Estimation of large dimensional conditional factor models in finance

This chapter surveys recent econometric methodologies 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 chapter starts with a historical perspective on conditional factor models with a small number of assets for comparison purpose. Then, it outlines the concept of approximate factor structure in the presence of conditional information, and reviews an arbitrage pricing theory for large dimensional factor models in this framework. For inference, we distinguish between two different cases 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 provide new empirical findings based on a broad set of factor models 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.