Working Paper: NBER ID: w28327
Authors: Shakeeb Khan; Arnaud Maurel; Yichong Zhang
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 paper 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: factor structures; binary response models; treatment effects; identification
JEL Codes: C14; C21; C25; C38
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| Imposing a factor structure (C38) | Point identification of the coefficient associated with the endogenous regressor in the outcome equation (C20) |
| Weaker assumptions (D89) | Identification of parameters compared to traditional models (C51) |
| Factor structure (C38) | Identification of the relationship between unobservables in the treatment and outcome equations (C32) |
| Access to at least two continuous measurements of the common factor (C39) | Sufficient for identification in more general factor structures (C38) |