Inference with High-dimensional Weak Instruments and the New Keynesian Phillips Curve

Inference on macroeconomic relations using instrumental variables (IVs) is often characterised by weak and high-dimensional IVs. I propose a weak-IV robust method that remains valid under dependent data, arbitrarily weak identification, and a number of IVs that can increase exponentially with the sample size. I show by simulation that using methods that are not robust to weak and high-dimensional IVs can lead to substantially biased inference, while the proposed test has good size and power properties. Conducting inference on a US New Keynesian Phillips Curve with 473 IVs and 116 observations, I find substantially wider confidence sets than those commonly reported in the literature.