GMM Estimation of the Number of Latent Factors

We propose a generalized method of moment (GMM) estimator of the number of latent factors in linear factor models. The method is appropriate for panels a large (small) number of cross-section observations and a small (large) number of time-series observations. It is robust to heteroskedasticity and time series autocorrelation of the idiosyncratic components. All necessary procedures are similar to three stage least squares, so they are computationally easy to use. In addition, the method can be used to determine what observable variables are correlated with the latent factors without estimating them. Our Monte Carlo experiments show that the proposed estimator has good finite-sample properties. As an application of the method, we estimate the number of factors in the US stock market. Our results indicate that the US stock returns are explained by three factors. One of the three latent factors is not captured by the factors proposed by Chen Roll and Ross 1986 and Fama and French 1996.