##### STATSCALE SEMINARS

##### PREVIOUS SEMINAR - 12th February 2021

Speaker: Matteo Barigozzi (Università di Bologna)

Title: Quasi Maximum Likelihood Estimation and Inference of Large Approximate Dynamic Factor Models via the EM algorithm

Abstract: This paper studies Quasi Maximum Likelihood estimation of dynamic factor models for large panels of time series. Specifically, we consider the case in which the autocorrelation of the factors is explicitly accounted for and therefore the model has a state-space form. Estimation of the factors and of their loadings is implemented by means of the Expectation Maximization (EM) algorithm, jointly with the Kalman smoother. We prove that, as both the dimension of the panel n and the sample size T diverge to infinity: (i) the estimated loadings are sqrt(T)-consistent and asymptotically normal if sqrt(T) /n → 0; (ii) the estimated factors are sqrt(n)-consistent and asymptotically normal if sqrt(n)/T → 0; (iii) the estimated common component is min(sqrt(T), sqrt(n))-consistent and asymptotically normal regardless of the relative rate of divergence of n and T . Although the model is estimated as if the idiosyncratic terms were cross-sectionally and serially uncorrelated, we show that these mis-specifications do not affect consistency. Moreover, the estimated loadings are asymptotically as efficient as those obtained with the Principal Components estimator, whereas numerical results show that the loss in efficiency of the estimated factors becomes negligible as n and T increase. We then propose robust estimators of the asymptotic covariances, which can be used to conduct inference on the loadings and to compute confidence intervals for the factors and common components. In a MonteCarlo simulation exercise and an analysis of US macroeconomic data, we study the performance of our estimators and we compare them with the traditional Principal Components approach.