for the average treatment response by imposing smoothness conditions alone, by combining them with monotonicity …

able to impose monotonicity of the estimated function. The use of such a shape restriction may signi cantly improve the … constrained estimator that imposes the monotonicity, on the other hand, signi cantly reduces variance by removing oscillations of …

treatment. This last condition, the so-called monotonicity condition, is often implausible. This paper starts by showing that … actually, IVs are still valid under a weaker condition than monotonicity. It then derives conditions that are sufficient for … applications where this weaker condition is applicable while monotonicity is not. Overall, this paper extends the applicability of …

identification through a monotonicity assumption in the treatment choice equation. We discuss the key conditions, the role of control …

and the IV estimand is no longer interpretable as a causal effect under a weaker version of monotonicity, i.e. when there …