Inference in Unstable Time Series Models

计量经济学时间序列模型参数的不稳定性在理论上是合理的，在经验上是普遍存在的现象。 过去的研究主要集中在测试模型的稳定性。 这个建议涉及到自然的下一步：如何在不稳定的时间序列模型中进行推理？第一个项目涉及一般似然模型中参数的时变路径的有效推断，包括参数路径的有效估计的特殊情况。路径的知识对于许多目的都是主要的兴趣：（i）它有助于了解不稳定的根源，（ii）路径的终点与有效预测密切相关，（iii）经济理论有时意味着特定形式的不稳定性，这样，对路径的推断就成了对经济理论的检验。主要结果是，渐近有效的推理路径上可以通过治疗的序列得分向量，在通常的最大似然估计，忽略了不稳定性，作为一个高斯局部水平模型进行评估。这特别意味着可以通过将简单的卡尔曼平滑器应用于分数序列来获得有效的路径估计器。第二个项目解决的问题，如何进行有效的推理的一个子集的稳定参数的广义矩量法（GMM）框架时，其他参数是时变的。当优化代理适应策略变化时，部分稳定模型自然会出现，这会导致其简化形式的行为方程（如欧拉方程）随时间变化。该研究的许多可能的应用之一是如何对稳定的结构参数进行推断，描述技术和偏好。主要的和可能的结果是，标准的GMM推断，忽略时间变化，仍然是渐近有效的稳定的参数子集。 第三个和无关的项目开发“强大的”长期方差估计。 该项目解决应用时间序列计量经济学家的一阶问题。方法创新，论证细致，解决了技术难题.从计量经济学理论的角度来看，结果可以说是在不稳定的时间序列模型的理解的实质性进展。有些结果是通用的，可以在其他上下文中使用。更广泛的影响：虽然基于技术上复杂的论点，这项研究的主要成果是非常直接的应用。鉴于参数不稳定性在实践中的流行，因此，这项研究应该有一个重大的影响，实证研究。这包括经济理论，预测和政策分析的测试。将通过在大学和会议上的介绍以及免费提供计算机代码来促进传播该项目的想法和成果。最后，通过与研究生的合作和研究援助，该提案对学生培训产生了直接影响。

Instabilities in the parameters of econometric time series models are a theoretically plausible and empirically widespread phenomenon. Past research has largely focused on testing the stability of models. This proposal is concerned with the natural next step: How does one do inference in unstable time series models? The first project concerns efficient inference on the time varying path of the parameters in general likelihood models, including the special case of efficient estimation of the parameter path. Knowledge of the path is of primary interest for many purposes: (i) it helps understand the source of the instability, (ii) the endpoint of the path is intimately linked to efficient forecasting and (iii) economic theory sometimes implies specific forms of instability, such that inference on the path becomes a test of economic theory. The main result is that asymptotically efficient inference on the path may be obtained by treating the sequence of score vectors, evaluated at the usual maximum likelihood estimator that ignores the instability, as a Gaussian local level model. This in particular implies that an efficient path estimator can be obtained by applying a simple Kalman smoother to the sequence of scores. The second project addresses the question of how to conduct valid inference on a subset of stable parameters in a Generalized Methods of Moments (GMM) framework when other parameters are time varying. Partially stable models arise naturally when optimizing agents adapt to policy changes, which induces time variation in their reduced form behavioral equations, such as Euler equations. One of many possible applications of this research is how to conduct inference on the stable structural parameters, describing technology and preferences. The main-and maybe surprising-result is that standard GMM inference, ignoring the time variation, remains asymptotically valid on the stable subset of parameters. A third and unrelated project develops 'robust' long-run variance estimators. The projects address first order problems for applied time series econometricians. The approaches are innovative, and careful arguments are employed to solve the technical difficulties. From an econometric theory point of view, the results arguably represent substantial advances in the understanding of unstable time series models. Some of the results are generic and may be used in other contexts. Broader Impacts: While based on technically sophisticated arguments, the main results of this research are very straightfoward to apply. Given the prevalence of parameter instability in practice, this research should therefore have a major impact on empirical research. This includes tests of economic theory, forecasting and policy analysis. Dissemination of the project's ideas and results will be facilitated through presentations at universities and conferences, as well as freely available computer code. Finally, through collaborations with graduate students and research assistance, the proposal has a direct impact on student training.