PHASE DATING AND CONTAGION IN THE GFC: A SMOOTH TRANSITION STRUCTURAL GARCH APPROACH

George Milunovich – Macquarie UniversitySusan Thorp – University of Technology SydneyMinxian Yang – University of New South Wales

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MOTIVATION Real estate shocks preceded the 2007-2009

financial crisis but other asset classes including debt and equities received, transmitted and possibly amplified the shocks.

We dissect the crisis at the level of structural shocks, tracking changes in simultaneous links between equities, T-bonds and real estate. Stocks (SP 500) Real Estate (FTSE NAREITs) T-Bonds (BOA Merrill Lynch US Treasury Index)

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DATA AND COMPLICATIONS Data sample:

Time Period: June 2001 – September 2010 Sampling Frequency: Daily No. of Observations: 2296

Investigate possible breaks in the structural relationships due to the GFC

Modeling Challenges: Endogenous data Possibility of several regime shifts during the

period of the GFC

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-10

-5

0

5

10

15

1000 1500 2000 2500

SP500

-2

-1

0

1

2

3

1000 1500 2000 2500

TBOND

-30

-20

-10

0

10

20

1000 1500 2000 2500

REIT

Included observations: 2296 after adjustments SP500 TBOND REIT Mean 0.002861 0.022405 0.038848

Maximum 10.24540 2.117925 16.35494 Minimum -9.459519 -1.957185 -20.59137 Std. Dev. 1.360837 0.340871 2.269040 Skewness -0.340865 -0.172506 -0.096049 Kurtosis 10.44911 5.003489 16.29085

Jarque-Bera 5352.939 395.3904 16902.72 Probability 0.000000 0.000000 0.000000

Observations 2296 2296 2296

Correlation Probability SP500 TBOND REIT

SP500 1.000000 -----

TBOND -0.349065 1.000000 0.0000 -----

REIT 0.743164 -0.220409 1.000000 0.0000 0.0000 -----

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MODEL Basic Structure for filtered returns

Or in vector notation:

500, 12 , 13 , 1,

, 21 500, 23 , 2,

, 31 500, 32 , 3,

SP t TBond t REIT t t

TBond t SP t REIT t t

REITs t SP t TBond t t

r r r u

r r r u

r r r u

t tL y r

1

, , , 1

~ 0,

is diagonal diagonal elements follow GARCH(1, 1):

t t t

t

i t i i i t i i t

I N G

Gg u g

u

t tBr u

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ENDOGENOUS DATING AND ESTIMATING THE IMPACT OF THE GFC In order to account for possible regime shifts

in the relationships across the three markets we extend the model as follows

where

t t tB r u

3 2 1 0 1 1 2 2 3 31 1 1t S S S S S S B B B B B

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1 for and 1,2,3j t jx cj t

tS e x jT

t tBr u

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SMOOTH TRANSITION FUNCTIONS SJ

1. the speed of transition through γ > 0. As γ →∞ transition becomes abrupt and the model jumps between the states.

2. the location of transition through c > 0. We allow up to three changes in regime, i.e. four phases 0<c1<c2<c3<1. For a large value of γ if c1≤ xt <c2 then Bt=B1 etc.

For information on smooth transition models see Granger (1993), van Dijk, Terasvirta, Frances (2002), Silvennoinen and Terasvirta (2009), amongst others

Shape of the transitions function depends on:

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1 j t jx cjS e

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IDENTIFICATION STRATEGY When the error vector ut=Byt is homoskedastic, the structural matrix B

cannot be recovered from the reduced VAR without identifying restrictions. Examples of such restrictions include a) exclusion restrictions, see for example

Sims(1980) and Bernanke (1986), b) sign constraints on parameters in B (Blanchard and Diamond (1989)) or c) assumptions about long-run multipliers (Blanchard and Quah (1989))

Recently a number of papers used identification via heteroskesticity to avoid imposing such constraints Sentana and Fiorentini (2001) provide sufficient conditions for identification of

factor models in which the factors are heteroskedastic Rigobon (2003) uses discrete regime shifts in volatility to identify SVAR models Rigobon and Sack (2003) suggest that ARCH in structural errors could be used

to identify structural VAR models but do not provide exact conditions for identification.

Lanne et al (2010) obtain identification of a structural model where heteroskedasticity follows a Markov switching process

Klein and Vella (2010) and Lewbel (2010) exploit relationships between heteroskedasticity and exogenous explanatory variables to prove identification

Milunovich and Yang (2010) prove joint identification of all structural parameters of SVAR models with ARCH variances

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IDENTIFICATION STRATEGY In this paper we use Milunovich and Yang (2010)

arguments and extend them to take into account the possibility of regimes shifts as described in this paper.

All structural parameters are locally identified at any regular point in the parameter space1. γ is sufficiently large2. B0, B1, B2, B3 are all invertible and different3. at least n-1 structural shocks have ARCH

effects

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ESTIMATED CRISIS REGIME DATES500 12 13SP TBond REITr r r

21 500 23TBond SP REITr r r

31 500 32REITs SP TBondr r r

13 Sep – bailout of Northern Rock18 Sep – lowering of Fed Funds rate1 Oct – UBS announces a large write-down of its portfolios5 Oct – Merrill Lynch reports large losses10 Oct – establishment of the HOPE NOW alliance to stave off mortgage foreclosures

9 Aug – large European banks report falls in earnings of between 28%-63% one year after the start of the crisis7 Sep – Fannie Mae and Freddie Mac passed into conservatorship, $100bn provided to each company , both CEOs replaced 10 Sep – Lehman announces $3.9bn loss in 3rd quarter15 Sep – Lehman files for bankruptcy, BOA buys Merrill Lynch , AIG debt downgraded by all three major rating agencies

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VARIANCE DECOMPOSITIONS Since the structural parameters are identified and we

obtain the estimates of the B matrices in the next step is to try to identify the structural shocks

We use the following strategy developed in Dungey et al (2010) A shock is named after the market to which it contributes the

largest fraction of its variance Two variable example

If then is called the ri variable shock.

1t t t

r B u

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2

| | 1 | 2

| 1|

| 1 | 2

| 2|

| 1 | 2

t j t i t t j t t t j t

t t j tut j t

t t j t t t j t

t t j tut j t

t t j t t t j t

Var r Var u Var u

Var uVD

Var u Var u

Var uVD

Var u Var u

1 2| |

u ut j t t j tVD VD 1u

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VARIANCE DECOMPOSITIONS

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MODEL FIT – RESIDUAL DIAGNOSTICS

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CONCLUSIONS We develop an identified Structural GARCH model with smooth

transition functions We are able to endogenously date 3 structural breaks and 4 regimes

Significant changes are found in the linkages between gov’t debt, real estate and equity which persist into the post-GFC period Direct linkages to and from T-bonds and the other two markets

become insignificant over the crisis Impact of equities on real estate increases dramatically during the

first phase of the GFC and remains high Impact of real estate on stocks doesn’t change over the crisis but

almost halves over the post-GFC period Impact from T-bonds on REITs corrects sign from in the post-GFC

period Variance decompositions illustrate the propagation of risk

across the three assets, with real estate shocks starting to grow in importance in 2003-2004 period.