More on monotone instrumental variables

Econometric analyses of treatment response often use instrumental variable (IV) assumptions to identify treatment effects. The traditional IV assumption holds that mean response is constant across the sub-populations of persons with different values of an observed covariate. Manski and Pepper (2000) introduced monotone instrumental variable assumptions, which replace equalities with weak inequalities. This paper presents further analysis of the monotone instrumental variable (MIV) idea. We use an explicit response model to enhance the understanding of the content of MIV and traditional IV assumptions. We study the identifying power of MIV assumptions when combined with the homogeneous linear response assumption maintained in many studies of treatment response. We also consider estimation of MIV bounds, with particular attention to finite-sample bias.