4Non-technical summary 5

This paper shows consistency of a two step estimator of the parameters of a dynamic approximate factor model when the panel of time series is large (n large). In the first step, the parameters are first estimated from an OLS on principal components. In the second step, the factors are estimated via the kalman smoother. This projection allows to consider dynamics in the factors and heteroskedasticity in the idiosyncratic variance. The analysis provides theoretical backing for the estimator considered in Giannone, Reichlin, and Sala (2004) and Giannone, Reichlin, and Small (2005).JEL Classification: C51, C32, C33.

This paper considers quasi-maximum likelihood estimations of a dynamic approximate factor model when the panel of time series is large. Maximum likelihood is analyzed under different sources of misspecification: omitted serial correlation of the observations and cross-sectional correlation of the idiosyncratic components. It is shown that the effects of misspecification on the estimation of the common factors is negligible for large sample size (T) and the cross-sectional dimension (n). The estimator is feasible when n is large and easily implementable using the Kalman smoother and the EM algorithm as in traditional factor analysis. Simulation results illustrate what are the empirical conditions in which we can expect improvement with respect to simple principle components considered by Bai (2003), Bai and Ng (2002), Forni, Hallin, Lippi, and Reichlin (2000, 2005b, Stock and Watson (2002a,b).