README.md
In affinitymatrix: Estimation of Affinity Matrix

affinitymatrix

The goal of affinitymatrix is to provide a set of tools to estimate matching models without frictions and with Transferable Utility starting from matched data. The package contains a set of functions to implement the tools developed by Dupuy and Galichon (2014), Dupuy, Galichon and Sun (2019) and Ciscato, Galichon and Gousse (2020).

estimate.affinity.matrix estimates the affinity matrix of the matching model of Dupuy and Galichon (2014), performs the saliency analysis and the rank tests. The user must supply a matched sample that is treated as the equilibrium matching of a bipartite one-to-one matching model without frictions and with Transferable Utility. For the sake of clarity, in the documentation we take the example of the marriage market and refer to “men” as the observations on one side of the market and to “women” as the observations on the other side. Other applications may include matching between CEOs and firms, firms and workers, buyers and sellers, etc. An example is provided below.
estimate.affinity.matrix.lowrank estimates the affinity matrix of the matching model of Dupuy and Galichon (2014) under a rank restriction on the affinity matrix, as suggested by Dupuy, Galichon and Sun (2019). In their own words, “to accommodate high dimensionality of the data, they propose a novel method that incorporates a nuclear norm regularization which effectively enforces a rank constraint on the affinity matrix.” This function also performs the saliency analysis and the rank tests. This function is a potential alternative to estimate.affinity.matrix when the number of matching variables is low relatively to the number of observed matches or when the researcher believes that the number of dimensions of the matching problem is much lower than the number of observed variables considered.
estimate.affinity.matrix.unipartite estimates the affinity matrix of the matching model of Ciscato, Gousse and Galichon (2020), performs the saliency analysis and the rank tests. The model is called unipartite (otherwise known as the “roommate problem”) and differs from the original Dupuy and Galichon (2014) since all agents are pooled in one group and can match within the group. For the sake of clarity, in the documentation we take the example of the same-sex marriage market and refer to “first partner” and “second partner” in order to distinguish between the arbitrary partner order in a database (e.g., survey respondent and partner of the respondent). Note that in this case the variable “sex” is treated as a matching variable rather than a criterion to assign partners to one side of the market as in the bipartite case. Other applications may include matching between coworkers, roommates or teammates.