1. Deviations from Rules-Based Policy and Their Effects
Alex Nikolsko-Rzhevskyy
Lehigh University
David Papell and Ruxandra Prodan
University of Houston

2. Policy Rules Monetary Policy Rules Rules versus Discretion Taylor Rule
Friedman (1959)
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
Policy Rule Deviations
Absolute Value of the Difference Between the Federal Funds Rate and the Rate Prescribed by Various Policy Rules
Tests for Multiple Structural Changes
Rules-Based Eras with Lower Deviations
Discretionary Eras with Higher Deviations
Compare Economic Performance Between the Eras

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
Can’t Use Federal Funds Rate After 2008
Use Shadow Federal Funds Rate from Wu and Xia (2014)

6. Real-Time 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
Output Gap
No Internal Fed (Greenbook) Output Gaps Before 1987
Real-Time Detrending Starting in 1947:Q1
Linear, Quadratic, and Hodrick-Prescott Detrending

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

8. The Federal Funds Rate and the Prescribed Original Taylor Rule Rate

9. Deviations from the Original Taylor Rule

10. Modified Taylor Rule Deviations
it = pt (pt – 2.0) yt + 2.0
it = pt yt
Analyzed in Yellen’s 2012 Speeches
“Taylor (1999) Rule” or “Balanced Approach Rule”
Construct Modified Taylor Rule Deviations

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

12. Deviations from the Modified Taylor Rule

13. The Estimated Taylor Rule
Real-Time Data from 1965:Q4 – 2013:Q4
it = pt yt
(0.30) (0.07) (0.05)
Coefficients on pt and yt Close to Original Taylor Rule
Smaller Intercept
Inflation Target of 3.33 Percent with R* = 2.0
R* = 1.35 with Inflation Target of 2 Percent

14. The Federal Funds Rate and the Prescribed Estimated Taylor Rule Rate

15. Deviations from the Estimated Taylor Rule

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

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

18. Restricted Structural Change Tests
Bai and Perron Tests do Not Determine Whether the Higher Means are Statistically Different from the Lower Means
Perron and Qu (2006) Tests
Choose Number of Breaks from the Bai and Perron test
Constrain Consecutive Breaks to be Equal with Opposite Signs
3 breaks: g1 + g2 = 0 and g2 + g3 = 0
4 breaks: g3 + g4 = 0

19. Restricted Structural Change Tests Original Taylor Rule
SupF test
Critical values (1%)
Break dates
Coefficients
95% Confidence Intervals
85.46*
17.17
γ0 = 1.075
1974:Q3
γ1 = 1.531
1971:Q1 - 1975:Q3
1985:Q1
γ2 =
1984:Q :Q3
2001:Q1
γ0 = 1.531
1999:Q :Q3

20. Restricted Structural Change Tests Original Taylor Rule

21. Structural Change Tests Modified Taylor Rule
SupF test
(sequential method)
Critical values (1%)
Break dates
Coefficients
95% Confidence Intervals
γ0 = 1.782
SupF(4| 3) = 63.05*
8.58
1977:Q4
γ1 = 2.616
1975:Q :Q1
SupF(1| 0) = 11.42*
10.13
1984:Q4
γ2 =
1984:Q :Q2
SupF(2| 1) = 65.41*
11.14
1999:Q1
γ3 = 2.631
1999:Q :Q4
SupF(3| 2) = 62.95*
11.83
2006:Q3
γ4 =
2005:Q4 - 2007:Q4

22. Restricted Structural Change Tests Modified Taylor Rule
SupF test
Critical values (1%)
Break dates
Coefficients
95% Confidence Intervals
100.14*
18.82
γ0 = 1.344
1977:Q2
γ1 = 2.629
1974:Q4 - 1978:Q3
1984:Q3
γ2 =
1984:Q :Q1
1999:Q2
γ3 = 2.629
1998:Q :Q3
2006:Q3
γ4=
2006:Q :Q1

23. Restricted Structural Change Tests
Modified Taylor Rule

24. Structural Change Tests Estimated Taylor Rule
SupF test
(sequential method)
Critical values (1%)
Break dates
Coefficients
95% Confidence Intervals
γ0 = 1.20
SupF(1| 0) = 34.95*
8.58
1974:Q3
γ1 = 1.867
1972:Q :Q4
SupF(2| 1) = 56.47*
10.13
1987:Q2
γ2 =
1987:Q :Q4
SupF(3| 2) = 11.15*
11.14
1995:Q1
γ3 = 0.664
1990:Q :Q3

25. Restricted Structural Change Tests Estimated Taylor Rule
SupF test
Critical values (1%)
Break dates
Coefficients
95% Confidence Intervals
85.46*
17.17
γ0 = 1.077
1974:Q3
γ1 = 1.259
1968:Q :Q1
1987:Q2
γ2 =
1986:Q :Q1
2003:Q1
γ0 = 1.259
2000:Q :Q4

26. Structural Change Tests
Estimated Taylor Rule

27. “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

28. Average Loss During Discretionary Eras
Loss Functions
Average Loss During
Rules-Based Eras
(1)
Average Loss During Discretionary Eras
(2)
Misery Index L = Inflation + Unemployment
8.50
<
9.34
<
9.12
<
Linear Absolute Loss Function L = |Inflation - 2%| + |Unemployment - Natural Rate|
2.31
<
2.86
<
2.92
<
Quadratic Loss Function L = (Inflation - 2%)2 + (Unemployment - Natural Rate)2
5.06
<
8.26
<
7.13
<

29. Additional Quadratic Loss Functions
Quadratic Loss Function with Higher Weight on Inflation
3/2*(inflation - 2%)2 + 1/2*(unemployment rate - natural rate)2
Quadratic Loss Function with Higher Weight on Unemployment
1/2*(inflation - 2%)2 + 3/2*(unemployment rate - natural rate)2
Quadratic Loss Function with All Weight on Inflation
(inflation - 2%)2

30. Additional Quadratic Loss Functions
Average Loss During
Rules-Based Eras
(1)
Average Loss During Discretionary Eras
(2)
Quadratic Loss Function L = 3/2*(Inflation - 2%)2 + 1/2*(Unemployment - Natural Rate)2
6.19
<
9.43
<
8.88
<
Quadratic Loss Function L = 1/2*(Inflation - 2%)2 + 3/2*(Unemployment - Natural Rate)2
3.93
<
7.09
<
5.38
<
Quadratic Loss Function L = (Inflation - 2%)2
3.66
<
5.30
<
5.31
<

31. “Monetary Policy Rules Work and Discretion Doesn’t”
Economic Loss Always Greater During Discretionary Eras than During Rules-Based Eras
Three Policy Rules and Six Loss Functions
Choice Among Policy Rules
Calculate Loss Ratios
Average Loss During Discretionary Eras / Average Loss During Rules-Based Eras
Policy Rules with Larger Loss Ratios are Preferable
Greater Benefit from Following the Rule

32. Discretionary Loss/Rules-Based Loss
Loss Ratios
Discretionary Loss/Rules-Based Loss
Misery Index L = Inflation + Unemployment
1.31 ↓ ↓
Linear Absolute Loss Function L = |Inflation - 2%| + |Unemployment - Natural Rate|
1.72 ↓ ↓
Quadratic Loss Function L = (Inflation - 2%)2 + (Unemployment - Natural Rate)2
3.17 ↓ ↓

33. Additional Quadratic Loss Ratios
Discretionary Loss/Rules-Based Loss
Quadratic Loss Function L = 3/2*(Inflation - 2%)2 + 1/2*(Unemployment - Natural Rate)2
3.19 ↓ ↓
Quadratic Loss Function L = 1/2*(Inflation - 2%)2 + 3/2*(Unemployment - Natural Rate)2
3.15 ↓ ↑
Quadratic Loss Function L = (Inflation - 2%)2
3.21 ↓ ↓

34. Conclusions Identify Rules-Based and Discretionary Eras
Original Taylor Rule
Rules-Based Eras for 1965 – 1974 and
Discretionary Eras for 1974 – 1985 and
Modified Taylor Rule
First Discretionary Era Starts in 1977
Rules-Based Era for 2007 – 2013
Discretionary with Original and Rules-Based with Modified Taylor Rule

35. Conclusions Monetary Policy Rules Work and Discretion Doesn’t
Compare Economic Loss for Three Rules and Six Loss Functions
Always Greater in Discretionary than Rules-Based Periods
The Choice Among Policy Rules Matters
Loss Ratios for Discretionary and Rules-Based Periods
Always Largest for the Original Taylor Rule

36. Conclusions John Taylor at Janet Yellen’s Inaugural Hearing
“It’s because of this success of policy rules that I recommend that legislation be put in place to require the Fed to report on its policy rule. It would be a rule of its own choosing – that’s the responsibility of the Fed.”
What Policy Rule Should the Fed Choose?
Maximize Gain from Rules-Based Policy
Fed Should Adopt the Original Taylor Rule