Abstract:

Economic or econometric models often predict that a small number of latent factors drive a large number of response variables. Factor analysis is a natural approach to estimate such models. Given that the factors are variables the econometrician does not observe directly, two fundamental questions arise when analyzing factor models: what are these factors and how many of them there are. Various estimators for the number factors exist, but they can be problematic. Previous estimators, for example, require the use of an ad hoc penalty function. This dissertation develops two new estimators, which do not require ad hoc penalty function, for determining the number of factors (r) in approximate factor models when using large panels of data. It is a well known fact that the r eigenvalues of the variance matrix of N response variables grow unboundedly as N increases while the others are bounded. The new estimators exploit this fact and are obtained simply by maximizing the ratio of two adjacent eigenvalues. Results found that they have better finite sample properties in simulation as long as the signal to noise ratio between the factors does not diverge substantially.

This dissertation also contains an application for US stock returns using the latest tools developed to analyze factor models. The Capital Asset Pricing Model (CAPM) of Sharpe, Lintner, Treynor and Mossin was the first model to coherently explain the risk return relationship for risky assets. However, the model failed empirically in the sense that it left many assets or portfolios of assets unexplained, a problem due to the use of miss-specified model. This dissertation develops an estimated Beta Pricing Model Results show that this model works in sample as well as models used in the empirical asset pricing literature and generates very few abnormal returns. Evidence for the presence of only one common factor in US stock returns is found.