How can I solve the cross-sectional dependence and heteroscedasticity in the model of fixed effects?
You can use the different estimators FGLS (Feasible Generalized Least Squares) or CPSE (Panel-Corrected Standard Error').
This link can be useful for you: https://www.youtube.com/watch?v=zXzKRkQtZQ8
Hi: Inference in stochastic frontier function is based on approach of DGP. So to find how to solve the concerns of individual specific effect and the latent heterogeneity you must start by understand first your goal and then use all estimators operators that the literature of panel datasets approach propose to us. William Greene' s book 5 th edition on econometrics in chapter 11 will give you more references and is a Good starting.
You may like to consider random effects model which explicitly deals with these issues and represents more than a 'technical fix' to get better standard errors
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In the presence of cross-sectional dependence and heteroscedasticity, you are most likely to be suffering from endogeneity of some regressors in your FE model. You could use System-GMM, with robust standard errors.
You can use the Driscoll-Kraay nonparametric covariance estimator to compute the standard errors. The standard errors are heteroskedacity and autocorrelation consistent and robust to cross sectional and temporal dependence. To achieve this in stata and since your model is a fixed-effects model, type xtscc dv iv, fe. Ensure you have downloaded the xtscc stata command before following the procedure. Note that dv and iv stand for dependent variable and independent variable(s) respectively, and fe stands fixed effects. FGLS and PCSE are mostly appropriate when you are ignoring fixed effects. FGLS would be appropriate when T > N while PCSE is otherwise.
Fixed Effect Model with SUR (Seemingly Unrelated Regression)
I agree with Gary King that using robust SE's is like taking a canary down the mine; if the robust SE's give different results , there is something wrong with the model, it is not OK to interpret it. I think it is better to have an explicit model that does take the dependency/ heteroscedasticity into account (see earlier post) and not just treat as a nuisance to be corrected.
http://gking.harvard.edu/publications/how-robust-standard-errors-expose-methodological-problems-they-do-not-fix
You could use Pesaran- panel smoothing transition regression (PSTR) estimator.
It depends also on the dimensions of your panel (N, T). You can go, as suggested by Olufemi Adewale Aluko with Driscoll and Kraay (1998) robust standard errors (robust to heteroscedasticity, autocorrelation, and cross-sectional dependency). See Table 1 in Hoechle (2006). Moreover, you can try panel corrected standard errors (Beck and Katz, 1995). Eventually, if you are dealing with a time-series panel, as suggested by Kazi Sohag, you can try CS-ARDL or CS-DL (e.g. Chudik, Mohaddes, Pesaran, and Raissi, 2015).
Please @ Kazi Sohag can you share the CS-ARDL STATA code
using FGLS OR PCSE estimators you can solve the hettro, auto and csd problem or you can use robust options and xtscc
how do you solve the problem of cross sectional dependence when you have a micro panel? I mean when your T is very small?
You may add time fixed effects and use proper robust standard errors, such as Driscoll and Kraay (1998).
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