Regularized GMM for Time-Varying Models with Applications to Asset Pricing

We develop a novel regularized GMM (RegGMM) approach to estimating time-varying coefficient models via a ridge fusion penalty with a high-dimensional set of moment conditions. Our RegGMM procedure only requires a mild condition on the total amount of oscillations between consecutive parameter values over the whole sample period, which allows for both abrupt structural breaks and smooth changes. While enjoying a closed-form solution for linear models, RegGMM avoids smoothed nonparametric estimation and implements a global one-step procedure. We establish consistency and derive the convergence rate and limiting distribution of the RegGMM estimator for independent and dependent observations. The simulation study shows its robust finite sample performance over existing methods under various scenarios. When applied to asset pricing modeling, RegGMM provides an alternative solution for estimating the time-varying stochastic discount factor model by utilizing a large cross section and/or many conditioning variables. We apply our method to U.S. equity data from 1972 to 2021. Reflecting the macroeconomic information, our time-varying estimate paths for factor risk prices respond to changing performance for multiple risk factors and summarize potential regime-switching scenarios. By outperforming alternative methods, we document the gains in asset pricing and investment performance from RegGMM for both in-sample and out-of-sample analysis.