In panel data analysis, if all the variables are stationary at level (in case of observations greater than 30), can we use fixed and random effect? Please suggest some support too.
You can use both fixed effect models and the random but then it would be advisable to apply the Hausman test to choose between the two models...intuitively, hausman is a general implementation of Hausman’s (1978) specification test, which compares an
estimator that is known to be consistent (1-fiixed) with an estimator (2-random)that is efficient under the assumption being tested. The null hypothesis is that the estimator (2-random) is indeed an efficient (and consistent) estimator of the true parameters. If this is the case, there should be no systematic difference between the two estimators. If there exists a systematic difference in the estimates, you have reason to doubt the assumptions on which the efficient estimator is based. The assumption of efficiency is violated if the estimator is pweighted or the data are clustered, so hausman cannot be used. The test can be forced by specifying the force option with hausman. For an alternative to using hausman in these cases.
Panel data is one of the regression estimation methods. All variable need to be stationary, so you can apply any of the panel data approach. However, it is good to choose the appropriate model based on the Hausman test and before you finalize the model you need to confirm the model is robust.
In addition to the answers provided above, it is equally advisable to include year dummies in the panel data so as to take care of time dimension idiosyncratic randomness, and regional/sector dummies to take care of regional/sector dimension idiosyncratic randomness, if the units of analysis are from different rehgions/sectors This ensures that the Hausman test is not misleading.