My colleague Ben Friedman recently drew my attention to an ariticle in the NY Times (June 20) with this piece of news:
Over all, each hour spent exercising (up to 30 hours a week) adds about two hours to a person's life expectancy, according to the Harvard Alumni Study, which has tracked deaths among 17,000 men for more than two decades.This sounds like a good deal. But there are two problems with this information, both of which are familiar to economists.
The first problem is discounting. The cost of exercise is paid today. The benefit of a longer life is obtained at the end of life--at my age, about 30 or 40 years from now. Even with a discount rate of 3 percent, that two hours of future benefit is worth less in present value than the one hour of present cost.
The second, more serious issue is the identification problem. This was aptly summarized in a letter to the Times a few days later:
If those who run regularly are less likely to have a heart attack, does that prove that running regularly is good for the heart? Or does it simply indicate that those with a strong heart and good health otherwise are more likely to enjoy running and do it more regularly? Your advice is probably right. But to know for sure is probably one of the most difficult problems in epidemiology. It would require telling one randomly selected group, ''You run,'' and another similarly selected group, ''You be a couch potato.'' Tricky to organize and tricky to avoid defectors' messing up the study.Absent a controlled experiment, it is hard to know if vigorous exercise is the cause of good health, or good health is the cause of vigorous exercise.
Some years ago, while I was applying for life insurance, I had the chance to chat with a cardiologist about the issue. I was on a treadmill at the time, and his job was to check on my heart to make sure I wasn't likely to die right after the policy was approved. Because he was a captive audience, I took the opportunity to quiz him about the identification problem. He essentially agreed with the point raised in this letter. Running the right controlled experiment, he said, is too costly. As a result, it is almost impossible to know if the derivative of two asserted in the Times article is really the right number. It seems very likely that this estimate is biased upward.
By the way, I did get the life-insurance policy, and it has not turned out to be a good investment so far. Maybe I am getting too much exercise.