When we compare the sexual activity of those with high and low wages, we might worry that there are confounding factors that lead a person to succeed in both the mating market and labor market. For example, if you are persuasive enough to talk someone out of their pants, you may well be persuasive at talking yourself into a raise. If you have the health and energy to be productive at work, those traits help you be more reproductive, too. Simultaneity bias is also plausible: the relationship could run the other way, with higher wages leading to more success in the sex market.
If we wanted to apply gold-standard research methods to this question, we would gather up volunteers, randomize them into treatment and control groups, and expose members of the the treatment group to an intervention that increases their sexual activity. I will leave this intervention to your imagination. We would then compare the wages of the treatment and control group to get the effect of the intervention. A bit more statistical fiddling would get us the causal impact on sex on wages, at least for those who were stimulated to action by the intervention.
In this paper, the author does not run a randomized trial, but instead uses observational data to draw his conclusions - specifically, an instrumental-variables strategy. The idea here is to find a variable (the "instrument") that is correlated with the "treatment" of interest (sex) but is correlated with the outcome (wages) only through that treatment.
In this particular context, an instrument is valid if it 1) is correlated with sexual activity and 2) is not correlated with wages through any channel except sexual activity. The first condition is called the relevance condition and the second the exclusion restriction.
In this paper, the author's identifying assumption is that religiosity has no relationship with economic activity except through its (negative) correlation with sexual activity.
Could religion have a relationship with wages, other than through its "effect" on sex? Are these results believable?
I now channel Max Weber (who penned The Protestant Ethic and the Spirit of Capitalism):
Max says "Ja," and "Nein."