Panel Data Models

1
Panel Data Models

• Dynamic panels and unit roots

2
Introduction

• To describe the dynamic panel and motivate its
  use (This is mostly a practical guide to its
  use).
• To differentiate between the Arellano-Bond and
  Arellano-Bovver approaches.
• To discuss the problems of unit roots in panel
  data.
• To introduce the concept of cointegration in
  panel data.

3
Dynamic Panel Data Models

• This approach to panel data models involves the
  use of a dynamic effect, in this case adding a
  lagged dependent variable to the explanatory
  variables.
• In addition the model is estimated using
  Generalised Method of Moments (GMM), which works
  in a similar way to Two Stage least squares,
  overcoming problems of endogeneity.
• This approach requires that NgtT, i.e. the cross
  section observations exceed the time series.

4
Theoretical Reason for the Dynamic Panel

• The main theoretical reason for the dynamic panel
  is that it is modelling a partial adjustment
  based approach.
• If it is a partial adjustment process, the
  coefficient on the lagged dependent variable
  measures the speed of adjustment (i.e. 1
  coefficient is speed of adjustment)
• In addition the lagged dependent variable can
  remove any autocorrelation.

5
Individual Effects

• The dynamic panel approach accounts for the
  individual effects, as with other panel data
  models. In the main approach of Arellano-Bond,
  this entails differencing the data.
• This means it is difficult to include dummy
  variables in these models.
• Although the individual effects applies to the
  cross section, two way individual effects can
  also be included, using time dummy variables.

6
Generalised Method of Moments

• This technique is basically a method that chooses
  parameter estimates, such that the theoretical
  model is satisfied as closely as possible. The
  estimates are chosen to minimise the weighted
  distance between the theoretical and actual
  values.
• This method requires that the theoretical
  relations between the parameters satisfies so
  called orthogonality conditions, which mean
  that the sample correlations between the
  explanatory variables and instruments is as close
  to zero as possible.
• OLS is a special case of GMM, where we assume no
  correlation between the explanatory variables and
  error term. (GMM is similar to 2SLS, in that we
  need to specify the instrument list)

7
Dynamic Panel Approaches

• There are basically 2 approaches, the
  Arellano-Bond and Arellano-Bovver approach.
• They differ in terms of the way that the
  individual effects are included in the model,
  with the Arellano-Bond method using differencing
  and the Arellano-Bovver approach using orthogonal
  deviations.
• Although the Arellano-Bond approach has proven
  most popular, the Arellano-Bovver approach has
  better small sample properties and also is better
  at modelling non-stationary data.

8
Dynamic Panel Models

• Criticisms of both approaches centre around the
  basic dynamic model, as dynamics are usually more
  complicated than a single lagged dependent
  variable.
• Also when accounting for unobserved
  heterogeneity, the methods for modelling this are
  limited.
• The stationarity of the variables tends to be
  ignored, although given that these models are
  restricted to short time series, this may not be
  too much of a problem.

9
Example

• The most well known example is the modelling of
  dividends (div) and earnings (earn)

10
Steps for estimating a dynamic panel data model

1. Specify model.
2. Choose whether to use differencing or orthogonal
   deviations to account for fixed effects.
3. Specify instruments (often lagged values of all
   variables in model)
4. Choose method for adjusting standard errors, to
   overcome heteroskedasticity. This is usually
   Whites adjustment.
5. Use the Sargan test to determine if the
   instruments are suitable (Test for
   overidentifying restrictions)

11
Panel Unit Root Tests

• Panel unit root tests can have the usual benefits
  of using a panel, in so far as increasing the
  number of observations
• In addition Levin and Lin (1992) have shown that
  the panel approach substantially increases the
  power of the test relative to the time series ADF
  tests.

12
Levin and Lin approach (LL)

• In the 1993 test, they adopt a similar approach
  to the ADF test for a unit root, where the null
  hypothesis is that there is a unit root.
• In effect ADF tests are carried out for each
  individual in the panel, then adjusted to account
  for any heteroskedasticity, a pooled t-test is
  then produced to test the null, which are
  asymptotically distributed under the normal
  distribution.
• Different lags are allowed across different cross
  sections.

13
Levin and Lin

• The 1993 model takes the following form (to
  remove autocorrelation lagged dependent variables
  included)

14
Levin Lin

• The error terms across the cross sections are
  assumed to be independent.
• It is assumed the ? is the same across all the
  cross sections.
• The lag length for the lagged dependent variables
  is chosen in the usual way.
• As with ADF tests, a trend can also be included
  in the test.

15
Im Pesaran and Shin Test (IPS)

• The IPS test is an example of an alternative to
  the LL test, as instead of assuming a common unit
  root process, where all the ? are identical, it
  tests for individual unit root processes.
• This in effect tests for all i cross sections to
  be stationary.
• The IPS test averages all the individual ADF
  test statistics.
• The null hypothesis in this case is that each
  series contains a unit root for all i cross
  sections.

16
IPS Test

• The IPS test in effect follows the model below

17
IPS and LL tests Compared

• The main difference between the tests, is that
  one assumes a common unit root, the other
  individual unit root, also the IPS has an
  alternative hypothesis stating that at least one
  of the I cross section series is stationary, so
  LL requires all to be stationary, IPS only some.
• Both suffer from the assumption that the error
  terms across the cross sections are independent,
  which rules out any cointegration between them.
  This may not always be the case, particularly
  where the cross sections are financial markets or
  banks.
• Depending on different values of the N and T
  components, the two test statistics can give
  different results

18
Panel Unit Root Test

• There are a variety of different tests with panel
  data, which differ in terms of the assumptions
  regarding the null hypothesis and how the
  autocorrrelation is removed.
• For instance the Fisher PP test removes the
  autocorrelation using an adjustment to the
  standard errors, as with the usual
  Phillips-Perron (PP) test.

19
Panel Cointegration

• The main approaches to cointegration have the
  same advantages as the panel unit root tests, in
  that they increase the power of the test.
• There are essentially two approaches, one based
  on the Engle-Granger approach and the other using
  a Johansen ML type methodology.
• There are in turn variations of both approaches,
  for example in the Engle Granger approach, there
  is the Kao test, which assumes the same values
  across all cross sections, whereas Pedroni
  assumes they can vary across the cross sections,
  in effect allowing considerable differences in
  the dynamics across the cross sections.

20
Conclusion

• The dynamic panel allows dynamic effects to be
  introduced into the model.
• There are basically two different methods, which
  differ in how the fixed effects are measured.
• Both unit root tests and tests for cointegration
  can be conducted with panel data, which increases
  the power of the tests.