Help with mixed models (spss, time-invariant main predictor, not a growth model)

I have practically no experience with longitudinal data, and really need your help.

I am looking at a sample of firms in a certain industry, and trying to determine whether ownership (foreign or domestic) is a significant predictor of productivity, when controlling for a number of firm-level factors (capital intensity, size, labour skills etc.). The only reason I collected time series data (2004-2008) is in order to maximize the number of observations (many firms only have data for certain years), but also because I was advised to control for firm-level unobserved effects (presumably through fixed-effects regression).

The only statistical software I am familiar with is SPSS, and standard repeated measures analyses cannot handle unbalanced panels (my sample is full of missing data). Also, since my main predictor is time-invariant, I was not sure how to handle that in a fixed-effects regression (as I said, I am not very familiar with panel data). I was therefore advised to use a multilevel-model (SPSS mixed procedure). However, most of the readings available on these models contain instructions on modeling change - which I am absolutely not interested in, as my main interest is in the average difference in productivity between foreign and domestically owned firms (and I don't think there would be much change on this variable in a mere 4 years).

I would be extremely grateful if you could help me figure out an SPSS procedure that would fit my needs better (use longitudinal data simply to control for within-firm unobserved effects, and focus on the across-group time-invariant effect of ownership).

Many, many thanks for your help!