Terms of Endearment: An Equilibrium Model of Sex and Matching

May 2013
Peter Arcidiacono, Andrew Beauchamp, Marjorie McElroy

We develop a two-sided directed search model of relationship formation which disentangles male and female preferences over partner characteristics and different relationship terms, using only a cross-section of observed matches. Individuals gain utility from relationships and direct their search for a partner on the basis of (i) the terms of the relationship, (ii) the partners' characteristics, and (iii) the endogenously determined probability of matching. If men outnumber women, in equilibrium 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 this equilibrium matching model with high school relationships. Variation in gender ratios is used to uncover male and female preferences. Estimates from this 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. Counterfactual simulations show the matching environment black women face is the primary driver of the large differences in sexual activity among white and black women.