Uniform Inference in Linear Error-in-Variables Models: Divide-and-Conquer

TL;DR

This paper introduces a divide-and-conquer estimator for linear error-in-variables models that remains consistent regardless of the true coefficient value, improving inference accuracy over traditional moments-based methods.

Contribution

The paper proposes a novel divide-and-conquer estimator that is consistent for all coefficient values, addressing limitations of existing moments-based estimators.

Findings

The new estimator provides more reliable effect estimates in empirical applications.

It reveals periods where the effect of Tobin's q is statistically insignificant.

Higher-order moment estimates are reduced with the new method.

Abstract

It is customary to estimate error-in-variables models using higher-order moments of observables. This moments-based estimator is consistent only when the coefficient of the latent regressor is assumed to be non-zero. We develop a new estimator based on the divide-and-conquer principle that is consistent for any value of the coefficient of the latent regressor. In an application on the relation between investment, (mismeasured) Tobin's $q$ and cash flow, we find time periods in which the effect of Tobin's $q$ is not statistically different from zero. The implausibly large higher-order moment estimates in these periods disappear when using the proposed estimator.