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### Taylor Rules and the Euro

Tanya Molodtsova, Alex Nikolsko-Rzhevskyy

and David H. Papell

CIRANO Workshop on Data Revision

October 10-11, 2008

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

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

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)

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

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

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

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

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

Questions We Ask:Do Taylor Rules provide a reasonable approximation of interest rate setting in the U.S. and Euro Area?

Does evidence of predictability come from Taylor rule fundamentals, as opposed to either inflation or the output gap, but not both?

(Yes)

Do models with Taylor rule fundamentals provide evidence of Euro/USD exchange rate predictability?

(Yes)

(Yes)

10

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

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

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

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

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

Question We Do Not Ask

How Did the Fed and ECB Conduct Monetary Policy?

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

Taylor Rules (2)

Extended Taylor Rule: Clarida, Gali and Gertler (1998)

is the real exchange rate

Introduce interest rate smoothing

After combining two equations

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

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

“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

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)

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)

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

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

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

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

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

The Adjusted Statistic

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

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

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

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

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

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

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

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

Forecasting Equation Coefficients (1)

Output Gap Differential Coefficient

Inflation Differential Coefficient

HP Filtered Output Gap

OECD Output Gap

Forecasting Equation Coefficients (2)

Inflation Differential Coefficient

Unemployment Differential Coefficient

Unemployment Rate

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

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

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

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