A penalized two-pass regression to predict stock returns with time-varying risk premia

Under the arbitrage pricing theory (Ross, 1976; Chamberlain and Rothschild, 1983), we know that risk premia are drivers of expected excess returns. Hence, estimating them should be useful for prediction of future equity excess returns. The workhorse to estimate equity risk premia in a linear multi-factor setting is the two-pass crosssectional regression method developed by Black et al. (1972) and Fama and MacBeth (1973). A series of papers address its large and finite sample properties for linear factor models with time-invariant coefficients; see, for example, Shanken (1985, 1992), Jagannathan and Wang (1998), Shanken and Zhou (2007), Kan et al. (2013), and the review paper of Jagannathan et al. (2010) (see Bryzgalova et al. (2019) for a recent Bayesian approach). In a time-varying setting, Gagliardini et al. (2016) (henceforth referred as GOS) study how we can infer the dynamics of equity risk premia from large stock return data sets under conditional linear factor models (see also Gagliardini