Measuring the Natural Rate of Interest Redux

Conference on “The Long Term Equilibrium Interest Rate” October 30, 2015

Thomas Laubach, Federal Reserve Boardand

John Williams, Federal Reserve Bank of San Francisco

The views presented here are those of the authors and not necessarily those of anyone else in the Federal Reserve System.

Measuring the Natural Rate of Interest Redux 2

Summary

• Univariate measures of natural rate of interest (NRI) are unreliable, ignore persistent deviations from stable inflation and potential output.

• Laubach-Williams (LW) model uses Kalman filter to jointly estimate output gap, trend potential GDP growth, and the natural rate of interest.

• NRI fell to near zero in 2009 and shows no signs of recovering; robust to alternative model specifications.

• Monetary policy strategies need to cope with persistently low NRI and high degree of NRI uncertainty.

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Defining the Natural Rate

“There is a certain rate of interest on loans which is neutral in respect to commodity prices, and tends neither to raise nor to lower them.”

Knut Wicksell, 1898

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Determination of the NRI

GDP

IS CurveNatural rate of interest

Potential GDP

Real interest rate

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Univariate Measures of Trend Rates

• Sizable persistent variation over time

• Can be distorted by periods of rising or falling inflation (late 1960s; early 1980s)

• Mechanically implies very low level today

Trend component of ex post real short-term rate

-4

-2

0

2

4

6

8

10

12

1961 1966 1971 1976 1981 1986 1991 1996 2001 2006 2011

Stock-Watson UCSV model

Hodrick-Prescott filter

Bandpass filter

Real federal funds rate, 5year average

Percent

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The Implicit Natural Rate

“The natural rate is an abstraction; like faith, it is seen by its works. One can only say that if the bank policy succeeds in stabilizing prices, the bank rate must have been brought in line with the natural rate, but if it does not, it must not have been.”

John H. Williams, 1931

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Laubach-Williams NRI Estimates

• LW Model of r*:

=

• g*: trend GDP growth.

• Z: other highly-persistent influences on r*.

• Ex post and real-time estimates track closely over past decade.

-1

0

1

2

3

4

1980 1983 1986 1989 1992 1995 1998 2001 2004 2007 2010 2013

Percent

Currentestimates

Real-timeestimates

One-sided estimates

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The Declining NRI

Estimates Changes in estimates*

1990 2007 2015H1 1990-2007 2007-15H1

Blue Chip survey 3.1 2.4 1.2 -0.7 -1.2

TIPS yields (5-10 years ahead) n/a 2.5 0.9 n/a -1.6

Laubach-Williams 3.4 2.1 -0.2 -1.3 -2.3

contribution from trend growth -0.4 -1.1

contribution from other factors -0.9 -1.2

*Numbers may not sum due to rounding.

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Robustness of NRI Estimates

• Main findings robust: large decline in, and very low current NRI.

• Alternative model; same key results:

• Fleischman-Roberts output gap

• = : no growth term

One-sided estimates of natural rate of interest

-3

-2

-1

0

1

2

3

4

5

6

1980 1985 1990 1995 2000 2005 2010 2015

Percent

LW with percapita GDP

Based on alternativeoutput gap

Standard LW

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Is the NRI Permanently Lower?

• LW estimates show no signs of rebounding.

• DSGE model estimates assume NRI returns to long-run mean.

• So far, DSGE estimates show no signs of returning to normal.

-5

-4

-3

-2

-1

0

1

2

3

4

5

2006 2008 2010 2012 2014 2016 2018 2020

Percent

2006q4

2008q4

2010q4 2012q42015q3

Curdia (2015) DSGE est. of short-run NRI

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Short-run vs. Long-Run NRI

• Alternative LW model where “other” factors assumed temporary:

=

• Short-run r* volatile; currently close to 0.

• Long-run r* = 0.8-8

-6

-4

-2

0

2

4

6

8

1980 1985 1990 1995 2000 2005 2010 2015

Percent

Alternative model:short-run R*

StandardLW model

Alternative model:long-run R*

One-sided estimates

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Some Monetary Policy Arithmetic

• mismeasurement:

• Difference rules: Policy strategies that are robust to ZLB and mismeasurement

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Consequences of Low

• and the lower bound on nominal interest rates:

Lower → higher frequency of hitting lower bound.

• Potential responses to persistently low : o Large CB balance sheet? Costs/benefits?oHigher ? But, risks to credibility, uncertain formation

of inflation expectationsoNegative short-term interest rates? Costs/benefits?o → Raise through policies other than monetary policy

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NRI after Financial Crises

Normal 0 1 2 3 4 5 Normal 0 1 2 3 4 5-4

-2

0

2

4

6

8

10

PreWW2 PostWW2

Short terminterest

CPI

Real shortterm interest

Percent