Time-Varying Factor Selection: A Sparse Fused GMM Approach

Abstract

This paper introduces a new method for estimating a time-varying coefficient model under time-varying sparsity within the GMM framework. By building a folded concave penalized high-dimensional moment restriction framework, we introduce a sparse fused GMM (SFGMM) approach.  SFGMM allows for consistently estimating time-varying parameters, accommodating changes in the relevant risk factors and their values across different regimes.  We provide large sample properties for our estimator, both with and without prior knowledge of structural changes, and test the conditional stochastic discount factor (SDF) model by offering a new perspective for time-varying factor selection. We estimate the conditional SDF for U.S. equity factors from 1973 to 2022 and find our SFGMM strategy achieves one of the best risk-adjusted investment performances with the model-implied SDF loadings.

Keywords: SCAD, structural breaks, stochastic discount factor, time-varying coefficient model, variable selection

JEL Classification: C14, G11, G12