Background
I have (unbalanced) panel data of a set of agricultural firms. I am attempting to estimate the effect of the surface area of crops (wheat, potatoes, onions, sugar-beets, corn) on the fixed yearly cost of a farm.
Regrettably (but not surprisingly), a fixed effects estimation of the data shows that very little variation in the dependent variable (fixed costs) is explained by variation within an agricultural firm.
As a result I have to resort to a random effects model (to make use of the "between" variation), which will regrettably be biased since $a_{i}$ is extremely unlikely to be uncorrelated with any of the $x_{itj}$
To mitigate this bias, as much as possible, I will include controls that do not change over time. One of the controls I am thinking of including, is farm type. However, farm type, is essentially based on the mix of surface area per crop. As an example, if the total surface area of a farm is more than 50% potatoes, it is a potato farmer. If the wheat is more than 50%, it is a wheat farmer. If it no crop covers more than 50% of the total surface area of the farm, it is a mixed farmer.
Questions
The issue with including farm type that I have is that it feels artificial, since farm type, is essentially determined on the basis of variables that are already included in the model. What is (from an econometric perspective) the effect of including farm type? Is it a good idea to include it? And why or why not?
Are there other approaches that deal with the problem of almost all variation being "between" variation, that might solve my problem?