Using unbalanced panel-data (Unbalanced Panel: n=54, T=81-307, N=11138), I estimated both FE and FD models. My understanding that they are analogous for T>2 and if they produce different results, then it usually indicates a violation of the strict exogeneity assumption and therefore the FD is more consistent as it uses a weaker form of strict exogeneity than FE.
In R
, using the package plm
, the FD results show an estimate of the intercept (and in this case, it turns out to be significant). I am wondering what does the intercept mean and how to interpret its value?
Is it common/correct to force the intercept to zero? The results are a bit different when dropping the intercept but not by much.
Best Answer
The FD intercept is the linear time trend coefficient in levels:
$$y_{i,t+1}-y_{i,t}=\alpha_i-\alpha_i + \beta\cdot (x_{i,t+1}-x_{i,t})+\gamma \cdot (t+1-t)+\varepsilon_{i,t+1}-\varepsilon_{i,t}$$
You can add time to your FE spec to check if this is the culprit.
Also some good ideas in this question on why $FD \ne FE$.