Can we apply 2sls and 3sls and GMM without test stationary in panel data and if data are not stationary at level and stationary at first difference can we perform such tests?
Ans1: I think that you may no need to panel stionarity tests, you may directly apply 2SLS/3SLS/GMM as these tests helpful to minimize the possible endogeneity from the given model
Ans 2 Saed Meao: FOR GMM, 2SLS STIONARITY NOT EQUIRED,as gmm is mostly preferred where we have short time period,so no need of stionarity, while if we have large enough data then we go for co- integration etc not gmm
2SLS, 3SLS and GMM does not assume stationarity or unit roots so we apply it without these tests. You can safely run GMM on panel time series data if you control for autocorrelation and when your data has T greater than 10 or 20 time periods.
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