Thursday, January 21, 2010

Two new matching papers from Cal Tech

Federico Echenique, emailing from the left coast, sends along links for two new papers:

1) "Aggregate Matchings," joint with SangMok Lee and Matt Shum.

An aggregate matching market is a matching market (M,W,>) in the usual sense, but where we imagine that the elements of M and W are "types" of men and women, and that there may be more than one agent of each type. You can then study "aggregate matchings." For example with 3 types of men and women, these are matrices like

2 3 0
0 1 3
0 0 2

where there are 5 men of type m_1; 2 are married to women of type w_1 and 3 are married to women of type w_2; and so on.

Aggregate matchings are interesting because matching data often comes in this form, and many empirical papers use aggregate matchings.

The focus of the paper is on the empirical implications of stability for aggregate matchings. We ask when there are preferences that make an aggregate matching stable. It turns out that one has to look at a graph defined by the matrix; it's a graph you can draw on the matrix where the vertexes are all the non-zero entries, and there is an edge between v and v' iff they lie on the same row or column. Then the matrix is rationalizable iff the graph does not have two connected cycles. We also look a the model with transfers, and find that rationalizability with transfers is equivalent to the absence of cycles.

In the paper we develop econometric techniques for estimating preference parameters from imposing stability. The techniques are based on a moment inequality we obtain from stability. We have an illustration with US marriage data.
A PDF is in:

2) "Clearinghouses For Two-Sided Matching: An Experimental Study," joint with Alistair Wilson and Leeat Yariv.

This is an experimental paper. We wanted to test the Gale-Shapley mechanism in the lab. We were worried about the effects of direct revelation on experimenter demand: if you give subjects a preference, and then you ask them to report their preference, then they may start thinking about the motives behind the study. So we have a design where subjects go through the steps of the algorithm, making offers and holding on to proposals. We also think this design makes it easier to map actions into outcomes, compared to the direct revealaion alternative.

The findings are: First, 48% of the observed match outcomes are fully stable.
Among those markets ending at a stable outcome, a large majority culminates in the best stable matching for the receiving-side. Second, contrary to the theory, participants on the receiving-side of the algorithm rarely truncate their true preferences. In fact, it is the proposers who do not make offers in order of their preference, frequently skipping potential partners. Third, market char- acteristics affect behavior and outcomes: both the cardinal representation and the span of the core influence whether outcomes are stable or close to stable, as well as the number of turns it takes markets to converge to the final outcome.
A PDF is in:

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