Identifying the Average Treatment Effect in a Two Threshold Model

Assume individuals are treated if a latent variable, containing a continuous instrument, lies between two thresholds. We place no functional form restrictions on the latent errors. Here unconfoundedness does not hold and identification at infinity is not possible. Yet we still show nonparametric point identification of the average treatment effect. We provide an associated root-n consistent estimator. We apply our model to reinvestigate the inverted-U relationship between competition and innovation, estimating the impact of moderate competitiveness on innovation without the distributional assumptions required by previous analyses. We find no evidence of an inverted-U in US data.