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Systemic Real and Financial Risks:
Measurement, Forecasting,
and Stress Testing
Gianni De Nicolò
International Monetary Fund and CESifo
Marcella Lucchetta
University of Venice
The views expressed in this paper are those of the authors and do not necessarily
represent those of the IMF.
Motivation

Available monitoring technologies failed to
provide early warnings on the crisis in 20072008.
Building on De Nicolò and Lucchetta (2010),
we develop a model that can be useful for
 positive analysis, and
 as a systemic risk monitoring system.

Limitations of current modeling
DSGE models
1. Incorporation of interactions between financial and
real sectors still in its infancy
2. Forecasting performance not yet firmly established.


1.
2.
Stress testing procedures
“shocked” variables typically endogenous (shock to
the “cause” or the “symptom”?)
difficult to assess the quantitative results.
Our contribution

Our model complements DSGE modeling by
exploiting:

the forecasting power of a Dynamic Factor Model
(DFM) with many predictors

structural identification based on explicit
theoretical constructs (such as DSGE models)

Flexibility (applicable to multiple countries/sector
datasets, and different data frequencies).
Output of the Model
a)
density forecasts of indicators of systemic
real risk and systemic financial risk;
b)
reduced-form stress tests, as historical
simulations;
c)
structural stress-tests, as impulse
responses of systemic risk indicators to
structural shocks identified by standard
macroeconomic and banking theory.
Systemic Real Risk

Systemic Real Risk is measured by GDPExpected Shortfall (GDPES), given by the
expected loss in GDP growth conditional on a
given level of GDP-at-Risk (GDPaR)

GDPaR is the worst predicted realization of
quarterly growth in real GDP at a given (low)
probability
Systemic Financial Risk

A financial health indicator (FS) : return of a
portfolio of financial firms less the return of the
market

Systemic Financial Risk is measured by FSExpected Shortfall (FSES) , given by the
expected loss in FS conditional on a given level
of FS-at-Risk (FSaR)

FSaR is the worst predicted realization of the FS
indicator at a given (low) probability level
The statistical models

GDP growth and FS are modeled through a
version of a factor-augmented VAR (FAVAR)
model (e.g. Stock and Watson, 2002 and 2005)

Density forecasts of GDPG and FS obtained
estimating a set of quantile auto-regressions

Systemic Risk Indicators constructed using
density forecasts
STRESS TESTING =
Measurement of impact and persistence of
configurations of unexpected (structural) shocks
on systemic risk indicators

Reduced-form stress tests:
based on shocks recovered from a statistical model of the
quantiles (distribution) of GDP growth and FS

Structural stress tests:

based on shocks derived from theoretical models
Identification of structural shocks accomplished with
theory-based sign restrictions (Canova and De Nicolò, JME
2002)

Implementation

We use macroeconomic and financial series for the
G-7 economies for the period 1980:Q1-2010:Q1

For each country, the vector of quarterly series
includes about 95 series classified into
equity markets data
credit conditions
indicators of real activity
1.
2.
3.
Main Results
1.
2.
3.



Significant forecasting power for tail risk
realizations of real activity and financial
health
Both reduced-form and structural stress
tests provide early warnings of real and
financial vulnerabilities
In all countries:
aggregate demand shocks drive the real cycle
bank credit demand shocks drive the bank
lending cycle
real drives financial
Plan of the presentation

The Model

Estimation and Forecasting (details)

Forecast Evaluation
Reduced-Form Stress Tests
Structural Stress Tests
Modeling Developments



The Dynamic Factor Model (DFM)
(static form)
X it  i Ft   i X it 1  vit
Ft  (L)Ft 1  Gt
GDPGt 1   R Ft   R ( L)GDPGt  ut11
FSt 1   F  Ft   F ( L) FSt  ut21
(5)
(6)
(7)
(8)
Density Forecasts

Density forecasts of GDP growth and FS obtained
estimating 99 quantile auto-regressions:
ˆ R ( ) F  ˆ ( )( L)GDPG
GDPGQt 1 ( )  ˆ1 ( )  
t
R
t
ˆ F  ( ) F  ˆ ( )( L) FS
FSQt 1 ( )  ˆ 2 ( )  
t
F
t

These “raw” quantile estimates are “rearranged” at each
date to overcome potential “crossing” (novel
application of Chernuzikhov et al. , Econometrica 2010)
Density Forecasts
(2008q3 and 2010q2)
U n it e d S t a t e s
.08
F S I n d ic a t o r
.06
D e n s it y F o r e c a s t s
0
0
.2
.02
.4
.04
.6
.8
G D P G r o w th
D e n s it y F o r e c a s t s
-3 -2 . 5 -2 -1 . 5 -1
-. 5
k d e n s it y s r 2 0 0 8 q3
0
x
.5
1
1 .5
2
2 .5
k d e n s it y s r 2 0 1 0 q 3
3
-3 5 -3 0 -2 5 -2 0 -1 5 -1 0 -5
k d e n s it y s f 2 0 0 8 q 3
0
x
5
10 15 20 25 30 35
k d e n s it y s f 2 0 1 0 q 3
Systemic Risk Indicators

For any given  (0,1)
GDPESt ( )   t (GDPGt | GDPGt  GDPaRt ( ))
FSESt ( )   t ( FSt | FSt  FSaRt ( ))
Systemic Risk Fan Charts
U nited States: Systemic Risk Fan Charts
-2 0 2 4 6
System ic Real Risk
1980q1
gesX = G DP Expected Shortfall with probability X
1990q1
2000q1
2010q1
time
ges20
ges5
fesX = FS Expected Shortfall with probability X
0
20 40 60
Syste m ic Finan cia l Risk
1980q1
1990q1
2000q1
time
fes20
fes5
2010q1
Estimation and Forecasting
(details)
Four steps:
1) Number of factors and lags
2) Quantile estimation
3) Density estimates and Expected
Shortfalls
4) Forecasting
(1) Number of Factors and Lags


Extract all factors with eigenvalues greater than 1
Order factors according to the explanatory power
of the variance of the data and construct
F  {( Fr 1 ), ( F1 , Fr  2 ),...., ( F1 , F2 ,..., Fr  R )}

Choose the number of lags L and the number of
static factors r  F that maximize BIC Criterion
among 4 by R specifications of the FAVAR
(2) Quantile Estimation
*

use the optimal number of lags L, the number
*
of static factors r , and the estimated factors
to estimate quantile auto-regressions for
  1,2....99 specified as in (7) and (8)

address the crossing problem by adopting the
“rearrangement” procedure introduced by
Chernuzukhov, Fernandez-Val and Galichon
(2010)
(3) Continuous Density Estimates

obtain continuous densities and compute expected
shortfalls as
ES( )  
1


0

F ( y)dy  
1


0
Q( y)dy
where Q( ) is the quantile corresponding to
probability  and Q( )  F  ( ) with
F ( )  inf(x | F(x)   )

(4) Expected Shortfall

Regress the series of 99 quantiles to obtain the
continuous function
m
i
ˆ ( ) 
ˆ
Q
a

 i
t
i 0

Then, the expected shortfall estimates are
2
m1
1  ˆ
1  m



ESt ( )    Qt ( y)dy     aˆi y i dy  (aˆ0  aˆ1  aˆ2  ...  aˆm
)
0
0

 i 0
2
3
m
Forecasting in 3 steps
1.
construct forecasts of conditional densities
and of systemic risk indicators
2.
use the VAR of static factors to compute
dynamic forecasts k quarters ahead
3.
use these forecasts are used to obtain
recursive forecasts of quantile estimates
Forecast Evaluation 1

Density forecasts are satisfactory if the Probability
Integral Transforms (PIT) based on estimated
quantiles satisfies independence and uniformity

We constructed PITs for both our real activity and FS
indicators for each of the seven countries

Properties broadly satisfied
Forecast Evaluation 2
Test based on Pearson’s Q statistics

Is the fraction of observed realizations of GDPG
and FS close to the fractions implied by estimated
or forecast quantiles?

In sample partitions
[<Q5,Q5-Q10,Q10-Q20,>Q20] : left-tail
[<Q10,Q10-Q25,Q25-Q50,Q50-Q75,Q75-Q90,>Q90].

entire distribution
Out –of- sample partition: [<Q20,>Q20] left tail

BROADLY SATISFIED
Forecast Evaluation
Table 4. Out-of–Sample Goodness of Fit
Each column reports the Q statistics corresponding to the forecast horizon k (in quarters).
Significance of the Q- statistics at a 5 percent confidence level is reported in boldface.
GDPG
U.S.
Canada
Japan
France
Germany
Italy
U.K.
FS
k=1
k=2
k=3
k=4
k=1
k=2
k=3
k=4
0.03
2.19
5.30
2.19
2.19
1.14
2.19
2.19
2.19
1.14
3.57
1.14
1.14
0.03
1.14
2.19
1.14
5.30
1.14
5.30
0.06
3.57
7.36
1.14
1.14
1.14
7.36
1.14
0.43
2.19
1.14
0.06
7.36
0.97
2.19
2.19
0.33
1.14
0.06
2.19
0.97
0.43
2.19
0.33
0.43
0.03
0.43
1.95
0.43
0.43
0.03
0.43
0.03
0.43
1.95
0.43
Reduced-Form Stress Tests

A historical sequence of shocks to the
distributions of GDP growth and the FS
indicator is obtained by assuming that each
quantile follows a AR(1) process
GDPGQt ( )  aR ( )  bR ( )GDPGQt 1( )  tR ( )
FSQt ( )  aF ( )  bF ( )GDPGQt 1( )  tF ( )
Reduced-Form Stress Tests Statistics

Stressed quantile series
SGDPGQT  H ,t ( )  GDPGQT  H ( )  tR ( )
SFSQT  H ,t ( )  FSQT H ( ) tF ( )

Expected Shortfall ST deviations (ESSTDs)
GDPESt ( )  SGDPGEST  H ,t ( )  GDPESt ( )
FSESt ( )  SFSEST  H ,t ( )  FSESt ( )

STATISTICS: Average ESSTDs for each   1...99
Average ESSTDs
(2008Q1 and 2008Q2)
S h o rt f a ll
T e s ts
D e lt a
2 0 0 8 Q 1
F in a n c ia l E x p e c t e d
S h o r tfa ll
.4
4
.6
6
8
de ltafes
.8
de ltag es
1
10
1.2
S ta te s : S tr e s s
R e a l E x p e c te d
12
U n it e d
D e lt a
0
2 0
4 0
6 0
8 0
1 0 0
0
2 0
4 0
q u a n tile
8 0
1 0 0
R e a l E x p e c te d
T e s ts
S h o rt f a ll
D e lt a
2 0 0 8 Q
2
F in a n c ia l E x p e c t e d
S h o r t f a ll
15
20
de ltafes
1.5
10
1
5
.5
de ltag es
2
25
2.5
S ta te s : S tr e s s
30
U n it e d
D e lt a
6 0
q u a n ti l e
0
2 0
4 0
6 0
q u a n ti le
8 0
1 0 0
0
2 0
4 0
6 0
q u a n ti l e
8 0
1 0 0
Structural Stress Testing



At a given date, the size of impulse responses to
identified shocks measures the sensitivity of systemic
risk indicators to these shocks.
Between dates, changes in the size of these
impulse responses provide a measure of changes in
the resilience of an economy to these shocks.
The impulse responses of observable variables can
be used to detect which sectors of the economy are
most sensitive to a particular shock (risk maps).
Theoretical Sign Restrictions
Table A. Responses of key variables to positive shocks
Aggregate Supply
Aggregate Demand
Positive
Negative
Positive
Positive
Bank Credit
Demand
Bank Credit Supply
Bank Credit Growth
Positive
Positive
Change in Lending
Rates
Positive
Negative
Macroeconomic
Model
GDP growth
Inflation
Banking Model
Identification

In all countries all identified shocks are
aggregate demand shocks associated with
bank credit demand shocks


Consistent with results in Canova and De
Nicolò (JIE 2003)
Slowdowns in aggregate bank credit growth are
the results of real activity downturns (consistent
with Berrospide and Edge, 2010)
A Simple Example of
Structural Stress Test



Gauge weather the stress test signals lower
resilience to structural shocks in the G-7
economies prior to 2007Q3 (pre-crisis)
Compute the difference of the cumulative impact
of the impulse response functions of GDPES
and FSES to each structural shock estimated for
(1980Q1-2007Q2) and (1993Q2-2007Q2)
A positive difference would indicate a lower
resilience of the economies to these shocks
Results

In all countries the first two shocks become
predominant in the last sub-period

Increased risk concentrations in these economies on
both the real and financial sides

The U.S. economy had increased its vulnerability to
shocks both on the real and financial sides, in
absolute terms as well as relatively to the other G-7
economies
Modeling Developments
 Extension
of our framework to the
simultaneous modeling of countries
and regions of the world
 Refinement
of stress testing statistics
and construction of risk maps