An Odd Couple: Monotone Instrumental Variables and Binary Treatments
研究了在非参数边界框架下，当处理变量为二元时，单调工具变量（MIV）能否帮助识别处理效应。发现MIV仅在特定条件下才能超越单调处理选择或单调处理响应假设的识别能力，并用犯罪定罪对工作匹配质量的影响数据进行了实证说明。
This article investigates Monotone Instrumental Variables (MIV) and their ability to aid in identifying treatment effects when the treatment is binary in a nonparametric bounding framework. I show that an MIV can only aid in identification beyond that of a Monotone Treatment Selection assumption if for some region of the instrument the observed conditional-on-received-treatment outcomes exhibit monotonicity in the instrument in the opposite direction as that assumed by the MIV in a Simpson's Paradox-like fashion. Furthermore, an MIV can only aid in identification beyond that of a Monotone Treatment Response assumption if for some region of the instrument either the above Simpson's Paradox-like relationship exists or the instrument's indirect effect on the outcome (as through its influence on treatment selection) is the opposite of its direct effect as assumed by the MIV. The implications of the main findings for empirical work are discussed and the results are highlighted with an application investigating the effect of criminal convictions on job match quality using data from the 1997 National Longitudinal Survey of the Youth. Though the main results are shown to hold only for the binary treatment case in general, they are shown to have important implications for the multi-valued treatment case as well.