3D-PCA: Factor Models with Restrictions

This paper proposes latent factor models for multidimensional panels called 3D-PCA. Factor weights are constructed from a small set of dimension-specific building blocks, which give rise to proportionality restrictions of factor weights. While the set of feasible factors is restricted, factors with long/short structures often found in pricing factors are admissible. I estimate the model using a 3-dimensional data set of double-sorted portfolios of 11 characteristics. Factors estimated by 3D-PCA have higher Sharpe ratios and smaller cross-sectional pricing errors than models with PCA or Fama-French factors. Since factor weights are subject to restrictions, the number of free parameters is small. Consequently, the model produces robust results in short time series and performs well in recursive out-of-sample estimations.