Efficient two-sample instrumental variable estimators with change points and near-weak identification

TL;DR

This paper develops efficient two-sample GMM estimators and change point tests for linear models with endogenous regressors, accommodating near-weak instruments and parameter shifts across samples, with applications to macroeconomic data.

Contribution

It introduces new estimators and tests that improve efficiency and detection of parameter changes in two-sample instrumental variable models with near-weak identification.

Findings

Proposed estimators outperform standard split-sample GMM in simulations.

New tests effectively detect change points even with weak or time-varying instruments.

Empirical application reveals time variation in the inflation-pass-through relationship.

Abstract

We consider estimation and inference in a linear model with endogenous regressors where the parameters of interest change across two samples. If the first-stage is common, we show how to use this information to obtain more efficient two-sample GMM estimators than the standard split-sample GMM, even in the presence of near-weak instruments. We also propose two tests to detect change points in the parameters of interest, depending on whether the first-stage is common or not. We derive the limiting distribution of these tests and show that they have non-trivial power even under weaker and possibly time-varying identification patterns. The finite sample properties of our proposed estimators and testing procedures are illustrated in a series of Monte-Carlo experiments, and in an application to the open-economy New Keynesian Phillips curve. Our empirical analysis using US data provides strong support for a New Keynesian Phillips curve with incomplete pass-through and reveals important time variation in the relationship between inflation and exchange rate pass-through.