Before revision:  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.
After revision:  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 , even in cases where all of the regressors from the outcome equation are discrete.