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In heterogeneous treatment effect models with endogeneity, identification of the local average treatment effect (LATE) typically relies on the availability of an exogenous instrument monotonically related to treatment participation. First, we demonstrate that a strictly weaker local monotonicity condition—invoked for specific potential outcome values rather than globally—identifies the LATEs on compliers and defiers. Second, we show that our identification results apply to subsets of compliers and defiers when imposing an even weaker local compliers-defiers assumption that allows for both types at any potential outcome value. We propose estimators that are potentially more efficient than two-stage least squares (2SLS) in finite samples, even in cases where 2SLS is consistent. Finally, we provide an empirical application to estimating returns to education using the quarter of birth instrument.

 

Abstract Orthotic treatments for knee osteoarthritis (OA) typically rely on simple mechanisms such as three-point bending straps and single-pin hinges. These commonly prescribed braces cannot treat bicompartmental knee OA, do not consider the muscle weakness that typically accompanies the condition, and employ hinges that restrict the knee's natural biomechanics. Utilizing a novel, personalized joint mechanism in conjunction with magnetorheological dampers, we have developed and evaluated a brace which attempts to address these shortcomings. This process has respected three principal design goals: reducing the load experienced across the entire knee joint, generating a supportive moment to aid the thigh muscles in shock absorption, and interfering minimally with gait kinematics. Two healthy volunteers were chosen to test the system's basic functionality through gait analysis in a motion capture laboratory. Combining the collected kinematic and force-plate data with data taken from sensors onboard the brace, we integrated the brace and leg system into a single inverse dynamics analysis, from which we were able to evaluate the effect of the brace design on the subjects' knee loads and moments. Of the three design goals: a reduction in knee contact forces was demonstrated; increased shock absorption was observed, but not to statistical significance; and natural gait was largely preserved. Taken in total, the outcome of this study supports additional investigation into the system's clinical effectiveness, and suggests that further refinement of the techniques presented in this paper could open the doors to more effective OA treatment through patient specific braces.