for some closed set C in$_{R}$ $^{2}$. This class of restrictions encompasses any restriction that can be written as for any continuous function g : $_{R}$×$_{R}$ → $_{R}$. For example, shape restrictions on the treatment response function such as MTR, concave response, and convex response can be written in the form (1). Furthermore, identifying the DTE under support restrictions opens the way to identify other parameters such as the DTE conditional on the treated and the untreated in the Roy model, and the DTE conditional on potential outcomes. Example 1 (Monotone Treatment Response) MTR only requires that the potential outcomes be weakly monotone in treatment with probability one: MTR restricts the support of ( Y$_{0}$, Y$_{1}$ ) to the region above the straight line Y$_{1}$ = Y$_{0}$, as shown in Figure 1(a). Example 2 (Concave/Convex Treatment Response) Consider panel data where the outcome without treat- ment and an outcome either with the low-intensity treatment or with the high-intensity treatment is observed for each individual. 5 Let W denote the observed outcome without treatment, while Y$_{0}$ and Y$_{1}$ denote potential outcomes under low-intensity treatment and high-intensity treatment, respectively. Suppose that the treat- ment response function is nondecreasing and that either ( W, Y$_{0}$ ) or ( W, Y$_{1}$ ) is observed for each individual. $^{5}$Various empirical studies are based on this structure, e.g. Newhouse et al. (2007), Bandiera et al. (2008), and Suri (2011), among others. 7 Pr ( Y$_{1}$ ≥ Y$_{0}$ ) = 1 . g ( Y$_{0}$, Y$_{1}$ ) ≤ 0 with probability one , (1) Figure 1: (a) MTR, (b) concave treatment response, (c) convex treatment response