As Good as Married? A Model of Premarital Cohabitation and Learning

Abstract

This article develops a two-sided search-matching model with imperfectly observed types and sequential learning. We use the metaphor of premarital cohabitation and assume that it is initiated to learn more about one's prospective spouse. We show that couples match within classes and that the classes of cohabiting and married couples partially overlap. Couples are more discriminating about whom they marry than whom they cohabit with. We demonstrate that cohabiting individuals eventually learn each other's true type. We show that sequential learning during cohabitation reduces signaling errors and that the Bayes estimator of true type converges almost surely to true type. As noisy information is filtered over time, the risk of mismatch disappears and the aggregate matching pattern based on true types is restored.

Keywords:

• Bayesian learning
• imperfect information
• marriage
• premarital cohabitation
• two-sided search-matching

Notes

¹Among studies in this literature are Collins and McNamara (1990), Smith (2006), Shimer and Smith (2000), Bloch and Ryder (2000), Burdett and Wright (1998), Chade (2001, 2006), and Rao Sahib and Gu (2002a, 2002b).

²In contrast, Hajeeh and Lairi (2009) consider the importance of different traits in marriageability using the analytical hierarchy process approach.

³Models with transferable utility have been used in the context of the labor market. See, for example, Shimer and Smith (2000).

⁴The joint distribution density of (X, Y), f(x, y), is involved in the calculation of Q(x | y) and F(m) in the following way:

When and ϵ ∼N(0, 1), the correlation coefficient ρ between X and Y is , and hence the joint distribution density is

In the case of normal distributions, and should be set equal to ∞ in the text of the article.

⁵For simplicity, we henceforth follow the convention of using lowercase letters to refer both to random variables and their realizations.

⁶Since x is stochastic ex ante, we know that x _t  ⇒ x _t prior to the realization of x. If x is realized, then we have only x _t , where x is a constant ex post. Mathematically, for m _t , a true type x can only be revealed after an infinite amount of time: t = ∞.