I am testing whether financial access is correlated with the education of young individuals using a longitudinal panel.

Among the controls I am using there is parents' education that is a determinant of child's education. Nevertheless, there are a lot of missing, thus adding it I drastically reduce my sample but with still a significant number of observations (more or less from 11,000 to 1,700). To remove it would increase the sample and gives me more significant results. I also include household income as control, that in part captures the information relative to parents' education since they are partially correlated.

My question is whether is better to keep the control losing most of the sample or to remove it with the risk of omitted variable bias.