Identification and Inference with Machine-Learned Instruments

Instrumental-variables estimation increasingly pools many or high-dimensional instruments into a single machine-learned first stage, with rich controls partialled out.

The resulting estimand, the partialled-out IV coefficient built from any signal of the instruments, is a signal-weighted average of the heterogeneous effects, which gives an opaque first stage a precise structural meaning.

The average is convex whenever a covariance-monotonicity condition holds, and we provide a microfoundation for that condition based on vector monotonicity.

With a learned signal, however, the usual debiased moment is not Neyman-orthogonal, and its first-order bias is a drift toward the learner's own signal-weighted average, so naive inference remains valid only for that learner-dependent target.

We construct a heterogeneity-robust orthogonal score that restores $\sqrt{N}$ inference on the fixed, learner-invariant target at no efficiency cost, and provide a Hausman-type diagnostic and identification-robust confidence sets.