Taylor Rules and the Euro

1. Taylor Rules and the Euro Tanya Molodtsova, Alex Nikolsko-Rzhevskyy and David H. Papell CIRANO Workshop on Data Revision October 10-11, 2008

2. Motivation • Out-of-Sample Predictability of the Dollar/Euro Exchange Rate • Most Research on Exchange Rate Predictability: Conventional Models of 1970’s Vintage (Monetary, PPP, Interest Rate Parity) Fully Revised Data • This paper: Models with Taylor Rule Fundamentals Real-Time Data

3. Literature: Taylor Rules and Real-Time Data Revised Data: Taylor (1993) Clarida, Gali, and Gertler (1998) Real-Time Data: Orphanides (2003, 2004) and Rudebusch (2006) for the U.S. Clausen and Meier (2003) and Gerberding, Worms and Seitz (2005) for Germany Nelson (2003) for UK Sauer and Sturm (2007), Gerdesmeier and Roffia (2004) Gorter, Jacobs and de Haan (2007), and Sturm and Wollmershauser (2008) for the Euro Area

4. Literature: Taylor Rules and Exchange Rates Clarida, Gali and Gertler (2002) and Clarida (2007): derive a two-country optimizing model with an open economy, IS curve, Philips curve, and Taylor rule Engel and West (2006), Mark (2007), and Engel, Mark and West (2007): examine the empirical performance of Taylor-rule based exchange rate models Clarida and Waldman (2007): introduce Taylor rules into an exchange rate model to explain how bad news about inflation can be good news for the exchange rate (an increase in inflation can cause currency appreciation)

5. Literature: Exchange Rate Predictability Meese and Rogoff (1983):economic models do not perform better out-of-sample than a naïve no change (random walk) model Cheung, Chinn, and Pascual (2005): same conclusion two decades later Faust, Rogers and Wright (2003): monetary model performs better using real-time data than using revised data, but not better than a random walk 5

6. Literature: Taylor Rules and Exchange Rate Predictability Molodtsova and Papell (2008): Exchange rate predictability for 1973-2006 using Taylor-rule fundamentals with quasi-revised data Molodtsova, Nikolsko-Rzhevskyy, and Papell (2008): Taylor rules and the Dollar/Mark rate Molodtsova (2007): Exchange rate predictability for 2000-2006 using Taylor-rule fundamentals with real-time data Engel, Mark, and West (2007): Exchange rate predictability using Taylor-rule fundamentals with revised data 6

7. Questions We Ask: Do Taylor Rules provide a reasonable approximation of interest rate setting in the U.S. and Euro Area? Do models with Taylor rule fundamentals provide evidence of Euro/USD exchange rate predictability? Does evidence of predictability come from Taylor rule fundamentals, as opposed to either inflation or the output gap, but not both? 7

8. Questions We Ask: Do Taylor Rules provide a reasonable approximation of interest rate setting in the U.S. and Euro Area? (Yes) Do models with Taylor rule fundamentals provide evidence of Euro/USD exchange rate predictability? Does evidence of predictability come from Taylor rule fundamentals, as opposed to either inflation or the output gap, but not both? 8

9. Questions We Ask: Do Taylor Rules provide a reasonable approximation of interest rate setting in the U.S. and Euro Area? (Yes) Do models with Taylor rule fundamentals provide evidence of Euro/USD exchange rate predictability? (Yes) Does evidence of predictability come from Taylor rule fundamentals, as opposed to either inflation or the output gap, but not both? 9

10. Questions We Ask: Do Taylor Rules provide a reasonable approximation of interest rate setting in the U.S. and Euro Area? (Yes) Do models with Taylor rule fundamentals provide evidence of Euro/USD exchange rate predictability? (Yes) Does evidence of predictability come from Taylor rule fundamentals, as opposed to either inflation or the output gap, but not both? (Yes) 10

11. Questions We Ask: Does predictability increase with real-time data? Is bad news about inflation good news for the forecasted exchange rate? Is good news about real economic activity good news for the forecasted exchange rate? Is the experience of the Bundesbank a good predictor for the actions of the ECB? 11

12. Questions We Ask: Does predictability increase with real-time data? (Yes) Is bad news about inflation good news for the forecasted exchange rate? Is good news about real economic activity good news for the forecasted exchange rate? Is the experience of the Bundesbank a good predictor for the actions of the ECB? 12

13. Questions We Ask: Does predictability increase with real-time data? (Yes) Is bad news about inflation good news for the forecasted exchange rate? (Yes) Is good news about real economic activity good news for the forecasted exchange rate? Is the experience of the Bundesbank a good predictor for the actions of the ECB? 13

14. Questions We Ask: Does predictability increase with real-time data? (Yes) Is bad news about inflation good news for the forecasted exchange rate? (Yes) Is good news about real economic activity good news for the forecasted exchange rate? (Yes) Is the experience of the Bundesbank a good predictor for the actions of the ECB? 14

15. Questions We Ask: Does predictability increase with real-time data? (Yes) Is bad news about inflation good news for the forecasted exchange rate? (Yes) Is good news about real economic activity good news for the forecasted exchange rate? (Yes) Is the experience of the Bundesbank a good predictor for the actions of the ECB? (No) 15

16. Question We Do Not Ask How Did the Fed and ECB Conduct Monetary Policy?

17. Taylor Rules (1) The Original Taylor Rule: Taylor (1993) is the target level of nominal interest rate is the inflation rate is the target level of inflation is the output gap is the equilibrium level of the real interest rate This equation can be rewritten as follows where and

18. Taylor Rules (2) Extended Taylor Rule: Clarida, Gali and Gertler (1998) is the real exchange rate Introduce interest rate smoothing After combining two equations

19. Real-Time Datasets US: Philadelphia Fed dataset: Croushore and Stark (2001) OECD Economic Outlook: output gap data SPF data: t+4 inflation forecasts Euro Area: OECD Original Release and Revision Database 1999:Q4-2007:Q4 Revised data: the 2007:Q4 vintage in both real-time datasets

20. Output Gap • To construct Taylor Rule fundamentals, we use the following measures of economic activity: • HP-detrended output gap • OECD estimates of the output gap • Unemployment rate • HP filter is applied taking into account the end-of-sample problem by forecasting and backcasting the series of industrial production by 12 quarters in both directions

21. Real-time vs. Revised Data (1) U.S. Euro Area Inflation HP Filtered Output gap

22. Real-time vs. Revised Data (2) U.S. Euro Area OECD Output Gap Unemployment Rate

23. Summary Statistics

24. “News” Versus “Noise” • Do Data Revisions Add “News” or Reduce “Noise”? • New Information or Measurement Error • News – Correlated with revised data and uncorrelated with real-time data • Noise – Correlated with real-time data and uncorrelated with revised data • Mixed Results

25. Descriptive Statistics of Revisions

26. Actual and Counterfactual Interest Rates Contemporaneous TR Forward-Looking TR U.S. FFR Euro Area MMR

27. Exchange Rate Predictability (1) Subtract Taylor rule for the Euro Area from Taylor rule for US: where ~ denotes Euro Area variables u and e are subscripts for the U.S. and Euro Area Suppose (for example) that U.S. inflation rises above its target level The Fed will raise the interest rate (immediately and/or gradually)

28. Exchange Rate Predictability (2) • Dornbusch Model with RE and UIRP: • Immediate Exchange Rate Depreciation • Forecasted Appreciation • Overshooting • Empirical Results Not Supportive: • Eichenbaum and Evans (1995) • Faust and Rogers (2003) • Scholl and Uhlig (2008) • Agreement About Sustained Appreciation Following Monetary Shock: • Disagreement About Delayed Overshooting (Identification)

29. Exchange Rate Predictability (3) Combine to produce a forecasting equation: Consistent with Forward Premium Puzzle Conditional on Monetary Policy Shocks Predictions Higher Inflation (Bad News) causes Forecasted Exchange Rate Appreciation Larger Output Gap (Good News) causes Forecasted Exchange Rate Appreciation

30. Taylor Rule Specifications • Symmetric vs. Asymmetric: • Symmetric - relative inflation and output gap terms only • Asymmetric - real exchange rate for the foreign country • Homogenous vs. Heterogeneous: • Homogenous – restricted cross-country coefficients on inflation and output gap • Heterogeneous – unrestricted cross-country coefficients • Smoothing vs. No Smoothing: • Smoothing – lagged interest rate • No smoothing – no lagged interest rate

31. Inference about Predictive Ability (1) • Compare two models based on the MSE comparisons: Model 1: , where Model 2: • Meese and Rogoff (1983a, 1983b) • Diebold-Mariano-West (DMW) Statistic - t-type statistic for testing that the two MSPE’s are equal: Diebold and Mariano (1995), West (1996) - inference is made using standard normal c.v.’s or bootstrap

32. Inference about Predictive Ability (2) • DMW Statistic only valid for non-nested models • Undersized for nested models • All models with random walk null and model-based alternative are nested • Clark and West (2006) Statistic - adjusted t-type statistic that has desirable size and power properties and can be used with standard normal cv’s

33. Why Do We Need to Adjust the Test Statistic? • Under the null of no predictability, the sample MSE of the alternative is greater than that of the random walk, while the population difference between the two MSPE’s is 0: • DMW statistic is undersized with nominal 10% tests having actual size of 2% • McCracken(2007) •  far too few rejections of the null

34. Why Do We Need to Adjust the Test Statistic? H0: H1: =0 >0

35. The Adjusted Statistic • The CW (Adjusted) Statistic: • Using asymptotic standard normal critical values with the adjusted CW statistic results in nicely sized tests

36. Inference about Predictive Ability (3) Use of the Clark and West Statistic Gourinchas and Rey (2007), Engel, Mark, and West (2007), Papell and Molodtsova (2008) Use of CW Statistic Criticized by Rogoff and Stavrakeva (2008) Measure of Predictability, not Forecasting

37. Evaluating Predictability • We start the sample in 2001:Q1 for the first vintage and estimate forecasting equation using rolling regressions with a 34-quarter window • Forecast one quarter ahead 32 exchange rate changes from 2000:Q1 to 2007:Q4 and record forecast errors of the model • Calculate CW statistic • Evaluate predictive ability using standard normal critical values

38. One-Quarter-Ahead Euro/USD Forecasts with Real-Time Data

39. One-Quarter-Ahead Euro/USD Forecasts with Real-Time Data and Either Inflation or the Output Gap

40. One-Quarter-Ahead Euro/USD Forecasts with Revised Data

41. One-Quarter-Ahead Euro/USD Forecasts with Real-Time Data and Period-t+4 Inflation Forecasts

42. One-Quarter-Ahead Euro/USD Forecasts with Real-Time Data and t+4 Inflation Forecasts and Output Gap Growth

43. Controlling for Multiple Hypotheses Testing Multiple hypotheses are tested simultaneously 24 alternative models Significant p-values could be generated by chance Perform test for Superior Predictive Ability (SPA) to increase reliability of results Hansen (2005) SPA test is designed to compare MSE of the benchmark to the MSE of a set of alternatives Rejecting the null indicates that at least one of the models from the set has superior predictive ability than the benchmark Takes into account search over specifications 43

44. Tests for Superior Predictive Ability

45. Forecasting Equation Coefficients • Is Good News About Inflation Bad News for the Forecasted Exchange Rate? • Negative Coefficient on the Inflation Differential • Higher U.S. Inflation causes Forecasted Dollar Appreciation • Is Good News About Real Economic Activity Good News for the Forecasted Exchange Rate? • Negative Coefficient on the Output Gap Differential • Positive Coefficient on the Unemployment Differential • Better U.S. Real Economic Activity Causes Forecasted Dollar Appreciation

46. Forecasting Equation Coefficients (1) Output Gap Differential Coefficient Inflation Differential Coefficient HP Filtered Output Gap OECD Output Gap

47. Forecasting Equation Coefficients (2) Inflation Differential Coefficient Unemployment Differential Coefficient Unemployment Rate

48. Is the Bundesbank a Good Predictor for the ECB? • Forecasting the Dollar/Mark Rate During the EMS • Molodtsova, Nikolsko-Rzhevskyy, and Papell (2007) • Strongest Evidence of Predictability • Heterogeneous Coefficients • No Smoothing • Asymmetric Specification • Forecasting the Dollar/Euro Rate with the Same Specification • No Evidence of Predictability

49. Conclusions Null hypothesis of no predictability can be rejected with Taylor rule fundamentals The results are robust to: Whether or not the coefficients on inflation and the real economic activity measure are homogeneous or heterogeneous Whether or not there is interest rate smoothing Evidence of predictability is only found for specifications that do not include the real exchange rate

50. Conclusions Evidence of predictability is: Stronger for real-time than for revised data About the same with inflation forecasts as with inflation rates Weakens if output gap growth is included in the forecasting regression Bad news about inflation and good news about real economic activity lead to out-of-sample predictability through forecasted exchange rate appreciation The Bundesbank is not a good predictor for the ECB