Wald inference on varying coefficients

TL;DR

This paper introduces Wald-type statistics for nonparametric inference on varying coefficients in regression models, accommodating spatial dependence and misspecification, with applications to economic data and housing prices.

Contribution

It provides a general nonparametric inference framework for linear restrictions on varying coefficients, covering diverse dependence structures and robustness features.

Findings

Evidence of constant returns to scale in Chinese mineral industry

Nonlinear response of Boston house prices to proximity to employment centers

Simulation confirms good finite-sample performance of the tests

Abstract

We present simple to implement Wald-type statistics that deliver a general nonparametric inference theory for linear restrictions on varying coefficients in a range of regression models allowing for cross-sectional or spatial dependence. We provide a general central limit theorem that covers a broad range of error spatial dependence structures, allows for a degree of misspecification robustness via nonparametric spatial weights and permits inference on both varying regression and spatial dependence parameters. Using our method, we first uncover evidence of constant returns to scale in the Chinese nonmetal mineral industry's production function, and then show that Boston house prices respond nonlinearly to proximity to employment centers. A simulation study confirms that our tests perform very well in finite samples.