Tweaks & tests on my first essay - revisions

The Breusch-Pagan Lagrange multiplier test for random effects tests if variances of groups are zero. The BP LM values reject the null only in the first and second model, suggesting that random effects should be used in these cases against an OLS estimator.
Using a likelihood-ratio test, homoskedasticity is rejected firmly in all models. Thus I take this into account by using White cross-sectional standard errors which are robust. Beyond this, serial correlation could be biasing the estimates so I use the test described by Wooldridge (2002) and implemented in Stata. However, the null of no serial correlation can be rejected at 5 percent significance lavels in all relevant models, proving that this is not an issue for these estimations.
To make sure that my regressions are not spurious, I perform the most common two panel unit root tests involving regressions on lagged difference: Levin Lin and Chu (2002) which assumes a cross-sectional common unit root and Im, Pesaran and Shin (2003) that allow for individual unit root processes across sections.