1. (Taylor) Rules versus Discretion in U.S. Monetary Policy
Alex Nikolsko-Rzhevskyy
Lehigh University
David Papell and Ruxandra Prodan
University of Houston
Texas Camp Econometrics – February 22, 2014

2. Motivation Monetary Policy Rules Rules versus Discretion Taylor Rule
Friedman (1960)
Rules versus Discretion
Kydland and Prescott (1977)
Taylor Rule
Taylor (1993)

3. “Monetary Policy Rules Work and Discretion Doesn’t: A Tale of Two Eras”
Taylor (2012) JMCB Lecture
The Rules-Based Era
The Ad Hoc (or Discretionary) Era ?
Chose Eras Based on Historical Experience
Temptation – Choose Eras Based on Success or Failure
Good Outcomes Become Rules-Based Eras
Bad Outcomes Become Ad Hoc Eras

4. Plan for the Paper
Identify Rules-Based and Discretionary Eras from the Data
Not Influenced by Economic Outcomes
Define Taylor Rule Deviations
Absolute Value of the Difference Between the Federal Funds Rate and the Rate Prescribed by the Original Taylor Rule
(Taylor) Rule-Based Eras
Lower Deviations
Discretionary Eras
Higher Deviations
Tests for Multiple Structural Changes
Markov Switching Models

5. Taylor Rule Deviations
Original Taylor (1993) Rule
it = pt (pt – 2.0) yt + 2.0
it = pt yt
Construct Taylor Rule Deviations
Calculate Actual Minus Prescribed Federal Funds Rate
Take Absolute Value to Measure Deviations
The Deviations are Calculated – Not Estimated

6. Data Real-Time Data Set for Macroeconomists (Philadelphia Fed)
GDP and GDP Deflator
Vintages Starting in 1965:Q4 – Data Starts in 1947:Q1
Inflation
Annual Percentage Change in GDP Deflator
Can’t Get Long Series for Other Measures

7. Data Output Gap Policy Rate
No Internal Fed (Greenbook) Output Gaps Before 1987
Real-Time Detrending Starting in 1947:Q1
Linear, Quadratic, and Hodrick-Prescott Detrending
No Necessity for Positive and Negative Output Gaps to be Equal
Policy Rate
Federal Funds Rate Until 2008:Q4
Shadow Federal Funds Rate Starting in 2009:Q1
Shadow Rate Term Structure Model of Wu and Xia (2013)

8. Real-time output gaps using linear, quadratic, and HP detrending

9. Real-Time Output Gaps Linear Detrending HP Detrending
Consistently Negative Since 1974
HP Detrending
Gaps Too Small During the 1970s and Early 1980s Recessions
Real-Time Okun’s Law Metric
Gaps for the 1990 and 2001 Recessions Almost as Large as Gaps for the 1980 and 1982 Recessions
Quadratic Detrending
Fits Gaps for 1970s and 1980s Recessions
Reasonable for 1980s through 2000s and

10. Taylor Rule Deviations
Real-Time GDP Inflation
Real-Time Quadratic Detrended Output Gaps
Negative in the 1970s
Positive in the Early 1980s
Negative in the 2000s

11. The Federal Funds Rate and the Prescribed Taylor Rule Rate

12. The Difference Between the Actual and Prescribed Rates

13. Taylor Rule Deviations

14. Structural Change Tests
Bai and Perron (1998) Tests for Multiple Structural Breaks
Changes in the Mean of the Taylor Rule Deviations
Dt = g0 + g1DU1t +…+gmDUmt + ut
Dt are Taylor Rule Deviations
DUmt = 1 if t>Tbt, 0 Otherwise, for All Breakpoints Tbt
sup Ft (l+1/l) Test with 15% Trimming
Search for a Break, Split Sample, Search Sub-Samples

15. Structural Change Tests
SupF test
(sequential method)
Critical values (1%)
Break dates
95% Confidence Intervals
SupF(1| 0) = 32.63
12.29
1985:Q1
1984:Q4 - 1986:Q2
SupF(2| 1) = 53.27
13.89
2000:Q4
1999:Q :Q2
SupF(3| 2) = 50.74
14.80
1974:Q3
1972:Q :Q2
Coefficients
γ0 = 1.468
γ1 = 1.835
γ2 =
γ3 = 1.174

16. Structural Change Tests

17. Structural Change Tests
Mean of the Taylor Rule Deviations
1.47 for 1965:Q4 – 1974:Q3
3.30 for 1974:Q4 – 1985:Q1
0.80 for 1985:Q2 – 2000:Q4
1.97 for 2001:Q1 – 2013:Q4
Highest in the 1970s and Early 1980s
Lowest in the Great Moderation

18. Restricted Structural Change Tests
Bai and Perron Tests do Not Determine Whether the Two Higher Means are Statistically Different from the Two Lower Means
Perron and Qu (2006) Tests
Add Two Constraints to Bai and Perron test
g1 + g2 = 0 and g2 + g3 = 0

19. Restricted Structural Change Tests
Restricted SupF test
Critical value (1%)
Break dates
95% Confidence Intervals
85.46*
17.17
1974:Q3
1971:Q :Q3
1985:Q1
1984:Q4 - 1988:Q3
2001:Q1
1999:Q :Q3
Coefficients
γ0 = 1.075
γ1 = 1.531
γ2 =
γ3 = 1.531

20. Restricted Structural Change Tests
Same Break Dates as in Bai and Perron
Mean of the Taylor Rule Deviations
1.05 for 1965:Q4 – 1974:Q3 and 1985:Q2 – 2001:Q1
2.58 for 1974:Q4 – 1985:Q1 and 2001:Q2 – 2013:Q4
Rules-Based and Discretionary Eras
The Differences are Statistically Significant

21. Structural Change Tests with Inflation Forecasts
Greenbook Inflation Forecasts Instead of Inflation Rates
Four-Quarter-Ahead Forecasts
Available from 1973:Q3 – 2007:Q4
SPF Forecasts for 2008:1 – 2013:4

22. Structural Change Tests with Inflation Forecasts
SupF test
(sequential method)
Critical values (1%)
Break dates
95% Confidence Intervals
SupF(1| 0) = 53.17*
12.29
1984:Q3
1983:Q2 - 1986:Q4
SupF(2| 1) = 42.36*
13.89
2001:Q1
1998:Q :Q1
Coefficients
γ0 =
γ1 =
γ2 = 0.893

23. Structural Change Tests with Inflation Forecasts

24. Markov Switching Models
Two State Models
Similar to the Restricted Structural Change Model
Allow for Changes in the:
Mean and Variance of the Taylor Rule Deviations
Transition Probabilities
Rules-Based Eras
Lower Mean and Variance
Discretionary Eras
Higher mean and Variance

25. Markov Switching Model: Switching Mean and Variance
State s=1
(Rules-Based)
State s=2
(Discretionary) μs
0.781
2.779
(0.070)
(0.137) σs
0.548
1.177
(0.052)
(0.089)
pss
0.942
0.952
(0.026)
(0.024)

26. Markov Switching Model: Switching Mean and Variance
Similar Regime Switches to Structural Change Break Dates
First Rules-Based Era Ends in 1974:Q3
Discretionary Era from 1974:Q4 – 1986:Q1
Rules-Based Era from 1986:Q2 – 2001:Q1
Discretionary Era from 2001:Q2 – 2006:Q2
Additional Regime Switches
Discretionary Era from 1965:Q4 – 1968:Q4
Rules-Based Era from 2006:Q3 – 2007:Q4
Discretionary Era from 2008:Q1 – 2009:Q1
Rules Based Era from 2009:Q :Q1
Discretionary Era from 2011:Q2 – 2013:Q4
No Trimming with Markov Switching Models
Discretionary Eras When Deviations > Two Percent

27. Markov Switching: Switching Mean and Variance

28. Markov Switching Model: Switching Mean, Constant Variance
State s=1
(Rule-based policy)
State s=2
(Discretion) μs
1.050
3.202
(0.103)
(0.175) σs
0.896
(0.051)
pss
0.916
0.957
(0.043)
(0.021)

29. Markov Switching: Switching Mean, Constant Variance

30. Markov Switching Model: Switching Mean and Independently Switching Variance
State s=1
(Rule-based policy)
State s=2
(Discretion) μs
0.786
2.492
(0.069)
(0.089) σs
0.598
2.089
(0.039)
(0.350)
pmeanss
0.985
0.906
(0.203)
(0.303)
pvarss
0.946
0.942
(0.161)
(0.155)

31. Markov Switching: Independently Switching Mean and Variance

32. Historical Perspective
Taylor and Meltzer
1985 – 2003 a Rules-Based Era
2003 – 2012 a Discretionary Era
1985 Start of the Rules-Based Era Accords with our Results
We Date the Start of Discretionary Era as 2001
Clear from the Taylor Rule Deviations
Is This Caused by our Data and/or Detrending?
Same Result from Poole (2007) Diagram in Taylor (2012)
Deviations Start in 2001
Become Larger Starting in 2003

33. Taylor Rule Deviations

34. Updated Poole (2007) Diagram

35. Historical Perspective
Rules-Based Era from 2006:Q3 – 2007:Q4
Taylor (2007)
Actual and Prescribed Paths Diverge in 2002:Q2 and Converge in 2006:Q3
Discretionary Era from 2008:Q1 – 2008:Q4
Response to Financial Market Stress
Taylor (2008) Proposed Lowering FFR by LIBOR-OIS Spread
Discretionary Era from 1965:Q4 – 1968:Q4
Change from Johnson to Nixon Administration
Discussed in Taylor’s First Principles Book

36. “Monetary Policy Rules Work and Discretion Doesn’t”
Taylor’s Assertion
Evaluate with Our Results
Use Revised Data on Inflation and Unemployment
Calculate Loss Functions for Rules-Based and Discretionary Eras
Okun’s Misery Index
(Inflation Plus Unemployment)
Linear absolute loss function
|inflation - 2%|+|unemployment rate - natural rate|
Quadratic loss function
(inflation - 2%)2+(unemployment rate - natural rate)2

37. Inflation and Unemployment

38. Loss Functions Average Loss During Taylor-Rule Eras
Average Loss During Taylor-Rule Eras
Average Loss During
Discretionary Eras
Panel A: Misery Index L = Inflation + Unemployment
Markov Switching
8.74
10.83
Structural Change
8.52
11.11
Panel B: Linear Absolute Loss Function L = |Inflation - 2%| + |Unemployment - Natural Rate|
2.37
3.87
2.32
3.95
Panel C: Quadratic Loss Function L = (Inflation - 2%)2 + (Unemployment - Natural Rate)2
5.91
14.86
5.10
15.91

39. Loss Functions Average Loss During Taylor-Rule Eras
Average Loss During Taylor-Rule Eras
Average Loss During
Discretionary Eras
Panel A: Misery Index L = Inflation + Unemployment
Markov Switching
9.70
9.89
Structural Change
9.41
10.63
Panel B: Linear Absolute Loss Function L = |Inflation - 2%| + |Unemployment - Natural Rate|
2.80
3.55
2.90
3.61
Panel C: Quadratic Loss Function L = (Inflation - 2%)2 + (Unemployment - Natural Rate)2
8.71
12.65
8.49
14.72

40. Identify (Taylor) Rules-Based and Discretionary Eras
Conclusions
Identify (Taylor) Rules-Based and Discretionary Eras
Tests for Structural Change and Markov Switching Methods
Our Statistical Results Provide Support for Taylor’s Results
The Dates Closely Correspond
Not Subject to Being Influenced by Outcomes
Different Perspective on Start of the Recent Discretionary Era
2001 Instead of 2003
Validated by Poole’s Diagram
Monetary Policy Rules Work and Discretion Doesn’t