1. The Taylor Principles Alex Nikolsko-Rzhevskyy
Lehigh University
David Papell and Ruxandra Prodan
University of Houston
University of Texas
October 27, 2015

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. The Taylor Rule Original Taylor Rule it = pt + f(pt – p*) + gyt + R*
it = m + apt + gyt
a = 1 + f and m = R* - fp*
Taylor’s Coefficients
it = pt (pt – 2.0) yt + 2.0
it = pt yt

4. Monetary Policy Evaluation with the Taylor Rule
The Taylor Rule as Normative
Based on Simulations of Econometric Models
Approximately Optimal in Woodford (2003)
The Taylor Rule as Positive
Estimate Taylor Rules over Various Periods
Periods Chosen Exogenously (Fed Chairs)
Periods Chosen Endogenously through Parameter Estimation
Focus on the Taylor Principle
The Nominal Interest Rate Should be Increased More than Point-for-Point with Inflation, so that the Real Interest Rate Rises

5. The Taylor Principle and the Taylor Rule
The Taylor Principle is Necessary, but Not Sufficient, for the Taylor Rule
First Taylor Principle
a = 1.5
a is Greater than and Significantly Different from One
Second Taylor Principle
g = 0.5
g is Greater than Zero, Less than One, and Significantly Different from both Zero and One

6. The Taylor Principle and the Taylor Rule
Third Taylor Principle
Constant Inflation Target
p* = 2.0
Fourth Taylor Principle
Constant Equilibrium Real Interest Rate
R* = 2.0

7. Plan for the Paper Start with the Original Taylor (1993) Rule
it = pt yt
Construct Taylor Rule Deviations
Calculate Actual Minus Prescribed Federal Funds Rate
The Deviations are Calculated – Not Estimated
Structural Change Tests to Define Monetary Policy Eras
Estimate Taylor Rules for the Different Eras
Link Deviations to Violations of Taylor Principles

8. Plan for the Paper Intercept of the Taylor Rule
m = R* - fp*
Cannot Separately Identify R* and p*
Cannot Make Sense of the 2000s
Two Alterations of the Taylor Rule
Higher Coefficient on the Output Gap
Time-Varying Equilibrium Real Interest Rate
Focus on Periods When:
Large Deviations for Original Taylor Rule
Small Deviations for Altered Taylor Rule
Results for

9. Starting Point for the Paper
Nikolsko-Rzhevskyy, Papell, and Prodan (2014a,b)
Calculate Taylor Rule Deviations
Take Absolute Value
Identify Rules-Based (Low Deviations) and Discretionary (High Deviations) Eras
Compare Loss Functions from Different Rules and Eras
Economic Performance Better in Rules-Based Eras
Difference Sharper with Original Taylor Rule than Alternatives
Pervious Papers Normative, this Paper is Positive
Normative Motivation for Positive Economics

10. 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
No Necessity for Positive and Negative Output Gaps to be Equal

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

12. 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

13. Federal Funds Rate Zero Lower Bound after 2008
Not Complete Measure of Monetary Policy
Use Shadow Rate from Wu and Xia (2015)
Nonlinear Term Structure Model
Incorporates Quantitative Easing and Forward Guidance
Not Real-Time Data
Credit Controls of 1980
FFR = 15.05% in 1980:Q1, 12.69% in 1980:Q2, 9.84% in 1980:Q3, and 15.85% in 1980:Q4
Interpolate for 1980:Q2 and 1980:Q3

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

15. Deviations from the Original Taylor Rule

16. Deviations from the Original Taylor Rule
Negative in the Late 1960s and 1970s
Great Inflation
Positive in the Early-to-Mid 1980s
Volcker Disinflation
Low in the Late 1980s and 1990s
Great Moderation
Negative in the 2000s
Great Deviation and Not-so-Great Recovery

17. Modified Taylor Rule Modified Taylor Rule
it = pt (pt – 2.0) yt + 2.0
it = pt yt
Featured in Yellen (2012)
Calculate Deviations in Same Way as Original Taylor Rule
Differences Starting in 2007

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

19. Deviations from the Modified Taylor Rule

20. Time-Varying Equilibrium Real Interest Rate
Taylor Rule with Time-Varying Equilibrium Real Interest Rate
it = pt (pt – 2.0) yt + Rt*
it = Rt* pt yt
Calculate Rt*
Trend Growth Rate (Real Time Data)
Property of Some Growth Models
Used by Taylor (1993) to Calculate R=2.0
Laubach and Williams Estimates (Real Time Data Since 2005)
Real Rate to Make Output Equal Potential Output
Woodford (2003)

21. The Federal Funds Rate and the Time-Varying (Trend Growth) Implied Rate

22. Deviations from the Trend Growth Taylor Rule

23. The Federal Funds Rate and the Time-Varying (Laubach-Williams) Implied Rate

24. Deviations from the (Laubach-Williams) Taylor Rule

25. Estimated Taylor Rule Estimated Taylor Rule for Full Sample
Real-Time Data from 1965:Q4 – 2014:Q4
it = pt yt
(0.43) (0.14) (0.07)
Coefficients on pt and yt Close to Original Taylor Rule
Smaller Intercept
Inflation Target of 3.36 Percent with R* = 2.0
R* = 1.20 with Inflation Target of 2 Percent

26. 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
Straightforward Application of Structural Change Tests

27. Original Taylor Rule Deviations Structural Change Tests
SupF test
(sequential method)
Critical values (1%)
Break dates
Coefficients
Deviations
95% Confidence Intervals
γ0 = -1.87
-1.87
SupF(1| 0) = 64.44*
12.29
1979:Q3
γ1 = 4.74
2.87
1979:Q :Q1
SupF(2| 1) = 94.01*
13.89
1987:Q2
γ2 = -2.86
0.01
1987:Q1 - 1988:Q2
SupF(3| 2) = *
14.80
2000:Q4
γ3= -2.09
-2.08
1999:Q :Q2

28. Original Taylor Rule Deviations

29. Original Taylor Rule Deviations Taylor Rule estimatesμ α γ
π*(R*=2)
R* (π*=2)
1965:Q4-1979:Q3
1.48
(0.68)
1.04
(0.14)
0.46
(0.07)
1.56
1979:Q4-1987:Q2
3.38
(0.58)
1.43
(0.10)
0.10
(0.09)
-3.20
4.23
1987:Q3-2000:Q4
1.21
(0.43)
1.32
(0.11)
0.64
2.50
1.84
2001:Q1-2014:Q4
-0.72
(0.76)
1.27
(0.38)
0.44
(0.05)
-0.18

30. Counterfactuals for Original Taylor Ruleα γ P y
Dev
1965:Q4-1979:Q3
1.04
1.50
0.46
5.17
-0.62
-1.87
0.51
1979:Q4-1987:Q2
1.43
0.10
0.50
5.19
-2.21
2.87
1.99
2001:Q1-2014:Q4
1.27
0.44
1.87
-1.22
-2.08
-1.73

31. Modified Taylor Rule Deviations Structural Change Tests
SupF test
(sequential method)
Critical values (1%)
Break dates
Coefficients
Deviations
95% Confidence Intervals
γ0 = -1.50
-1.50
SupF(2| 1) = *
13.89
1979:Q4
γ1 = 5.35
3.85
1979:Q :Q2
SupF(1| 0) = 16.77*
12.29
1987:Q4
γ2 = -4.61
-0.76
1987:Q3 - 1988:Q4
SupF(4| 3) = *
15.28
1999:Q3
γ3 = -2.69
-3.45
1999:Q :Q4
SupF(3| 2) = 31.23*
14.80
2007:Q2
γ4 = 3.73
0.29
2006:Q :Q3

32. Modified Taylor Rule Deviations

33. Modified Taylor Rule Deviations Taylor Rule estimatesμ α γ
π*(R*=2)
R* (π*=2)
1965:Q4-1979:Q4
1.17
(0.74)
1.12
(0.15)
0.49
(0.08)
1.40
1980:Q1-1987:Q4
3.11
(0.51)
1.49
(0.10)
0.13
-2.25
4.09
1988:Q1-1999:Q3
(0.37)
1.27
(0.11)
0.82
(0.07)
3.27
1.66
1999:Q4-2007:Q2
-1.71
(0.76)
(0.39)
0.81
(0.13)
-0.91
2007:Q3-2014:Q4
2.06
(1.09)
0.22
(0.46)
0.67

34. Counterfactuals for Modified Taylor Ruleγ Π y
Dev
1965:Q4-1979:Q4
1.12
1.50
0.49
5.17
-0.62
-1.50
0.46
1980:Q1-1987:Q4
1.49
0.13
0.50
5.19
-2.02
3.85
3.10
1999:Q4-2006:Q4
1.18
0.89
2.03
2.83
-3.60
-3.00

35. How Can a = 0? Original Taylor Rule it = pt + f(pt – p*) + gyt + R*
it = m + apt + gyt
a = 1 + f and m = R* - fp*
a = 0 if f = -1
Taylor Rule
it = p* + gyt + R*
FFR = Equilibrium FFR + Output Gap Adjustment

36. How Can a = 0? Woodford’s Version of the Taylor Rule
it = p* + f(pt – p*) + gyt + Rt*
it = m + fpt + gyt
m = R* + (1- f)p*
First Taylor Principle if f >1
Taylor Rule when f = 0
it = p* + gyt + Rt*
FFR = Equilibrium FFR + Output Gap Adjustment

37. Structural Change Tests
Taylor Rule Deviations with a Time-Varying (Trend Growth) Equilibrium Real Interest Rate
Structural Change Tests
SupF test
(sequential method)
Critical values (1%)
Break dates
Coefficients
Deviations
95% Confidence Intervals
γ0 = -3.47
-3.47
SupF(1| 0) = 92.20*
12.29
1979:Q3
γ1 = 5.72
2.26
1979:Q :Q4
SupF(2| 1) = *
13.89
1987:Q4
γ2 = -2.84
-0.58
1987:Q2 - 1988:Q3
SupF(3| 2) = 55.93*
14.80
1999:Q4
γ3= -2.89
1999:Q :Q2
SupF(4| 3) = 50.97*
15.28
2007:Q1
γ4= 2.04
-1.43
2006:Q :Q1

38. Taylor Rule Deviations with a Time-Varying (Trend Growth) Equilibrium Real Interest Rate

39. Taylor Rule Deviations with a Time-Varying (Trend Growth) Equilibrium Real Interest Rate
Taylor Rule estimates μ α γ π*
1965:Q4-1979:Q3
-2.92
(0.81)
1.19
(0.16)
0.40
(0.08)
1979:Q4-1987:Q4
1.45
(0.52)
1.33
(0.11)
0.13
(0.09)
-4.47
1988:Q1-1999:Q4
-0.29
(0.43)
0.91
(0.14)
0.64
(0.10)
2000:Q1-2007:Q1
-5.48
(0.84)
1.78
(0.44)
0.65
(0.15)
2007:Q2-2014:Q4
-0.74
(0.73)
0.50
(0.32)

40. Structural Change Tests
Taylor Rule Deviations with a Time-Varying (Laubach and Williams) Equilibrium Real Interest Rate
Structural Change Tests
SupF test
(sequential method)
Critical values (1%)
Break dates
Coefficients
Deviations
95% Confidence Intervals
γ0 = -4.24
-4.24
SupF(1| 0) = *
12.29
1979:Q3
γ1 = 5.88
1.64
1979:Q :Q4
SupF(2| 1) = 71.82*
13.89
1987:Q2
γ2 = -2.23
-0.59
1986:Q4 - 1988:Q4
SupF(4| 3) = 87.93*
15.28
1999:Q3
γ3= -2.24
-2.83
1998:Q :Q2
SupF(3| 2) = 22.87*
14.80
2006:Q4
γ4= 2.65
-0.18
2006:Q :Q2

41. Taylor Rule Deviations with a Time-Varying (Laubach and Williams) Equilibrium Real Interest Rate

42. Taylor Rule Deviations with a Time-Varying (Laubach and Williams) Equilibrium Real Interest Rate - Taylor Rule Estimates m α γ π*
1965:Q4-1979:Q3
-3.45
(0.79)
1.14
(0.16)
0.41
(0.08)
1979:Q4-1987:Q2
0.68
(0.56)
1.30
(0.10)
0.03
(0.09)
-2.26
1987:Q3-1999:Q3
-0.41
(0.43)
0.93
(0.13)
0.69
1999:Q4-2006:Q4
-4.51
(0.82)
1.51
(0.42)
0.72
2007:Q1-2014:Q4
1.01
(0.75)
0.21
(0.31)
0.49
(0.06)
Real-time
0.37
(0.66)
0.39
(0.28)
0.45
(0.07)

43. Conclusions The Anna Karenina Principle
“All happy families are alike, each unhappy family is unhappy in its own way”
Endeavor where a Deficiency in Any of its Factors Dooms it to Failure
All Four Taylor Principles Satisfied During the Great Moderation
Violations of Taylor Principles
First Principle During the Great Inflation
Second Principle During the Volcker Disinflation
All Four Principles Between 2000 and 2006
Different Rule Between 2007 and 2014