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Taylor Rules and the Euro

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Out-of-Sample Predictability of the Dollar/Euro Exchange Rate ... Cheung, Chinn, and Pascual (2005): same conclusion two decades later ... – PowerPoint PPT presentation

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Title: 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)

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 t4 inflation forecasts
  • Euro Area
  • OECD Original Release and Revision Database
  • 1999Q4-2007Q4
  • Revised data the 2007Q4 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
    MSPEs 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 cvs

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 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

34
Why Do We Need to Adjust the Test Statistic?
  • H0
  • H1

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 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

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-t4 Inflation Forecasts
42
One-Quarter-Ahead Euro/USD Forecasts with
Real-Time Data and t4 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
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