Estimation of Large Dimensional Conditional Factor Models in Finance

This chapter provides an econometric methodology for inference in large-dimensional conditional factor models in finance. Changes in the business cycle and asset characteristics induce time variation in factor loadings and risk premia to be accounted for. The growing trend in the use of disaggregated data for individual securities motivates our focus on methodologies for a large number of assets. The beginning of the chapter outlines the concept of approximate factor structure in the presence of conditional information, and develops an arbitrage pricing theory for large-dimensional factor models in this framework. Then we distinguish between two different cases for inference depending on whether factors are observable or not. We focus on diagnosing model specification, estimating conditional risk premia, and testing asset pricing restrictions under increasing cross-sectional and time series dimensions. At the end of the chapter, we review some of the empirical findings and contrast analysis based on individual stocks and standard sets of portfolios. We also discuss the impact on computing time-varying cost of equity for a firm, and summarize differences between results for developed and emerging markets in an international setting.