Identifying the average treatment effect in ordered treatment models without unconfoundedness

We show identification of the Average Treatment Effect (ATE) when treatment is specified by ordered choice in cross section or panel models. Treatment is determined by location of a latent variable (containing a continuous instrument) relative to two or more thresholds. We place no functional form restrictions on latent errors and potential outcomes. Unconfoundedness of treatment does not hold and identification at infinity for the treated is not possible. Yet we still show nonparametric point identification and estimation of the ATE. We apply our model to reinvestigate the inverted-U relationship between competition and innovation, and find no inverted-U in US data.