Monotone Instrumental Variables: With an Application to the Returns to Schooling

Abstract

Econometric analyses of treatment response commonly use instrumental variable (IV) assumptions to identify treatment effects.Yet the credibility of IV assumptions is often a matter of considerable disagreement.There is therefore good reason to consider weaker but more credible assumptions.To this end, we introduce monotone instrumental variable (MIV) assumptions and the important special case of monotone treatment selection (MTS).We study the identifying power of MIV assumptions alone and combined with the assumption of monotone treatment response (MTR).We present an empirical application using the MTS and MTR assumptions to place upper bounds on the returns to schooling.1 Whereas a variable v was originally called an instrumental variable if v has zero covariance with a residual ,, the modern usage of the term has broadened to embrace assumptions that specified functions of v and , are orthogonal.Hence it is now necessary to specify the type of IV assumption one has in mind.Mean independence, quantile independence, and statistical independence assumptions (or the orthogonality conditions that these assumptions yield) have all been prominent in the literature.See Manski (1988) pp.25-26 and Section 6.1 for discussion of the history and exposition of the variety of modern IV assumptions.2 Several contributors to this literature have examined the identifying power of IV assumptions in the absence of parametric restrictions on the form of response functions.Manski (1990Manski ( , 1994) ) showed that mean independence assumptions imply sharp bounds on mean outcomes and average treatment effects.Robins (1989) and Balke and Pearl (1997) have considered the statistical independence assumption that holds in classical randomized experiments, where response functions are statistically independent of assigned treatments.Hotz, Mullins, and Sanders (1997) have studied contaminated instrument assumptions.These suppose that a mean-independence assumption holds in a population of interest, but the observed population is a probability mixture of the population of interest and one in which the assumption does not hold.