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空间动态面板非线性Logistic平滑转移模型（SDPD-LSTAR）是一个灵活性较好、应用广泛的新模型，刻画了变量的空间交互、时间依赖、时空协变和非线性空间区制平滑转换特征。不过，如果不考虑时间依赖、时空协变或非线性特征而直接建立空间模型，会影响估计精度和有效性。本文对双向固定效应SDPD-LSTAR模型，提出拟极大似然（QML）转换和直接估计法，证明参数估计量的一致性，并进一步推导修正估计量，证明修正估计量具有更好的有限样本性质。同时，本文通过Monte Carlo模拟和实例应用检验估计效果。模拟结果表明：QML转换和直接估计量偏差均较小，随着N和T不断增大，估计准确性增加；修正QML比未修正QML估计量更精确，转换估计的准确性优于直接估计。实例应用不仅重新评估了城市碳排放与经济发展水平的空间动态非线性关系，也很好地验证和展示了理论结论和实践性。
Abstract：Spatial dynamic panel Logistic smooth transfer autoregression model(SDPD-LSTAR) is a flexible and widely used new model. The model can effectively describe the spatial interaction, time dependence, spatio-temporal covariant and nonlinear spatial partitioning smooth transfer characteristics of panel data. Direct spatial modeling without considering the time dependence, spatio-temporal covariant and nonlinear characteristics will affect the accuracy and effectiveness of parameter estimation. We propose the quasi maximum likelihood(QML) transformation and direct estimation method for the SDPD-LSTAR model with two-way fixed effects. We show the consistency of these estimators. The modified estimator is further derived. We prove the better small sample properties of the modified estimator. The Monte Carlo simulation shows that the deviation of the QML transformation and direct estimator is small. The estimation accuracy increases with the increase of T and N. The modified QML estimator is more accurate than the unmodified QML. The accuracy of transformation estimation is better than that of direct estimation. The empirical application not only reevaluates the spatial dynamic nonlinear relationship between urban carbon emissions and economic development, but also well confirms the theoretical conclusions and their practicability.
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(1)因篇幅所限，具体证明过程以附录1展示，见《统计研究》网站所列附件。下同。
(2)因篇幅所限，具体证明过程以附录2展示。
(1)因篇幅所限，具体证明过程以附录1展示。
(2)因篇幅所限，具体证明过程以附录2展示。
(1)因篇幅所限，具体证明过程以附录3展示。
(2)因篇幅所限，具体证明过程以附录3展示。
(1)因篇幅所限，本文仅给出参数组合10θ的模拟结果，参数组合20θ的模拟结果以附录4展示。
基本信息:
DOI：10.19343/j.cnki.11-1302/c.2023.10.010
中图分类号:O212.1
引用信息:
[1]徐晔,欧阳婉桦.空间动态面板非线性Logistic模型的QML估计[J].统计研究,2023,40(10):124-137.DOI:10.19343/j.cnki.11-1302/c.2023.10.010.
基金信息:
国家自然科学基金地区科学基金项目“数字赋能视阈下创新要素配置促进制造业高质量发展的机制研究”（72163008）
2023-10-25
2023-10-25