Identifying and interpreting the factors in factor models via sparsity: Different approaches

This paper considers different approaches for identifying the factor structure and interpreting the factors without imposing their interpretation via restrictions: sparse PCA and factor rotations. We establish a new consistency result for the factors estimated by sparse PCA. Monte Carlo simulations show that our methods accurately estimate the factor structure, even in small samples. We apply them to large datasets about international business cycles and the US economy. For each empirical application, they identify the same factor structure, offering a clear economic interpretation. These exploratory methods can in particular justify or complement approaches that impose the factor structure a priori.