The Sex and Money Study Is Misleading.--

Todd Zywicki mentioned the release of a study of sex, money, and happiness by economists David Blanchflower and Andrew Oswald. When I followed the SSRN link he gave, it required $25 to download it. Instead, I went through my university's online library card catalog, which directed me to a free link for university subscribers, so others at universities might try to get the paper for free that way. The Blanchflower/Oswald article was first posted online last May as a working paper on SSRN and the National Bureau of Economic Research .

In June, the study caused a flurry of comments, from the Wall Street Journal to the Jay Leno show. The main finding discussed in public was not the one that Todd noted (that sex leads to happiness), but rather that those with higher incomes did not have sex more often than those with lower incomes. But it appears that actually people with higher incomes do have more frequent sex, as I discovered when I reran some of their analyses using the same database they used, the General Social Survey.

Unfortunately, in their May working paper Blanchflower and Oswald had misunderstood the database they were using and all their data analysis needed to be redone (as they agreed when I pointed this out to them). Let me explain. In their working paper, Blanchflower and Oswald were under the impression that the General Social Survey (GSS), which they used, was a random sample of individuals. But the GSS, like nearly all large surveys of the general public, is a multi-stage probability sample, not a random sample. More seriously, the GSS is a household survey, not an individual survey. They interview only one person in each household. If you don't weight their results by the number of adults in the household, then households with only one adult are oversampled compared to married couples or larger households. For example, in their working paper Blanchflower and Oswald reported that 22% of subjects reported no sexual partners in the last year. Once one properly weights for household size, the real numbers for people in their database, the 1989-2002 GSS, is 17.6% having no sexual partners in the last year. People who live alone have less frequent sex, so it is important not to overweight those who live alone.

In the article they just published, Blanchflower and Oswald corrected this error as well as a minor one that I also pointed out in an email to them. They reran their data accounting for the number of adults in each household, and acknowledged my help in recommending the weighting protocol that they used to do this.

Last summer I raised one other concern that they did not substantially deal with in the final paper. And as I rerun numbers tonight using the same database they used, I think this third concern is even more of a problem than I thought when I corresponded with them last summer. That is the finding that was most trumpeted by the press in June, that money does not buy sex. In their published paper, they write:

What is the connection between income and frequency of sex? Interestingly, Table 5 finds that it is zero for both men and women. We know from these equations that money does seem to buy greater happiness. But it does not buy more sex. In both columns 5 and 6 of Table 5, family income enters with rather weak t statistics.

But the simple correlation in the GSS database that they used between family income and the frequency of sex is .12, which is statistically significant. (Also significant are measures more commonly used for ordinal variables, such as Somer's d, gamma, Spearman's rho, and Kendall's tau.) So, contrary to their paper, there is a "connection between income and frequency of sex." Why didn't they find any in their Table 5? The answer is that Blanchflower and Oswald did regression equations that computed the effect of family income on sexual activity, net of other predictors, such as marital status and full-time employment.

The Blanchflower/Oswald study finds that married people have much more frequent sex. And the GSS shows that married people have much higher family incomes, in part because they often have two incomes to pool. Thus, it is not surprising that the relationship between family income and sexual frequency is primarily through the path of marital status. So net of marriage and some other variables, family income has no additional effect on sexual frequency. Another way of telling a story consistent with the data is:

1. Adults with higher family incomes have somewhat more frequent sex.
2. This is mostly because married people have much more sex, and adults who are married tend to have much higher family incomes.

Thus, people should recognize that there is a positive relationship between income and sexual frequency, but this relationship appears to occur through other variables (such as marriage) that are related both to sexual frequency and to family income.

UPDATE: Ann Althouse thoughtfully raises a point that I had intended to discuss but my post was already long--the causal order of all this. Are people with money (or expectations to earn money) more attractive to the opposite sex, or is it simply that when two people marry, their family income tends to go up because their family is more likely to have 2 incomes? Does expected income cause marriage or does marriage cause higher family income--or both?