Collaborative Research: Methods for Analyzing Large Dimensional Data

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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.