Generalised Canonical Correlation Estimation of the Multilevel Factor Model

Abstract

We develop a novel approach based on the generalised canonical correlation (GCC) analysis to
analyse the high dimensional panel data model with the multilevel factor structure. Importantly,
our approach is shown to be valid even if some blocks share the common local/regional factors.
We establish the consistency of the estimated factors and loadings, and derive their asymptotic
normal distributions under fairly standard conditions. We also propose a GCC selection criterion for
identifying the number of global factors. Via Monte Carlo simulations, we confirm the validity of our
asymptotic theory, and also demonstrate the superior performance of the GCC selection criterion
over existing approaches. Finally, we demonstrate its usefulness with an application to the housing
market in England and Wales using a large disaggregated panel data of the real house price growth rates for the 331 local authorities over the period 1996Q1 to 2021Q2.

Keywords: Multilevel Factor Models, Principal Components, Generalised Canonical Correlation, Housing Market Cycles

JEL Classification: C55,R31