Lecture 10.ppt

‘Introductory Econometrics for Finance’ © Chris Brooks 2013 1
Chapter 11
Panel Data

The Nature of Panel Data
• Panel data, also known as longitudinal data, have both time series and cross-
sectional dimensions.
• They arise when we measure the same collection of people or objects over a
period of time.
• Econometrically, the setup is
where yit is the dependent variable,  is the intercept term,  is a k  1 vector
of parameters to be estimated on the explanatory variables, xit; t = 1, …, T;
i = 1, …, N.
• The simplest way to deal with this data would be to estimate a single, pooled
regression on all the observations together.
• But pooling the data assumes that there is no heterogeneity – i.e. the same
relationship holds for all the data.
it
it
it u
x
y 

 


The Advantages of using Panel Data
There are a number of advantages from using a full panel technique when a panel
of data is available.
• We can address a broader range of issues and tackle more complex problems
with panel data than would be possible with pure time series or pure cross-
sectional data alone.
• It is often of interest to examine how variables, or the relationships between
them, change dynamically (over time).
• By structuring the model in an appropriate way, we can remove the impact of
certain forms of omitted variables bias in regression results.

Seemingly Unrelated Regression (SUR)
• One approach to making more full use of the structure of the data would be
to use the SUR framework initially proposed by Zellner (1962). This has
been used widely in finance where the requirement is to model several
closely related variables over time.
• A SUR is so-called because the dependent variables may seem unrelated
across the equations at first sight, but a more careful consideration would
allow us to conclude that they are in fact related after all.
• Under the SUR approach, one would allow for the contemporaneous
relationships between the error terms in the equations by using a generalised
least squares (GLS) technique.
• The idea behind SUR is essentially to transform the model so that the error
terms become uncorrelated. If the correlations between the error terms in the
individual equations had been zero in the first place, then SUR on the system
of equations would have been equivalent to running separate OLS
regressions on each equation.

Fixed and Random Effects Panel Estimators
• The applicability of the SUR technique is limited because it can only be
employed when the number of time series observations per cross-sectional
unit is at least as large as the total number of such units, N.
• A second problem with SUR is that the number of parameters to be estimated
in total is very large, and the variance-covariance matrix of the errors also
has to be estimated. For these reasons, the more flexible full panel data
approach is much more commonly used.
• There are two main classes of panel techniques: the fixed effects estimator
and the random effects estimator.

Fixed Effects Models
• The fixed effects model for some variable yit may be written
• We can think of i as encapsulating all of the variables that affect yit cross-
sectionally but do not vary over time – for example, the sector that a firm
operates in, a person's gender, or the country where a bank has its
headquarters, etc. Thus we would capture the heterogeneity that is
encapsulated in i by a method that allows for different intercepts for each
cross sectional unit.
• This model could be estimated using dummy variables, which would be
termed the least squares dummy variable (LSDV) approach.
it
i
it
it v
x
y 


 



Fixed Effects Models (Cont’d)
• The LSDV model may be written
where D1i is a dummy variable that takes the value 1 for all observations on
the first entity (e.g., the first firm) in the sample and zero otherwise, D2i is a
dummy variable that takes the value 1 for all observations on the second
entity (e.g., the second firm) and zero otherwise, and so on.
• The LSDV can be seen as just a standard regression model and therefore it
can be estimated using OLS.
• Now the model given by the equation above has N+k parameters to estimate.
In order to avoid the necessity to estimate so many dummy variable
parameters, a transformation, known as the within transformation, is used to
simplify matters.
it
i
N
i
i
i
it
it v
DN
D
D
D
x
y 






 




 
3
2
1 3
2
1

The Within Transformation
• The within transformation involves subtracting the time-mean of each entity
away from the values of the variable.
• So define as the time-mean of the observations for cross-sectional
unit i, and similarly calculate the means of all of the explanatory variables.
• Then we can subtract the time-means from each variable to obtain a
regression containing demeaned variables only.
• Note that such a regression does not require an intercept term since now the
dependent variable will have zero mean by construction.
• The model containing the demeaned variables is
• We could write this as
where the double dots above the variables denote the demeaned values.
• This model can be estimated using OLS, but we need to make a degrees of
freedom correction.


T
t it
i y
y 1
i
it
i
it
i
it u
u
x
x
y
y 



 )
(

it
it
it u
x
y 
 




 

The Between Estimator
• An alternative to this demeaning would be to simply run a cross-sectional
regression on the time-averaged values of the variables, which is known as
the between estimator.
• An advantage of running the regression on average values (the between
estimator) over running it on the demeaned values (the within estimator) is
that the process of averaging is likely to reduce the effect of measurement
error in the variables on the estimation process.
• A further possibility is that instead, the first difference operator could be
applied so that the model becomes one for explaining the change in yit rather
than its level. When differences are taken, any variables that do not change
over time will again cancel out.
• Differencing and the within transformation will produce identical estimates
in situations where there are only two time periods.

Time Fixed Effects Models
• It is also possible to have a time-fixed effects model rather than an entity-
fixed effects model.
• We would use such a model where we think that the average value of yit
changes over time but not cross-sectionally.
• Hence with time-fixed effects, the intercepts would be allowed to vary over
time but would be assumed to be the same across entities at each given point
in time. We could write a time-fixed effects model as
where t is a time-varying intercept that captures all of the variables that
affect y and that vary over time but are constant cross-sectionally.
• An example would be where the regulatory environment or tax rate changes
part-way through a sample period. In such circumstances, this change of
environment may well influence y, but in the same way for all firms.
it
t
it
it v
x
y 


 



Time Fixed Effects Models (Cont’d)
• Time-variation in the intercept terms can be allowed for in exactly the same
way as with entity fixed effects. That is, a least squares dummy variable
model could be estimated
where D1t, for example, denotes a dummy variable that takes the value 1 for
the first time period and zero elsewhere, and so on.
• The only difference is that now, the dummy variables capture time variation
rather than cross-sectional variation. Similarly, in order to avoid estimating a
model containing all T dummies, a within transformation can be conducted to
subtract away the cross-sectional averages from each observation
• Finally, it is possible to allow for both entity fixed effects and time fixed
effects within the same model. Such a model would be termed a two-way
error component model, and the LSDV equivalent model would contain both
cross-sectional and time dummies
it
t
T
t
t
it
it v
DT
D
D
x
y 




 


 ...
2
1 2
1

Investigating Banking Competition with a Fixed Effects
Model
• The UK banking sector is relatively concentrated and apparently extremely
profitable.
• It has been argued that competitive forces are not sufficiently strong and that
there are barriers to entry into the market.
• A study by Matthews, Murinde and Zhao (2007) investigates competitive
conditions in UK banking between 1980 and 2004 using the Panzar-Rosse
approach.
• The model posits that if the market is contestable, entry to and exit from the
market will be easy (even if the concentration of market share among firms is
high), so that prices will be set equal to marginal costs.
• The technique used to examine this conjecture is to derive testable
restrictions upon the firm's reduced form revenue equation.

Methodology
• The empirical investigation consists of deriving an index (the Panzar-Rosse
H-statistic) of the sum of the elasticities of revenues to factor costs (input
prices).
• If this lies between 0 and 1, we have monopolistic competition or a partially
contestable equilibrium, whereas H < 0 would imply a monopoly and H = 1
would imply perfect competition or perfect contestability.
• The key point is that if the market is characterised by perfect competition, an
increase in input prices will not affect the output of firms, while it will under
monopolistic competition. The model Matthews et al. investigate is given by
where REVit is the ratio of bank revenue to total assets for firm i at time t, PL
is personnel expenses to employees (the unit price of labour); PK is the ratio
of capital assets to fixed assets (the unit price of capital); and PF is the ratio
of annual interest expenses to total loanable funds (the unit price of funds).
it
i
t
it
it
it
it
it
it
it
v
GROWTH
BR
ASSET
RISKASS
PF
PK
PL
REV



















1
3
2
1
3
2
1
0
ln
ln
ln
ln
ln
ln
ln

Methodology (Cont’d)
• The model also includes several variables that capture time-varying bank-
specific effects on revenues and costs, and these are: RISKASS, the ratio of
provisions to total assets; ASSET is bank size, as measured by total assets; BR
is the ratio of the bank's number of branches to the total number of branches
for all banks.
• Finally, GROWTHt is the rate of growth of GDP, which obviously varies
over time but is constant across banks at a given point in time; i is a bank-
specific fixed effects and vit is an idiosyncratic disturbance term. The
contestability parameter, H is given as 1 + 2 + 3
• Unfortunately, the Panzar-Rosse approach is only valid when applied to a
banking market in long-run equilibrium. Hence the authors also conduct a
test for this, which centres on the regression
it
i
t
it
it
it
it
it
it
it
w
GROWTH
BR
ASSET
RISKASS
PF
PK
PL
ROA



















'
ln
'
ln
'
ln
'
ln
'
ln
'
ln
'
'
ln
1
3
2
1
3
2
1
0

Methodology (Cont’d)
• The explanatory variables for the equilibrium test regression are identical to
those of the contestability regression but the dependent variable is now the
log of the return on assets (lnROA).
• Equilibrium is argued to exist in the market if 1' + 2' + 3'
• Matthews et al. employ a fixed effects panel data model which allows for
differing intercepts across the banks, but assumes that these effects are fixed
over time.
• The fixed effects approach is a sensible one given the data analysed here
since there is an unusually large number of years (25) compared with the
number of banks (12), resulting in a total of 219 bank-years (observations).
• The data employed in the study are obtained from banks' annual reports and
the Annual Abstract of Banking Statistics from the British Bankers
Association. The analysis is conducted for the whole sample period, 1980-
2004, and for two sub-samples, 1980-1991 and 1992-2004.

Results from Test of Banking Market Equilibrium
by Matthews et al.
Source: Matthews, Murinde and Zhao (2007)

Analysis of Equilibrium Test Results
• The null hypothesis that the bank fixed effects are jointly zero (H0: i = 0) is
rejected at the 1% significance level for the full sample and for the second
sub-sample but not at all for the first sub-sample.
• Overall, however, this indicates the usefulness of the fixed effects panel
model that allows for bank heterogeneity.
• The main focus of interest in the table on the previous slide is the equilibrium
test, and this shows slight evidence of disequilibrium (E is significantly
different from zero at the 10% level) for the whole sample, but not for either
of the individual sub-samples.
• Thus the conclusion is that the market appears to be sufficiently in a state of
equilibrium that it is valid to continue to investigate the extent of competition
using the Panzar-Rosse methodology. The results of this are presented on the
following slide.

Results from Test of Banking Market Competition
by Matthews et al.
Source: Matthews, Murinde and Zhao (2007)

Analysis of Competition Test Results
• The value of the contestability parameter, H, which is the sum of the input
elasticities, falls in value from 0.78 in the first sub-sample to 0.46 in the
second, suggesting that the degree of competition in UK retail banking
weakened over the period.
• However, the results in the two rows above that show that the null
hypotheses that H = 0 and H = 1 can both be rejected at the 1% significance
level for both sub-samples, showing that the market is best characterised by
monopolistic competition.
• As for the equilibrium regressions, the null hypothesis that the fixed effects
dummies (i) are jointly zero is strongly rejected, vindicating the use of the
fixed effects panel approach and suggesting that the base levels of the
dependent variables differ.
• Finally, the additional bank control variables all appear to have intuitively
appealing signs. For example, the risk assets variable has a positive sign, so
that higher risks lead to higher revenue per unit of total assets; the asset
variable has a negative sign, and is statistically significant at the 5% level or
below in all three periods, suggesting that smaller banks are more profitable.

The Random Effects Model
• An alternative to the fixed effects model described above is the random
effects model, which is sometimes also known as the error components
model.
• As with fixed effects, the random effects approach proposes different
intercept terms for each entity and again these intercepts are constant over
time, with the relationships between the explanatory and explained variables
assumed to be the same both cross-sectionally and temporally.
• However, the difference is that under the random effects model, the
intercepts for each cross-sectional unit are assumed to arise from a common
intercept  (which is the same for all cross-sectional units and over time),
plus a random variable i that varies cross-sectionally but is constant over
time.
• i measures the random deviation of each entity’s intercept term from the
“global” intercept term . We can write the random effects panel model as
it
i
it
it
it
it v
x
y 



 



 ,

How the Random Effects Model Works
• Unlike the fixed effects model, there are no dummy variables to capture the
heterogeneity (variation) in the cross-sectional dimension.
• Instead, this occurs via the i terms.
• Note that this framework requires the assumptions that the new cross-
sectional error term, i, has zero mean, is independent of the individual
observation error term vit, has constant variance, and is independent of the
explanatory variables.
• The parameters ( and the  vector) are estimated consistently but
inefficiently by OLS, and the conventional formulae would have to be
modified as a result of the cross-correlations between error terms for a given
cross-sectional unit at different points in time.
• Instead, a generalised least squares (GLS) procedure is usually used. The
transformation involved in this GLS procedure is to subtract a weighted mean
of the yit over time (i.e. part of the mean rather than the whole mean, as was
the case for fixed effects estimation).

Quasi-Demeaning the Data
• Define the ‘quasi-demeaned’ data as and similarly for xit,
•  will be a function of the variance of the observation error term, v
2, and of
the variance of the entity-specific error term, 
2:
• This transformation will be precisely that required to ensure that there are no
cross-correlations in the error terms, but fortunately it should automatically
be implemented by standard software packages.
• Just as for the fixed effects model, with random effects, it is also
conceptually no more difficult to allow for time variation than it is to allow
for cross-sectional variation.
• In the case of time-variation, a time period-specific error term is included and
again, a two-way model could be envisaged to allow the intercepts to vary
both cross-sectionally and over time.
i
it
it y
y
y 


*
2
2
1
v
v
T 



 



Fixed or Random Effects?
• It is often said that the random effects model is more appropriate when the
entities in the sample can be thought of as having been randomly selected
from the population, but a fixed effect model is more plausible when the
entities in the sample effectively constitute the entire population.
• More technically, the transformation involved in the GLS procedure under
the random effects approach will not remove the explanatory variables that
do not vary over time, and hence their impact can be enumerated.
• Also, since there are fewer parameters to be estimated with the random
effects model (no dummy variables or within transform to perform), and
therefore degrees of freedom are saved, the random effects model should
produce more efficient estimation than the fixed effects approach.
• However, the random effects approach has a major drawback which arises
from the fact that it is valid only when the composite error term it is
uncorrelated with all of the explanatory variables.

Fixed or Random Effects? (Cont’d)
• This assumption is more stringent than the corresponding one in the fixed
effects case, because with random effects we thus require both i and vit to be
independent of all of the xit.
• This can also be viewed as a consideration of whether any unobserved
omitted variables (that were allowed for by having different intercepts for
each entity) are uncorrelated with the included explanatory variables. If they
are uncorrelated, a random effects approach can be used; otherwise the fixed
effects model is preferable.
• A test for whether this assumption is valid for the random effects estimator is
based on a slightly more complex version of the Hausman test.
• If the assumption does not hold, the parameter estimates will be biased and
inconsistent.
• To see how this arises, suppose that we have only one explanatory variable,
x2it that varies positively with yit, and also with the error term, it. The
estimator will ascribe all of any increase in y to x when in reality some of it
arises from the error term, resulting in biased coefficients.

Credit Stability of Banks in Central and Eastern
Europe: A Random Effects Analysis
• Foreign participants in the banking sector may improve competition and
efficiency to the benefit of the economy that they enter.
• They may have a stabilising effect on credit provision since they will
probably be better diversified than domestic banks and will therefore be more
able to continue to lend when the host economy is performing poorly.
• But on the other hand, it is also argued that foreign banks may alter the credit
supply to suit their own aims rather than that of the host economy.
• They may act more pro-cyclically than local banks, since they have
alternative markets to withdraw their credit supply to when host market
activity falls.
• Moreover, worsening conditions in the home country may force the
repatriation of funds to support a weakened parent bank.

The Data
• There may also be differences in policies for credit provision dependent upon
the nature of the formation of the subsidiary abroad – i.e. whether the
subsidiary's existence results from a take-over of a domestic bank or from the
formation of an entirely new startup operation (a ‘greenfield investment’).
• A study by de Haas and van Lelyveld (2006) employs a panel regression
using a sample of around 250 banks from ten Central and East European
countries.
• They examine whether domestic and foreign banks react differently to
changes in home or host economic activity and banking crises.
• The data cover the period 1993-2000 and are obtained from BankScope.

The Model
• The core model is a random effects panel regression of the form:
where the dependent variable, grit, is the percentage growth in the credit of
bank i in year t; Takeover is a dummy variable taking the value one for
foreign banks resulting from a takeover and zero otherwise; Greenfield is a
dummy taking the value one if bank is the result of a foreign firm making a
new banking investment rather than taking over an existing one; crisis is a
dummy variable taking the value one if the host country for bank i was
subject to a banking disaster in year t.
• Macro is a vector of variables capturing the macroeconomic conditions in the
home country (the lending rate and the change in GDP for the home and host
countries, the host country inflation rate, and the differences in the home and
host country GDP growth rates and the differences in the home and host
country lending rates).
)
(
5
4
3
2
1
it
i
it
it
it
i
it
it
Contr
Macro
Crisis
Greenfield
Takeover
gr

















The Model (Cont’d)
• Contr is a vector of bank-specific control variables that may affect the
dependent variable irrespective of whether it is a foreign or domestic bank.
• These are: weakness parent bank, defined as loan loss provisions made by
the parent bank; solvency is the ratio of equity to total assets; liquidity is the
ratio of liquid assets / total assets; size is the ratio of total bank assets to total
banking assets in the given country; profitability is return on assets and
efficiency is net interest margin.
•  and the 's are parameters (or vectors of parameters in the cases of 4 and
5), i is the unobserved random effect that varies across banks but not over
time, and it is an idiosyncratic error term.

Estimation Options
• de Haas and van Lelyveld discuss the various techniques that could be
employed to estimate such a model.
• OLS is considered to be inappropriate since it does not allow for differences
in average credit market growth rates at the bank level.
• A model allowing for entity-specific effects (i.e. a fixed effects model that
effectively allowed for a different intercept for each bank) is ruled out on the
grounds that there are many more banks than time periods and thus too many
parameters would be required to be estimated.
• They also argue that these bank-specific effects are not of interest to the
problem at hand, which leads them to select the random effects panel model.
• This essentially allows for a different error structure for each bank. A
Hausman test is conducted, and shows that the random effects model is valid
since the bank-specific effects i are found “in most cases not to be
significantly correlated with the explanatory variables.”

Results
Source: de Haas and van Lelyveld (2006)

Analysis of Results
• The main result is that during times of banking disasters, domestic banks
significantly reduce their credit growth rates (i.e. the parameter estimate on
the crisis variable is negative for domestic banks), while the parameter is
close to zero and not significant for foreign banks.
• There is a significant negative relationship between home country GDP
growth, but a positive relationship with host country GDP growth and credit
change in the host country.
• This indicates that, as the authors expected, when foreign banks have fewer
viable lending opportunities in their own countries and hence a lower
opportunity cost for the loanable funds, they may switch their resources to
the host country.
• Lending rates, both at home and in the host country, have little impact on
credit market share growth.

Analysis of Results (Cont’d)
• Interestingly, the greenfield and takeover variables are not statistically
significant (although the parameters are quite large in absolute value),
indicating that the method of investment of a foreign bank in the host country
is unimportant in determining its credit growth rate or that the importance of
the method of investment varies widely across the sample leading to large
standard errors.
• A weaker parent bank (with higher loss provisions) leads to a statistically
significant contraction of credit in the host country as a result of the reduction
in the supply of available funds.
• Overall, both home-related (‘push’) and host-related (‘pull’) factors are found
to be important in explaining foreign bank credit growth.

Panel Unit Root and Cointegration Tests - Background
• Dickey-Fuller and Phillips-Perron unit root tests have low power, especially
for modest sample sizes
• It is believed that more powerful versions of the tests can be employed when
time-series and cross-sectional information is combined – as a result of the
increase in sample size
• We could increase the number of observations by increasing the sample
period, but this data may not be available, or may have structural breaks
• A valid application of the test statistics is much more complex for panels than
single series
• Two important issues to consider:
– The design and interpretation of the null and alternative hypotheses needs careful
thought
– There may be a problem of cross-sectional dependence in the errors across the
unit root testing regressions
• Early studies that assumed cross-sectional independence are sometimes
known as ‘first generation’ panel unit root tests

The MADF Test
• We could run separate regressions over time for each series but to use
Zellner’s seemingly unrelated regression (SUR) approach, which we might
term the multivariate ADF (MADF) test
• This method can only be employed if T >> N, and Taylor and Sarno (1998)
provide an early application to tests for purchasing power parity
• However, that technique is now rarely used, researchers preferring instead to
make use of the full panel structure
• A key consideration is the dimensions of the panel – is the situation that T is
large or that N is large or both? If T is large and N small, the MADF
approach can be used
• But as Breitung and Pesaran (2008) note, in such a situation one may
question whether it is worthwhile to adopt a panel approach at all, since for
sufficiently large T, separate ADF tests ought to be reliable enough to render
the panel approach hardly worth the additional complexity.

The LLC Test
• Levin, Lin and Chu (2002) – LLC – develop a test based on the equation:
• The model is very general since it allows for both entity-specific and time-
specific effects through αi and θt respectively as well as separate
deterministic trends in each series through δit, and the lag structure to mop
up autocorrelation in Δy
• Of course, as for the Dickey-Fuller tests, any or all of these deterministic
terms can be omitted from the regression
• The null hypothesis is H0: ρi ≡ ρ = 0 ∀ i and the alternative is H1: ρ < 0 ∀ i.
So the autoregressive dynamics are the same for all series under the
alternative.

The LLC Test and Nuisance Parameters
• One of the reasons that unit root testing is more complex in the panel
framework in practice is due to the plethora of ‘nuisance parameters’ in the
equation which are necessary to allow for the fixed effects (i.e. αi, θt, δit)
• These nuisance parameters will affect the asymptotic distribution of the test
statistics and hence LLC propose that two auxiliary regressions are run to
remove their impacts
• The resulting test statistic is asymptotically distributed as a standard normal
variate (as both T and N tend to infinity)
• Breitung (2000) develops a modified version of the LLC test which does
not include the deterministic terms and which standardises the residuals
from the auxiliary regression in a more sophisticated fashion.

The LLC Test – How to Interpret the Results
• Under the LLC and Breitung approaches, only evidence against the non-
stationary null in one series is required before the joint null will be rejected
• Breitung and Pesaran (2008) suggest that the appropriate conclusion when
the null is rejected is that ‘a significant proportion of the cross-sectional
units are stationary’
• Especially in the context of large N, this might not be very helpful since no
information is provided on how many of the N series are stationary
• Often, the homogeneity assumption is not economically meaningful either,
since there is no theory suggesting that all of the series have the same
autoregressive dynamics and thus the same value of ρ

Panel Unit Root Tests with Heterogeneous Processes
• This difficulty led Im, Pesaran and Shin (2003) – IPS – to propose an
alternative approach where the null and alternative hypotheses are now H0:
ρi = 0 ∀ i and H1: ρi < 0, i = 1, 2, . . . , N1; ρi = 0, i = N1 + 1, N1 + 2, . . . , N
• So the null hypothesis still specifies all series in the panel as nonstationary,
but under the alternative, a proportion of the series (N1/N) are stationary,
and the remaining proportion ((N − N1)/N) are nonstationary
• No restriction where all of the ρ are identical is imposed
• The statistic in this case is constructed by conducting separate unit root
tests for each series in the panel, calculating the ADF t-statistic for each one
in the standard fashion, and then taking their cross-sectional average
• This average is then transformed into a standard normal variate under the
null hypothesis of a unit root in all the series
• While IPS’s heterogeneous panel unit root tests are superior to the
homogeneous case when N is modest relative to T, they may not be
sufficiently powerful when N is large and T is small, in which case the LLC
approach may be preferable.

The Maddala and Wu (1999) and Choi (2001) Tests
• Maddala and Wu (1999) and Choi (2001) developed a slight variant on the
IPS approach based on an idea dating back to Fisher (1932)
• Unit root tests are conducted separately on each series in the panel and the
p-values associated with the test statistics are then combined
• If we call these p-values pvi, i = 1, 2, . . . ,N, under the null hypothesis of a
unit root in each series, pvi will be distributed uniformly over the [0,1]
interval and hence the following will hold for given N as T → ∞
• Note that the cross-sectional independence assumption is crucial
• The p-values for use in the test must be obtained from Monte Carlo
simulations.

Allowing for Cross-Sectional Heterogeneity
• The assumption of cross-sectional independence of the error terms in the
panel regression is highly unrealistic
• For example, in the context of testing for whether purchasing power parity
holds, there are likely to be important unspecified factors that affect all
exchange rates or groups of exchange rates in the sample, and will result in
correlated residuals.
• O’Connell (1998) demonstrates the considerable size distortions that can
arise when such cross-sectional dependencies are present
• We can adjust the critical values employed but the power of the tests will
fall such that in extreme cases the benefit of using a panel structure could
disappear completely
• O’Connell proposes a feasible GLS estimator for ρ where an assumed form
for the correlations between the disturbances is employed

Allowing for Cross-Sectional Heterogeneity 2
• To overcome the limitation that the correlation matrix must be specified
(and this may be troublesome because it is not clear what form it should
take), Bai and Ng (2004) propose to separate the data into a common factor
component that is highly correlated across the series and a specific part that
is idiosyncratic
• A further approach is to proceed with OLS but to employ modified standard
errors – so-called ‘panel corrected standard errors’ (PCSEs) – see, for
example Breitung and Das (2005)
• Overall, however, it is clear that satisfactorily dealing with cross-sectional
dependence makes an already complex issue considerable harder still
• In the presence of such dependencies, the test statistics are affected in a
non-trivial way by the nuisance parameters.

Panel Cointegration Tests
• Testing for cointegration in panels is complex since one must consider the
possibility of cointegration across groups of variables (what we might term
‘cross-sectional cointegration’) as well as within the groups
• Most of the work so far has relied upon a generalisation of the single
equation methods of the Engle-Granger type following the pioneering work
by Pedroni (1999, 2004)
• For a set of M variables yit and xm,i,t that are individually integrated of order
one and thought to be cointegrated, the model is
• The residuals from this regression are then subjected to separate Dickey-
Fuller or augmented Dickey-Fuller type regressions for each group
• The null hypothesis is that the residuals from all of the test regressions are
unit root processes and therefore that there is no cointegration.

The Pedroni Approach to Panel Cointegration
• Pedroni proposes two possible alternative hypotheses:
– All of the autoregressive dynamics are the same stationary process
– The dynamics from each test equation follow a different stationary process
• In the first case no heterogeneity is permitted, while in the second it is –
analogous to the difference between LLC and IPS as described above
• Pedroni then constructs a raft of different test statistics
• These standardised test statistics are asymptotically standard normally
distributed
• It is also possible to use a generalisation of the Johansen technique
• We could employ the Johansen approach on each group of series
separately, collect the p-values for the trace test and then take −2 times the
sum of their logs following Maddala and Wu (1999) above
• A full systems approach based on a ‘global VAR’ is possible but with
considerable additional complexity – see Breitung and Pesaran (2008).

Panel Unit Root Example: The Link between Financial
Development and GDP Growth
• To what extent are economic growth and the sophistication of the country’s
financial markets linked?
• Excessive government regulations may impede the development of the
financial markets and consequently economic growth will be slower
• On the other hand, if economic agents are able to borrow at reasonable rates
of interest or raise funding easily on the capital markets, this can increase
the viability of real investment opportunities
• Given that long time-series are typically unavailable developing economies,
traditional unit root and cointegration tests that examine the link between
these two variables suffer from low power
• This provides a strong motivation for the use of panel techniques as in the
study by Chrisopoulos and Tsionas (2004)

Panel Unit Root Example: The Link between Financial
Development and GDP Growth 2
• Defining real output for country i as yit, financial ‘depth’ as F, the
proportion of total output that is investment as S, and the rate of inflation as
, the core model is
• Financial depth, F, is proxied by the ratio of total bank liabilities to GDP
• Data are from the IMF’s International Financial Statistics for ten countries
(Colombia, Paraguay, Peru, Mexico, Ecuador, Honduras, Kenya, Thailand,
the Dominican Republic and Jamaica) over the period 1970-2000
• The panel unit root tests of Im, Pesaran and Shin, and the Maddala-Wu chi-
squared test are employed separately for each variable, but using a panel
comprising all ten countries
• The number of lags of Δyit is determined using AIC
• The null hypothesis in all cases is that the process is a unit root.

Panel Unit Root Example: Results
• The results, are much stronger than for the single series unit root tests and
show conclusively that all four series are non-stationary in levels but
stationary in differences:

Panel Cointegration Test: Example
• The LLC approach is used along with the Harris-Tzavalis technique, which
is broadly the same as LLC but has slightly different correction factors in
the limiting distribution
• These techniques are based on a unit root test on the residuals from the
potentially cointegrating regression
• Christopoulos and Tsionis investigate the use of panel cointegration tests
with fixed effects, and with both fixed effects and a deterministic trend in
the test regressions
• These are applied to the regressions both with y, and separately F, as the
dependent variables
• The results quite strongly demonstrate that when the dependent variable is
output, the LLC approach rejects the null hypothesis of a unit root in the
potentially cointegrating regression residuals when fixed effects only are
included in the test regression, but not when a trend is also included.

Panel Cointegration Test: Findings
• In the context of the Harris-Tzavalis variant of the residuals-based test, for
both the fixed effects and the fixed effects + trend regressions, the null is
rejected
• When financial depth is instead used as the dependent variable, none of
these tests reject the null hypothesis
• Thus, the weight of evidence from the residuals-based tests is that
cointegration exists when output is the dependent variable, but it does not
when financial depth is
• In the final row of the table, a systems approach to testing for cointegration
based on the sum of the logs of the p-values from the Johansen test shows
that the null hypothesis of no cointegrating vectors is rejected
• The conclusion is that one cointegrating relationship exists between the
four variables across the panel.

Panel Cointegration Test: Table of Results

Lecture 10.ppt

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