I intend to conduct a panel VAR with N = 39 (banks) and T = 14. My variables are: Stability (STAB_Low-T), Return on Assets (ROA), Gross NPA ratio (GNPA), Liquidity (LR2), Governance Quality (GQI_un), and Customer Orientation (COI_un). The dataset I am working with is an unbalanced panel due to the merger of certain banks.
With an unbalanced panel, I gravitated towards either the Im-Pesharan-Shin (IPS) or Fisher unit root test. While reading the STATA help manual xtunitroot (attached), I had some doubts as under.
1. Asymptotics of IPS test indicates:
Question 1: Whether the IPS test more appropriate for panels with N > T or those with T > N or it can be used in both cases?
2. Using the same rationale, can we interpret that the asymptotics for Fisher type test, i.e., T→∞, N either finite or infinite, suggests its suitability for panels with T > N? If yes, isn't it contradicting that example 6 (page #17) uses a panel with N = 151 and T = 34?
Question 2: Whether the Fisher unit root test could be applied even for a panel with N > T?
3. The -xtcsd- test with pesaran, frees and friedman options indicated the presence of cross-sectional dependence among panels. Some of the appropriate tests under cross-sectional correlations were -xtcips- (Peasran, 2007), -breitung- with robust option (Breitung and Das, 2006), and -xtpanic- (Bai and Ng, 2004), as mentioned in Cameron, 2013; page #56 (attached), all of which need a balanced panel. For the unbalanced panel, I used the -pescadf- (Peasran, 2007) test. However, the inferences varied depending on the number of lags used, as indicated in the table below.
Results of Pesaran unit root test (without time trend, the constant term included)
pescadf varname, lags(#)
H0: All panels contain a unit root
H1: At least one panel is stationary
Question 3: Under such circumstances, what inference should I draw regarding the stationarity of my variables?
Question 4: Further is there any general rule of thumb for the number of lags to be tested, in the absence of options to select lags based on AIC/BIC/HQIC as in the case of xtunitroot fisher or pescadf?
I would indeed appreciate any guidance and input on this matter. Thanks in advance.
Kind regards
Pankaj Swain
With an unbalanced panel, I gravitated towards either the Im-Pesharan-Shin (IPS) or Fisher unit root test. While reading the STATA help manual xtunitroot (attached), I had some doubts as under.
1. Asymptotics of IPS test indicates:
- N→∞ and fixed T or N and T fixed
- (T, N) →seq ∞
Question 1: Whether the IPS test more appropriate for panels with N > T or those with T > N or it can be used in both cases?
2. Using the same rationale, can we interpret that the asymptotics for Fisher type test, i.e., T→∞, N either finite or infinite, suggests its suitability for panels with T > N? If yes, isn't it contradicting that example 6 (page #17) uses a panel with N = 151 and T = 34?
Question 2: Whether the Fisher unit root test could be applied even for a panel with N > T?
3. The -xtcsd- test with pesaran, frees and friedman options indicated the presence of cross-sectional dependence among panels. Some of the appropriate tests under cross-sectional correlations were -xtcips- (Peasran, 2007), -breitung- with robust option (Breitung and Das, 2006), and -xtpanic- (Bai and Ng, 2004), as mentioned in Cameron, 2013; page #56 (attached), all of which need a balanced panel. For the unbalanced panel, I used the -pescadf- (Peasran, 2007) test. However, the inferences varied depending on the number of lags used, as indicated in the table below.
Results of Pesaran unit root test (without time trend, the constant term included)
pescadf varname, lags(#)
H0: All panels contain a unit root
H1: At least one panel is stationary
| Variable | Lags(0) | Lags(1) | Lags(2) | Lags(3) | Lags(4) | Lags(5) |
| Stab-Low_T | H0 rejected | Fail to reject H0 | Fail to reject H0 | Fail to reject H0 | Fail to reject H0 | Fail to reject H0 |
| ROA | H0 rejected | H0 rejected | Fail to reject H0 | Fail to reject H0 | Fail to reject H0 | Fail to reject H0 |
| GNPA | H0 rejected | H0 rejected | Fail to reject H0 | Fail to reject H0 | Fail to reject H0 | Fail to reject H0 |
| LR2 | H0 rejected | H0 rejected | Fail to reject H0 | Fail to reject H0 | Fail to reject H0 | Fail to reject H0 |
| GQI_un | Fail to reject H0 | Fail to reject H0 | Fail to reject H0 | Fail to reject H0 | Fail to reject H0 | Fail to reject H0 |
| COI_un | Fail to reject H0 | Fail to reject H0 | Fail to reject H0 | Fail to reject H0 | Fail to reject H0 | Fail to reject H0 |
Question 3: Under such circumstances, what inference should I draw regarding the stationarity of my variables?
Question 4: Further is there any general rule of thumb for the number of lags to be tested, in the absence of options to select lags based on AIC/BIC/HQIC as in the case of xtunitroot fisher or pescadf?
I would indeed appreciate any guidance and input on this matter. Thanks in advance.
Kind regards
Pankaj Swain
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