Title: Taylor Rules and the Euro
1Taylor Rules and the Euro
- Tanya Molodtsova, Alex Nikolsko-Rzhevskyy
- and David H. Papell
- CIRANO Workshop on Data Revision
- October 10-11, 2008
2Motivation
- 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
3Literature 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
4Literature 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)
5Literature 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
6Literature 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
7Questions 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
8Questions 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
9Questions 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
10Questions 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
11Questions 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
12Questions 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
13Questions 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
14Questions 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
15Questions 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
16Question We Do Not Ask
- How Did the Fed and ECB Conduct Monetary Policy?
17Taylor 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
-
18Taylor Rules (2)
- Extended Taylor Rule Clarida, Gali and Gertler
(1998) -
- is the real exchange rate
- Introduce interest rate smoothing
-
- After combining two equations
19Real-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
20Output 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
21Real-time vs. Revised Data (1)
U.S. Euro Area
Inflation
HP Filtered Output gap
22Real-time vs. Revised Data (2)
U.S. Euro Area
OECD Output Gap
Unemployment Rate
23Summary Statistics
24News 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
25Descriptive Statistics of Revisions
26Actual and Counterfactual Interest Rates
Contemporaneous TR Forward-Looking TR
U.S. FFR
Euro Area MMR
27Exchange 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) -
28Exchange 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)
29Exchange 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
30Taylor 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
31Inference 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
32Inference 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
33Why 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
34Why Do We Need to Adjust the Test Statistic?
35The Adjusted Statistic
- The CW (Adjusted) Statistic
-
- Using asymptotic standard normal critical values
with the adjusted CW statistic results in nicely
sized tests
36Inference 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
37Evaluating 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
38One-Quarter-Ahead Euro/USD Forecasts with
Real-Time Data
39One-Quarter-Ahead Euro/USD Forecasts with
Real-Time Data and Either Inflation or the Output
Gap
40One-Quarter-Ahead Euro/USD Forecasts with
Revised Data
41One-Quarter-Ahead Euro/USD Forecasts with
Real-Time Data and Period-t4 Inflation Forecasts
42One-Quarter-Ahead Euro/USD Forecasts with
Real-Time Data and t4 Inflation Forecasts and
Output Gap Growth
43Controlling 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
44Tests for Superior Predictive Ability
45Forecasting 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
46Forecasting Equation Coefficients (1)
Output Gap Differential Coefficient
Inflation Differential Coefficient
HP Filtered Output Gap
OECD Output Gap
47Forecasting Equation Coefficients (2)
Inflation Differential Coefficient
Unemployment Differential Coefficient
Unemployment Rate
48Is 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
49Conclusions
- 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
50Conclusions
- 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