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，但是用来消化所有信息的计量经济学工具仍然相当有限。将N（横截面单位数）视为固定并让T（时间序列观测数）趋于无穷大的渐近分析的标准假设不再适用于分析大型数据面板。PI研究的主题是有效利用大数据面板中的信息，比如x。PI的工作将围绕三个项目组织。项目A延续了pi之前的工作，使用因子模型来降低x的维数。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，这些误差并不普遍到足以被称为共同因素，但却足以对估计的共同因素的精度产生不利影响。在这笔拨款中，PI寻求开发更有效的主成分估算器来处理这两个问题。项目B继续利用X中的相关信息，但现在的目标是预测因子框架之外的级数、y和PI的步长。这里的问题是为y挑选出一组合理的强预测因子，但这些预测因子之间的相关性不是很高，否则就会有太多的信息重叠。PI将使用惩罚回归来研究最佳收缩。目标是为时间序列设置中的惩罚参数建立与数据相关的规则。例如，平稳和非平稳预测器将以不同的比率受到惩罚。样本内和样本外的预测都将被考虑。项目C旨在开发一个有效的估计面板协整的横截面共同冲击的存在，这推动了经济变量的运动。该框架允许横截面相关误差，并将固定效应模型作为一种特殊情况。目前，在许多预测工作和政策分析中都使用了标准主成分估计。改进的因素估计将不可避免地影响这些工作。项目A应该直接导致对因素数量的更好估计，这在资产定价模型和需求分析中具有自然的作用。除了为预测者提供即时使用的结果外，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/条件预期没有正确建模时，经济假设就不能得到公平的检验。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。许多预测器框架在更广泛的背景下可能有用。在处理经济数据时，假设各个单位的误差相同是没有吸引力的。当误差是横截面相关时，项目C处理有效的估计。其结果将对涉及国家/行业/公司数据的经济分析有用。

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.