Como medir o invis\'ivel? Guerras, pizzarias do Pent\'agono e o uso de vari\'aveis proxy em econometria

TL;DR

This paper examines how proxy variables can address the challenge of unobservable latent factors in econometric models, proposing a protocol for evaluating proxy quality and illustrating with geopolitical tension data.

Contribution

It formalizes the impact of omitted latent variables, distinguishes perfect and imperfect proxies, and introduces a practical evaluation protocol for proxies in econometrics.

Findings

Including proxies can reduce bias from unobserved factors.

Imperfect proxies lead to attenuated effect estimates.

Application to geopolitical data demonstrates the method's utility.

Abstract

Many economically relevant variables (risk, confidence, uncertainty) are latent and therefore not directly observable, which creates identification challenges in applied regressions. This text formalizes how omitting latent factors generates omitted-variable bias and discusses when including a proxy variable can mitigate it. We distinguish the case of a perfect proxy, which can eliminate the bias, from the more realistic case of an imperfect proxy, where residual bias remains and the estimated effect is attenuated. We propose a practical evaluation protocol based on four properties: relevance, conditional sufficiency, exogeneity, and stability. As an illustration, we use micromobility data from Arlington together with the U.S. Geopolitical Risk Index, estimating cointegration and a bivariate VEC model to interpret local activity as a high-frequency signal of the latent component of geopolitical tension.