Collaborative Research: Methods for Analyzing Large Dimensional Data

经济学家很幸运能够接触到大量的数据，但是能够用来消化所有信息的计量经济学工具仍然相当有限。渐近分析的标准假设是将N（横截面单位数）视为固定的，而T（时间序列观测值的数目）趋于无穷大，这种假设不再适用于分析大数据面板。PI的工作将围绕三个项目组织。项目A继续PI先前的工作，使用因子模型来降低X的维度。当N较大时，需要仔细地降低噪声数据的权重。更困难的问题是处理特殊误差中的横截面相关性，这些特殊误差不足以被称为共同因素，但足够强，足以对估计的共同因素的精度产生不利影响。项目B继续利用X中的相关信息，但现在的目标是预测一些系列y，以及PI在因子框架之外的步骤。这里的问题是为y选择一组合理的强预测因子，但是这些预测因子之间的相关性不是很高，否则会有太多的信息重叠。PI将使用惩罚回归来研究最佳收缩率。我们的目标是建立数据依赖规则的惩罚参数在一个时间序列设置。例如，平稳和非平稳预测变量将以不同的比率受到惩罚。项目C的目标是在存在共同冲击的情况下，为面板协整建立一个有效的估计器，共同冲击驱动经济变量的协动。该框架允许横截面相关的错误，并包括固定效应模型作为一个特例。更广泛的影响和智力价值标准主成分估计现在用于许多预测练习和政策分析。改进的因素估计将不可避免地影响这些工作。项目A应直接导致更好地估计因素的数量，这在资产定价模型和需求分析中具有自然的作用，除了为预测者提供立即使用的结果外，项目B还影响宏观经济分析，因为许多经济模型涉及预期变量。当预测/有条件的预期没有正确建模时，经济假设无法得到公平的检验。此外，研究人员可能只想预测y是更高、更低还是保持不变，而不是预测y。多预测因子框架在更广泛的背景下可能有用，在处理经济数据时，假设误差在各个单位之间是独立的是没有吸引力的。项目C解决了当误差在横截面上相关时的有效估计。其结果将有助于涉及国家/行业/公司数据的经济分析。

Economists are fortunate to have access to lots of data, but the econometric tools that can beused to digest all the information remain rather limited. The standard assumption underlyingasymptotic analysis that treats N (number of cross-section units) as fixed and let T (the number oftime series observations) to tend to infinity is no longer appropriate for analyzing large data panels.The theme of the PIs research is efficient use of information in a large panel of data, say, X. The PI'swork will be organized around three projects. Project A continues the PIs previous work in using factor models to reduce the dimension of X. With N large, there is a need to carefully downweigh noisy data. The more difficult problem is to deal with the cross-section correlation in idiosyncratic errors that are not pervasive enough to be called common factors, but are strong enough to adversely affect the precision of the estimated common factors. In this grant, the PI's seek to develop moreefficient principal component estimators to deal with both problems.Project B continues to exploit the relevant information in X, but now the goal is to predictsome series, y, and the PI's step outside of the factor framework. The problem here is to pick out a setof reasonably strong predictors for y, but that the predictors are not very highly correlated witheach other, or else there will be too much information overlap. The PI's will use penalized regressions tostudy optimal shrinkage. The goal is to establish data dependent rules for the penalty parametersin a time series setting. For example, stationary and non-stationary predictors will be penalized atdifferent rates. Both in and out-of-sample predictions will be considered.Project C aims to develop an efficient estimator for panel cointegration in the presence of cross-section common shocks, which drive the comovement of economic variables. The framework allowsfor cross-sectionally correlated errors and encompasses the fixed effects model as a special case.Broader Impact and Intellectual Merit Standard principal component estimates are nowused in many forecasting exercises and in policy analysis. Improved factor estimates will inevitablyimpact these work. Project A should lead directly to better estimates for the number of factors,which has a natural role in asset pricing models and in demand analysis.In addition to providing results of immediate use to forecasters, Project B also impacts macroe-conomic analysis, as many economic models involve expectational variables. Economic hypothesescannot be fairly tested when the forecasts/conditional expectations are not properly modelled. Fur-thermore, instead of predicting y, a researcher might just want to predict if y is higher, lower, or stays thesame. The many predictors framework is potentially useful in broader contexts.When working with economic data, the assumption that the errors are iid across units is un-appealing. Project C tackles efficient estimation when the errors are cross-sectionally correlated.The results will be useful for economic analysis involving data for countries/industries/firms.