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 1970s 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)

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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

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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

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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?

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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?

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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)

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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?

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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?

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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?

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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)

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Question We Do Not Ask

• How Did the Fed and ECB Conduct Monetary Policy?

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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

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Taylor Rules (2)

• Extended Taylor Rule Clarida, Gali and Gertler
  (1998)
• is the real exchange rate
• Introduce interest rate smoothing
• After combining two equations

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Real-Time Datasets

• US
• Philadelphia Fed dataset Croushore and Stark
  (2001)
• OECD Economic Outlook output gap data
• SPF data t4 inflation forecasts
• Euro Area
• OECD Original Release and Revision Database
• 1999Q4-2007Q4
• Revised data the 2007Q4 vintage in both
  real-time datasets

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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

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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
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Summary Statistics
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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

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Descriptive Statistics of Revisions
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Actual and Counterfactual Interest Rates
Contemporaneous TR Forward-Looking TR
U.S. FFR
Euro Area MMR
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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)

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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)

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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

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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

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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
  MSPEs are equal Diebold and Mariano (1995),
  West (1996)
• - inference is made using standard normal
  c.v.s or bootstrap

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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 cvs

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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 MSPEs is 0
• DMW statistic is undersized with nominal 10
  tests having actual size of 2
• McCracken(2007)
• ? far too few rejections of the null

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Why Do We Need to Adjust the Test Statistic?

• H0
• H1

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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

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Evaluating Predictability

• We start the sample in 2001Q1 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 2000Q1 to 2007Q4 and record
  forecast errors of the model
• Calculate CW statistic
• Evaluate predictive ability using standard normal
  critical values

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One-Quarter-Ahead Euro/USD Forecasts with
Real-Time Data
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One-Quarter-Ahead Euro/USD Forecasts with
Real-Time Data and Either Inflation or the Output
Gap
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One-Quarter-Ahead Euro/USD Forecasts with
Revised Data
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One-Quarter-Ahead Euro/USD Forecasts with
Real-Time Data and Period-t4 Inflation Forecasts
42
One-Quarter-Ahead Euro/USD Forecasts with
Real-Time Data and t4 Inflation Forecasts and
Output Gap Growth
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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

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Tests for Superior Predictive Ability
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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

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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

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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

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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