Sparse Modeling Under Grouped Heterogeneity with an Application to Asset Pricing

Sparse models, though long preferred and pursued by social scientists, can be ineffective or unstable relative to large models, for example, in economic predictions (Giannone et al., 2021). To achieve sparsity for economic interpretation while effectively exploiting big data for superior empirical performance, we introduce a general framework that jointly clusters observations (via new decision trees) and locally selects variables (with Bayesian priors) for modeling panel data with potential grouped heterogeneity. We derive analytical marginal likelihoods as global split criteria in our Bayesian Clustering Model (BCM), to incorporate economic guidance, address parameter and model uncertainties, and prevent overfitting. We apply BCM to asset pricing and estimate uncommon-factor models for data-driven asset clusters and macroeconomic regimes. We find (i) cross-sectional heterogeneity linked to (non-linear interactions of) return volatility, size, and value, (ii) structural changes in factor relevance over time primarily predicted by market volatility and valuation, and (iii) MKTRF and SMB as common factors and multiple uncommon factors across characteristics-managed-market-timed clusters. BCM helps explain volatility- or size-related anomalies, validate within-group tests, and mitigate the “factor zoo” problem. Overall, BCM outperforms benchmark commonfactor models in pricing and investments in U.S. equities, e.g., attaining out-ofsample
cross-sectional R2s exceeding 25% for multiple clusters and Sharpe ratio of tangency portfolios tripling that obtained from ME-B/M 5 × 5 portfolios.