Taylor Rule Exchange Rate Forecasting during the Financial Crisis (2013)

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