More on Monotone Instrumental Variables

Econometric analyses of treatment response often use instrumental variable (IV) assumptions to identify treatment effects. The traditional IV assum ption holds that mean response is constant acros s the subpopulations of persons with different values of an observed covariate. Manski and Pepper (2000) introduced monotone instrumental variable (MIV) assumptions, which replace equalities with weak inequalities. This paper presents further ana lysis of the MIV idea. We use an e xplicit response m odel to en hance 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. This paper was prepared for the tenth anniversary issue of the Econometric Journal. Our research on monotone in strumental variables (MIVs) was first circulated in 1998, th e y ear that the journal beg an publication. We are grateful for this opportunity to report further findings on MIVs and, in doing so, to mark the tenth anniversary of both the journal and the subject. We have benefitted from the comments of a referee. Manski’s research was supported in part by NSF Grant SES-0549544.