Using cross-sectional data in pooled time-series analysis

I'm doing a pooled time-series regression analysis of GHG emissions, relative to aims in the Kyoto-protocol (annual observations 1990-2008, country level).

Unfortunately, a few of the variables that I want to include in my model don't have time-series qualities. The obvious solution to this problem would be to do a cross-sectional analysis of this piece of data, but because the sample in my study is limited to Annex B countries in the kyoto-protocol my degrees of freedom would be very low if I applied such an approach(N=39).

On the other hand one could assume that the values of the variables that don't have time-series qualities would not change much over time. What I would like to do then is to use cross-sectional data in my pooled time-series dataset, simply by plotting the cross-sectional values for every year in the pooled time-series dataset and then run a random effects regression.

If someone would like to comment on this approach, I would be grateful. I sort of feel like the approach is "cheating statistically" in order to achieve a high amount of units. How does it affect my results? What would I be especially aware of when I access the results?