Inference on varying coefficients in spatial autoregressions

2025-02-05

AI Summary

This paper addresses time-varying coefficient regression models exhibiting cross-sectional or spatial dependence. We propose a general nonparametric Wald-type inference framework, built upon nonparametric kernel estimation and robust standard errors. The method accommodates arbitrary spatial error dependence structures and flexible nonparametric spatial weight matrices. It constitutes the first unified, misspecification-robust inferential framework enabling joint linear hypothesis testing on both time-varying regression coefficients and spatial autoregressive parameters. The procedure is computationally straightforward and implementation-friendly. Monte Carlo simulations under small-sample settings demonstrate accurate size control and high statistical power. Empirical applications yield two key findings: (i) the Chinese non-metallic mineral products industry exhibits constant returns to scale; and (ii) Boston housing prices respond significantly and nonlinearly to distance from employment centers.

Technology Category

• Machine Learning: Kernel Methods
• Search and Optimization: Non-convex Optimization
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Economics, Online Markets and Human Computation: Sustainability of Web economics

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 spatial autoregressive models. Our theory covers error dependence of a general form, allows for a degree of misspecification robustness via nonparametric spatial weights and permits inference on both varying regression and spatial coefficients. One application of our method finds evidence for constant returns to scale in the production function of the Chinese nonmetal mineral industry, while another finds a nonlinear impact of the distance to the employment center on housing prices in Boston. A simulation study confirms that our tests perform well in finite-samples.

Problem

• Develops Wald tests for varying coefficient restrictions
• Enables inference under spatial dependence and misspecification
• Analyzes production functions and housing price relationships

Innovation

• Wald-type statistics for nonparametric varying coefficients inference
• General central limit theorem with spatial dependence robustness
• Nonparametric spatial weights enabling misspecification-robust inference