Meyer, Viscusi and Durbin (MVD) measured the impact of increases in workers compensation on the amount of time a person would stay out of work if they were injured. They say in the paper that benefits are a function of wages before injury and at the same time previous earning influence your desire to return to work so the "benefits of returning to work and the economics gains from receiving benefits are largely influence by a common variable"
Kruger used the same approach and said there is
"difficulty of identifying separate benefit and wage effects because benefits are typically determined as a function of the worker's pre-disability wage."
I understand why using difference in difference is a desirable methodology to use in this context because we have a policy that has been implemented on high earners (treatment group) but not low earner (control group) and we have data before and after. However I don't understand how what they have described in the 2 quotes causes a problem.
Intuitively I understand that people with more benefits now may choose to stay on them for longer because they are more comfortable, and people who would not have bothered claiming in the past when they would have received less money now do claim because they receive more. But I still don't feel like I really get their explanations.
I guess what confuses me is that we have a control variable for wages and we know how much a person will be paid in benefits so why is diff n diff superior to OLS over the 2 time periods using the coefficient of benefits paid as the impact of benefits on duration of injury compensation.
Can anyone give their own interpretation to these 2 quotes and the reason the both authors feel that the influence of a common variable results in the need for difference in difference.