1. Esman M. Nyamongo Central Bank of Kenya
Panel data analysis
Econometrics Course organized by the COMESA Monetary Institute (CMI), 9-13 February 2015, Kampala, Uganda
Esman M. Nyamongo
Central Bank of Kenya

2. stationary panel data

3. Non stationary panel data
Previous panel data tools did not deal with the possibility of non-stationary data
Data limitations- T was short
Large T dimensions:
Allow estimation of heterogenous panels
Allow investigation of non-stationary spurious regression and cointegrtion

4. The treatment given to panel has a basis in time series
Background knowledge of stationarity/unit root in time series environment is assumed here.
The treatment given to panel has a basis in time series
Tests of panel unit root
Panel cointegration

5. A. Panel unit-root tests
A number of tests are available:
Levin and Lin panel unit root test
The Im, Pesaran and Shin (IPS) panel unit root test
Hadri test
The Maddala and Wu (1999) panel unit root test
etc

6. 1A. The Levin and Lin (1993) panel unit-root test
Pioneering work by Levin and Lin ( ).
Allows fixed individual and time effects (through an individualized trend); is homogenous across the panel
The test is ‘Dickey-Fuller’ based:
But can assume a case of

7. Step1- conduct separate ADF for cross sections
The model:
Step1- conduct separate ADF for cross sections
Then estimate 2 auxiliary regressions to get orthogonalised residuals

8. Step 3: compute the panel test statistic.
Standardize these residuals to control for difference variances across i.
Step 2: estimate the ratio of the long-run and short-run standard deviations
Step 3: compute the panel test statistic.
Run the pooled regression:
Then test hypothesis.

9. 1B. Levin, lin and chu (LLC) test
Based on ADF and not DF
The maintained hypothesis
Steps:
Step1- conduct separate ADF for cross sections
Then estimate 2 auxiliary regressions to get orthogonalised residuals

10. Step 3: compute the panel test statisitic. Run the pooled regression:
Standardize these residuals to control for difference variances across i.
Step 2: estimate the ratio of the long-run and short-run standard deviations
Step 3: compute the panel test statisitic. Run the pooled regression:
Then test hypothesis.
Caution: LLC recommend N= 10 – 250 and T=
Outside this range the test is not ideal

11. Example

12. 2. Im, pesaran and shin (IPS)
IPS allow for heterogeneity. They construct a panel test first on DF-test and then ADF test:
Because the lag lengths, pi, can differ across equations, separate lag length test for each equation is advised.
However, it works within a balanced panel setup.
In addition, if time trend is included in one equation it should be included in all.
Hypothesis testing
for all i
for at least one cross-section

13. Then construct the statistic as follows:
Once all the pi have been estimated, we obtain the t-statistic. We then compute the sample mean of the n different t-statistics:
Then construct the statistic as follows:
where:
t bar is the average ADF test statistic of all the individual cross-section statistics
E(tbar) and var(tbar) are means and variances that must be computed based on Monte Carlo simulated moments provided by IPS in their paper.
Paper to be provided, if possible.
Practical exercises to be done as well

14. Example: IPS test on fer

15. 3. Maddala and wu (2000)
This test is constructed with the idea of concentrating on the shortcomings of Levin and Lin and IPS.
IPS assumes T is constant for all i.
Both Levin and Lin, and IPS have critical values which depend on pi.
This test:
Does not require balanced panel (as IPS)
Can accommodate different unit root tests
Can be adapted for less restrictive assumptions about cross-correlations
The Maddala and Wu test is a Fisher (1932) based test that combines information on the unit root test p- values
It has the advantage of being exact
Does not depend on asymptotics for distribution

16. The test is stated as follows:
This test suggests that we can do any number of individual tests and combine them.

17. Hadri test
Unlike other tests it tests the null hypothesis of stationarity.
Practical exercises to follow

18. Example: Adf- angola