The fair way to compare the two systems, to each other and to systems in other countries, would be to conduct something like a PISA for higher education. That had never been done until late 2013, when the O.E.C.D. published exactly such a study.

The project is called the Program for the International Assessment of Adult Competencies (known as Piaac, sometimes called “pee-ack”). In 2011 and 2012, 166,000 adults ages 16 to 65 were tested in the O.E.C.D. countries (most of Europe along with the United States, Canada, Australia, Japan and South Korea) and Cyprus and Russia.

Like PISA, Piaac tests people’s literacy and math skills. Because the test takers were adults, they were asked to use those skills in real-world contexts. They might, for example, be asked to read a news article and an email, each describing a different innovative method of improving drinking water quality in Africa, and identify the sentence in each document that describes a criticism common to both inventions. The test also included a measure of “problem-solving in technology-rich environments,” reflecting the nature of modern work.

As with the measures of K-12 education, the United States battles it out for last place, this time with Italy and Spain. Countries that traditionally trounce America on the PISA test of 15-year-olds, such as Japan and Finland, also have much higher levels of proficiency and skill among adults.

Of course, all 15-year-olds are required to go to school. College is voluntary. But when the Piaac numbers are calculated for people with different levels of education, America stills falls short of most other countries.

Only 18 percent of American adults with bachelor’s degrees score at the top two levels of numeracy, compared with the international average of 24 percent. Over one-third of American bachelor’s degree holders failed to reach Level 3 on the five-level Piaac scale, which means that they cannot perform math-related tasks that “require several steps and may involve the choice of problem-solving strategies.” Americans with associate’s and graduate degrees also lag behind their international peers.