Robust determination for the number of factors in constrained approximate factor models

This article introduces a new method called the constrained transformed growth ratio (CTGR) for determining the number of factors in a constrained factor model. Under certain mild conditions, the resulting estimator can be proven to be consistent. To illustrate the effectiveness of the proposed method, Monte Carlo simulation experiments and a real data application are well conducted. It is worth mentioning that the new estimator performs better than the existing methods in accurately selecting the number of common factors, particularly when weak factors are present or when the constraint dimension is large in the constrained factor model. The empirical findings indicate that Chinese housing prices are shaped by the dynamic interplay of market supply-demand dynamics, government policy interventions, and the persistent trend of deurbanization.