Forecasting with Dynamic Panel Data Models

样本外预测（Out-of-sample prediction）是数据科学的基本课题之一。传统的预测方法需要长时间序列的经济数据来实现，并且不能处理具有短时间跨度的经济数据，例如预测最近金融危机之后的初创公司业绩和银行业绩。本项目旨在开发一种新的方法，利用面板数据中的横截面信息生成短时间序列经济数据的预测。在这种预测中，“好的”预测不仅需要对面板数据中的共同组成部分进行“好的”估计，而且需要对面板模型中的个别具体组成部分进行“好的”估计，这是该项目的主要挑战。研究者将根据统计决策理论开发最佳预测，并研究如何实施。最终，该项目将提供更好的预测工具，以帮助个人决策者和政策制定者。为了开发新方法来生成对短时间序列经济数据的预测，研究人员将考虑具有未观察到的个体异质性的线性动态面板模型。由于对面板数据的“好”预测不仅需要对面板模型中的公共参数进行“好”的估计，而且还需要对面板模型中的各个特定参数进行“好”的估计，因此，它们通常不能在短时间跨度面板中得到一致的估计。现有的文献大多集中在建立良好的估计的公共参数在存在的大尺寸的个人特定的参数，但不一定建立良好的估计的个人特定的参数。该项目与以往文献的主要区别在于将未观察到的个体效应变量的条件均值与贝叶斯框架中个体效应变量的后验均值相关联。在贝叶斯后验推理的基础上，研究者将推导出最优预测公式，并开发出几种估计方法来实现最优预测。本项目将进一步研究有趣的实证应用，包括预测美国银行在2008年金融危机后的表现。

Out-of-sample prediction or forecasting is one of the fundamental subjects of data science. The conventional forecasting methods require long time series economic data for implementation, and cannot handle economic data with short time span such as predicting, for example, start-up companies' performances and bank performances after the recent financial crises. This project aims at developing a new method to generate forecasts for short time series economic data using cross sectional information in panel data. In such forecasting, "good" forecasts require not only "good" estimates of the common components in the panel data but also the individual specific components in the panel model, which is the main challenge of the project. The investigator will develop the optimal forecast based on statistical decision theory and investigate how to implement it. Ultimately, this project will provide better forecasting tools to help individual decision makers and policymakers. To develop new methods to generate forecasts for short time series economic data, the investigator will consider a linear dynamic panel model with unobserved individual heterogeneity. Because "good" forecasts for panel data require not only "good" estimates of the common parameters but also the individual specific parameters in the panel model, they cannot be estimated consistently with short time span panel in general. The existing literature mostly focuses on establishing good estimates of the common parameters in the presence of the large dimensional individual specific parameters, but not necessarily on establishing good estimates of the individual specific parameters. The key departure of this project from the previous literature is to relate the conditional mean of the unobserved individual effect variable to the posterior mean of the individual effect variable in the Bayesian framework. Building on Bayesian posterior inference, the investigator will derive an optimal forecast formula and develop several estimation methods to implement the optimal forecast. This project will further investigate interesting empirical applications, including forecasting the performances of US banks after 2008 financial crisis.