Factors contained in the unobserved effect? I try to study differences in health care cost between counties over a several years period, using a fixed effects model. I use a cost measure as dependent variable and have some demographic, geographical, social and size-related factors as explanatory variables.
What are some of the factors you think could be contained in the unobserved effect, $a_i$?
 A: Given that you mention geographical factors, the geography and size of a county will typically not change over time. So if these are unobserved fixed effects that have an effect on health care spending, e.g. counties with a moderate climate might need to spend less than counties with extreme weather conditions, then this will be in $a_i$.
Depending on the length of your time dimension, this might also include infrastructure (for instance, it takes a lot of time to build a new hospital) or industry structure (counties with heavy industries might have more accidents per capita and thus higher health care costs). The last example with the industries is perhaps seemingly far fetched but all of this is speculation. Unless you actually observe the fixed factors you do not know what is included in $a_i$. In this sense, if you want to interpret the fixed effects it is also worth remembering that $a_i$ is a kitchen sink. All of the mentioned effects will be somehow absorbed in this one fixed effect per county.
