Abstract
This paper extends the threshold regression to threshold effect in varying coefficient model. We allow for either cross-section or time series observations. Estimation of the regression parameters is considered. An asymptotic distribution theory for the regression estimates (the threshold and the regression slopes) is developed. The distribution of threshold estimates is found to be non-standard. Under some sufficient conditions, we show that the proposed estimator for regression slopes is root-n consistent and asymptotically normally distributed, and that the proposed estimator for the varying coefficient is consistent and also asymptotically normal distributed but at a rate slower than root-n. Consistent estimators for the asymptotic variances of the proposed estimators are provided. Monte Carlo simulations are presented to assess the performance of the asymptotic approximations. The empirical relevance of the theory is illustrated through an application to the relationship between environmental regulation and regional technological innovation study.
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Acknowledgements
We appreciate the editors, guest editors and anonymous reviewers for their helpful comments. Zhang’s work is supported by grants from the National Social Sciences Funding (No.21FJYB027 and 22 &ZD160). Ai’s work is supported by grants from the Key National Natural Science Funding (No.72133005)
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Zhang, Y., Ai, C. & Feng, Y. Threshold effect in varying coefficient models with unknown heteroskedasticity. Comput Stat 39, 1165–1181 (2024). https://doi.org/10.1007/s00180-023-01335-7
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DOI: https://doi.org/10.1007/s00180-023-01335-7