UCLA

Many social processes studied by demographers can be viewed as two-sided matching markets. For example, heterosexual marriages, job searching, and residency assignments for medical school graduates all require members of two disjoint groups to mutually consent to form a relationship, or ``match.'' Yet the underlying mechanisms dictating such processes are often opaque. Demographers require statistical models for partnership formation that separate the underlying preferences individuals have for various types of partners from the availability of such partners.

To address this need, in my dissertation I develop a revealed preferences model (RPM) which captures the complex interplay between discrete characteristics, both observed and unobserved, of individuals and the availabilities of potential partners to form a stable set of partnerships in networks of different sizes. The major contribution of this work is the introduction of a model that not only estimates partnership outcomes in a two-sided matching market, but also is flexible enough to handle realistic data drawn from various sampling schemes and population types.

Contextualizing the problem in the heterosexual marriage market setting, in the first two chapters I present background information on the two-sided matching market problem and and introduce the revealed preferences model novel statistical methodology to compute point estimates for preferences parameters. I validate the approaches with multiple simulation studies and demonstrate RPM’s key novel contribution, the ability to recover societal preferences for partners independent of the types of partners available. I additionally use these simulation studies to conduct a comprehensive study of model performance under different conditions, such as varying population and sample sizes and different sampling schemes.

To facilitate the use of the model in practical settings, I propose additional novel tools such as bootstrap procedures for bias-correcting parameter estimation and empirical and analytical approaches for computing uncertainty intervals for the preference parameter estimates. I discuss the process of model selection and propose several methods for assessing the goodness-of-fit, including quantitative and visual procedures. To my knowledge this is the first time these procedures have been discussed in literature.

To aid continued development of models for two-sided matching markets, I present a review of the two major frameworks that have been hypothesized as underlying the partnership process. While developments in marriage modeling under these different frameworks have continued in parallel over the last several years, this is the first time that the assumptions and implications of the two frameworks have been compared clearly side-by-side using consistent notation. I bridge the gap in literature between the two settings by demonstrating how RPM can be adapted to model the marriage process in either scenario.

Throughout the dissertation, I continue to validate the proposed procedures through extensive simulation studies, and I show how the model can be applied and interpreted given survey data from the 2008 Survey on Income and Program Participation.