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

Policy Rules Monetary Policy Rules Rules versus Discretion Taylor Rule Friedman (1959) Rules versus Discretion Kydland and Prescott (1977) Taylor Rule Taylor (1993)

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 + 0.5 (pt – 2.0) + 0.5 yt + 2.0 it = 1.0 + 1.5 pt + 0.5 yt

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

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

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

Plan for the Paper Start with the Original Taylor (1993) Rule it = 1.0 + 1.5 pt + 0.5 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

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 2007 - 2014

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

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

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

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

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

The Federal Funds Rate and the Prescribed Original Taylor Rule Rate

Deviations from the Original Taylor Rule

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

Modified Taylor Rule Modified Taylor Rule it = pt + 0.5 (pt – 2.0) + 1.0 yt + 2.0 it = 1.0 + 1.5 pt + 1.0 yt Featured in Yellen (2012) Calculate Deviations in Same Way as Original Taylor Rule Differences Starting in 2007

The Federal Funds Rate and the Prescribed Modified Taylor Rule Rate

Deviations from the Modified Taylor Rule

Time-Varying Equilibrium Real Interest Rate Taylor Rule with Time-Varying Equilibrium Real Interest Rate it = pt + 0.5 (pt – 2.0) + 0.5 yt + Rt* it = Rt* - 1.0 + 1.5 pt + 0.5 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)

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

Deviations from the Trend Growth Taylor Rule

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

Deviations from the (Laubach-Williams) Taylor Rule

Estimated Taylor Rule Estimated Taylor Rule for Full Sample Real-Time Data from 1965:Q4 – 2014:Q4 it = 0.03 + 1.58 pt + 0.51 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

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

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:Q1 - 1980:Q1 SupF(2| 1) = 94.01* 13.89 1987:Q2 γ2 = -2.86 0.01 1987:Q1 - 1988:Q2 SupF(3| 2) = 117.01* 14.80 2000:Q4 γ3= -2.09 -2.08 1999:Q4 - 2001:Q2

Original Taylor Rule Deviations

Original Taylor Rule Deviations Taylor Rule estimates μ 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

Counterfactuals for Original Taylor Rule α 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

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) = 100.06* 13.89 1979:Q4 γ1 = 5.35 3.85 1979:Q1 - 1980:Q2 SupF(1| 0) = 16.77* 12.29 1987:Q4 γ2 = -4.61 -0.76 1987:Q3 - 1988:Q4 SupF(4| 3) = 146.74* 15.28 1999:Q3 γ3 = -2.69 -3.45 1999:Q1 - 1999:Q4 SupF(3| 2) = 31.23* 14.80 2007:Q2 γ4 = 3.73 0.29 2006:Q3 - 2007:Q3

Modified Taylor Rule Deviations

Modified Taylor Rule Deviations Taylor Rule estimates μ 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

Counterfactuals for Modified Taylor Rule γ 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

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

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

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:Q2 - 1979:Q4 SupF(2| 1) = 173.92* 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:Q2 - 2000:Q2 SupF(4| 3) = 50.97* 15.28 2007:Q1 γ4= 2.04 -1.43 2006:Q2 - 2008:Q1

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

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)

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) = 196.47* 12.29 1979:Q3 γ1 = 5.88 1.64 1979:Q2 - 1979: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:Q4 - 2000:Q2 SupF(3| 2) = 22.87* 14.80 2006:Q4 γ4= 2.65 -0.18 2006:Q2 - 2007:Q2

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

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)

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