Using spatial modeling to address covariate measurement error

TL;DR

This paper introduces a novel spatial modeling approach to correct covariate measurement error using neighboring data points, applicable to nonlinear models without strict distributional assumptions.

Contribution

It develops a new estimation method leveraging spatial data and operator diagonalization, applicable to general nonlinear models with nonclassical errors.

Findings

Method effectively corrects measurement error in simulations.

Application reveals insights into pre-colonial political influence on economic development.

Combines sieve semiparametric likelihood with kernel and simulation techniques.

Abstract

We propose a new estimation methodology to address the presence of covariate measurement error by exploiting the availability of spatial data. The approach uses neighboring observations as repeated measurements, after suitably controlling for the random distance between the observations in a way that allows the use of operator diagonalization methods to establish identification. The method is applicable to general nonlinear models with potentially nonclassical errors and does not rely on a priori distributional assumptions regarding any of the variables. The method's implementation combines a sieve semiparametric maximum likelihood with a first-step kernel estimator and simulation methods. The method's effectiveness is illustrated through both controlled simulations and an application to the assessment of the effect of pre-colonial political structure on current economic development in Africa.