Inference on the New Keynesian Phillips Curve with Very Many Instrumental Variables

TL;DR

This paper develops a robust inference method for the New Keynesian Phillips Curve using a large number of instrumental variables, addressing issues of weak identification and dependence, and demonstrates its effectiveness through simulations and empirical analysis.

Contribution

It introduces a Sup Score test that remains valid with many IVs, weak identification, and dependent data, improving inference accuracy in high-dimensional settings.

Findings

Wider confidence sets than traditional methods in empirical NKPC analysis

The proposed test remains valid with exponentially many IVs and dependent data

Simulation shows ad-hoc procedures can cause substantial biases

Abstract

Limited-information inference on New Keynesian Phillips Curves (NKPCs) and other single-equation macroeconomic relations is characterised by weak and high-dimensional instrumental variables (IVs). Beyond the efficiency concerns previously raised in the literature, I show by simulation that ad-hoc selection procedures can lead to substantial biases in post-selection inference. I propose a Sup Score test that remains valid under dependent data, arbitrarily weak identification, and a number of IVs that increases exponentially with the sample size. Conducting inference on a standard NKPC with 359 IVs and 179 observations, I find substantially wider confidence sets than those commonly found.