Finding relevant variables in sparse Bayesian factor models

This paper considers factor estimation from heterogenous data, where some of the variables are noisy and only weakly informative for the factors. To identify the irrelevant variables, we search for zero rows in the loadings matrix of the factor model. To sharply separate these irrelevant variables from the informative ones, we choose a Bayesian framework for factor estimation with sparse priors on the loadings matrix. The choice of a sparse prior is an extension to the existing macroeconomic literature, which predominantly uses normal priors on the loadings. Simulations show that the sparse factor model can well detect various degrees of sparsity in the data, and how irrelevant variables can be identified. Empirical applications to a large multi-country GDP dataset and disaggregated CPI inflation data for the US reveal that sparsity matters a lot, as the majority of the variables in both datasets are irrelevant for factor estimation.