Identification, estimation and inference of nonlinear dynamic causal effects in macroeconometrics

本研究计画主要研究非线性脉冲响应函数的辨识与估计。虽然结构线性向量自回归（VAR）模型经常用于计算IRF，但线性模型过于简单，无法正确描述表征宏观经济变量之间关系的复杂数据生成过程。例如，它们没有考虑到IRF是不对称的可能性，这取决于冲击的信号。为了捕捉非线性，我们需要超越标准的线性VAR模型，并考虑该模型的非线性变化。现有文献考虑了两大类模型：（i）线性模型，包括被删失或以其他方式非线性变换的回归量，以及（ii）非线性VAR模型，包括具有状态依赖性的模型，其中冲击的影响例如可能取决于经济是否处于衰退。一个流行的例子是平滑过渡VAR模型，其中允许参数从一个状态到下一个状态变化。我在这个研究项目中的目标是提出新的估计和推断方法的非线性脉冲响应函数来自这些结构动力模型。我将首先推导出（i）中模型类所隐含的IRF的封闭形式表达式。结构性冲击对目标变量的影响将通过该变量的两个样本路径之间的差异来衡量：经济受到冲击的扰动路径和没有冲击的基准路径。在线性模型中，该差异是恒定的，并识别线性IRF。在具有非线性的模型中，它取决于冲击序列的当前值和未来值。我将考虑无条件的IRF（它整合了这些冲击）和有条件的IRF，其中期望是以过程的给定历史为条件的。第二个目标将是提出一个新的插件估计的IRF的基础上，样本模拟的封闭形式的表达式获得的IRF。最后，我将提出自助置信区间的IRF的基础上，新提出的插件估计。对于非线性VAR模型，除非我们对误差项的条件分布假设强条件，否则不存在封闭形式的表达式。因此，蒙特卡罗积分（MCI）方法在这种情况下是有吸引力的。这些相当于一个自助式的IRF估计，从估计的结构模型的基础上rescovery。我的第一个目标是证明MCI估计量的一致性，这是文献中缺乏的结果。第二个目标是扩展的适用性的自助推断的非线性IRF的MCI估计的基础上。这将需要一个双重引导，我将探索这种方法的快速版本。最后，在本建议的第三部分，我将考虑流行的局部投影方法的变化，估计非线性IRF。

This research proposal studies the identification and estimation of nonlinear impulse response functions (IRFs). While structural linear vector autoregressive (VAR) models are often used to compute IRFs, linear models are too simple to properly describe the complex data generating processes that characterize the relationship among macroeconomic variables. For instance, they do not accommodate the possibility that the IRF is asymmetric, depending on the sign of the shock. In order to capture nonlinearities, we need to move beyond the standard linear VAR model and consider nonlinear variations of this model. The existing literature has considered two main classes of models: (i) linear models that include regressors that are censored or otherwise nonlinearly transformed, and (ii) nonlinear VAR models, which include models with state dependence where the effect of a shock, for example, may depend on whether the economy is in recession or not. A popular example is the smooth transition VAR model, where the parameters are allowed to change from one regime to the next. My goal in this research project is to propose new estimation and inference methods for nonlinear impulse response functions derived from these structural dynamic models. I will first derive closed-form expressions for the IRFs implied by the class of models in (i). The effect of a structural shock on a target variable will be measured by the difference between two sample paths for this variable: a perturbed path where the economy is subject to a shock and a benchmark path without the shock. In linear models, this difference is constant and identifies the linear IRF. In models with nonlinearities, it depends on the current and future values of the shock sequence. I will consider both an unconditional IRF (which integrates out these shocks) and a conditional IRF, where the expectation is conditional on a given history of the process. The second goal will be to propose a new plug-in estimator of the IRF, based on the sample analogue of the closed-form expression obtained for the IRF. Finally, I will propose bootstrap confidence intervals for the IRF, based on the newly proposed plug-in estimator. For a nonlinear VAR model, no closed-form expression exists unless we assume strong conditions on the conditional distribution of the error terms. Therefore, Monte Carlo Integration (MCI) methods are appealing in this context. These amount to a bootstrap-based estimator of the IRF, based on resampling from the estimated structural model. My first goal will be to show the consistency of the MCI estimator, a result that is lacking in the literature. The second goal is to extend the applicability of the bootstrap for inference on the nonlinear IRF based on the MCI estimator. This will require a double bootstrap and I will explore fast versions of this method. Finally, in the third part of this proposal, I will consider variations of the popular local projection approach to estimating nonlinear IRFs.