Download Estimation of Panel Data Regression Models

Macro stress Testing Credit Risk: A Panel Econometric Estimation with
Ugandan Data
by
Charles Augustine Abuka
Director, Financial Stability Department
BANK OF UGANDA
Prepared for the CMI Course on Macro stress testing
August 22, 2013
KSMS, Nairobi, Kenya
OUTLINE
2
Outline
•
•
•
•
•
Applications in modelling the financial sector
Introduction to Panel Data Models
Practical Applications Using Ugandan Data
Further Topics
Concluding Remarks
3
APPLICATIONS IN MODELLING
SOURCES OF SYSTEMIC RISK IN THE
BANKING SECTOR
4
The empirical literature overview
Author (s)
Methodology and Economies
Results
Gambera [2000]
The authour used bivariate VAR
(employing
variables
such
as
unemployment, sector income, number
of bankrupcies, car sales and
agricultural, commercial, industrial
and real estate loans) and investigated
the impact of economic development
on loan portfolio quality for the case of
the USA.
This study revealed the link between
macroeconomics dynamics and banks
asset quality, where yields can be used
to make accurate predictions of future
effects of the business cycle on assets
quality and cyclical factors can be used
for asset quality forecasting.
Arpa et al [2001]
The authours used single equation
regression analysis, focusing on risk
provisions and the operating income of
Austrian banks.
The authours conclude that the share
of risk provisions in the total loans of
the banking sector varies indirectly
with real GDP and real interest rates
and directly with CPI inflation and real
estate price inflation.
Blaschke and Jones [2001]
The
authors
applied
a
VAR
methodology to investigate the
transmission from real GDP, inflation,
nominal interest rate and the terms of
trade to NPL ratio for the case of the
USA.
The authours discuss the impact of
GDP growth and the business cycle on
credit risk and also on the quality of
bank loans
5
The empirical literature overview
Author (s)
Methodology and Economies
Results
Gropp et al [2002]
The authours suggested a comparison of an equitybased indicator (distance to default) and a bondmarket related (subordinated debt spread) in emerging
market economies.
The spreads do contract in line with a
positive outlook for economies, corporate
bond yield decline, generally maintaining
their spreads to government bonds at
fairly low levels, amid signs of stable-toimproving credit quality and favourable
liquidity conditions.
Gerlach et al, [2005]
The author relied on regression analysis (for the case of
Hong Kong) and employed nominal interest rates, the
CPI, property prices, equity prices, and number of
bankruptcies, the unemployment rate and real GDP as
explanatory variables.
The analysis indicates that the NPL ratio
rises with increasing nominal interest
rates and an increasing number of
bankruptcies, but decreases with higher
CPI inflation, economic growth, and
property
price
inflation.
Deflation
squeezes out corporate profitability and
adversely affects borrowers ability to pay.
Quagliariello [2003]
The authour presents a regression between the
evolution of NPLs as a dependent variable and a set of
explanatory variables for the case of Italy: the real GDP
growth rate, the growth of real gross fixed investment
and consumption, changes in the unemployment rate,
the CPI, the real exchange rate and the M2 growth rate.
The authour concluded that decreasing
real GDP growth and increasing
unemployment have a significantly
adverse effect on loan portfolio quality,
while the real exchange rate and consumer
price index fail to significantly affect it.
6
The empirical literature overview
Author (s)
Methodology and Economies
Results
Popiera [2006]
The author explored the relationship
between banking sector performance and
the quality of regulation and supervision
as measured by the Basel Core Principles
for Effective Supervision using the panel
data for 65 economies.
The study revealed the significant positive
impact of higher compliance with the
Basel Core Principles on banking sector
performance as measure by NPL and net
interest margin (after controlling for the
level of development of the economy and
financial system).
Manasoo and Mayes [2009]
The authours presented a panel logit
model for the CEE between the evolution
of NPLs and set of explanatory variables:
liquidity ratio, inverse liquidity ratio, loan
to asset ratio, equity to asset ratio, cost to
income
ratio
and
macroeconomic
variables.
The authours claim that declining GDP
growth and the instability of external and
internal environments leads to a
worsening of banking sector results and
financial stability indicators in the CEE.
Baboucek and Jankar [2005]
The authours investigated economic
developments in the Czech banking sector
through unemployment, real GDP growth,
exports, imports, the real effective
exchange rate, the CPI and credit growth
as indicators of NPL ratio performance
using an unrestricted VAR methodology.
The study showed that the appreciation of
the real effective exchange rate does not
deteriorate the NPL ratio; increasing
unemployment and inflation deteriorate
the NPL ratio, while faster GDP growth
decelerates the NPL ratio.
7
The empirical literature overview
Author (s)
Methodology and Economies
Results
Hoggarth et al [2005]
The authours applied the VAR approach to investigate
the link between loan write-offs and the output gap,
retail prices, real estate prices, the nominal short term
interest rates and the real exchange rate for the case of
the United Kingdom.
The important factors indirectly influencing financial
stability and loan portfolio quality are the dynamics
of inflation and interest rates.
Chihak et al [2007]
The authours compared system focused stress testing
methods (VAR, Monte Carlo Simulations, etc) and
discussed issues related to the design of stress tests for
the Czech banking system.
The authours suggest (besides banking sector
indicators such as capital adequacy, credit risk and
other relevant factors) incorporating different
shocks into models, non bank financial indicators
and relevant macroeconomic factors ( e.g. the
exchange rate and the interest rate) in order to
perform stress testing
Babihuga [2007]
The authour investigated the relationship between
macroeconomic variables and financial stability
indictors (like capital adequacy, asset quality and
profitability) in the case of the European, Asian and
Sub-Saharan Africa economies. The authour presented
a regression between the evolution of NPL as a
dependent variable and a set of explanatory variables:
the quality of banking sector supervision measured by
an index of compliance with the Basel Core Principles,
terms of trade, unemployment, lending rates, the real
effective exchange rate and the business cycle
component of GDP.
The authour showed that financial stability
indicators fluctuate strongly with the business cycle
and the inflation rate.; and that the cycle component
of real GDP has a negative relationship with capital
adequacy and NPLs. There is also an important
degree of heterogeneity across the sample of
countries (European, Asian and Sub-Saharan Africa
economies) between macroeconomic and financial
stability indicators. The relationship between the
business cycle and capital adequacy is more
ambiguous and it appear to be counter cyclical
(except in Asian and Sub Saharan African, where it is
procyclical).
8
The empirical literature overview
Author (s)
Methodology and Economies
Results
Jakubik [2007]
The authour employed the regression
method for NPL inflow estimation (in
the case of the Czech Republic) using
real GDP, real effective exchange rates,
the CPI, the loan to GDP ratio,
unemployment, and the real interest rate
as explanatory variables.
The default rate for the corporate sector is
determined by the appreciation of the real
effective exchange rate and by the increase
in the loan to GDP ratio; meanwhile, the
default rate for households deteriorates via
unemployment and interest-rate increases.
Zeman and Jurca
[2008]
The authors applied the multivariate
regression method using real GDP, the
output
gap,
exports,
industrial
production, oil prices, the CPI, M1,
nominal interest rates, and nominal
exchange rates as explanatory variables
for NPL dynamics in the case of slovakia.
Real GDP, the nominal exchange rate and
nominal interest rate are the most
important variable influencing NPL
dynamics. A slow down in GDP growth is
not expected to substantially threaten the
banking system. Exposure to interest rate
growth through direct channels and
foreign currency risk through indirect
channels was shown to be due to the high
level of openness of the economy.
9
The empirical literature overview
Author (s)
Methodology and Economies
Results
Uhde and Heimeshoff
[2009]
The authours provided empirical
evidence in the case of the EU-25,
that the national banking market
concentration has a negative impact
on European Banks’ financial
soundness as measured by the Z
score technique (while controlling
for macroeconomic, bank-specific
regulatory and institutional factors.
The authours reveal that Eastern
European Banking markets exhibit a lower
level
of competitive pressure, fewer
diversification opportunities and a higher
fraction of government-owned banks,
which are more prone to financial fragility.
10
PANEL DATA REGRESSION MODELS
11
Time Series Example
Year = t
System NPLs=Yi
LAR=X1
Inflation rate=x2
2009
3.8
55.0
7.0
2010
5.0
60.8
10.0
2011
8.5
66.5
12.0
2012
10.6
70.5
15.0
12
Panel Data Example
Year=t
Bank = I
NPL=Y
LAR=X1
Inflation=X2
2009
CITI
3.4
48.0
7.0
2010
CITI
3.5
50.0
10.0
2011
CITI
3.6
60.0
12.0
2012
CITI
4.0
65.0
15.0
2009
BOB
3.2
60.0
7.0
2010
BOB
3.4
64.0
10.0
2011
BOB
3.7
66.0
12.0
2012
BOB
4.0
70.4
15.0
2009
KCB
4.0
30.4
7.0
2010
KCB
4.6
35.6
10.0
2011
KCB
4.4
40.5
12.0
2012
KCB
5.0
50.6
15.0
13
Panel Data Regression Models
• Same cross-section unit (family or firm or a state) is surveyed over
time.
• Panel data have space as well as time
Advantages
1.
2.
Panel data estimation takes into account heterogeneity in individuals,
firms states, countries, etc. This is done by allowing for individual
specific variables.
By combining time series of cross-section observations, panel data
gives “more informative data, more variability, less collinearity among
variables, more degrees of freedom and more efficiency”
14
Panel Data Regression Models
3.
4.
5.
6.
Panel is suited to study dynamics of change because it studies
repeated cross sections of observations.
Panel data can better detect and measure effects that simply
cannot be observed in pure-cross-section or pure time series
data.
Enables study of more complicated behavioural modes than
purely time series or cross section data e.g. economies of scale
and technological change.
Panel data can minimize bias that might result if we aggregate
individuals or firms into broad aggregates.
15
Panel Data Regression Models
• Limitations of Panel data include:
– Design and data collection problems – problems of
coverage, non response, recall etc,
– Distortions of measurement errors – faulty responses
due to unclear questions, memory errors etc.
– Selectivity problems
• Self selectivity
• Non response
• Attrition
• Short time series dimension
16
Panel Data Regression Models
EXAMPLE
• Non performing loans depend on loan to
asset ratio and macroeconomic variables .
For four banks BOB, BOA, CITI and DFCU.
1993-2013.
17
Estimation of Panel Data Regression Models
•
•
•
•
Four cross sectional units
20 time periods
80 observations
Instead of running 20 cross-sectional regressions and
getting into degrees of freedom problems, we can pool all
the 80 observations as follows:
Yit  1   2 X 2it  3 X 3it  it
i  1,2,3,4
1
t  1,2,................20
18
Estimation of Panel Data Regression Models
• Estimation depends on the assumptions we make about the
intercept, the slope coefficients and the error term unit.
There are several possibilities:
1. Assume the intercept and slope coefficients are constant across
time and space and the error term captures differences over
time and individuals i.e. a pooled regression.
2. The slope coefficients are constant but the intercept varies
over individuals.
3. The slope coefficients are constant but the intercept varies
over individuals and time.
4. All coefficients (the intercept as well as slope coefficient) vary
over individuals.
19
Estimation of Panel Data Regression Models
1. All coefficients constant across time and individuals.
• Simplest & naïve approach, disregards space and time
dimensions of data
• Pooled regression
• Note significance of coefficients as well as the signs
• Comment on the value of Durbin-Watson-if low suggest
autocorrelation in data or specification errors
• Model assumes intercepts of BOB, BOA, CITI and DFCU are the
same
• It assumes slope coefficients of X2 and X3 are the same for
all the banks.
• Highly restrictive assumptions.
20
Estimation of Panel Data Regression Models
2. Slope coefficients constant but the intercept varies across
individuals
• Fixed effects or least-square Dummy Variable (LSDV) regression
modes.
• One way to take into account “individuality” of each bank or
each cross section is to let the intercept vary for each bank but
assume that the slope coefficients are constant across banks.
Yit  1i   2 X 2it  3 X 3it  it
•
2
• The subscript on the intercept term suggests that the intercepts
of the four banks may be different due to differences in
managerial style or managerial philosophy.
21
Estimation of Panel Data Regression Models
• Each individual’s intercept does not vary over time. It is
time invariant.
• To implement this we use the dummy variable technique
(differential intercept dummies)
Y    D  D  D   X   X  
3
if the observation belongs to BOA, 0 other wise
D 1
D 1
if the observation belongs to CITI, 0 other wise
D 1
if the observation belongs to DFCU, 0 other wise
it
1
2
2i
3
3i
4
4i
2
2it
3
3it
it
2i
3i
4i
22
Estimation of Panel Data Regression Models
• Three dummy variables are used because we have 4 banks
and need to avoid dummy variable trap (perfect collinearity)
• If there is no dummy for BOB a1 represents the intercept of
BOB and  2 ,  and  4 the differential coefficients that
tell by how much the intercepts of BOA, CITI and DFCU
differ from the intercept of BOB. BOB is the comparison
bank.
3
• THINGS TO NOTE
23
Estimation of Panel Data Regression Models
i. Significance of coefficients
ii. Differences in intercepts are due to features that
are unique to each bank.
iii. R squared tends to increase may be due to more
variables.
iv. Note what happens to the Durbin Watson
statistic.
• To test model 1 (the restricted which imposes a
common slope to all banks) and model 2 (the
unrestricted) we use an F test.
24
Estimation of Panel Data Regression Models
• The time effect – Time effect allows the NPL function to
shift over time because of factors such as:
 Technological changes
 Changes in government regulatory and/or tax policies
 External effects such as wars or other conflicts
• These are handled by use of time dummies, one for each year.
Since we have 20 years from 1993 to 2013 we can introduce 19
time dummies as:
• Yit  0  1Dum1993  2 Dum1994.......  19 Dum20124i   2 X 2it  3 X 3it  it
4
Dum1993 takes a value 1 for observation in year 1993 and 0
otherwise, etc.
• Year 2013 is the base year and intercept will be given by 0
•
25
Estimation of Panel Data Regression Models
THINGS TO NOTE
Significance of time dummies
Any change in R2
Look at the F test – if it is not significant, it suggests that
the credit function has not changed over
time.
3. Slope coefficients constant but the intercept varies over
individuals as well as time.
• We combine 3 and 4 to get:
•
•
•
•
Yit  1   2 DBOAi   3 DCITI i   4 DDFCU i  0  1Dum1993  2 Dum1994.......
 19 Dum 20124i   2 X 2it  3 X 3it  it
5
26
Estimation of Panel Data Regression Models
Are bank dummies as well as coefficients of X significant
Are time dummies significant
All coefficients vary across individuals
Intercepts and slope coefficient are different for all
individuals, or cross-section units. Are the NPL functions of
BOB, BOA, CITI and DFCU all different.
• Interactive or differential slope dummies hence:
•
•
4.
•
Yit  1   2 D2i   3 D3i   4 D4i   2 X 2it  3 X 3i 
 1 ( D2i X 2it )  2 ( D2i X 3it )  3 ( D3i X 2it ) 
 4 ( D3i X 3it )  5 ( D4i X 2it )  6 ( D4i X 3it )  it
6
27
Estimation of Panel Data Regression Models
• The  ' s are the differential slope coefficients
• While 2 , 3 and  4 are the differential intercepts.
• If all the differential intercepts and all the
differential slope coefficients are statistically
significant we conclude that the NPL functions of
BOA, CITI and DFCU are different from that of BOB.
No need to estimate a pooled regression.
28
Problems of LSDV Model
1.
Introduces to many dummy variables and you run into the
degrees of freedom problem. Given 80 observations:
55 d.f = 80 -3 d.f for three banks
-19 d.f for year dummies
-2 d.f for two slope coefficients
-1 d.f for the common intercept.
2. Possibility of multicollinearity because of so many variables in
the model – precise estimation of parameters is difficult.
3. May not be able to identify impact of time-invariant variables
such as sex, colour or ethnicity (these do not change over
time).
4. Assume the error term follows the classical assumptions of
normality. However, the error term may need to be modified.
29
Estimation of Panel Data Regression Models
• The One way error component model
– The Fixed Effects Model
– The Random Effects Model
• The two way Error Component Model
– The Fixed Effects Model
– The Random Effects Model
30
Estimation of Panel Data Regression Models
• One Way Error Component Regression Model
– Given a Panel data regression model of the
form:
Yit    X it    it ..........................7
i  1,....., N ; t  1,...., T
– Most Panel data applications utilize a one way
error component model for the disturbances,
with
 it  i   it
31
Estimation of Panel Data Regression Models
–  i = the unobservable individual specific
effect
–  it = the remainder of the disturbance
– Example: For a production function utilizing
data on banks across time Yit will capture
output and X will measure inputs.
it
– The  i
will capture things such as
entrepreneurial or managerial skills of the
banks executive.
32
Estimation of Panel Data Regression Models
• The Fixed Effects Model
– In this model the  i are assumed to be
fixed effects to be estimated and the
remainder disturbances are stochastic
with  it independent and identically
distributed
IID (0,  2 )
– for all i and t .
33
Estimation of Panel Data Regression Models
• This model is appropriate when inference is
restricted to a specific set of N Known
firms whose behavior we are interested in.
• The Fixed Effects (FE) Least Squares is also
known as the Least Squares Dummy
Variables (LSDV).
34
Estimation of Panel Data Regression
Models
• The Random Effects Model
– There too many parameters in the fixed effects
model and the loss of degrees of freedom can be
avoided if  i is assumed to be random. In this
case:
i  IID(0,  2 )
 i  IID (0,  )
2
– and
 i are independent of  it .
35
Estimation of Panel Data Regression
Models
– In addition, theX are independent of the
it
 i and  it for all i and t.
– The random effects model is an appropriate
specification if we are drawing N individuals
randomly from a large population.
– The individual effect is characterized as random
and inference pertains to the population that the
sample was randomly drawn.
36
Estimation of Panel Data Regression
Models
• Two Way Error Component Regression
Model
– In this case the regression model in equation
(7) above has two-way error component
disturbances i.e.:
 it  i  t  it
i  1,....., N ; t  1,....T ......................................8
 i = the unobservable individual effect
37
Estimation of Panel Data Regression
Models
t
–  it
–
=
the unobservable time effect
=
is the remainder stochastic disturbance term.
– Note that t is individual – invariant and accounts for
any time specific effect not included in the regression.
– These include strike year effects that disrupt, oil
embargo effects that disrupt supply of oil and affect its
price, government laws that affect consumption e.t.c.
38
Estimation of Panel Data Regression
Models
• The Fixed Effects Model
– The  i and t
are assumed to be fixed
parameters to be estimated and the remainder
of the disturbances are stochastic with
 it  IID (0,  2 )
• then equation (8) represents a two way fixed
effects error component model.
39
Estimation of Panel Data Regression
Models
– The X it
are assumed independent of all
the  it for all i and t .
– However, inference is conditional on the
particular N Individuals and over the specific
time periods observed.
40
Estimation of Panel Data Regression
Models
• The Random Effects Model
– If i  IID(0, 2 ),   IID0, 2 and it  IID(0,2 )
– Independent of each other then the equation
(8) is the two way random effects model.
– In addition, if X it is independent of  i , t and  it
for all i and t then inference in that case
pertains to the large population from which this
sample was randomly drawn.
41
SOME PRACTICAL APPLICATIONS WITH
UGANDAN DATA
42
III. Practical Applications
• The Data:
• Quarterly bank and macro level data from Uganda
from 2000q1 to 2013q1. This dataset is found in
a file (bank_data.WF1).
• Contains quarterly macroeconomic variables real
GDP, exchange rate change, inflation and interest
rates 2000q1-2013q1.
• Contains bank level data on non performing loans,
market share of banks assets, total loans loans to
total assets. There are twelve banks.
43
III. Practical Applications
Macroeconomic variables
No.
Variable
Measures
Identification
1
Real GDP
Real GDP
rgdp
Growth Rate of Real GDP
rgdpg
Real effective exchange
rate
reer
Nominal exchange
ner
Headline consumer price
index
hcpi
Annual Inflation rate
infla
Average Lending Rate
lr
Real lending rate
rir
Treasury securities
tb364, tb91
2
3
4
Exchange Rate
Inflation
Interest rates
44
III. Practical Applications
Bank level variables
No.
Variable
Measures
Identification
1
Nonperforming loans
Nonperforming loans
ratio
npl
2
Bank size
Market share
size
Total assets
ta
3
Loans extended
Total loans
tl
4
Deposits
Total deposit liabilities
dep
5
Loans to total assets
Loans to total assets ratio
lota
45
III. Practical Applications: Static Model
• The dependent variable is non performing
assets (LNPL)other regressors are:
– real GDP growth rate (RGDPG),
– real interest rate (RIR),
– change in the exchange rate (DLNER),
– the inflation rate (INFLA),
– the market share (SIZE),
– loans to total assets (LLOTA).
46
Estimating a Panel Least Squares Equation: One way error fixed
• Using: bank_data.WF1
• Quick/Estimate Equation
• Type equation in the command window
– i.e. lnpl c rgdpg rir dlner infla lsize llota
• Panel options:
– Cross section – Fixed
– Period
- None
47
Estimating a Panel Least Squares Equation: One way error fixed
48
Estimating a Panel Least Squares Equation: One way error Random
• Using Using: bank_data.WF1
• Quick/Estimate Equation
• Type equation in the command window
– i.e. lnpl c rgdpg rir dlner infla lsize llota
• Panel options:
– Cross section – Random
– Period
- None
49
Estimating a Panel Least Squares Equation: One way error Random
50
Estimating a Panel Least Squares Equation: Two way error Fixed
• Will not be estimated, nature of the data set.
51
Estimating a Panel Least Squares Equation: Two way error Random
• Using Using: bank_data.WF1
• Quick/Estimate Equation
• Type equation in the command window
– i.e. lnpl c rgdpg rir dlner infla lsize llota
• Panel options:
– Cross section – Random
– Period
- Random
52
Estimating a Panel Least Squares Equation: Two way error Random
53
III. Practical Applications: Dynamic Model
• Estimate a dynamic panel least equations using:
– The nonperforming assets ratio (LNPL) and other
regressors such namely regressors are
•
•
•
•
•
•
•
•
lagged NPL ratio (LNPL(-1),
real GDP rate (LRGDP), RGDPG
real interest rate (RIR), LTB364, LTB91, LR
change in the exchange rate (DLNER), LREER
the inflation rate (INFLA), LHCPL, DLHCPI
the market share (SIZE),
loans to total assets (LLOTA), LTA
growth in total loans (DLTL). LTL
54
III. Practical Applications: Dynamic Model
• Estimate the following Dynamic Panel Least Squares Equations:
– One way error fixed (cross section- fixed; period –none)
– One way error random (cross section- Random; period –none)
– Two way error random (cross section- Random; period –
Random)
– Equation: LNPL C LNPL(-1) LRGDP RIR DLNER INFLA LSIZE LLOTA
DLTL
• What are your results and how might they compare with the
static model results?
• What are some of the problems with these regression
equations?
• What are the implications for model search?
55
III. Practical Applications: Dynamic Model
One way error fixed
56
III. Practical Applications: Dynamic Model
One way error random
57
III. Practical Applications: Dynamic Model
Two way error random
58
FURTHER TOPICS
59
Further Topics
• Further Topics
– Non Stationary Panel Data Models
– Panel Cointegration
– GMM estimation etc, etc
60
REFERENCES
61
REFERENCES
• Baltagi B.D., 2001 Econometric Analysis of
Panel Data, John Willwy and Sons, LTD.
• Eviews 6 and 7 Users Guides
• Green, W.H., 2005 Econometric Analysis,
Prentice Hall.
• Wooldridge, J.M, 2002 Econometric Analysis
of Cross Section and Panel Data, The MIT
Press.
62