  We provide various norm-based definitions of different types of
cross-sectional dependence and the relations between them. These definitions
facilitate to comprehend and to characterize the various forms of
cross-sectional dependence, such as strong, semi-strong, and weak dependence.
Then we examine the asymptotic properties of parameter estimators both for
fixed (within) effect estimator and random effect (pooled) estimator for linear
panel data models incorporating various forms of cross-sectional dependence.
The asymptotic properties are also derived when both cross-sectional and
temporal dependence are present. Subsequently, we develop consistent and robust
standard error of the parameter estimators both for fixed effect and random
effect model separately. Robust standard errors are developed (i) for pure
cross-sectional dependence; and (ii) also for cross-sectional and time series
dependence. Under strong or semi-strong cross-sectional dependence, it is
established that when the time dependence comes through the idiosyncratic
errors, such time dependence does not have any influence in the asymptotic
variance of $(\hat{\beta}_{FE/RE}). $ Hence, it is argued that in estimating
$Var(\hat{\beta}_{FE/RE}),$ Newey-West kind of correction injects bias in the
variance estimate. Furthermore, this article lay down conditions under which
$t$, $F$ and the $Wald$ statistics based on the robust covariance matrix
estimator give valid inference.
