The National Academy of Sciences warned a decade ago that young scientists in biomedicine were struggling to launch careers for lack of research money. A NAS report released in January says the situation has grown more “arresting” in all fields: “Without their own funding, young researchers are prevented from starting their own laboratories, pursuing their own research,” writes Johns Hopkins University President Ronald Daniels.

Few would disagree. Research money has been drying up at universities and government research labs since the turn of the century, and young scientists have suffered in particular. Many budding researchers are jumping to the corporate world and applied research, where money and opportunities are more certain. A 2013 study by the Brookings Institution showed a huge, unmet demand for science and math-oriented applicants with advanced degrees. It found workers earning 21% more in jobs requiring STEM skills, and five job openings for every unemployed computer worker compared with one for most other industries. Why not go where you’re wanted?

According to Mr. Daniels, a researcher now lands her first National Institutes of Health grant at 45 years of age, compared with age 38 in 1980. The number of grant recipients younger than 36 in 2010 fell to 3% from 18% in 1983. How many important discoveries haven’t happened as a result?

What’s behind the shortage? Mr. Daniels suggests several reasons, including longer postdoctoral training; a system of applications, demonstrable data and peer review, and a shift in research costs to universities—which typically narrows awards to seasoned, tenured researchers. But perhaps the simplest explanation came from Nobel laureate Michael Levitt of Stanford, who said last year that senior scientists were once able to renew their existing grants and let young scientists compete for unawarded grant money. Now after budget cuts, older scientists are competing “against the kids,” and usually winning.

Mr. Daniels’s proposed solutions are all too predictable: more government investment in research, extended grant periods, more studies on young researchers and a new government committee. The prospect of these solutions working is nil. There simply isn’t enough government money to cover every grant application. Even if the current economic “recovery” continues, it will takes years to return to the golden days of government grants in the late 1980s.