To be sure, lowering the price of community college may improve the chances that students who would not otherwise have attended any college will go somewhere. We also have to recognize, however, that by changing the relative price of education in the two and four-year sectors, the Obama proposal may actually lower degree completion rates for students induced to choose a community college option over the chance to enroll from the start at a four-year institution.”

The broader question is to what extent completion rates are lowered by failures of students to attend academically strong institutions for which they are qualified.

By now there is a considerable literature documenting the importance of an appropriate “match” in determining educational outcomes. In brief, these studies show that students who enroll at institutions with test scores (and other academic credentials) at or above their own levels do much better in earning degrees, and in earning them in a timely way, than do students who “undermatch” — by which we mean simply that they go to schools that are less selective than schools for which their qualifications could well have led to their admission.

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