A0154
Title: Gaussian maximum likelihood estimation of static and dynamic-var factor models
Authors: Peter Zadrozny - Bureau of Labor Statistics (United States) [presenting]
Abstract: Static factor models have unknowns of constant factor-loading coefficients, constant factor covariances, constant data-disturbance covariances, time-varying factors, and time-varying data disturbances. Dynamic-VAR factor models have additional unknowns of constant VAR-factor coefficients and time-varying factor disturbances. For Gaussian distribution, the aim is to derive in a single step: (i) maximum likelihood estimates (MLE) of all unknowns; (ii) an expectation-maximization algorithm for computing them; (iii) finite-sample and asymptotic (as sample periods and number of variables to go infinity)covariances of estimates; (iv) proof of statistical consistency of estimates. The literature has obtained these results mostly by separate steps: (a)estimating constant unknowns by principal components or MLE; (b) estimating factors by weighted least squares or projection; (c) estimating vector autoregressive (VAR) models of factors. The MLE has been obtained mostly for diagonal disturbance-covariance matrices, which are unrestricted here. Advantages of the single-step MLE are: (1) avoiding logical inconsistencies over (a)-(c); (2) asymptotically efficient estimates of all unknowns; (3)comprehensive and more accurate accounting of estimate uncertainty; (4) easy derivations and considerably shorter and easier to understand proofs using differential form of matrix differentiation in standard matrix-algebraic notation.
