Search for a Metric for Financial StabilityBy C.A.E. Goodhart

It is easier to define, measure, model, analyse and control price stability than to do so for financial stability.

We (Dimitri Tsomocos, Oriol Aspachs, Ton Sunirand, Lea Zicchino) have an ongoing program of work to make a start on such issues.

In several ways the problem of measurement should have priority. Economics is a quantitative social science. Need to compare and analyse. The current unit of measurement is the event of a ‘bank crisis’, but problems of timing of onset, duration, choice of event, intensity, and throwing away non-crisis data.

Our work began with an attempt to model financial fragility, GST, ‘A model to analyse financial fragility’, Economic Theory. When we came to take this model to the data, first by simulation, (GST, Journal of Financial Stability, 2004), and then by calibration, (GST, Annals of Finance, 2006), two key factors were what was effect of shock on (i) bank profitability, (ii) default rates of banks and their customers.

Price Stability Financial Stability

a) Measurement and Definition

Yes, subject to technicalqueries

Hardly, except by its absence

b) Instrument for control Yes, subject to lags Limited, and difficult to adjust

c) Accountable Yes Hardly

d) Forecasting Structure Central tendency ofdistribution

Tails of distribution

e) Forecasting Procedure Standard Forecasts Simulations or Stress Tests

f) Administrative Procedure

Simple Difficult

A Framework for Financial Stability

Contrasts between Price and Financial Stability

A typical example from our latest paper (AGTZ 2006) shows the effects of a change in default penalties on interest rates, and bank profits, capital, capital ratio and repayment rates (default probabilities).

In this example repayment rates go up, (i.e. default probabilities decline), whereas profits decline, primarily because banks choose a safer, less risky investment strategy. While normally the expectation is that profitability and default probabilities are inversely correlated, this is not always the case, especially when banks (are induced to) choose riskier (or less risky) strategies. Greater risk implies profits and PD should rise.

Indeed, in our data base, the correlation between the % change in equity values, (our proxy measure of profitability) and estimated P.D. is only about -0.32 on a quarterly, and -0.61 on an annual, basis, being the average of the simple correlations in our seven countries.

Bank -9.2 -3.3 -14.8 -27.6 -1.4 -0.9 -0.38 0.2 0.24 0.14

Bank -18 -10 -13.2 -34.4 -2.8 -8.9 -1.8 -8 0.24 0.58

Bank -18 -10 -16.9 -23.3 -3.5 -3.5 -2.6 -2.6 0.44 0.29

-3.2 -0.9 -1.5

Table 4: % change in key variables given a 2% increase in default penalties imposed on banks on both states of the world

Interest rates

bdr

br bi b

ii bie b

iie bik b

i bii iGDP iiGDPb

iik

Legend: br lending rate offered by bank b∈ B={δ,γ,τ}, b

dr deposit rate offered by bank b,

ρ= interbank rate, b

s profits of bank b in state of the world s={i,ii},

bse capital held by bank b in state s,

bsk ratio of capital to risk-weighted assets of bank b in state s,

bs repayment rate of bank b to all its creditors in state s,

sGDP = GDP in state s.

So we felt forced to move to a two factor model, profitability and PD, regretfully so since we are seeking a single metric, and to achieve that from a 2 factor model requires some (estimated) factor weighting.

Initially tried data from bank accounts, e.g. profits, NPLs, write-offs, etc., but did not work well:-

(i) Accounting inconsistencies, both between countries and over time;

(ii) Manipulation and smoothing;(iii) Long lags in reporting, especially write-offs.

So we turned to market variables, equity values (as a proxy for profits) and PD, with the latter taken from the IMF.

Note that estimate of PD incorporates both equity valuation and market volatility. So why is it not a sufficient statistic in itself?

Answers:-

(i) Low correlation, already noted;(ii) What are the relevant weightings; e.g. Vol Ai = f (Vol Market,

Vol Sector, Vol Company + covariances);(iii) Empirical Test.

Our procedure was to examine relationships between GDP, our measure of social welfare, inflation, PD of banking sector and equity values of banking sector.

Initial exercises, however, indicated that both PD and % changes in Eq were threshold variables. They only adversely affected GDP if worse than some level. Theshold levels chosen to maximise fit (n.b. small data set, few countries, short period).

Anyhow individual and panel VAR, with four variable VAR and plus property prices, and plus interest rates as well.

Data set includes: Finland, Germany, Japan, Korea, Norway, Sweden and UK over period 1990, Q4 – 2004, Q4, (n.b. bank equity values only available for Norway and Finland from 1996 onwards, and for Sweden from 2000 onwards).

Results: Surprisingly good for Panel; Supportive, but not totally so for individual countries.

What does this suggest:-

(a) for weighting of Eq and PD?

(b) for effects on GDP of individual countries?

Impulse-responses for 3 lag VAR of pod gdp equity inf propprice

Errors are 5% on each side generated by Monte-Carlo with 1000 reps

response of pod to pod shocks

(p 5) pod po d (p 95) pod

0 6-0.1208

0.3400

response of pod to gdp shocks

(p 5) g dp gdp (p 95) gdp

0 6-0.1444

0.0336

response of pod to equity shocks

(p 5) equi ty eq uit y (p 95) equi ty

0 6-0.0652

0.0855

response of pod to inf shocks

(p 5) i nf inf (p 95) inf

0 6-0.1200

0.0568

response of pod to propprice shocks

(p 5) p roppric e pro pprice (p 95) proppri ce

0 6- 0.2900

0.0700

response of gdp to pod shocks

(p 5) pod po d (p 95) pod

0 6-0.4019

0.8707

response of gdp to gdp shocks

(p 5) g dp gdp (p 95) gdp

0 60.0000

1.2075

response of gdp to equity shocks

(p 5) equi ty eq uit y (p 95) equi ty

0 6-0.3117

0.3057

response of gdp to inf shocks

(p 5) i nf inf (p 95) inf

0 6-0.3164

0.2891

response of gdp to propprice shocks

(p 5) p roppric e pro pprice (p 95) proppri ce

0 6- 0.4519

0.5568

response of equity to pod shocks

(p 5) pod po d (p 95) pod

0 6-3.2531

3.7811

response of equity to gdp shocks

(p 5) g dp gdp (p 95) gdp

0 6-0.8613

3.9331

response of equity to equity shocks

(p 5) equi ty eq uit y (p 95) equi ty

0 6-0.2362

6.9194

response of equity to inf shocks

(p 5) i nf inf (p 95) inf

0 6-1.1659

2.8479

response of equity to propprice shocks

(p 5) p roppric e pro pprice (p 95) proppri ce

0 6- 3.0746

1.6112

response of inf to pod shocks

(p 5) pod po d (p 95) pod

0 6-0.2202

0.3229

response of inf to gdp shocks

(p 5) g dp gdp (p 95) gdp

0 6-0.2418

0.1214

response of inf to equity shocks

(p 5) equi ty eq uit y (p 95) equi ty

0 6-0.1607

0.1498

response of inf to inf shocks

(p 5) i nf inf (p 95) inf

0 6-0.0670

0.5989

response of inf t o propprice shocks

(p 5) p roppric e pro pprice (p 95) proppri ce

0 6- 0.1808

0.1977

response of propprice to pod shocks

(p 5) pod po d (p 95) pod

0 6-13.5533

2.7656

response of propprice to gdp shocks

(p 5) g dp gdp (p 95) gdp

0 6-9.5867

0.4280

response of proppri ce to equity shocks

(p 5) equi ty eq uit y (p 95) equi ty

0 6-8.9184

0.0000

response of propprice to inf shocks

(p 5) i nf inf (p 95) inf

0 6-11.363 8

0.3923

response of propprice to propprice shocks

(p 5) p roppric e pro pprice (p 95) proppri ce

0 60.0000

11.7293

Quartersahead

10 97.32 0.87 1.45 0.3520 97.18 0.96 1.48 0.3610 11.12 86.38 2.09 0.3820 11.28 86.13 0.27 0.410 41.19 6.09 50.77 1.6320 41.27 6.39 50.63 1.6910 16.19 10.71 10.11 62.9720 16.42 10.87 11.02 61.68

pod

inf

gdp

equity

Table 9. Variance decompositions: percent of variation in the row variable explained by the column variable

Model (1) pod gdp equity inf

Table 10: Variance-decompositions: percent of variation in the row variable explained by column variable

Model (2) Quarters

ahead pod gdp equity inf propprice

10 63.40 8.59 1.35 3.30 23.35 pod

20 62.96 8.57 1.42 3.85 23.19 10 7.36 85.44 0.48 1.78 4.92

gdp 20 7.56 84.12 0.57 2.35 5.38 10 16.16 16.00 58.94 5.17 3.70

equity 20 16.12 15.79 58.67 5.30 4.10 10 6.60 3.90 1.20 87.96 0.32

inf 20 6.81 4.31 1.48 86.67 0.71 10 10.96 10.73 15.99 20.46 41.84

propprice 20 12.04 10.77 19.41 21.12 36.63

Can we get a single metric, comparable over time and across countries for financial stability?

Yes, conditional on:-

(i) methods (transformation, etc.) used to estimate PD(ii) estimation of relative weights of PD and Eq from

empirical exercises

What does it look like in our case?

Note that PD much stronger influence on GDP than Eq, (as might have been expected), so what determines PD? Further, separate work by Goodhart, Hofmann and Segoviano, ‘Default, Credit Growth and Asset Prices’, IMF (2005/6).

-8

-6

-4

-2

0

2

4

6

8

1996

q4

1997

q2

1997

q4

1998

q2

1998

q4

1999

q2

1999

q4

2000

q2

2000

q4

2001

q2

2001

q4

2002

q2

2002

q4

2003

q2

2003

q4

2004

q2

2004

q4

Index Sweden Index Norway Index Finaland

-8-6-4-202468

10

1991

q4

1992

q4

1993

q4

1994

q4

1995

q4

1996

q4

1997

q4

1998

q4

1999

q4

2000

q4

2001

q4

2002

q4

2003

q4

2004

q4

Index Korea Index Japan

-10

-8

-6

-4

-2

0

2

4

6

8

1991

q4

1992

q4

1993

q4

1994

q4

1995

q4

1996

q4

1997

q4

1998

q4

1999

q4

2000

q4

2001

q4

2002

q4

2003

q4

2004

q4

Index Germany Index UK

Welfare indexes of financial fragility: