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

With the usual estimation methods of factor models, the estimated factors are notoriously difficult to interpret, unless their interpretation is imposed via restrictions. This paper considers different approaches for identifying the factor structure and interpreting the factors without imposing their interpretation: sparse PCA and factor rotations. We establish a new consistency result for the factors estimated by sparse PCA. Monte Carlo simulations show that our exploratory methods accurately estimate the factor structure, even in small samples. We also apply them to two standard 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 of the estimated factors. These exploratory methods can justify or complement approaches which impose the factor structure a priori, and can also be useful for applications in which factor interpretation is usually overlooked.