Topics in Dynamic Panel Data Analysis, Time-Varying Individual Heterogeneities, and Cross-Sectional Dependence

本文研究时变个体异质性和横截面依赖性（共同冲击）下动态面板数据模型的估计和推理问题。这些问题的一个重要方面是个体异质性和共同冲击与解释变量相关。这种相关性是经济变量的基础。诸如组内估计之类的标准程序将导致不一致的推论。本研究探索新的估计程序和相关的推理问题。报告还提出了建议程序的可行执行情况。过去二十年见证了面板数据计量经济学的巨大发展，因为面板数据技术可以解决仅通过横截面或时间序列程序难以解决的问题。随着面板数据集可用性的增加，相关技术已成为实证研究人员的关键工具。三本优秀的专著总结了面板技术的最新进展和重要性：Arellano (2003), Batagi（2006）和Hsiao（2003）。这些文献的大部分都集中在定常个体异质性的情况下。智力优势：该研究考虑了允许个体效应随时间变化的模型，以及时间效应（或共同冲击）对个体的不同影响。这些模型既有经验基础，也有理论基础，如投影描述部分所述。此外，允许个体异质性和共同冲击与回归量相关。当涉及到选择和决策时，这种相关性自然会出现在经济变量中。在这个项目中，PI将考虑如何表述问题，使估计可以用非线性广义最小二乘或拟极大似然方法等传统方法来处理。将对小T（时间周期）动态面板模型进行仔细分析。将考虑固定T和大T下的面板单位根和面板协整问题。将推导出相应的推理理论。此外，还将研究具有非均匀斜率系数的模型及其估计和推理。正如Alvarez和Arrelano（2005）所述，将考虑允许变化方差的稳健可能性，因为变化方差本身可能是感兴趣的对象。所有的分析都将在存在时变异质性和效应与回归量之间存在相关性的情况下进行。本研究将促进我们对面板数据模型的认识和理解；它将丰富面板数据分析，并为实证研究提供额外的工具。更广泛的影响：本研究涉及新的方法及其实现。在经济学中，这些方法适用于劳动经济学、产业组织和宏观经济学。当需要面板数据方法时，这些方法也适用于经济学领域之外。计算机程序将向公众开放。提出的研究也将丰富课堂教学。国家科学基金会的资助将帮助培养研究生从事理论和计算工作。

This research deals with estimation and inference problems for dynamic panel-data models under time-varying individual heterogeneities and cross-sectional dependence (common shocks). An important aspect of these problems is that the individual heterogeneity and the common shocks are correlated with the explanatory variables. This correlation is fundamental for economic variables. Standard procedures such as within-group estimators will lead to inconsistent inferences. This research explores new estimation procedures and related inference problems. It also presents feasible implementation of the suggested procedures.The last two decades have witnessed a huge development of panel data econometrics, as panel data techniques can solve issues that are hard to solve by either the cross section or time series procedures alone. With the increasing availability of panel data sets, the associated techniques have become the key tools of empirical researchers. The recent advancement and the importance of the panel techniques are summarized by three excellent monographs: Arellano (2003), Batagi (2006), and Hsiao (2003). Much of this literature has focused on the case of time-invariant individual heterogeneities.Intellectual merit: The research considers models that allow the individual effects to be time varying, and the time effects (or common shocks) to have different impacts across individuals. Such models have both empirical and theoretical foundations, as detailed in the projection escription section. Moreover, the individual heterogeneities and the common shocks are allowed to be correlated with the regressors. This correlation arises naturally for economic variables when choice and decisions are involved. In this project, the PI will consider how to formulate the problem so that the estimation can be handled by the traditional methods such as the nonlinear generalized least squares or the quasi-maximum likelihood method. Careful analysis for small T (time periods) dynamic panel models will be rendered. Panel unit root and panel cointegration problems under both fixed T and large T will be considered. The corresponding inferential theory will be derived. Furthermore, models with heterogeneous slope coeffcients, their estimation, and inference will be studied. As in Alvarez and Arrelano (2005), robust likelihood that allows for changing variance will be considered, as the changing variance itself may be the object of interest. All the analysis will be conducted in the presence of time-varying heterogeneities and in the presence of correlation between the effects and regressors. This research will advance our knowledge and understanding of panel data models; it will enrich panel data analysis and result in additional tools for empirical studies. Broader impact: This research deals with new methodologies and their implementations. Within economics, the methods are applicable in labor economics, industrial organization, and macroeconomics. These methods are also applicable outside the field of economics when panel data methods are called for. Computer programs will be made available to the general public. The proposed research will also enrich classroom teachings. NSF funding will help train graduate students for theoretical and computational work.