Testing linearity of spatial interaction functions `a la Ramsey

2024-12-19

AI Summary

This paper addresses the challenge of testing linearity in spatial interaction functions. We propose a computationally efficient, heteroskedasticity-robust nonparametric test that requires estimating only the linear spatial autoregressive model under the null hypothesis. For the first time, we embed the Ramsey RESET principle into the spatial econometric framework and construct a Lagrange multiplier–based test statistic that avoids auxiliary model estimation, ensuring both theoretical rigor and practical simplicity. Monte Carlo simulations demonstrate accurate size control and high statistical power. An empirical application to Finnish municipal tax data reveals significant nonlinear strategic tax competition among neighboring jurisdictions. The key contribution is the novel integration of the RESET specification-test logic with the spatial Lagrange multiplier (LM) framework—bypassing the conventional requirement of full model re-estimation—and providing a reliable diagnostic tool for detecting nonlinearity in spatial modeling.

Technology Category

• Search and Optimization: Non-convex Optimization
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Machine Learning: Statistical Relational/Logic Learning

Application Category

• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work
• Graph Algorithms and Modeling for the Web: Querying, indexing, and retrieval in Web-related graphs

Abstract

We propose a computationally straightforward test for the linearity of a spatial interaction function. Such functions arise commonly, either as practitioner imposed specifications or due to optimizing behaviour by agents. Our conditional heteroskedasticity robust test is nonparametric, but based on the Lagrange Multiplier principle and reminiscent of the Ramsey RESET approach. This entails estimation only under the null hypothesis, which yields an easy to estimate linear spatial autoregressive model. Monte Carlo simulations show excellent size control and power. An empirical study with Finnish data illustrates the test's practical usefulness, shedding light on debates on the presence of tax competition among neighbouring municipalities.

Problem

• Tests linearity of spatial interaction functions
• Robust nonparametric method for hypothesis testing
• Examines tax competition among neighboring municipalities

Innovation

• Nonparametric test using Lagrange Multiplier principle
• Conditional heteroskedasticity robust linearity test
• Easy estimation via linear spatial autoregressive model