Mathematics – Optimization and Control
Scientific paper
2010-12-09
Mathematics
Optimization and Control
Scientific paper
Choo-Siow (2006) proposed a model for the marriage market which allows for random identically distributed noise in the preferences of each of the participants. The randomness is McFadden-type, which permits an explicit resolution of the equilibrium preference probabilities. The purpose of this note is to prove uniqueness of the resulting equilibrium marriage distribution, and find a representation of it in closed form. This allows us to derive smooth dependence of this distribution on exogenous preference and population parameters, and establish sign, symmetry, and size of the various substitution effects, facilitating comparative statics. For example, we show that an increase in the population of men of any given type in this model leads to an increase in single men of each type, and a decrease in single women of each type. We show that an increase in the number of men of a given type increases the equilibrium transfer paid by such men to their spouses, and also increases the percentage of men of that type who choose to remain unmarried. The verification of such properties helps to substantiate the validity of the model. Moreover, we make unexpected predictions which could be tested: the percentage change of type $i$ unmarrieds with respect to fluctuations in the total number of type $j$ men or women turns out to form a symmetric positive-definite matrix $r_{ij}=r_{ji}$ in this model, and thus to satisfy bounds like $|r_{ij}| \le (r_{ii}r_{jj})^{1/2}$. Along the way, we give a new proof for the existence of an equilibrium, based on a strictly convex variational principle and a simple estimate, rather than a fixed point theorem. Fixed point approaches to the existence part of our result have been explored by others \cite{CSS} \cite{Dag} \cite{Fox}, but are much more complicated and yield neither uniqueness, nor comparative statics, nor an explicit representation of the solution.
Decker Colin
Lieb Elliott H.
McCann Robert J.
Stephens Benjamin K.
No associations
LandOfFree
Unique equilibria and substitution effects in a stochastic model of the marriage market does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Unique equilibria and substitution effects in a stochastic model of the marriage market, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Unique equilibria and substitution effects in a stochastic model of the marriage market will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-76422