Mixed-Frequency Panel Regressions with Sparse and Heterogeneous Structures

Thomas M. Menino Convention & Exhibition Center 

This paper develops a mixed frequency panel regression framework for nowcasting and
forecasting a low frequency outcome using a large set of high frequency predictors. We
propose a method that captures both sparsity in distributed lag predictors and heterogeneity
across cross sectional units through latent group structures. In this setting, slope coefficients
are homogeneous within groups but heterogeneous across them. To estimate the model, we
introduce a doubly penalized least squares estimator that simultaneously selects the relevant
high frequency predictors and uncovers the underlying group structure without prior knowledge
of the number of groups or sparsity patterns. We establish oracle properties for the estimator
and show that it consistently identifies both the relevant predictors and the group memberships
in large samples. Monte Carlo experiments demonstrate strong finite sample performance. An
empirical application to U.S. metropolitan statistical area housing prices illustrates the gains
in mixed frequency nowcasting and forecasting achieved by incorporating sparsity and group
heterogeneity.

High dimensionality

Mixed data sampling (MIDAS)

Parameter Heterogeneity

Penalized regression

Sparsity

Oracle property