I'm dealing with panel data and I chose to do a regression with cross-sectional fixed effects. Some of my explanatory variables (such as $debt_{it}$) do not show very much variation over the time dimension. In fact, the most interesting variation in $debt_{it}$ (but also in some other variables), is probably the cross-sectional variation (i.e. one country having a higher debt over the entire period under investigation) rather than the variation of debt over time within each country.
Therefore, I believe that demeaning the data by using cross-section fixed effects may elimate a lot of interesting information. The $H_{0}$ of redundant fixed effects is strongly rejected, and the Hausman test strongly rejects the consistency of the random effects estimator. Doing a pooled estimation, rather than F.E. estimation, more than doubles the estimated coefficient to debt.
In an attempt to 'retrieve' the valuable cross-sectional information, I plotted each country's fixed effect against each country's average level of debt over the time period. There was a significant correlation $(p<0,01)$ between the averaged debt and the fixed effect. Intuitively, it seems to me that I can conclude that (even though the coefficient to $debt_{it}$ is possibly insignificant, depending on the specification, I'm still working on this) a higher debt does result in higher interest rate spreads (which is the dependent variable).
These are my questions:
- Is my intuition correct?
- If it is not, which I assume to be the case since I have never come across a similar reasoning, where exactly does my reasoning fail? Can you provide some intuition or an accessible reference dealing with the issue?
- Are there any estimators that are better equipped to use cross-sectional variation in the data than the within-estimator?