Threshold spatial panel regression with fixed effects

doi:10.1016/j.jeconom.2026.106271

Threshold spatial panel regression with fixed effects

2026-06-01

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DOI：10.1016/j.jeconom.2026.106271

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Abstract

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We introduce general estimation and inference methods for threshold spatial panel regression with two-way fixed effects in a diminishing-threshold-effects framework. A valid objective function is obtained through a simple adjustment on the concentrated quasi loglikelihood with fixed effects being concentrated out, which leads to a consistent estimation of all common parameters. We show that the estimation of threshold parameter has a negligible effect on the asymptotic distribution of the main parameter estimators and thereby regular inference methods apply, though a bias correction may be necessary. The limiting distribution of the threshold parameter estimator is shown to be non-regular and infeasible, and for inference, a likelihood ratio test procedure is proposed. The test for the non-existence of threshold effects faces an identification issue at the null. To overcome this difficulty, we propose a sup-Wald test and a bootstrap method for its critical values. Monte Carlo results show that the proposed methods perform well in finite samples. An empirical application is presented on age-of-leader effects on political competitions across Chinese cities.

Keywords:

Fixed effects

Spatial panels

Threshold effects

Sup-Wald test

Bootstrap critical values

Time-varying spatial weights

Threshold spatial panel regression with fixed effects

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