Identification of Nonseparable Models Using Instruments With Small Support
研究连续内生变量下不可分工具变量模型的非参数识别，发现只要结果方程和第一阶段方程关于标量不可观测变量严格递增，即使工具变量支撑很小（如离散或二元），也能点识别结果方程的水平，这与需要大支撑连续工具变量的现有研究形成对比。
I consider nonparametric identification of nonseparable instrumental variables models with continuous endogenous variables. If both the outcome and first stage equations are strictly increasing in a scalar unobservable, then many kinds of continuous, discrete, and even binary instruments can be used to point-identify the levels of the outcome equation. This contrasts sharply with related work by Imbens and Newey, 2009 that requires continuous instruments with large support. One implication is that assumptions about the dimension of heterogeneity can provide nonparametric point-identification of the distribution of treatment response for a continuous treatment in a randomized controlled experiment with partial compliance.