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 paper we attempt to formally quantify their informational content in a bivariate system often employed in the treatment eﬀects literature. Our main ﬁndings are that under the factor structures often imposed in the literature, point identiﬁcation of parameters of interest, such as both the treatment eﬀect and the factor load, is attainable under weaker assumptions than usually required in these systems. For example, we show is that an exclusion restriction, requiring an explanatory variable in the outcome equation not present in the treatment equation is no longer necessary for identiﬁcation. Furthermore, we show support conditions of included instruments in the outcome equation can be substantially weakened, resulting in settings where the identiﬁcation results become regular. Under such settings we propose a estimators for the treatment eﬀect parameter, the factor load, and the average structural function that are root-n consistent and asymptotically normal. The estimators’ ﬁnite sample properties are demonstrated through a simulation study and in an empirical application, where we implement our method to the estimation of the civic returns to college, revisiting the work by Dee (2004).
Factor Structures, Discrete Choice, Treatment Eﬀects
Information Security | Management Information Systems
KHAN, Shakeeb; MAUREL, Arnaud; and ZHANG, Yichong.
Informational content of factor structures in simultaneous discrete response models. (2015). 1-42. Research Collection School Of Economics.
Available at: http://ink.library.smu.edu.sg/soe_research/2057
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