Parameter cascading for panel models with unknown number of unobserved factors: An application to the credit spread puzzle

The iterative least squares method for estimating panel models with unobservable factor structure is extended to cover the case where the number of factors is unknown a priori. The proposed estimation algorithm optimizes a penalized least squares objective function to estimate the factor dimension jointly with the remaining model parameters in an iterative hierarchical order. Monte Carlo experiments show that, in many configurations of the data, such a refinement provides more efficient estimates in terms of MSE than those that could be achieved if the feasible iterative least squares estimator is calculated with an externally selected factor dimension. The method is applied to the problem of the credit spread puzzle to estimate the space of the missing risk factors jointly with the effects of the observed credit and illiquidity risks.