Whether the nation faces a doctor shortage is a matter of debate. But a new study suggests there are already fewer doctors practicing than had been estimated, because of a lag in reporting retirements.

The new study, published in the Oct. 21 issue of The Journal of the American Medical Association, estimates that the United States has 788,000 active doctors  65,000 fewer than calculations have suggested. The doctor work force is also younger than previously estimated, with a greater proportion of doctors in their 20s and 30s and fewer who are 65 and older.

By 2020, there will be 957,000 physicians, the new estimates show, rather than the 1.05 million previously projected. Only 9 percent will be 65 or older, or half as many as had been predicted.

The new analysis used census data to make projections.

“From 2005 to 2020, we project a 20 to 22 percent growth in the number of physicians,” said the paper’s lead author, Douglas O. Staiger, a Dartmouth economist. “But because you start with a lower number, you end up with a lower number in the future  with 9 percent fewer physicians by 2020.”