Let's talk about sex

No date for the weekend?Feeling a bit desperate? This NBER paper (No. 16517) tells you what you need to know (who says economics isn't useful?).
Terms of Endearment: An Equilibrium Model of Sex and Matching
Peter Arcidiacono, Andrew W. Beauchamp, Marjorie B. McElroy

We develop a directed search model of relationship formation which can disentangle male and female preferences for types of partners and for different relationship terms using only a cross-section of observed matches. Individuals direct their search to a particular type of match on the basis of (i) the terms of the relationship, (ii) the type of partner, and (iii) the endogenously determined probability of matching. If men outnumber women, they tend to trade a low probability of a preferred match for a high probability of a less-preferred match; the analogous statement holds for women. Using data from National Longitudinal Study of Adolescent Health we estimate the equilibrium matching model with high school relationships. Variation in gender ratios is used to uncover male and female preferences. Estimates from the structural model match subjective data on whether sex would occur in one's ideal relationship. The equilibrium result shows that some women would ideally not have sex, but do so out of matching concerns; the reverse is true for men.

Regression as a matching estimator: Oaxaca-Blinder rides again

Propensity score matching is a well known method of estimating treatments effects with observational data where the treatment is binary and it is assumed there is no selection on unobservables. To recall: one has data on individuals who have been treated. One would like to form a control who are otherwise identical (on average) but who were not treated.
One could match on characteristics but if the dimension of the X's is high that gets very difficult. It turns out that, due to a famous result of Rosenbaum & Rubin, given a key assumption, matching on the probability of being treated (the propensity) is equivalent.
So the norm is to model this probability with say a logit or probit, estimate the predicted probability and form your control group. There are several ways of doing this.
So what if you used a linear probability model instead? Well it turns out that, like speaking prose, you may have been doing this all along without realizing it. In a recent paper P. Kline shows that such a procedure is equivalent to our old friend the Oaxaca-Blinder estimator well known to de-composers. Aside from being easy to do it has several other nice features like being unbiased in finite samples and ensuring exact covariate balance between the two groups in circumstances where it is not guaranteed by other estimators.
For a nice introduction to matching methods see Conniffe et al.