Model Selection for Factor Analysis: Some New Criteria and Performance Comparisons

This paper derives Akaike?s (1973) Akaike information criterion (AIC), Hur- vich and Tsai?s (1989) corrected AIC, the Bayesian information criterion (BIC) of Akaike (1978) and Schwarz (1978), and Hannan and Quinn?s (1979) informa- tion criterion for factor models and studies the consistency properties of these information criteria. It also reports extensive simulation results comparing the performance of the extant and new procedures for the selection of the number of factors. The data generating process for the simulation consists of serially cor- related factors and serially and cross-sectionally correlated idiosyncratic errors. The idiosyncratic errors are either homoskedastic or heteroskedastic. Idiosyn- cratic errors with fat tails and those with outliers having a much larger variance than the rest of the errors are also considered. The simulation results show the di¡Ë culty of determining which criterion performs best. In practice, it is advisable to consider several criteria at the same time, especially BIC, Hannan and Quinn?s information criterion, Bai and Ng?s (2002) IC p2 and BIC3, and Onatski?s (2010) and Ahn and Horenstein?s (2009) eigenvalue-based criteria. The model-selection criteria considered in this paper are also applied to Stock and Watson?s (2002, 2005) data sets. The results di¢´er considerably depending on the model-selectioncriterion in use, but evidence suggesting four factors for Stock and Watson?s (2002) data and six or seven factors for Stock and Watson?s (2005) is obtainable.