I'm trying to understand the implications of an intervention which is not randomly allocated in a quasi-experimental setting. The intervention is receiving a license for shale gas exploration in the UK. Receipt of licensure is based on certain characteristics, such as viability of shale gas development, population density, the impact on local residents etc. What does this non-random licensure imply? Does it mean that there is unobserved heterogeneity or an endogeneity problem? Any pointers would be appreciated!!
First of all, it is necessary to identify the outcome(s). In the case you describe, if the variables that differ in distribution between treated and non-treated are also associated with the potential outcomes (i.e. the outcomes in case of treatment and non-treatment respectively), they are confounders. This means that, if you don't control for them, you can't get an unbiased estimate of the treatment effect. Thus, in this case:
1) Yes, there is an endogeneity problem: the treatment effect you would estimate by simple regression would be biased by the fact that there is a correlation between the treatment and the error term (given the error term, in such equation, would also include the effect of confounders, since they are excluded from the regression).
2) Yes, there is unobserved heterogeneity as long as there are factors you don't observe (basically, that you don't include in your model, thus all apart from the treatment itself) that are associated with the outcome.
your case is a one where you have an endogeneity problem due to unobserved heterogeneity.
To address the bias deriving from this issue, there are several methods; however, before thinking at them, a precise definition of the treatment assignment procedure is needed. Thus, how was decided whether the license was granted or not?