Panel data: OLS assumptions I am trying to run an econometric panel data (fixed effects) model with about 4000 observations (so not a small dataset). My data consists of transactions (buy and sell). The transactions are linked to a rank (1 to 5) based on the B/M ratio for the company related to the transaction. However, I am having enormous amount of trouble with the following aspect: According to the kdensity plot and the qnorm plot, the residuals does not pass the test of normality. What does this implicate? Are the p-values not to be trusted? What are the minimum requirements to a OLS regression run on panel data?
 
 A: In Econometrics a linear panel data model with the name fixed effects usually refers to estimating the within transformed model by OLS. What are the requirements for this model? Well, let us see. 
Model
We assume a population model of the form:
$$
y_t = x_t \beta +c+u_t,
$$
where $y_t$ is $1\times 1$, $x_t$ is $1\times K$, $\beta$ is $K\times 1$, $c$  is $1\times 1$ and $u_t$ is $1\times 1$. The within transformation subtracts the individual average from all periods:
$$
y_t-\bar y=(x_t-\bar x)\beta +(u_t-\bar u)\\
\tilde y_t = \tilde x_t \beta + \tilde u_t,
$$
where $\sim$ indicates within transformed variables and $c$ disappears because it is time constant.
Identification and consistency
In order to achieve identification and estimate our parameters consistently we need two conditions fulfilled. The first is akin to the population orthogonality assumed in our pooled OLS. Basically we often assume:
$$
E(u_{it}|x_1,x_2,\ldots,x_T,c_i)=0, ~ \forall t \in\{ 1,...T\}.
$$
This assumption is often called strict exogeneity. This implies $E(\tilde u_t|\tilde x_t)=0$. 
The second assumption is a rank condition saying:
$$
rank(E(\tilde x_t ' \tilde x_t^{\,}))=K
$$
In most cases this just tells us to remember to remove time constant observables. 
Efficiency
Under the following condition, the estimator is also efficient:
$$
E(uu'|x,c)=\sigma_u^2 I_T
$$
This basically rules out serial correlation in the (non-transformed) errors. This is usually not the case in empirical work, so that is why a robust variance-covariance matrix is often computed:
$$
\hat{Avar}(\hat\beta)=(\tilde X' \tilde X)^{-1}\left(\sum^N_{i=1}\tilde x_i'\hat{\tilde u}_i\hat{\tilde u}'_i x_i\right)(\tilde X' \tilde X)^{-1},
$$
where big X is $x_i$'s stacked. Notice, we do not need normality of the $u$'s or the $\tilde u$'s.
A: Those deviations from the normal look like they are largely driven by a few outliers.  See what happens when you trim those, and look closely at them to see whether they belong in your model in the first place.  They may have high leverage and thereby drive your estimates.  If you know why they are what they are, and have data on the mechanism, you should control for it, and possible interact it with your regressor of interest.
Also, on a semi-related note, inference in standard OLS depends on an assumption that observations are independent and identically distributed.  The first is almost always violated in panel data, and the second is often violated in general, if you assume that heteroskedasticity is the norm, and that homoskedasticity is a special case.  To get around this, applied econometricians "cluster their standard errors", which corrects for both problems.  Google clustered standard error if you haven't heard of this before; you'll find lecture notes from universities on the subject.  It looks like you're using stata, on which this procedure is trivial to implement: xtreg y x, cluster(clustvar), where the cluster variable is usually the cross-sectional unit, but may be a higher-level unit into which cross-sectional units are aggregated.
