Time-varying dynamics in panel data sets with stochastic trends

面板数据在应用经济学中已经变得普遍，例如，以多国数据或企业级数据的形式出现。与时间序列或横截面数据相比，面板数据可以为确定经济增长或股票收益的决定因素等问题提供更丰富的经验证据。最初的提案认为，在存在横截面依赖性的情况下，持续性和随时间变化的波动性的相互作用可能会使研究人员在应用标准工具时得出误导性结论，并着手提供稳健的方法。（见“Beschreibung_des_Vorhabens”的详细贡献清单），我们在第一个融资期间认识到，时变波动率往往与时变自相关性（动态）相结合。目前尚不清楚这种时变动态如何影响标准面板推理工具的属性。然而，鉴于随时间变化的波动性的经验，预计面板方法受到特别严重的影响，因为小的单位特定的扭曲通常累积在panel.该项目的扩展旨在量化随时间变化的动态引起的扭曲，并讨论解决方案和校正，以考虑到这个问题。另外，一些前期研究问题还需要关注，前期项目计划了三年，只批准了两年。首先，我们将完成一些已经开始但尚未完成的工作，例如，关于面板可预测性检验的论文;考虑预测器中随时间变化的动态方面也会特别有意义。测试方法的组合也应得到充分重视。由于时间的限制，这一点到目前为止还没有达到预期的程度，尤其是因为我们在过去18个月里在项目范围内确定并探讨了一些额外的富有成效的主题。第二，我们将讨论对波动性和动态变化的监测。目前大多数用于检测波动性或自相关变化的程序仅适用于事后方式，而从业人员通常需要实时信息。第三，我们将讨论处理时变相关性的不同方法。虽然我们努力尽可能提供通用解决方案，但情况并非总是如此，而且通常情况下，针对具体问题的具体解决方案效果更好。此外，在两种方法都适用的情况下，具体的比较是必不可少的。第四，我们将提供实证分析，突出理论研究的相关性。我们计划研究，除其他外，具体国家的同期金融不稳定指标在多大程度上可以作为未来产出和产出波动的领先指标。

Panel data have become pervasive in applied economics - for example, in form of multi-country or of firm-level data - and, compared to time series or cross-sectional data, may provide richer empirical evidence for questions such as the identification of the determinants of economic growth or of stock returns.The empirical analysis needs, as always, to take the stylized facts of the data into account. The initial proposal argued that the interaction of persistence and time-varying volatility in the presence of cross-sectional dependence may take researchers to misleading conclusions when applying standard tools, and set out to provide robust methods.While a large part of the initial project is completed (see Beschreibung_des_Vorhabens" for a detailed list of contributions), we realized during the first funding period that time-varying volatility is often paired with time-varying autocorrelations (dynamics). It is not clear at this time how such time-varying dynamics affect the properties of standard panel inference tools. In view of the experience with time-varying volatility, it is however to be expected that panel methods are particularly badly affected, since small unit-specific distortions typically cumulate over the panel.The extension of the project aims to quantify the distortions induced by time-varying dynamics and to discuss solutions and corrections to take this problem into account. Also, some of the initial research questions still need attention, the initial project having been planned for three years, only two of which were granted.First, we will complete some work already started, but not yet finished, e.g., the paper on panel predictability testing; it will be of particular interest to consider the aspect of time-varying dynamics in the predictor as well. The combination of tests approach shall also receive full attention. This was not possible to the desired extent so far due to time restrictions, not least because we identified and explored some additional fruitful topics within the scope of the project during the past 18 months.Second, we will discuss the monitoring of changes in volatility as well as dynamics. Most current procedures for detecting volatility or autocorrelation changes are applicable in an ex-post fashion only, while practitioners typically require real-time information. Third, we will discuss different approaches for dealing with time-varying dependence. While we strive to provide generic solutions whenever possible, this will not always be the case, and, often, specific solutions to specific problems fare better. Moreover, concrete comparisons are indispensable when both approaches are available.Fourth, we shall provide empirical analyses highlighting the relevance of the theoretical research. We plan to study, among others, the extent to which country-specific indicators of contemporaneous financial instability can be useful as leading indicators of future output and output volatility.