Bootstrap inference for nondifferentiable functionals under weak instruments

Develop bootstrap inference procedures for Hadamard directionally differentiable, nondifferentiable functionals—specifically the breakdown frontiers for the Local Average Treatment Effect (LATE) and the Intention-to-Treat (ITT) in binary-outcome instrumental variable models—that yield valid inference in the presence of weak instruments, such as uniform confidence bands, extending beyond existing bootstrap methods designed for differentiable functionals under standard assumptions.

Background

The study proposes breakdown frontiers to assess robustness of LATE and ITT conclusions under joint relaxations of instrument independence and monotonicity. Estimation relies on functionals that are Hadamard directionally differentiable, for which standard nonparametric bootstrap methods are known to be inconsistent, motivating the use of numerical-derivative-based bootstrap procedures.

While specialized bootstrap methods exist to address weak instruments when standard differentiability conditions hold, extending such improvements to nondifferentiable functionals like breakdown frontiers remains unresolved. The paper explicitly notes the gap and calls for future work to address bootstrap improvements under weak instruments for these functionals.