The empirical distribution of sequential LS factors in Multi-level Dynamic Factor Models

TL;DR

This paper investigates whether the asymptotic distribution for Principal Components factors can accurately approximate the empirical distribution of the sequential LS estimator in multi-level dynamic factor models, supported by Monte Carlo experiments.

Contribution

It demonstrates that the asymptotic distribution effectively approximates the finite-sample distribution of SLS factors in ML-DFMs, and evaluates improved MSE estimators accounting for cross-sectional correlation.

Findings

Asymptotic distribution approximates empirical distribution well

Monte Carlo confirms effectiveness under general covariance structures

Best MSE estimator accounts for cross-sectional correlation and estimation uncertainty

Abstract

The research question we answer in this paper is whether the asymptotic distribution derived by Bai (2003) for Principal Components (PC) factors in dynamic factor models (DFMs) can approximate the empirical distribution of the sequential Least Squares (SLS) estimator of global and group-specific factors in multi-level dynamic factor models (ML-DFMs). Monte Carlo experiments confirm that under general forms of the idiosyncratic covariance matrix, the finite-sample distribution of SLS global and group-specific factors can be well approximated using the asymptotic distribution of PC factors. We also analyse the performance of alternative estimators of the asymptotic mean squared error (MSE) of the SLS factors and show that the MSE estimator that allows for idiosyncratic cross-sectional correlation and accounts for estimation uncertainty of factor loadings is best.