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 systems . In particular, we show that an exclusion restriction , requiring an explanatory variable in the outcome equation to be excluded from the treatment equation , is no longer necessary for identification . Under such settings, we propose a rank estimator for both the factor loading and the causal effect parameter that are root-n consistent and asymptotically normal. The estimator's finite sample properties are evaluated through a simulation study. We also establish identification results in models with more general factor structures, that are characterized by nonparametric functional forms and multiple idiosyncratic shocks .
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 .
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systems
models
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an exclusion restriction , requiring
a "non-standard" exclusion restriction that requires
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,
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. Under such settings, we propose a rank estimator for both the factor loading and the causal effect parameter that are root-n consistent and asymptotically normal. The estimator's finite sample properties are evaluated through a simulation study.
, even in cases where all of the regressors from the outcome equation are discrete.
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results
of the coefficient of the endogenous regressor
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that are characterized by nonparametric functional forms and multiple idiosyncratic shocks
in situations where one has access to at least two continuous measurements of the common factor