Panel data estimation methods: different properties

[YoramV]

Dear e-views forum users,

I hope you can help me with the following question. For my thesis in econometrics, I would like to make a table on the following issue.

Suppose you have the following data generating process:


y_(i,t)=α_1 x_it^1+α_2 x_it^2+α_3 x_it^3+ η_i+ϵ_it i = 1…N t = 1…T (1)

In equation 1, x_it^1 x_it^2 x_it^3 are regressors with different properties. η_i are the individual specific effects, which are regarded as nuisance parameters. ϵ_it is the i.i.d. error term. To clarify this more:
x_it^1 is an endogenous regressor, i.e. E[x_it^1 ϵ_it ]≠0 for all t. x_it^2 is a predetermined regressor, i.e. E[x_it^2 ϵ_is ]≠0 for all t > s. x_it^3 is a exogenous regressor, i.e. E[x_it^3 ϵ_is ]=0 for s,t= 1…T. η_i is the individual effect, possibly correlated with the regressors x_it^1 x_it^2 x_it^3 . Please note that ^ does not represent a to the power operation in this case.

I would like to make the following table for pooled OLS, fixed effects, Arellano Bond (1 and 2 step) and Blundell bond (only 2-step) estimator for equation 1 (large N small t estimators).

Estimator - Transformation used by the estimator - Sufficient condition for a consistent estimate of α' in (1) - Necessary condition for a consistent estimate of α' in (1) -Necessary modifications of the standard errors for robust inference - Reference

However, most references i find do not distinguish between sufficient and necessary conditions for consistency. This is especially the case for the somehow simpler estimators, i.e. Pooled ols and Fixed effects. Does anybody know good references where the properties of these estimators are derived? Or can anybody help me out with distinguishing between (relevant) sufficient and necessary conditions.

Thanks in advance,
Yoram