<p><p>Suppose V and U are two independent mean zero random variables, where V has an asymmetric distribution with two mass points and U has a symmetric distribution. We show that the distributions of V and U are nonparametrically identified just from observing the sum V +U, and provide a rate root n estimator. We apply these results to the world income distribution to measure the extent of convergence over time, where the values V can take on correspond to country types, i.e., wealthy versus poor countries. We also extend our results to include covariates X, showing that we can nonparametrically identify and estimate cross section regression models of the form Y = g(X;D*)+U, where D* is an unobserved binary regressor.</p></p>
Authors
![Arthur Lewbel](/sites/default/files/styles/square_desktop/public/2022-07/Arthur%20Lewbel.png?itok=MXnJtTf7)
Research Associate Boston College
Arthur is a Research Associate of the IFS and holds the Barbara A. and Patrick E. Roche chair in economics at Boston College.
![Person graphic](/sites/default/files/styles/square_desktop/public/2022-06/IFS-person-graphic.png?itok=hWCtTSrz)
Yingyong Dong
Working Paper details
- DOI
- 10.1920/wp.cem.2009.1609
- Publisher
- IFS
Suggested citation
Dong, Y and Lewbel, A. (2009). Nonparametric identification of a binary random factor in cross section data. London: IFS. Available at: https://ifs.org.uk/publications/nonparametric-identification-binary-random-factor-cross-section-data (accessed: 3 July 2024).
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