Are FE estimate consistent when variables are integrated of different order

[Elizabeth Nedumparambil]

Hi All,

I have an unbalanced panel with data for 890 companies for 81 months. Since the period is long, it was suggested that I perform unit root test and check whether the variables used in the study are stationary. To account for cross-sectional dependence, the pescadf command was used for the unit root test. The results suggest that one of my variables is nonstationary.

Given this, are the fixed effect estimates obtained using the xtreg, fe command efficient and consistent?

It would be really helpful if someone could help me in this regard.

Thanks
Elizabeth

[Sebastian Kripfganz]

The within-groups transformation applied by the fixed-effects estimator does not turn nonstationary variables into stationary ones. Hence, under large-T asymptotics, a static fixed-effects regression with nonstationary variables might suffer from a spurious-regression problem (similarly to the pure time series context).

[Elizabeth Nedumparambil]

Thank you, Sebastian, for the clarification. What alternative method can I use in this case? Since differencing makes the variable stationary would it suffice to include the differenced variable as the explanatory variable and estimate a fixed effects model?

Also, is there any model that accounts for cross-sectional dependence and allows the use of I(0) and I(1) variables together in the model?

[Sebastian Kripfganz]

Differencing would be one way to deal with the problem. Another one would be to consider a dynamic model with lags of the dependent and/or independent variables. Your time dimension is certainly large enough to estimate a dynamic model with the fixed-effects estimator.

Regarding cross-sectional dependence, you might want to have a look at the xtdcce2 command, although I am not sure how it performs with such a large number of cross sections:
Dietzen, J. (2018). Estimating dynamic common-correlated effects in Stata. Stata Journal 18 (3), 585-617

[Elizabeth Nedumparambil]

Thank you, Sebastian.