Asset Price Bubbles and Monetary Policy: A Multivariate ExtensionBy Andrew Filardo, BIS

Prepared for a workshop on “Fundamental and Non-fundamental Asset Price Dynamics: Where Do We Stand?”, Venastul, Norway, 14-15 February 2008

General MotivationGreenspan, Bubbles and Policy

“In conclusion, the endeavors of policy makers to stabilize our economies require a functioning model of the way our economies work. Increasingly, it appears that this model needs to embody movements in equity premiums and the development of bubbles if it is to explain history.”

Jackson Hole 2002

Key Contributions Of This Paper

Methodology – relatively simple macro setup and “realistic” multivariate bubble specification do work and yield key insights

Modelling – endogenous multivariate bubbles in a dynamic macro model

Monetary policy – conventional wisdom about ‘benign neglect and mopping-up later approach’ may be too optimistic in the current policy environment

Preview Of Findings

Multivariate bubble considerations complicate the policy tradeoffs:

It is optimal to respond to asset prices generally and bubbles specifically!

Defensive strategies – preventing and pricking asset price bubbles

Opportunistic strategies – use bubbles to achieve stabilization goals

Monetary Policy And Asset Prices

Asset price booms and busts have been extreme developments that monetary authorities have had to face.

Monetary Policy and Asset Prices

Housing

Equity Equity

Housing

Monetary Policy and Asset Prices: Asia-Pacific

Equity Housing

Monetary Policy an Asset Prices

Asset price booms and busts are an important feature of the monetary policy landscape going forward. [Borio, English and Filardo (2003)]

The double-bubble aspect of this relationship has been underappreciated

Asset price booms and busts have been extreme developments that monetary authorities have had to face.

Road Map

Lay out monetary policy model

Multivariate bubble specification

Results

Policy implications and conclusions

The Greenspan Approach – Conventional Wisdom?

“ …Greenspan’s preferred approach to bubbles is to let them burst of their own accord, and then to use monetary policy (and other instruments), as necessary, to protect the banking system and the economy from the fallout…the ‘mop-up after’ strategy

“If the mopping up strategy worked this well after the mega-bubble burst in 2000, shouldn’t we assume that it will also work after other, presumably smaller, bubbles burst in the future?”

Blinder & Reis, Jackson Hole 2006

Three Modelling Blocks

Small-Scale Macro Model

1 1 , 1 1

1 1 , 1

( )

( )

t t t AP t t t

t t t NF t t

IS y r y

PC y

φ π π

βπ

Asset Price Block

, , ,( ) AP t F t NF tAP π π π

,, 1 1

,

,, 1 1

,

( )

( ) ( , )

e eeF t t

F t t th hhF t t

eB t

NF t t t thNF t

F i y

B y r

π

π

Monetary Policy Block

)1

()var()var( rrryL

Standard Loss Function

Optimal Monetary Policy

{ , , , }var( ) var( ) var( )

1Min

a ay F NFL y r rr

a a

subject to the model of the macroeconomy and asset prices:

,

,

,

,

1F t

F t

B t

B t

t

t

e

h

e

h

y

ttt AX BEX

, ,F F t NFt Ft tt Nyr a y a a π a π

3 Policy Specifications

tatyyatr

r a y tayt t t a APAP

r a y ayt t t a π a πF F,t NF NF,t

Modelling the BubbleTime-Varying Transition Probability (TVTP) Model For

Each Bubble

1,

0,

1,

it

bubble

I no bubble

bubble

Asset price bubble distribution

assuming I(t-1) = 0

0

0.2

0.4

0.6

0.8

-1 0 1

I(t)

Pro

ba

bilit

y

Modelling the Bubble

Time-Varying Transition Probability Model

Sample Path of a Bubble - “Blowing Bubbles”

-20

-15

-10

-5

0

5

10

15

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Time periods

Modelling the Bubble

No-Bubble State Transition Probability

10,0

1

exp(0.5 )0.96 1.92 0.5

1 exp(0.5 )i t

t

yP

y

10,1 0,0

1

exp( )(1 )

1 exp( )i i t

t

yP P

y

0, 1 0,0 0,11i i iP P P

0

0.5

1

-10 -5 0 5 10

y t-1

Function of yt-1

Modelling the Bubble

Bubble State Transition Probability

2 specifications

- weakly interacting multivariate bubbles

- strongly interacting multivariate bubbles

housinghousing 1 1 1

1,1 housing1 1 1

exp(2.5 1.1 0.4 0.1 )

1 exp(2.5 1.1 0.4 0.1 )t t t

t t t

y rP

y r

‘Own’

duration dependence

t-1equityAdd τ for strong version

Housing bubble

transition probability

Results for Optimal PolicyV

ari

anc

e o

f in

fla

tio

n

Variance of output

Optimal Monetary Policy Frontiers

tatyyatr **

Results for Optimal PolicyV

ari

anc

e o

f in

fla

tio

n

Variance of output

Optimal Monetary Policy Frontiers

Superior policy

Results for Optimal PolicyV

ari

anc

e o

f in

fla

tio

n

Variance of output

Optimal Monetary Policy Frontiers

Result for Standard Taylor Rule

Optimal Policy Frontiers

No response to AP

r a y ayt t t

Basic Result I: Pricking AP Is Optimal

Optimal Policy Frontiers

No response to AP

Responseto AP

r a y ayt t t t a APAP

Basic Result 2: Knowing NF and F not critical

Optimal Policy Frontiers

No response to AP

Responseto AP

Response to F and NF

r a y ayt t t a π a πF F,t NF NF,t

A Little Bit of Nonlinearity, Important Consequences

1 1

1 1

( , )

( , )t

t

t

t

et

te

h

h

t

t

t t

y r

y r

tE

Bubblepart

Complex Dynamics in Model

Output

Nonlinear Impulse Responses

Inflation

Nonlinear Impulse Responses Illustrate…

Endogenous bubble models admit richer dynamics

Chaotic behavior is possible

Monetary policy helps to stabilize the economy…

… by not only pricking bubbles but also by exploiting bubbles (Blanchard, 2000)

Expected Durations

How do the expected durations of a bubble change over time?

- Assume in the no-bubble steady state and a pickup in economic activity begins

- In simulations, an 8-period positive shock to y

Expected Durations – Monetary Policy Matters!1

, , , ,1 1 1

( | ) ( | ) (1 )i

t t i i t j j t i j j t ki i k

E D I j D F D I j i p p

Expected Duration for Housing Bubble

Expected Duration for Housing Bubble

Start with an equity bubble (1995)

• Then a housing bubble begins (1999)

• Then recessionary shocks start (2000) & soon after the equity price bubble collapses

• Subpar growth shocks end (2002)

• Equity price bubble restarts (2003)

Counterfactual simulation (?)

Expected Duration for Housing Bubble

Recession ends at point D and optimal R increases!E bubble

H bubble

Recession

Expected Duration for Housing Bubble

Too Low, Too Long Policy

Summary – So Far

Optimal policy indicates central banks should respond to asset price bubbles on the way up as on the way down in other words, no Greenspan benign neglect on the upside

Also, double bubbles are a double whammy on Greenspan approach don’t be too

aggressive on the downside

Consensus view a la Blinder/Reis not robust!

Extra Consideration – Closer to Reality: Incorporating Uncertainty Into Analysis

PAYOFF MATRIX

True macroeconomic structure

H price bubble matters H price bubble not matter H price bubble matters

Lmatter, matter=8.2 Lmatter, not matter=8.3 Monetary authority’s view

H price bubble does not matter

Lnot matter, matter=9.3 Lnot matter, not matter=8.2

Compare the expected gains and losses from reacting to asset prices – Risk Management!

PROBABILITY STRUCTURE

H price bubble matters H price bubble not matter

H price bubble matters

Pmatter Pnot matter Monetary authority’s view

H price bubble does not matter

Pmatter Pnot matter

Bayesian Expected Loss Analysis

Implications for Monetary Policy and Benign Neglect

Threshold

Degree of confidence in bubble matters!

Conclusions

In this class of models, generally monetary authorities want to respond to asset prices; it also optimal to “prevent and prick them.”

Findings about optimal monetary policy in multi-bubble environment:

- Intuition from single-bubble models might be misleading at this policy juncture

- Greenspan approach in 2000+ may not be as attractive in 2008+

Conclusions

What’s next on policy modelling front?

- Forward-looking behavior (lengthening horizon!)

- Uncertainty with small probability events (tail risk, insurance motives and ‘Greenspan/Bernanke put’)

- Optimal policy mix especially at the ZLB

Conclusions

What’s next on bubble modelling front?

Better micro-foundations for financial imbalances and bubbles

- What is the role of money and credit?

- What is the nature of the coordination failure?

- What is the role of rational herding and information cascades? Other behavioral models of asset prices?

So, here’s an alternative explanation for why the timing and size of the 75 basis point intermeeting cut in the federal funds rate target. Chairman Bernanke and his colleagues want us to know that when they see changes in the economy that compromise their medium-term stabilization objectives, they will act.

January 23, ???

Where do we stand?... Now, In Disarray

Investors expect the federal funds rate to be as low as 2.25% by the end of the year...In trying to prevent financial-market calamity, the (Bernanke) Fed may find itself pushed by Wall Street to leave interest rates too low for too long.

The Economist, 31 January 2008

Thank you