A link between a physical attribute and salary, or crime, does not necessarily mean cause and effect. Mr. Mocan pointed out that we do not know why someone who is overweight, unattractive or short is at a disadvantage in the labor market or more likely to commit a crime. It could be employer discrimination, customer preference or that the physical attribute may make the worker less productive. If a job involves carrying heavy loads, for instance, brawn would be an advantage.

That is what both Howard Bodenhorn, an economist at Clemson University, and Mr. Price concluded from 19th-century prison records. In that era increased body weight was associated with a lower risk of crime. In the 21st century, though, in which service jobs are much more common, Mr. Price found that being overweight was linked to a higher risk of crime.

Mr. Mocan and Erdal Tekin, an economist at Georgia State University, analyzed data from a national survey of adolescent health that involved 15,000 high school students who were interviewed in 1994, 1996 and 2002. They found that being unattractive in high school was correlated with a lower grade point average, more problems with teachers and suspensions.

Other studies have found that shorter students tend to participate less frequently in clubs and sports. As a result these students may suffer a drop in self-esteem or not develop certain kinds of social skills that are useful later in life, the two economists theorized.

According to their study, both men and women who were rated unattractive (as rated on a five-point scale) in high school were more likely to commit — or at least more likely to be caught while committing — one of seven crimes, including burglary and selling drugs, than those rated average or attractive.

Mr. Price said anthropometric economics was based on the work of economic historians — including the Nobel Prize-winner Robert Fogel, John Komlos at the University of Munich and Richard H. Steckel at Ohio State University — who have used height and weight to assess changing social conditions.

Since biologists believe that 80 percent of height is determined by genetics and 20 percent by environmental conditions, height — and sometimes weight — can be an index of childhood nutrition, health care and exposure to disease. Thus smaller stature may be a sign of an impoverished upbringing.