Is there a genetic cause of midgets?

Likely yes.: It is very likely that there is a genetic component to this. There are issues like achondroplasia or dwarfism that are definitely genetic in origin. Height is very often a result of genetic selection in plants and animals and people are no exception. Excess in height is also genetic. Abraham lincoln is a very good exmple of marfan's syndrome, a disorder with great height as a feature.