Crawford School of Public Policy

CAMACentre for Applied Macroeconomic Analysis

A comment on Wu and Xia (2015), and the case for two-factor Shadow Short Rates

CAMA Working Paper 48/2015December 2015

Leo KrippnerReserve Bank of New Zealand and Centre for Applied Macroeconomic Analysis (CAMA), ANU

Abstract

Shadow Short Rates (SSRs) estimated from shadow/lower-bound term structure models (SLMs) can be useful for monitoring of the stance of unconventional monetary policy and for quantitative analysis, but only if they are relatively robust. I show from several perspectives that SSRs from three-factor SLMs, which includes Wu and Xia (2015) SSRs, are not robust, and how that arises from the inherent flexibility of three-factor SLMs. Such SSRs should therefore be avoided. However, I also show that estimated SSRs from two-factor SLMs are relatively robust. Hence, two-factor SLM SSRs appear to be good candidates for monitoring and quantitative analysis, but ideally with appropriate robustness checks including alternative monetary policy metrics.

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Keywords

Shadow Short Rates, zero lower bound, unconventional monetary policy, term structure models.

JEL Classification

E43, G12, G13

Address for correspondence:

(E) cama.admin@anu.edu.au

ISSN 2206-0332

The Centre for Applied Macroeconomic Analysis in the Crawford School of Public Policy has been established to build strong links between professional macroeconomists. It provides a forum for quality macroeconomic research and discussion of policy issues between academia, government and the private sector.

The Crawford School of Public Policy is the Australian National University’s public policy school, serving and influencing Australia, Asia and the Pacific through advanced policy research, graduate and executive education, and policy impact.

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2008 2009 2010 2011 2012 2013 2014 2015

Perc

ent

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7Interest rate data

Federal Funds Rate3-month Tbill rateWX 3x1-month f orward rateWX 25 bp LB parameter

Time to maturity0 2 4 6 8 10

No

unit

0

0.2

0.4

0.6

0.8

1

WX shadow forward rate factor loadings

Factor 1Factor 2Factor 3

0 2 4 6 8 10

% p

oint

s

-2

0

2

4rLB = 25 bps (full)

FR dataLB FRSh. FR

0 0.5 1 1.5 2 2.5-0.2

0

0.2

0.4

0.6

0.8rLB = 25 bps (zoomed)

SSR (-1.42%) rLB

0 2 4 6 8 10

% p

oint

s

-2

0

2

4rLB = 19 bps (full)

FR dataLB FRSh. FR

0 0.5 1 1.5 2 2.5-0.2

0

0.2

0.4

0.6

0.8rLB = 19 bps (zoomed)

SSR (-0.59%) rLB

0 2 4 6 8 10

% p

oint

s

-2

0

2

4rLB = 14 bps (full)

FR dataLB FRSh. FR

0 0.5 1 1.5 2 2.5-0.2

0

0.2

0.4

0.6

0.8rLB = 14 bps (zoomed)

SSR rLB

Time to maturity0 2 4 6 8 10

% p

oint

s

-2

0

2

4rLB = 0 bps (full)

FR dataLB FRSh. FR

Time to maturity0 0.5 1 1.5 2 2.5

-0.2

0

0.2

0.4

0.6

0.8rLB = 0 bps (zoomed)

SSR rLB

0 2 4 6 8 10

No

unit

0

0.5

1

rLB = 25 bps

0 2 4 6 8 100

0.5

1

rLB = 19 bps (est.)

Time to maturity0 2 4 6 8 10

No

unit

0

0.5

1

rLB = 14 bps

Time to maturity0 2 4 6 8 10

0

0.5

1

rLB = 0 bps

0 2 4 6 8 10

% p

oint

s

-4

-2

0

2

rLB = 25 bps (full)

Y C dataLB YCSh. Y C

0 0.5 1 1.5 2 2.5-0.2

0

0.2

0.4

0.6

0.8rLB = 25 bps (zoomed)

SSR (-5.47%) rLB

0 2 4 6 8 10

% p

oint

s

-4

-2

0

2

rLB = 16 bps (full)

Y C dataLB YCSh. Y C

0 0.5 1 1.5 2 2.5-0.2

0

0.2

0.4

0.6

0.8rLB = 16 bps (zoomed)

SSR (-3.64%) rLB

0 2 4 6 8 10

% p

oint

s

-4

-2

0

2

rLB = 14 bps (full)

Y C dataLB YCSh. Y C

0 0.5 1 1.5 2 2.5-0.2

0

0.2

0.4

0.6

0.8rLB = 14 bps (zoomed)

SSR (-3.38%) rLB

Time to maturity0 2 4 6 8 10

% p

oint

s

-4

-2

0

2

rLB = 0 bps (full)

Y C dataLB YCSh. Y C

Time to maturity0 0.5 1 1.5 2 2.5

-0.2

0

0.2

0.4

0.6

0.8rLB = 0 bps (zoomed)

SSR (-1.92%) rLB

0 2 4 6 8 10

No

unit

0

0.5

1

rLB = 25 bps

0 2 4 6 8 100

0.5

1

rLB = 16 bps (est.)

Time to maturity0 2 4 6 8 10

No

unit

0

0.5

1

rLB = 14 bps

Time to maturity0 2 4 6 8 10

0

0.5

1

rLB = 0 bps

2008 2009 2010 2011 2012 2013 2014 2015

WX

ETZ

(yea

rs)

4

3

2

1

0

25 bps19 bps (est.)14 bps0 bps

2008 2009 2010 2011 2012 2013 2014 2015

K-AN

SM(2

) SSR

(% p

oint

s)

-5

0

SSR (RHS)

QE3taper