BASIC ECONOMETRICS - Panel data

Why are OLS standard errors invalid in panel data?

Repeated observations on the same individuals mean errors are likely correlated over time within an individual. OLS coefficients may remain unbiased and consistent, but standard errors will be incorrect unless clustering is used.

What is the RE assumption?

The unobserved individual effect (Xikt) must be uncorrelated with all explanatory variables (ui).

Why is the RE assumption often unrealistic? COV(Xikt,ui) =0

Unobserved time-invariant characteristics (ability) are often correlated with explanatory variables.

How do you identify the sign of omitted variable bias using FE and OLS estimates?

If B(ols) > B(FE) - then OLS is likely upward biased. If B(ols) < B(FE) - then OLS is likely downward biased.

What does it mean if the OLS coefficient is larger than the FE coefficient?

The omitted individual effect is positively correlated with both the regressor and the outcome, causing upward omitted variable bias.

Why does FE not report coefficients for time-invariant variables?

The FE estimator subtracts each individual's time mean. Therefore the variable is perfectly collinear with the individual fixed effect and cannot be estimated.

What are time invariant variables?

Variables that do not change during the sample period

What variation identifies FE estimates?

Within-individual variation over time.

Why are the coefficients on experience and the time trend not separately identified in a Fixed Effects model with a balanced panel? equation

Exper(it) = exper(i1) + (t – 1)

Why can't experience and a time trend be separately identified in FE?

Experience increases mechanically over time, so it is perfectly correlated with the time trend. Therefore, the Fixed Effects estimator cannot separately estimate the effects of experience and time.

Why are mean variables included in a CRE model?

To allow the individual effect to be correlated with the explanatory variables.

Why do time-invariant variables not appear as means in CRE?

For a time-invariant variable X(bar)i = Xi, Including both creates perfect multicollinearity.

What are the hypotheses for the CRE test?

H0: B(jm) = 0 ; H1: at least one B(j) not 0

What does the null hypothesis of the CRE test mean?

Chissq_q, where q is the number of restrictions

CRE test decision rule?

At the 5% significance level, reject H0 if Chissq > Chissq(0.95,q)

CRE test conclusion if χ2>χc2

We reject H0. There is sufficient evidence that the mean variables are jointly significant. Therefore, the Random Effects estimator is not appropriate and the Correlated Random Effects model is preferred.

CRE test conclusion if χ2<χc

We fail to reject H0. There is insufficient evidence that the mean variables are jointly significant and the sample evidence is consistent with Random Effects estimator being appropriate