People with a high school diploma earn significantly more than those without one. I haven't seen the statistics, but I'd imagine that people with a GED earn somewhat more than people who just drop out.
Why don't we scale unemployment benefits with education completed? As in, you get more in terms of unemployment benefits if you have completed high school than if you have just done a GED, and more for a GED than if you never got anything. You could even pay more for higher levels - Associates and Bachelors.That's a peripheral decision - the major point would be to get people to go back and get their high school diplomas, or prevent them from dropping out. So while it could be valuable to scale up unemployment benefits with each level of education, the scale is most important at the bottom, not the top - the bottom has higher unemployment, it's easiest to go and finish the degree and the education of the bottom is where the US is falling short, not education of the top, who remain extremely highly skilled by world standards.
Someone unemployed has time to go and advance towards those degrees; job searching doesn't usually take all of your time (you have to wait for interviews, etc).