdom and the Euro Area, the prospects for Taylor rule exchange rate forecasting were bleak. A second theme of the post, however, was that there was nothing particularly promising on the horizon. Going back to the monetary model, even in a regime of quantitative easing, faced doubtful prospects for success.5The events of 2007 to 2009 focused the attention of economists on the importance of financial conditions. On August 9, 2007, the spread between the dollar London interbank offer rate (Libor) and the overnight index swap (OIS), an indicator of financial stress in the interbank loan market, jumped from 13 to 40 basis points on concerns that problems in the subprime mortgage market were spreading to the broader mortgage market.6 The spreads mostly fluctuated between 50 and 90 basis points until September 17, 2008, when they spiked following the announcement that Lehman Brothers had filed for bankruptcy, peaking on October 10 at over 350 basis points. Following the end of the panic phase of the financial crisis in October, 2008, the spread gradually returned to near precrisis levels in September 2009. The spread increased again, although not nearly as sharply, in mid-2010 and late 2011. The spreads are depicted in figure 1.Fig. 1. Credit spreads and financial stress indexes with their differentialsView Large ImageDownload PowerPointThe deteriorating financial situation in late 2007 and 2008 inspired several proposals for linking monetary policy to financial conditions. Mishkin (2008) argued that, when a financial disruption occurs, the Fed should cut interest rates to offset the negative effects of financial turmoil on aggregate economic activity. McCully and Toloui (2008) suggested that, because of tightened financial conditions, the Fed needed to lower the policy rate by 100 basis points in early February 2008 in order to keep the neutral rate constant. Meyer (2009) argued that the Taylor rule without considerations of financial conditions could not explain aggressive Fed policy in early 2008.Taylor (2008) proposed adjusting the systematic component of monetary policy by subtracting a smoothed version of the Libor-OIS spread from the interest rate target that would otherwise be determined by deviations of inflation and real GDP from their targets according to the Taylor rule. He argued that such an adjustment, which would have been about 50 basis points in late February 2008, would be a more transparent and predictable response to financial market stress than a purely discretionary adjustment.Curdia and Woodford (2010) modify the Taylor rule with an adjustment for changes in interest rate spreads. Using a dynamic stochastic general equilibrium (DSGE) model with credit frictions, they show that incorporating spreads can improve upon a standard Taylor rule, although the optimal size of the adjustment is smaller than proposed by Taylor and depends on the source of variation in the spreads.The spread between the euro interbank offer rate (Euribor) and the euro OIS also jumped in August 2007 and spiked in September and October 2008, although not by as much as the US spread. While the Euribor-OIS spread came down in September 2009, it did not return to its precrisis levels. During August and December 2010, the spread jumped to as high as 40 basis points and, in December 2011, reached a maximum of 100 basis points. The end-of-quarter Libor-OIS, Euribor- OIS, and the difference between the Libor-OIS and Euribor-OIS spreads are depicted in figure 1. After the gap between the two spreads narrowed in 2008:Q4, the spread turned against the Euro Area, reaching a maximum in 2011:Q3 and 2011:Q4 before narrowing in 2012:Q1.This paper investigates out-of-sample exchange rate forecasting during the financial crisis with Taylor rule-based models that incorporate indicators of financial stress. We use one-quarter-ahead forecasts and estimate models with core inflation and both the output gap and the unemployment gap for the Taylor rule fundamentals and Taylor rule differentials models.7 When the Libor-OIS/Euribor-OIS differential is included in the forecasting regression, we call the models spread-adjusted Taylor rule fundamentals and differentials models. According to these models, when the Libor-OIS spread increases, the Fed would be expected to either lower the interest rate or, if it had already attained the zero lower bound, engage in quantitative expansion, depreciating the dollar. When the Euribor-OIS spread increases, the ECB would be expected to react similarly, depreciating the euro. We therefore use the difference between the Libor-OIS and Euribor-OIS spreads in addition to the difference between the United States and Euro Area inflation rates and output gaps for out-of-sample forecasting of the dollar/euro exchange rate.Another widely used credit spread is the Ted spread, the three-month Libor/three-month Treasury spread for the United States and the three-month Euribor/three-month Treasury spread for the Euro Area. As shown in figure 1, the US Ted spread was generally higher than the Euro Area Ted spread until 2008 and the Ted spread differential was more variable than the Libor-OIS/Euribor-OIS differential. The Euro Area Ted spread spiked with the US Ted spread in 2008:Q3, and so the differential does not display a spike at the peak of the financial crisis. Subsequent to the financial crisis, the Ted spread differential is similar to the Libor-OIS/Euribor-OIS differential. It turns against the Euro Area in 2009, reaches a maximum in 2011:Q3 and 2011:Q4, and narrows in 2012:Q1. We use the difference between the US and Euro Area Ted spreads as an alternative indicator of financial stress.Financial Conditions Indexes (FCIs) that summarize information about the future state of the economy contained in a number of current financial variables have received considerable attention in recent years. Hatzius et al. (2010) show that FCIs outperform individual financial variables that are considered to be useful leading indicators in their ability to predict the growth of different measures of real economic activity. We therefore augment the Taylor rule by using the difference between the Bloomberg and Organization for Economic Cooperation and Development (OECD) FCIs for the United States and the Euro Area for out-of-sample forecasting of the dollar/euro exchange rate.8 The Bloomberg and OECD FCIs are depicted in figure 1 where, in contrast to the credit spreads, an increase represents an improvement in financial conditions. Financial conditions deteriorate sharply for both the United States and the Euro Area in late 2008, but turn in favor of the United States starting in 2009.Real-time data for the United States is available in vintages starting in 1966, with the data for each vintage going back to 1947. Real-time data for the Euro Area, however, is only available in vintages starting in 1999:Q4, with the data for each vintage going back to 1991:Q1. While the euro/dollar exchange rate is only available since the advent of the euro in 1999, "synthetic" rates are available since 1993. We use rolling regressions to forecast exchange rate changes starting in 1999:Q4, with 26 observations in each regression. Keeping the number of observations constant, we report results ending in 2007:Q1, with 30 forecasts, through 2012:Q1, with 50 forecasts. We report the ratio of the mean squared prediction errors (MSPE) of the linear and random walk models and the CW test statistic of Clark and West (2006).9The Taylor rule fundamentals model with the unemployment gap produces very strong results. The MSPE of the Taylor rule model is smaller than the MSPE of the random walk model and the random walk null can be rejected in favor of the Taylor rule model using the CW test at the 5 percent level for the initial set of forecasts ending in 2007:Q1. As the number of forecasts increases, the MSPE ratios decrease and the strength of the rejections increases, peaking at the 1 percent level in 2008:Q1. In the following quarter, 2008:Q2, the MSPE ratios start to rise and continue to increase through 2009:Q1 (although the rejections continue at the 5 percent level or higher). Starting in mid-2009, the MSPE ratios stabilize and the random walk can be rejected in favor of the Taylor rule model at the 5 percent significance level for all specifications between 2009:Q2 and 2012:Q1.The results for the other models are not as strong. For the Taylor rule differentials model with the output gap, the random walk null can be rejected at the 10 percent level or higher from 2007:Q1 to 2008:Q3 and 2009:Q2 to 2009:Q4, but not otherwise. For the Taylor rule fundamentals model with the output gap and the Taylor rule differentials model with the unemployment gap, the random walk null can only be rejected at the 10 percent level or higher from 2007:Q1 to 2008:Q2.A major innovation in this paper is to incorporate indicators of fi-nancial stress, measured by the difference between the Libor-OIS and Euribor-OIS spreads, the US and Euro Area Ted spreads, the US and Euro Area Bloomberg FCIs, and the US and Euro Area OECD FCIs, for out-of-sample exchange rate forecasting with Taylor rule models. The strongest results are again for the Taylor rule fundamentals model with the unemployment gap. Using the OECD FCI, the random walk null can be rejected in favor of the linear model alternative at the 5 percent level for all but one set of forecasts, and at the 10 percent level for the remaining forecast. Using the three other indicators, the null can be rejected at the 10 percent level or higher for over half of the forecasts, with the strongest results for the forecasts ending between 2007 and 2009. As with the original Taylor rule model, the augmented Taylor rule differentials model with the output gap is the next most successful, with the random walk null rejected at the 10 percent level or higher for all forecasts using the OECD FCI and at the 10 percent level or higher for over half of the forecasts with the three other indicators. The rejections for the other two augmented models are concentrated in 2007 and 2008.We proceed to compare the original and augmented models for the two most successful specifications. For the Taylor rule fundamentals models with the unemployment gap, the original model null can be rejected in favor of the augmented model alternative at the 5 percent level for virtually every set of forecasts ending between 2007:Q1 to 2008:Q2 for all four financial stress indicators. For the forecasts ending between 2008:Q3 and 2012:Q1, however, the original model null is never rejected. For the Taylor rule differentials model with the output gap, there is some evidence in favor of the alternative specification with the Ted spread, Bloomberg FCI, and OECD FCI.We also compare the out-of-sample performance of the Taylor rule models with the monetary, PPP, and interest rate differentials models. For the interest rate differentials model, the MSPE ratios are below one and the random walk can be rejected with the CW tests from 2007:Q1 to 2008:Q2. Starting with the panic period of the financial crisis in 2008:Q3, the MSPE ratios rise above one and the random walk null can only be rejected for the forecasts ending in 2009:Q1 and 2012:Q1. The monetary and PPP models cannot outperform the random walk for any forecast interval. The evidence of out-of-sample exchange rate predictability is much stronger with the Taylor rule models than with the traditional models.II. Exchange Rate Forecasting ModelsEvaluating exchange rate models out of sample was initiated by Meese and Rogoff (1983), who could not reject the naïve no-change random walk model in favor of the existent empirical exchange rate models of the 1970s. Starting with Mark (1995), the focus of the literature shifted toward deriving a set of long-run fundamentals from different models, and then evaluating out-of-sample forecasts based on the difference between the current exchange rate and its long-run value. Engel, Mark, and West (2008) use the interest rate implied by a Taylor rule, and Molodtsova and Papell (2009) use the variables that enter Taylor rules to evaluate exchange rate forecasts.A. Taylor Rule Fundamentals ModelWe examine the linkage between the exchange rate and a set of variables that arise when central banks set the interest rate according to the Taylor rule. Following Taylor (1993), the monetary policy rule postulated to be followed by central banks can be specified aswhere it is the target for the short-term nominal interest rate, πt is the inflation rate, is the target level of inflation, yt is the output gap, the percent deviation of actual real GDP from an estimate of its potential level, and R is the equilibrium level of the real interest rate.10According to the Taylor rule, the central bank raises the target for the short-term nominal interest rate if inflation rises above its desired level and/or output is above potential output. The target level of the output deviation from its natural rate yt is 0 because, according to the natural rate hypothesis, output cannot permanently exceed potential output.The target level of inflation is positive because it is generally believed that deflation is much worse for an economy than low inflation. The unemployment gap, the difference between the unemployment rate and the natural rate of unemployment, can replace the output gap in equation (1) as in Blinder and Reis (2005) and Rudebusch (2010). In that case, the coefficient γ would be negative so that the Fed raises the interest rate when the unemployment rate is below the natural rate of unemployment. Taylor assumed that the output and inflation gaps enter the central bank's reaction function with equal weights of 0.5 and that the equilibrium level of the real interest rate and the inflation target were both equal to 2 percent.The parameters and R in equation (1) can be combined into one constant term, , which leads to the following equation, where λ = 1 + ϕ. Because λ > 1, the real interest rate is increased when inflation rises, and so the Taylor principle is satisfied. Following Taylor (2008) and Curdia and Woodford (2010), the original Taylor rule can be modified by subtracting a multiple of the spread between the dollar Libor rate and the OIS rate, where st is the spread.We do not incorporate several modifications of the Taylor rule that, following Clarida, Galí, and Gertler (1998), are typically used for estimation. Lagged interest rates are usually included in estimated Taylor rules to account for either (a) partial adjustment of the federal funds rate to the rate desired by the Federal Reserve, or (b) desired interest rate smoothing on the part of the Federal Reserve. Since the most successful exchange rate forecasting specifications for the dollar/euro rate in MNP (2011) did not include a lagged interest rate and Walsh (2010) shows that the Federal Reserve lowered the interest rate during the financial crisis faster than would be consistent with interest rate smoothing, we do not include lagged interest rates. The real exchange rate is often included in specifications that involve countries other than the United States. Since there is no evidence that the ECB uses the real exchange rate as a policy objective and inclusion of the real exchange rate worsens exchange rate forecasts in MNP (2011), we do not include it. Finally, while inflation forecasts are often used on the grounds that Federal Reserve policy is forward looking, there is no publicly available data on euro area core inflation forecasts.To derive the Taylor rule based forecasting equation, we construct the implied interest rate differential by subtracting the interest rate reaction function for the Euro Area from that for the United States: where asterisks denote Euro Area variables and α is a constant. It is assumed that the coefficients on inflation and the output gap are the same for the United States and the Euro Area, but the inflation targets and equilibrium real interest rates are allowed to differ.11Based on empirical research on the forward premium and delayed overshooting puzzles by Eichenbaum and Evans (1995), Faust and Rogers (2003) and Scholl and Uhlig (2008), and the results in Gourinchas and Tornell (2004) and Bacchetta and van Wincoop (2010), who show that an increase in the interest rate can cause sustained exchange rate appreciation if investors either systematically underestimate the persistence of interest rate shocks or make infrequent portfolio decisions, we postulate the following exchange rate forecasting equation:12where asterisks denote Euro Area variables, ω is a constant, and ωπ, ωy, and ωs are positive coefficients. Alternatively, the unemployment gap differential (with opposite sign) can substitute for the output gap differential in equation (5).The variable et is the log of the US dollar nominal exchange rate determined as the domestic price of foreign currency, so that an increase in et is a depreciation of the dollar. The reversal of the signs of the coefficients between (4) and (5) reflects the presumption that anything that causes the Fed and/or ECB to raise the US interest rate relative to the Euro Area interest rate will cause the dollar to appreciate (a decrease in et). Since we do not know by how much a change in the interest rate differential (actual or forecasted) will cause the exchange rate to adjust, we do not have a link between the magnitudes of the coefficients in (4) and (5).13The difference between the US and Euro Area Ted spreads, Bloomberg FCIs, and OECD FCIs can also be used as the measure of the spread differential. An increase in the US spreads relative to the Euro Area spreads would cause forecasted dollar depreciation. Because the FCIs are constructed so that an increase represents an improvement in financial conditions, the sign of the coefficient on the FCI differentials would be negative so that a relative deterioration in US financial conditions would still lead to forecasted dollar depreciation.B. Taylor Rule Differentials ModelEngel, Mark, and West (2008) propose an alternative Taylor rule based model, which we call the Taylor rule differentials model to differentiate it from both the interest rate differentials model and the Taylor rule fundamentals model. They posit, rather than estimate, coefficients for the Taylor rule and subtract the interest rate reaction function for the Euro Area from that for the United States to obtain implied interest rate differentials,where the constant is equal to zero, assuming that the inflation target and equilibrium real interest rate are the same for the United States and the Euro Area. Out-of-sample exchange rate forecasting is conducted using single equation and panel error correction models.14We estimate a variant of the Taylor rule differentials model with two measures of economic activity–OECD estimates of the output gap and the unemployment gap. In order to obtain an implied interest rate differential that corresponds to the implied interest rate differential (6) with the unemployment gap as the measure of real economic activity, we use a coefficient of -1.0. This is consistent with a coefficient of 0.5 on the output gap if the Okun's law coefficient is 2.0.The Taylor rule differential model using Taylor's original coefficients would have a coefficient of 1.5 on the inflation differential, 0.5 on the output gap differential, and would not include the real exchange rate.15 During 2009 and 2010, a number of commentators, most notably Rudebusch (2010), argued that the appropriate output or unemployment gap coefficient in the Taylor rule for the United States should be double the coefficient in Taylor's original rule. While there has been an active policy debate on the normative question of whether prescribed Taylor rule interest rates should be calculated using Taylor's original specification or with larger coefficients, it is clear that the latter provide a better fit for Fed policy in the 2000s.16 Since the same argument has not been made for the ECB, we implement this by estimating a Taylor rule differentials model with a coefficient of 1.0 on the output gap (or -2.0 on the unemployment gap) for the United States and 0.5 on the output gap (or -1.0 on the unemployment gap) for the ECB, where α is a constant.The implied interest rate differential can be used to construct an exchange rate forecasting equation, where, as in the Taylor rule fundamentals model, the signs of the coefficients switch and we do not have a

The study modeled the dynamic interaction between exchange rate, interest rate and agricultural export earnings using panel VAR Model. The specific objectives of the study include to; interdependencies in the dynamic interaction between exchange rate, interest rate and agricultural export earnings, parameters of panel VAR model using PVAR Stata code developed by Abrigo and love, determine the shocks associated with their dynamic interactions between these variables, investigate direction of causality between interest rate, exchange rate and agricultural export earnings from six African countries and make appropriate recommendations. The data used for the study was secondary data extracted from index mundi website and world data indicators for the period of 40 years (1980-2020). The data was on exchange rate, interest rate and agricultural export earnings. Geographically, the six African countries include; Algeria, Angola, Egypt, Libya, Gabon and Nigeria. The study uses vector Autoregressive model estimation results with PVAR Stata code developed by Abrigo and love. The post estimation test on the Vector Autoregressive (VAR) model shows a contemporary Co-efficient of Correlation analysis. It was found that lending interest rate and exchange rate are negatively associated with Co-efficient of Correlation of (-0.0873). Also, it was found that there exist a positive association between exchange rate and agricultural export earnings. Also, there is a positive association between lending interest rate and agricultural export earnings. The inverse roots of a characteristic polynomial of the estimated Panel VAR model satisfied the stability condition (of the diagnostic test) since no root lied outside the unit root circle. Therefore, the estimated VAR is stable. However, it was confirmed that there is no directional relationship that exist between the variables. Also, the results show that exchange rate and lending rate have positive on agricultural export earnings, whereas exchange rate is likely to reduce the level of lending interest rate slightly. Therefore, it is recommended that in estimating the dynamic interaction between variables in a panel data system, there is need for the inclusion of the lags of the response variable among the determinants to measures the dynamic interaction as well capture heterogeneities in the series and also, policies should be formulated to stabilized exchange and lending rates in order to improve and strengthen the countries’ agricultural economy amongst others

We study the out-of-sample forecasting performance of 32 exchange rates vis-a-vis the New Taiwan Dollar (NTD) in a 32-variable vector autoregression (VAR) model. The Bayesian approach is applied to a large-scale VAR model (LBVAR) and its forecasting performance is compared to the random-walk model in terms of both Diebold-Mariano and the Giacomini-Rossi fluctuation tests. Several results are found in the paper when we pay attention to the top three trading partner for Taiwan, particularly the China, U.S. and Japan, in which the corresponding bilateral exchange rates forecasts are denoted as CNY-NTD, USD-NTD and JPY-NTD respectively. First, a LBVAR model has a relatively better forecasting performance of CNY-NTD exchange rate in both medium-run and long-run. Second, a LBVAR model performs better than the random-walk model only in the short-run when forecasting USD-NTD exchange rate. Lastly, the random-walk model outperforms a LBVAR model all the time on forecasting JPY-NTD exchange rate.

Previous articleNext article FreeCommentMichael W. McCrackenMichael W. McCrackenFederal Reserve Bank of St. Louis Search for more articles by this author PDFPDF PLUSFull Text Add to favoritesDownload CitationTrack CitationsPermissionsReprints Share onFacebookTwitterLinked InRedditEmailQR Code SectionsMoreI. IntroductionThis paper makes me think of academic seminars. Not in the content per se or even its presentation, but rather in how I personally know when I think a seminar is “good” or “bad.” Since there exists no such thing as a perfect paper my definition of a good or bad seminar does not reflect whether the paper is perfect. For me, a good seminar is one where I like the paper enough to be willing to engage in an active discussion even if that means pointing out aspects of the paper I disagree with. In contrast, a bad seminar is one associated with a paper that is so bad that I don’t want to ask questions because that only prevents me from getting out of the seminar as soon as possible.This is a good paper. It has a question that I find intriguing and addresses the question in a reasonable fashion. And yet it is not perfect and there are many issues that can be criticized. These include focusing only on one quarter ahead forecasts, using rolling windows to estimate parameters despite very small sample sizes, the potential for data snooping over the many models and periods considered, using somewhat quirky and oddly timed OECD data, and so forth.Rather than spend time working my way through a list of referee-style suggestions that might improve the paper, in the remainder I’ll focus on what I think is a deeper issue in this paper and, more generally, the literature, on very standard empirical macroeconomic models of exchange rates. In particular I discuss some very pragmatic forecasting issues involving forecast origins and the relevant forecast horizons.II. Forecast Origins and HorizonsAs someone who works at a central bank I tend to think of forecasting in the context of (a) Federal Open Market Committee (FOMC) dates and (b) macroeconomic aggregates. The former implies a very specific set of forecast origins—dates on which a forecast must be produced. The latter implies a very specific set of forecast horizons–the difference between the FOMC date and the dates on which the macroeconomic variables are published by the Bureau of Economic Analysis (e.g., GDP), the Bureau of Labor Statistics (e.g., the unemployment rate), or even the Federal Reserve System (e.g., industrial production). Both are very convenient because they define the collection of data available at any given FOMC meeting (anything observed before that date) and it defines how far into the future we have to forecast (the day in which the data is released). In the notation of a forecasting model this tells me when my forecast origin t is and how far ahead into the future h my forecast horizon is. In contrast, in this paper these quantities are not very clearly motivated and hence the remainder of my discussion will focus on how that affects how we should view their results on the predictive content of macroeconomic models of exchange rate predictability.In this paper the authors consider a very standard forecasting exercise in which they investigate the predictability of bilateral US dollar/ euro exchange rate movements. To do so they consider a very standard collection of empirical models including the Monetary, Purchasing Power Parity, and interest rate differentials models, as well as variants of a Taylor rule based model developed in earlier work by Moltsdovoya and Papell (2009). Each of these models implies a set of predictors x that are observed at a quarterly frequency. In addition, following the literature, the y variable being predicted is measured as the log-difference of the exchange rate observed on the last business day of each quarter. For example, this implies that y2012:Q1 equals the natural log of the exchange rate measured on March 31, 2012, minus the same measured on December 31, 2011. In each case the predictive model is an OLS (ordinary least squares) estimated linear regression of the form in which measurements of macroeconomic aggregates obtained prior to the current quarter are used to predict the current quarter log-difference in the exchange rate.While standard, this modeling procedure is not obvious for someone who works in a very structured forecasting environment such as a central bank. For example, suppose that I observe my quarterly frequency xt value on December 31, 2011. Why is it that we forecast exchange rate movements at the one quarter horizon and not, say, at the one month horizon? In this framework we would define yt+1 as the log-difference in the exchange rate over the first month of quarter t + 1 and hence y2012:Q1 equals the natural log of the exchange rate measured on January 31, 2012, minus the same measured on December 31, 2011? The US dollar/euro exchange rate varies not only across the quarter but also does so monthly, weekly, daily, and even intra-daily. That’s not to say that the one quarter horizon isn’t potentially interesting, but rather there is nothing about the exchange rate market that implies that a one quarter ahead horizon is a natural forecast horizon given an information set of data available through the end of the previous quarter. It is perfectly possible that a quarterly frequency predictor xt would be useful for forecasting soon after its release date (a day, a week, or even a month) and yet at a one quarter ahead horizon a naive random walk forecast dominates. My fear is that the one quarter ahead horizon is chosen by default simply because the x variable is observed at a quarterly frequency.In the previous example I assumed that my quarterly frequency predictor xt was observed on the last day of the previous quarter, say December 31, 2011. If I am using it as a predictor of current quarter exchange rate movements, the earliest possible forecast origin is clearly December 31, 2011. But what if I am asked to provide a forecast of future current quarter exchange rate movements at an FOMC meeting dated January 31, 2012? I could still use it as a predictor but I would want to redefine my y variable. For example, suppose I define yt+1 = y2012:Q1 as the natural log of the exchange rate measured on March 31, 2012, minus the same measured on January 31, 2012. There is nothing stopping me from using the same regression framework from before to construct a forecast. In this hypothetical world, since xt is defined on the last day of the previous quarter, I could conduct this type of exercise for y variables defined over any subperiod of quarter t.In figure 1 we consider such an exercise for four distinct definitions of yt+1 when the Taylor rule fundamentals model uses the output gap for prediction.1 When defined relative to t + 1 = 2012:Q1, these take the values of the difference in the log-exchange rate between (a) March 31, 2012, and December 31, 2011 (the definition of yt+1 considered in the paper and elsewhere in the literature); (b) January 31, 2012, and December 31, 2011; (c) February 28, 2012, and January 31, 2012; and (d) March 31, 2012, and February 28, 2012. The figure consists of four lines. When , the line corresponds to the MSPE ratio path from table 1, panel A, of the paper (case (a)). The other lines are the MSPE ratio paths when the forecast origin and horizon are defined relative to cases (b), (c), and (d).Fig. 1. MSPE ratios Taylor rule fundamentals model with output gapView Large ImageDownload PowerPointWe immediately find there is considerable heterogeneity in the predictive content of this model across the quarter. Over the first month of the quarter (so that ) the model predicts quite poorly relative to the random walk benchmark, with MSPE ratios near 1.2. Over the second month of the quarter the model does a bit better with ratios near 1.1, but is still worse than the random walk model. Somewhat surprisingly, the model consistently outperforms the random walk model during the last month of the quarter with MSPE ratios generally below one with values ranging from 0.95 to 0.9. Integrating across these three lines we obtain the line that matches the numbers from table 1, panel A .The MSPE ratio paths lead to a somewhat odd conclusion: the model performs better, relative to the random walk model, the closer we get to the end of the quarter. This is despite the fact that the information content in the predictors is increasingly stale as we move from a forecast origin of the last day of the previous quarter to a forecast origin of the last day of the second month of the current quarter. If we take a deeper look at the raw MSPEs from the random walk and Taylor rule models (not shown) we find that both models contribute to this result: the random walk MSPE path associated with the first month of the quarter tends to be a bit lower than that from the third month of the quarter, while the Taylor rule model MSPE path associated with the first month of the quarter tends to be a bit higher than that from the third month of the quarter. Whether or not these paths are statistically distinct from one another is beyond the scope of the discussion, but the differences are interesting nevertheless.One potential explanation might arise from the derivation of the Taylor rule based models and in particular the timing of information flows within these models. As described in section II, subsection A, equation (1) of the text, the basic building block of this model is an equation of the form2 where it is the target for the short-term nominal interest rate, πt is the inflation rate, is the target level of inflation, gt is a measure of the output gap (or more generally some measure of economic slack in the economy), and R is the equilibrium level of the real interest rate. The equilibrium concepts and R are known constants chosen by the relevant monetary authority. Moreover, the preference parameters Φ and γ are also known to the monetary authority. The basic premise of this rule is that it provides a description of what the monetary authority should do when selecting the target for the short-term nominal interest rate i at time t based on the levels of π and g observed at time t.With this in mind consider the logic followed in developing the Taylor rule based predictive model for exchange rates. First we take the time t difference between the Taylor rule associated with the FOMC and that for the Governing Council of the ECB (GC hereafter) as the authors do for equation (4) of the text where asterisks denote observables for the euro area and the lack thereof denotes an observable for the United States. In addition we maintain that the policy parameters Φ and γ are common across the FOMC and GC and hence λ = 1 + Φ, while we aggregate R, R*, , and Φ into the constant term α. From here, with a bit of handwaving that links interest rate differentials to exchange rate movements, the authors obtain the predictive equation In the paper, t is linked one-to-one with quarters as defined by a calendar year where, as an example, January, February, and March together define the first quarter of a year. This is not entirely unreasonable and is the procedure followed throughout much of the literature including Mark (1995); Cheung, Chinn, and Pascual (2002); and Engel, Mark, and West (2008) in the context of other, non-Taylor rule based, quarterly frequency macroeconomic models of exchange rate determination. Moreover, with t defined relative to a sequence of quarters within a calendar year, setting h equal to 1 is not an unreasonable choice.And yet given the description of the Taylor rule from earlier, it’s not clear that is the correct way to view t. Recall that i is defined as the target for the short-term nominal interest rate. This rate typically only changes when the FOMC or the GC has its regularly scheduled meetings: eight times a year for the FOMC (twice per quarter; approximately the third and ninth week of each quarter), and twelve times a year for the GC (once per month and typically in the first two weeks of the month).3 This implies that irrelevant of the terms on the right-hand side of (4), the left-hand side will literally only change if either the FOMC or the GC changes its respective policy rate. Put differently, equation (4) implies that t is not so much indexed to calendar time as indexed to scheduled meetings of the FOMC or the GC.That is not to say that the right-hand side terms in (4) are irrelevant for exchange rate movements. Quite the contrary, these are very much the types of data the FOMC and GC looks at when making decisions about the short-term policy rate. The problem is that by transitioning from equation (4) to equation (5) you are changing a time index that is primarily associated with the timing of FOMC and GC meetings to one that is interpreted as being associated with (end of quarter) quarterly calendar dates.To see how this might affect the intra-quarter predictability of the Taylor rule based model, consider the following approximate time line of FOMC and GC meetings for the first quarter of 2012: January 12*, January 25, February 9*, March 8*, and March 13, where I’ve let an asterisk denote a GC meeting and the absence of an asterisk denotes an FOMC meeting. If the Taylor rule based predictive model is taken literally, exchange rate movements in 2012:Q1 due to changes in policy rates (it − it*) can only occur on or after these dates. These policy rates in turn will have changed only if the inflation rate or the output gap changed since the previous meeting. Since US RGDP for 2011:Q4 was released on January 28, 2012, euro area RGDP for 2011:Q4 was released on February 15, 2012, and the next GC and FOMC meetings do not occur until March, the only month within 2012:Q1 that the output gap component of the Taylor rule will be able to affect exchange rate movements is March–the third month of the quarter, in accordance with the MSPE ratio paths from figure 1.III. ConclusionAs I said in the introduction, I like this paper and a lot can be learned from it. Perhaps my favorite part is simply that the authors took the time to gather vintage data in order to conduct their forecasting exercises in something akin to a real-time environment—the kind of environment policymakers would have faced throughout the past decade and particularly during the Great Recession. Even so, there are many unanswered questions associated with the paper. And as I made clear in my discussion, the aspect of the paper that confuses me the most is the simple definition of the forecast origins and horizons implied by these quarterly frequency macroeconomic models of exchange rate predictability. And again, to be fair, this concern is not uniquely tied to this paper but it is exacerbated by the focus this paper puts on Taylor rule based models of exchange rate predictability—models that center around changes in the short-term policy rates set by both the FOMC and Governing Council of the ECB.EndnotesThe views expressed herein are solely those of the author and do not necessarily reflect the views of the Federal Reserve Bank of St. Louis or the Federal Reserve Board of Governors. For acknowledgments, sources of research support, and disclosure of the author’s material financial relationships, if any, please see http://www.nber.org/chapters/c12775.ack.1. The data was kindly provided by the authors.2. In the following I use g to denote an output gap rather than y, as is done in the text.I do so to distinguish it from the generic use of y as a dependent variable.3. The ECB Governing Council meets more like twice per month for a total of 24 times per year. However, the first meeting of the month is the one associated with decisions on the policy stance of the ECB.ReferencesCheung, Y., M. Chinn, and A. Pascual. 2002. “Empirical Exchange Rate Models of the Nineties: Are Any Fit to Survive?” Journal of International Money and Finance 24: 1150–75.First citation in articleGoogle ScholarEngel, Charles, Nelson C. Mark, and Kenneth D. West. 2008. “Exchange Rate Models Are Not As Bad As You Think.” In NBER Macroeconomics Annual 2007, edited by Daron Acemoglu, Kenneth Rogoff, and Michael Woodford, 381–441. Chicago: University of Chicago Press.First citation in articleGoogle ScholarMark, Nelson. 1995. “Exchange Rate and Fundamentals: Evidence on Long-Horizon Predictability.” American Economic Review 85: 201–18.First citation in articleGoogle ScholarMolodtsova, Tanya, and David H. Papell. 2009. “Exchange Rate Predictability with Taylor Rule Fundamentals.” Journal of International Economics 77: 167–80.First citation in articleGoogle Scholar Previous articleNext article DetailsFiguresReferencesCited by Volume 9, Number 12013 Article DOIhttps://doi.org/10.1086/669591 © 2013 by the National Bureau of Economic ResearchPDF download Crossref reports no articles citing this article.

Bayesian Model Averaging and exchange rate forecasts

We analyse how financial market analysts’ expectations in the Czech National Bank’s Financial Market Inflation Expectations survey perform relative to the random-walk forecast when it comes to predicting five financial variables. Using data from 2001 to 2022, our results indicate that the analysts are able to significantly outperform the random-walk forecast in terms of forecast precision for the repo rate and Prague Interbank Offered Rate at the one-month forecasting horizon. For the five- and ten-year interest rate swap rates, the random walk significantly outperforms the analysts at both the one-month and one-year forecasting horizons. For the CZK/EUR exchange rate, the random-walk forecast has a lower root mean squared forecast error than that of the analysts’ forecast at the one-month horizon whereas at the one-year horizon the opposite is found; however, none of these differences are statistically significant.

This paper presents a model that integrates money, relative prices, and the current account balance as factors ex- plaining movements in nominal (effective) exchange rates. Thus money and the current account are the proximate determinants of changes in real (effective) rates. The basic model is first analyzed under static expectations. It is an extension of Branson (1977) to include explicitly exogenous disturbances to the current account. Next, rational expectations are introduced, and it is shown that the nominal (and real) rate should be expected to jump instantaneously in response to new information or "innovations" in money, the current account, and relative prices.

This paper aims to investigate the predictive accuracy of the flexible price monetary model of the exchange rate, estimated by an approach based on combining the vector autoregressive model and multilayer feedforward neural networks. The forecasting performance of this nonlinear, nonparametric model is analyzed comparatively with a monetary model estimated in a linear static framework; the monetary model estimated in a linear dynamic vector autoregressive framework; the monetary model estimated in a parametric nonlinear dynamic threshold vector autoregressive framework; and the naive random walk model applied to six different exchange rates over three forecasting periods. The models are compared in terms of both the magnitude of their forecast errors and the economic value of their forecasts. The proposed model yielded promising outcomes by performing better than the random walk model in 16 out of 18 instances in terms of the root mean square error and 15 out of 18 instances in terms of mean return and Sharpe ratio. The model also performed better than linear models in 17 out of 18 instances for root mean square error and 14 out of 18 instances for mean returns and Sharpe ratio. The distinguishing feature of the proposed model versus the present models in the literature is its robustness to outperform the random walk model, regardless of whether the magnitude of forecast errors or the economic value of the forecasts is chosen as a performance measure.

Forecasting Euro Exchange Rates: How Much Does Model Averaging Help?

Exchange Rates and Prices: Sources of Sterling Real Exchange Rate Fluctuations, 1973-94

The purpose of this research is to investigate the forecasting performance of Artificial Neural Network models applied to foreign exchange rates. The study concentrates on the behavior of forecasts of exchange rates generated from the radial basis function (RBF) network models where little previous work exists;Exchange rates examined are the German mark/US dollar, Japanese yen/US dollar, and Italian lira/US dollar. One-step-ahead forecasts from univariate and multivariate RBF models are compared with those generated from ARIMA models, random walk forecasts and the forward rates. Interest rates and the money supply (M1) are used as explanatory variables in the multivariate analyses;Out-of-sample evaluation criteria include root mean squared error, correct direction, and speculative direction. Hypothesis tests are used to assess if differences in forecast accuracy from different models are significant and to assess if models can predict the direction of change with statistical significance. The tests employed are the Modified Diebold Marino test [Harvey et al. (1997)], the Pesaran-Timmerman (1992, 1994) non-parametric market timing test, and the chi2 test of independence [see Swanson and White (1997)];The main results of the study indicate that RBF models may be a useful alternative to the other models considered for forecasting exchange rates. In particular, out-of-sample forecasting results indicate that some multivariate RBF models using interest rates as economic variables do have forecasting value for some exchange rates. In the presence of interest rates, the M1 variable does not seem to possess much explanatory power for forecasting the three exchange rates.

Purpose- Exchange rate is the value of a country's national currency against foreign national currencies. In this context, the exchange rate is considered an important macroeconomic indicator in evaluating the country's economy. The failure to control the exchange rate may damage economy significantly. It is possible to understand this from the 2001 crisis in Turkey, known as 'Black Wednesday', and the foreign exchange crisis that started in Thailand in 1997 and affected many East Asian countries. Interest rate is one of the critical determinants affecting the exchange rates. Therefore, changes in interest rates are expected to affect the level of exchange rates. When there is an increase in interest rates, foreign capital flow is expected for that particular country. Hence, a decrease in exchange rates is expected for the excess capital flows. This study aims to analyze the relationship between exchange rates and interest rates, considering the last 10 announcements of the interest policy of the Central Bank of the Republic of Turkiye. These announcements are between January 19, 2023 and October 26, 2023. The study used the TL/USD exchange rates and 10-year government bond interest rates to measure the relationship in between these two variables. Methodology-The aim of this study is to analyze the relationship between the dollar exchange rate and government bond interest rates for Turkiye. For this purpose, data is collected for the days when the last 10 policy rates published by the CBRT were announced. Data is obtained investing.com. Vector Autoregression (VAR) is used to measure the relationship in between two variables. The VAR system is based on empirical regularities embedded in the data. The VAR model may be viewed as a system of reduced form equations in which each of the endogenous variables is regressed on its own lagged values and the lagged values of all other variables in the system. Vector Autoregressive models are widely used in time series research to examine the dynamic relationships exist in between variables that interact with one another. In addition, VAR models are viable forecasting tools used often by macroeconomic or policy-making institutions. . In this study first, the stationary levels of the variables are determined by using Unit Root Test. Second, pre-tests of autocorrelation, heteroscedasticity and normality are conducted for the validity of the VAR model. Third, the short-term relationship between variables is tested by using VAR Granger Causality Test. Fourth, VAR analysis is utilized by applying Impulse-Response Analysis and Variance Decomposition Analysis . And finally, the long-term relationship between variables is tested by using Johansen Cointegration Test. Vector Autoregressionmodel is employed in this study. Findings- According to the results of Granger Causality test, government bond interest rates strongly affect the changes of exchange rate. However, there is no causality from exhange rates to interest rates. Therefore, the changes of interest rates are the main determinants of the changes of exchange rates in this short period. The results of Impulse-Response Test show that an unexpected shock (an unexpected increase) in government bond interest rates affects the exchange rates and increases it significantly. More, an unexpected increase in the exchange rates causes the interest rates on government bond to increase. The results of the variance decomposition test show that 50% of the change in the variance of the exchange rates in the first period is explained by changes in bond interest while 30% of the change in the variance of bond interest rates is explained by the changes in exchange rates. The results of Johansen cointegration test support that there is a stable long-term relationship between dollar exchange rates and government bond interest rates. Conclusion-This study focuses on the relationship between government bond interest rates and the dollar exchange rates in Turkiye for the last 10 policy interest rates announcements by Cenral Bank of Turkiye. In summary, the changes in interest rates on bonds affect the changes in exchange rates more. Data for the days that the CBRT issued the last ten policy rates is gathered for this purpose. The association between two variables is measured using Vector Autoregression (VAR). According to overall results, the changes in interest rates on bonds affect the changes in exchange rates more. Keywords: Policy rate, exchange rate, interest rate, Turkiye, Granger Causality, VAR model JEL Codes: E40, E50, C10, C58

Iran is a country, which has experienced high, and chronic inflation period and fluctuating Exchange rates during past decades. After the revolution in Iran in 1979, followed by eight-year Iran-Iraq war and world oil crises, high inflation has been one of the Iran's most important problems. Especially during past years boycotts against trade caused instable Exchange rates and high inflation in Iran. These issues attract economists' interest toward this subject. Therefore, the aim of this study is to analyze the relationship between Exchange rate and inflation based on time series data, using Hendry General to Specific Modeling method and Vector Autoregression (VAR) model. To this end, we used annual data for the period 1976-2012 for Hendry method. We also used the quarterly data between 1997: 3 -2011: 4 to estimate VAR model. Due to economic instability in recent years and lack of valid data we estimated model up to 2012. As a result of the Hendry model, it is obtained that there is a direct relationship between Exchange rate and inflation. An increase in foreign exchange rates makes the inflation goes up. By including the money supply variable to VAR model the effects of money supply and the exchange rate on inflation has been investigated as well. According to the results, both the money supply and the exchange rate affect the inflation in the positive direction. Contribution of the money supply on inflation is greater than the exchange rate.

Background/Objectives: Export competitiveness of an economy is determined by exchange rate and price level movements. This paper endeavors to analyze relative price and exchange rate movements in selected Asian countries visà-vis India and theirimplications for trade policy. Methods/Statistical analysis: The trends in changes in relative prices, exchange rates and trade are analyzed for years 1993, 2003 and 2013. Unit value index for exports is used to calculate relative price ratios. The relative prices and exchange rates are calculated using simple mathematical equations. Then, the price ratios and exchange rates are compared with export and imports movements of each country vis-à-vis another to assess effects of these movements on trade competitiveness. Findings: The study elucidates thatthe greater the increase in the exchange rate than the increase in the relative price level, the beneficial it is for a country to trade with another country. India’s exports to selected five countries reflected an upward trend whenever the depreciation of currency was greater that the upward movements in the price levels. An analysis of percentage changes in price and exchange rates and growth rates of exports and imports also reflects that India experienced a slow growth in exports in all those years when price rise was not compensated equally by exchange rate depreciations.It also indicates that whenever the price rise was compensated by the equivalent or greater depreciation of currency, there was surplus in trade with the competing country. These findings are in tune with fundamental macroeconomic theory of exchange rates and price movements. This analysis clearly indicates that unlike other competing economies India lacks active policy interventions that will help in enhancing export competitiveness through precise exchange rate movements. Applications/Improvements: The study puts forward a strong case in favor of an exchange rate policy that brings about the movements in exchange rate in such a manner as to compensate for the changing price level in India. Keywords: Exchange Rate Movements, Export Competitiveness, Price Level, Trade Policy

PurposeThe random walk forecast of exchange rate serves as a standard benchmark for forecast comparison. The purpose of this paper is to assess whether this benchmark is unbiased and directionally accurate under symmetric loss. The focus is on the random walk forecasts of the dollar/euro for 1999‐2007 and the dollar/pound for 1971‐2007.Design/methodology/approachA forecasting framework to generate the one‐ to four‐quarter‐ahead random walk forecasts at varying lead times is designed. This allows to compare forecast accuracy at different lead times and forecast horizons. Using standard evaluation methods, this paper further evaluates these forecasts in terms of unbiasedness and directional accuracy.FindingsThe paper shows that forecast accuracy improves with a reduction in the lead time but deteriorates with an increase in the forecast horizon. More importantly, the random walk forecasts are unbiased and accurately predict directional change under symmetric loss and thus are of value to a user who assigns similar cost to incorrect upward and downward move predictions in the exchange rates.Research limitations/implicationsThe one‐ to four‐quarter‐ahead random walk forecasts evaluated here are for averages of daily figures and not for the (end‐of‐quarter) rates in 3‐, 6‐, 9‐ and 12‐months. Thus, the framework is of value to a market participant who is interested in forecasting quarterly average rates rather than the end‐of‐quarter rates.Originality/valueThe exchange rate forecasting framework presented in this paper allows the evaluation of the random walk forecasts in terms of directional accuracy which (to the best of knowledge) has not been done before.