We study the construction of nonlinear impulse responses in linear structural dynamic models that include nonlinearly transformed regressors. We derive the closed-form solution for the population impulse responses to a given shock and propose a control function approach to estimating these responses without taking a stand on how the remainder of the model is identified. Our plug-in estimator dispenses with the need for simulations and, unlike conventional local projection (LP) estimators, is consistent. A modified LP estimator is shown to be consistent in special cases, but less accurate in finite samples than the plug-in estimator.

中文翻译：

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具有非线性回归量的结构动力模型的脉冲响应分析

我们研究了线性结构动力学模型中非线性脉冲响应的构建，其中包括非线性变换的回归量。我们为给定冲击的总体脉冲响应推导出封闭形式的解决方案，并提出了一种控制函数方法来估计这些响应，而无需就如何识别模型的其余部分采取立场。我们的插件估计器无需模拟，并且与传统的局部投影 (LP) 估计器不同，它是一致的。修改后的 LP 估计器在特殊情况下是一致的，但在有限样本中不如插件估计器准确。