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

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

“Monetary Policy Rules Work and Discretion Doesn’t: A Tale of Two Eras” Taylor (2012) JMCB Lecture The Rules-Based Era 1985-2003 The Ad Hoc (or Discretionary) Era 2003 - ? 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

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

Taylor Rule Deviations Original Taylor (1993) Rule it = pt + 0.5 (pt – 2.0) + 0.5 yt + 2.0 it = 1.0 + 1.5 pt + 0.5 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)

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

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

The Federal Funds Rate and the Prescribed Original Taylor Rule Rate

Deviations from the Original Taylor Rule

Modified Taylor Rule Deviations it = pt + 0.5 (pt – 2.0) + 1.0 yt + 2.0 it = 1.0 + 1.5 pt + 1.0 yt Analyzed in Yellen’s 2012 Speeches “Taylor (1999) Rule” or “Balanced Approach Rule” Construct Modified Taylor Rule Deviations

The Federal Funds Rate and the Prescribed Modified Taylor Rule Rate

Deviations from the Modified Taylor Rule

The Estimated Taylor Rule Real-Time Data from 1965:Q4 – 2013:Q4 it = 0.37 + 1.49 pt + 0.47 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

The Federal Funds Rate and the Prescribed Estimated Taylor Rule Rate

Deviations from the Estimated Taylor Rule

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

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:Q3 - 1975:Q2 SupF(1| 0) = 32.63* 13.89 1985:Q1 γ2 = -2.506 1984:Q4 - 1986:Q2 SupF(2| 1) = 53.27* 14.80 2000:Q4 γ3 = 1.174 1999:Q2 - 2001:Q2

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

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 = -1.531 1984:Q4 - 1988:Q3 2001:Q1 γ0 = 1.531 1999:Q1 - 2001:Q3

Restricted Structural Change Tests Original Taylor Rule

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:Q2 - 1979:Q1 SupF(1| 0) = 11.42* 10.13 1984:Q4 γ2 = -3.494 1984:Q3 - 1986:Q2 SupF(2| 1) = 65.41* 11.14 1999:Q1 γ3 = 2.631 1999:Q1 - 1999:Q4 SupF(3| 2) = 62.95* 11.83 2006:Q3 γ4 = -2.041 2005:Q4 - 2007:Q4

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 = -2.629 1984:Q2 - 1987:Q1 1999:Q2 γ3 = 2.629 1998:Q4 - 1999:Q3 2006:Q3 γ4= -2.629 2006:Q1 - 2007:Q1

Restricted Structural Change Tests Modified Taylor Rule

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:Q2 - 1974:Q4 SupF(2| 1) = 56.47* 10.13 1987:Q2 γ2 = -2.342 1987:Q1 - 1988:Q4 SupF(3| 2) = 11.15* 11.14 1995:Q1 γ3 = 0.664 1990:Q4 - 1996:Q3

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:Q4 - 1975:Q1 1987:Q2 γ2 = -1.259 1986:Q4 - 1993:Q1 2003:Q1 γ0 = 1.259 2000:Q1- 2003:Q4

Structural Change Tests Estimated Taylor Rule

“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

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 < 11.16 9.34 < 10.80 9.12 < 10.13 Linear Absolute Loss Function L = |Inflation - 2%| + |Unemployment - Natural Rate| 2.31 < 3.98 2.86 < 3.70 2.92 < 3.22 Quadratic Loss Function L = (Inflation - 2%)2 + (Unemployment - Natural Rate)2 5.06 < 16.07 8.26 < 15.26 7.13 < 12.09

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

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 < 19.78 9.43 < 20.43 8.88 < 14.79 Quadratic Loss Function L = 1/2*(Inflation - 2%)2 + 3/2*(Unemployment - Natural Rate)2 3.93 < 12.36 7.09 < 10.09 5.38 < 9.38 Quadratic Loss Function L = (Inflation - 2%)2 3.66 < 11.75 5.30 < 12.80 5.31 < 8.75

“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

Discretionary Loss/Rules-Based Loss Loss Ratios   Discretionary Loss/Rules-Based Loss Misery Index L = Inflation + Unemployment 1.31 ↓ 1.15 ↓ 1.11 Linear Absolute Loss Function L = |Inflation - 2%| + |Unemployment - Natural Rate| 1.72 ↓ 1.29 ↓ 1.10 Quadratic Loss Function L = (Inflation - 2%)2 + (Unemployment - Natural Rate)2 3.17 ↓ 1.85 ↓ 1.70

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 ↓ 2.16 ↓ 1.66 Quadratic Loss Function L = 1/2*(Inflation - 2%)2 + 3/2*(Unemployment - Natural Rate)2 3.15 ↓ 1.42 ↑ 1.74 Quadratic Loss Function L = (Inflation - 2%)2 3.21 ↓ 2.42 ↓ 1.65

Conclusions Identify Rules-Based and Discretionary Eras Original Taylor Rule Rules-Based Eras for 1965 – 1974 and 1985 - 2000 Discretionary Eras for 1974 – 1985 and 2001 - 2013 Modified Taylor Rule First Discretionary Era Starts in 1977 Rules-Based Era for 2007 – 2013 2007-2013 Discretionary with Original and Rules-Based with Modified Taylor Rule

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

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