Graduate schools are seeing higher first-time enrollment. (Brian Davies/The Register Guard via AP)

International students drove enrollment up at graduate schools across the country last fall, delivering the largest one-year increase in first-time graduate enrollment since 2009, according to a study released by the Council of Graduate Schools on Thursday.

The numbers are striking because there is often an inverse relationship between the economy and graduate school enrollment. People pursued advanced degrees in high numbers at the outset of the financial crisis but pulled back amid a protracted recession and the rising cost of attendance. While job prospects have improved, the cost of graduate school continues to climb, along with student debt. The jump in enrollment from 2013 to 2014 shows that students are willing to make the gamble.

And with good reason. A recent study from the St. Louis Fed said people with advanced degrees have much higher lifetime earnings than those with just a bachelor’s or high school diploma. What’s more, the Bureau of Labor Statistics projected that employers will add nearly 2.4 million jobs requiring a graduate or professional degree between 2012 and 2022.

“Greater investments in graduate education and research — supporting both domestic and international students — will be required to keep up with the demand for graduate-level talent in the future,” said Suzanne T. Ortega, the council’s president.

The 636 institutions that responded to the council survey received more than 2 million applications, extended over 850,000 offers of admissions and enrolled nearly 480,000 first-time graduates last fall.

The 3.5 percent increase in new graduate students was bolstered by high enrollment in mathematics, computer science and engineering, all of which experienced double-digit growth with an influx of students from overseas.

Still, for the first time in several years, more domestic students were admitted into graduate programs than in the past five years. The overall number of students pursuing advanced degrees, however, grew by less than 1 percent, with  1.7 million graduates enrolled in certificate, master’s or doctoral programs.

“Total enrollment was really growing at quite a clip until 2009, when it began to peak, and then it dropped after the Great Recession. It’s more or less flat right now,” said Jeff Allum, assistant vice president for research and policy analysis at the council.

The number of new Hispanic students grew by almost 7 percent, while new enrollment by African American students crept up by only 2 percent. Women continue to make up more than half of students entering graduate programs, constituting at least three-quarters of new enrollees in health sciences and public administration. Yet they are still disproportionately underrepresented in science and engineering fields, according to the study.

International students have accounted for more than  two-thirds of the growth in first-time enrollment at graduate schools in the United States from 2004 to 2014. The number of new international graduate students coming to study in the United States rose 11.2 percent from 2013 to 2014, while first-time enrollment of domestic students inched up 1.3 percent.

“The increase in overall enrollments is good news, but the disparity between U.S. and international growth is a cause for concern,” Ortega said.

There is a noticeable gulf between international and domestic students pursuing advanced degrees in science, technology, engineering and math (STEM), fields that are in high demand. About 57 percent of students from abroad are in STEM-related programs, compared with 16 percent of American students, according to the report.

Last fall, 83 percent of all new graduate students were in programs leading to a master’s degree or graduate certificate, and education and business programs alone accounted for about 37 percent of graduate enrollment. At the doctoral level, the health sciences, education, social and behavioral sciences, and engineering  accounted for 56 percent of enrollment.

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