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Informational Content of Factor Structures in Simultaneous Binary Response Models

Shakeeb Khan (Boston College, US)

Arnaud Maurel (Duke University, US)

Yichong Zhang (Singapore Management University, Singapore)

Essays in Honor of Joon Y. Park: Econometric Methodology in Empirical Applications

ISBN: 978-1-83753-213-1, eISBN: 978-1-83753-212-4

Publication date: 24 April 2023

Abstract

We study the informational content of factor structures in discrete triangular systems. Factor structures have been employed in a variety of settings in cross-sectional and panel data models, and in this chapter we formally quantify their identifying power in a bivariate system often employed in the treatment effects literature. Our main findings are that imposing a factor structure yields point-identification of parameters of interest, such as the coefficient associated with the endogenous regressor in the outcome equation, under weaker assumptions than usually required in these models. In particular, we show that a “non-standard” exclusion restriction that requires an explanatory variable in the outcome equation to be excluded from the treatment equation is no longer necessary for identification, even in cases where all of the regressors from the outcome equation are discrete. We also establish identification of the coefficient of the endogenous regressor in models with more general factor structures, in situations where one has access to at least two continuous measurements of the common factor.

Keywords

Acknowledgements

Acknowledgments

We thank the Co-Editor, Simon Lee, an anonymous referee, Arthur Lewbel, Serena Ng, and seminar participants at Arizona State University, Emory, Michigan State, Shanghai University of Finance and Economics, University of Arizona, as well as conference participants at the 2015 SEA meetings for helpful comments. We also thank Zhangchi Ma and Qingsong Yao for excellent research assistance. Zhang acknowledges the financial support from Singapore Ministry of Education Tier 2 grant under grant MOE2018-T2-2-169 and the Lee Kong Chian fellowship.

Citation

Khan, S., Maurel, A. and Zhang, Y. (2023), "Informational Content of Factor Structures in Simultaneous Binary Response Models", Chang, Y., Lee, S. and Miller, J.I. (Ed.) Essays in Honor of Joon Y. Park: Econometric Methodology in Empirical Applications (Advances in Econometrics, Vol. 45B), Emerald Publishing Limited, Leeds, pp. 385-410. https://doi.org/10.1108/S0731-90532023000045B016

Publisher

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Emerald Publishing Limited