R * : EQUILIBRIUM INTEREST RATE. Yuriy Gorodnichenko UC Berkeley
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1 R * : EQUILIBRIUM INTEREST RATE Yuriy Gorodnichenko UC Berkeley
2 What is common across the following: Working of a black box device WHAT DO WE KNOW ABOUT R *? Location of black holes in the universe Equilibrium interest rate (R*) [the real interest rate consistent with output equaling its natural rate and constant inflation]
3 What is common across the following: Working of a black box device WHAT DO WE KNOW ABOUT R *? Location of black holes in the universe Equilibrium interest rate (R*) [the real interest rate consistent with output equaling its natural rate and constant inflation] None is observed directly but we can make inference from things we can observe.
4 What is common across the following: Working of a black box device WHAT DO WE KNOW ABOUT R *? Location of black holes in the universe Equilibrium interest rate (R*) [the real interest rate consistent with output equaling its natural rate and constant inflation] None is observed directly but we can make inference from things we can observe. Equilibrium interest rate R*: construct a macroeconomic model, estimate it, measure shocks, compute the interest rate when the economy is resting (not hit by shocks).
5 WHAT DO WE KNOW ABOUT R *? The typical prediction of macroeconomic models: RR = gg + ρρ gg = growth rate of (potential) output ρρ = a measure of how impatient consumers are ( time preference )
6 WHAT DO WE KNOW ABOUT R *? The typical prediction of macroeconomic models: gg = growth rate of (potential) output RR = gg + ρρ ρρ = a measure of how impatient consumers are ( time preference ) Since ρρ is approximately fixed, variation in RR likely comes from variation in gg, the growth rate of output under normal conditions.
7 WHAT DO WE KNOW ABOUT R *? The typical prediction of macroeconomic models: gg = growth rate of (potential) output RR = gg + ρρ ρρ = a measure of how impatient consumers are ( time preference ) Since ρρ is approximately fixed, variation in RR likely comes from variation in gg, the growth rate of output under normal conditions. But the growth rate of output under normal conditions (or potential output) is not observed either
8 WHY DOES R * MATTER? Policy rule for central banks: ii tt = ππ + RR tt + φφ ππ (ππ tt ππ ) + φφ xx (yy tt yy tt ) ii tt = nominal interest rate RR tt = equilibrium real interest rate ππ tt = inflation ππ = inflation target (set by a central bank) yy tt = output yy tt = potential output yy tt yy tt = output gap
9 WHY DOES R * MATTER? Policy rule for central banks: ii tt = ππ + RR tt + φφ ππ (ππ tt ππ ) + φφ xx (yy tt yy tt ) ii tt = nominal interest rate RR tt = equilibrium real interest rate (not observed directly) ππ tt = inflation ππ = inflation target (set by a central bank) yy tt = output yy tt = potential output (not observed directly) yy tt yy tt = output gap (not observed directly)
10 Policy rule for central banks: WHY DOES R * MATTER? ii tt = ππ + RR tt + φφ ππ (ππ tt ππ ) + φφ xx (yy tt yy tt ) ii tt = nominal interest rate RR tt = equilibrium real interest rate (not observed directly) ππ tt = inflation ππ = inflation target (set by a central bank) yy tt = output yy tt = potential output (not observed directly) yy tt yy tt = output gap (not observed directly) Recall that RR tt gg tt + cccccccccccccccc = (yy tt yy tt 1 ) + cccccccccccccccc
11 ACTUAL VS POTENTIAL OUTPUT log deviation from 2007Q actual
12 ACTUAL VS POTENTIAL OUTPUT log deviation from 2007Q CBO 2007 actual
13 ACTUAL VS POTENTIAL OUTPUT log deviation from 2007Q CBO 2007 CBO 2009 actual
14 ACTUAL VS POTENTIAL OUTPUT log deviation from 2007Q CBO 2007 CBO 2009 CBO 2011 actual
15 ACTUAL VS POTENTIAL OUTPUT log deviation from 2007Q CBO 2007 CBO 2009 CBO 2011 CBO 2013 actual
16 ACTUAL VS POTENTIAL OUTPUT log deviation from 2007Q CBO 2007 CBO 2009 CBO 2011 CBO 2013 CBO 2015 actual
17 ACTUAL VS POTENTIAL OUTPUT log deviation from 2007Q CBO 2007 CBO 2009 CBO 2011 CBO 2013 CBO 2015 CBO 2017 actual
18 R* AND POTENTIAL OUTPUT GROWTH RATE Source: Holston, Laubach and Williams (2017)
19 MEASURES OF POTENTIAL OUTPUT Fact #1: Revisions are not one-sided log deviation from 1994Q CBO 1995 CBO 1997 CBO 1999 CBO 2001 CBO 2003 actual
20 MEASURES OF POTENTIAL OUTPUT Fact #4: Estimates of pot. output can be proxied with moving averages of actual output Fact #5: Estimates of pot. output co-move with productivity percent per year Potential GDP (Orphanides 2004) Potential GDP (Greenbook)
21 MEASURES OF POTENTIAL OUTPUT Fact #2: Estimates of pot. output co-move with productivity Fact #5: Estimates of pot. output can be proxied with moving averages of actual output percent per year Potential GDP (Orphanides 2004) Potential GDP (Greenbook) MA(20) TFP
22 MEASURES OF POTENTIAL OUTPUT Fact #2: Estimates of pot. output co-move with productivity Fact #3: Estimates of pot. output can be proxied with moving averages of actual output percent per year Potential GDP (Orphanides 2004) Potential GDP (Greenbook) HP-filtered Actual GDP, λ=2m MA(20) TFP
23 MEASURES OF POTENTIAL OUTPUT Fact #4: Estimates of pot. output are sensitive to assumptions and methods log deviation from 2007Q Phillips Gali CBO Pre-crisis est. Blanchard Cochrane Actual Year Source: Coibion, Gorodnichenko and Ulate (2017)
24 Policy rule for central banks: WHY DOES R * MATTER? ii tt = ππ + RR tt + φφ ππ (ππ tt ππ ) + φφ xx (yy tt yy tt ) ii tt = nominal interest rate RR tt (yy tt yy tt 1 ) + cccccccccc equilibrium real interest rate, (not observed directly) ππ tt = inflation ππ = inflation target (set by a central bank) yy tt = output yy tt = potential output (not observed directly) yy tt yy tt = output gap (not observed directly) POLICYMAKERS HAVE AN INCREDIBLY HARD JOB!
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