Although never as popular in econometrics as in fields such as sociology or psychology, there has always been some interest in the application of factor models to economic data. This interest has been heightened in the past two decades by the rise of quantitative finance, where thinking in factor terms has been found to be very useful, with one representation, the arbitrage pricing theory of Ross (1976), becoming a key approach in the modeling of asset returns. Some of the lack of enthusiasm for factor models might be explained by a concern that the factors were unobservable, and such a qualification would naturally lead to a clear preference for identifying influences upon economic variables from forces that were capable of being directly measured. In this respect things have changed a good deal in many parts of economics, nowhere more so than in macroeconomics. Today unobserved factors such as technology shocks are prominent in many models, while the common trends apparent in many time series have become the basis of the expanding literature on cointegration between them.
Section 2 of the chapter sets out in more detail various applications of factor models. Such a review emphasizes the common structure underlying these models, making it possible to consider estimation issues from a general perspective, rather than through the extant specialized approaches. As we describe, direct estimation of the parameters of such models, θ, is frequently very difficult, and this leads us to propose the indirect estimation methods of Gourieroux, Monfort, and Renault (1993) and Gallant and Tauchen (1996) as good ways of finding estimates of θ at reasonable computational cost.