Latent indices in assortative matching models
A large class of two-sided matching models that include both transferable and non-transferable utility result in positive assortative matching along a latent index. Data from matching markets, however, may not exhibit perfect assortativity due to the presence of unobserved characteristics. This pape...
| Main Authors: | , |
|---|---|
| Other Authors: | |
| Format: | Article |
| Published: |
The Econometric Society
2018
|
| Online Access: | http://hdl.handle.net/1721.1/113699 https://orcid.org/0000-0001-5002-0374 |
| _version_ | 1811095051126702080 |
|---|---|
| author | Diamond, William Agarwal, Nikhil |
| author2 | Massachusetts Institute of Technology. Department of Economics |
| author_facet | Massachusetts Institute of Technology. Department of Economics Diamond, William Agarwal, Nikhil |
| author_sort | Diamond, William |
| collection | MIT |
| description | A large class of two-sided matching models that include both transferable and non-transferable utility result in positive assortative matching along a latent index. Data from matching markets, however, may not exhibit perfect assortativity due to the presence of unobserved characteristics. This paper studies the identification and estimation of such models. We show that the distribution of the latent index is not identified when data from one-to-one matches are observed. Remarkably, the model is nonparametrically identified using data in a single large market when each agent on one side has at least two matched partners. The additional empirical content in many-to-one matches is demonstrated using simulations and stylized examples. We then derive asymptotic properties of a minimum distance estimator as the size of the market increases, allowing estimation using dependent data from a single large matching market. The nature of the dependence requires modification of existing empirical process techniques to obtain a limit theorem. Keywords: matching; identification; estimation |
| first_indexed | 2024-09-23T16:09:44Z |
| format | Article |
| id | mit-1721.1/113699 |
| institution | Massachusetts Institute of Technology |
| last_indexed | 2024-09-23T16:09:44Z |
| publishDate | 2018 |
| publisher | The Econometric Society |
| record_format | dspace |
| spelling | mit-1721.1/1136992022-09-29T18:39:36Z Latent indices in assortative matching models Diamond, William Agarwal, Nikhil Massachusetts Institute of Technology. Department of Economics Agarwal, Nikhil A large class of two-sided matching models that include both transferable and non-transferable utility result in positive assortative matching along a latent index. Data from matching markets, however, may not exhibit perfect assortativity due to the presence of unobserved characteristics. This paper studies the identification and estimation of such models. We show that the distribution of the latent index is not identified when data from one-to-one matches are observed. Remarkably, the model is nonparametrically identified using data in a single large market when each agent on one side has at least two matched partners. The additional empirical content in many-to-one matches is demonstrated using simulations and stylized examples. We then derive asymptotic properties of a minimum distance estimator as the size of the market increases, allowing estimation using dependent data from a single large matching market. The nature of the dependence requires modification of existing empirical process techniques to obtain a limit theorem. Keywords: matching; identification; estimation 2018-02-15T20:10:59Z 2018-02-15T20:10:59Z 2017-11 2016-11 2018-02-13T17:33:34Z Article http://purl.org/eprint/type/JournalArticle 1759-7323 1759-7331 http://hdl.handle.net/1721.1/113699 Diamond, William, and Agarwal, Nikhil. “Latent Indices in Assortative Matching Models.” Quantitative Economics 8, 3 (November 2017): 685–728 © 2017 The Authors https://orcid.org/0000-0001-5002-0374 http://dx.doi.org/10.3982/QE736 Quantitative Economics Creative Commons Attribution-NonCommercial 4.0 International http://creativecommons.org/licenses/by-nc/4.0/ application/pdf The Econometric Society Wiley |
| spellingShingle | Diamond, William Agarwal, Nikhil Latent indices in assortative matching models |
| title | Latent indices in assortative matching models |
| title_full | Latent indices in assortative matching models |
| title_fullStr | Latent indices in assortative matching models |
| title_full_unstemmed | Latent indices in assortative matching models |
| title_short | Latent indices in assortative matching models |
| title_sort | latent indices in assortative matching models |
| url | http://hdl.handle.net/1721.1/113699 https://orcid.org/0000-0001-5002-0374 |
| work_keys_str_mv | AT diamondwilliam latentindicesinassortativematchingmodels AT agarwalnikhil latentindicesinassortativematchingmodels |