When forecasting from a large panel of time series, the dominant approach reduces the predictors to a few principal components (Stock-Watson diffusion indexes). De Mol, Giannone and Reichlin ask whether Bayesian shrinkage — Bayesian regression on all the predictors with a shrinkage prior — is a valid alternative. Considering a Normal prior (ridge regression) and a double-exponential prior (lasso), they show empirically that the resulting forecasts are highly correlated with, and forecast about as well as, the principal-component forecasts across a wide range of prior tightness, and they establish the asymptotic link between the two.
"This paper considers Bayesian regression with normal and double-exponential priors as forecasting methods based on large panels of time series. We show that, empirically, these forecasts are highly correlated with principal component forecasts and that they perform equally well for a wide range of prior choices."
A clarifying paper that dissolves a false dichotomy: "factor models vs. Bayesian regression" for big-data forecasting is largely a distinction without a difference, because both are doing the same thing — shrinking a high-dimensional coefficient vector toward the low-dimensional structure the data actually contain. Making the ridge-equals-PC link precise (and showing it holds empirically across prior settings) is genuinely useful, because it means a practitioner can pick whichever is convenient — principal components for a transparent factor interpretation, ridge for a one-line prior, lasso when sparsity/interpretability is wanted. It sits at the intersection of the diffusion-index and large-BVAR programmes the same authors advanced, and prefigures the modern view that machine-learning forecasting on macro panels is mostly a story about the right regularization.