Analytical GMM tests: asset pricing with time-varying risk premiums

We propose alternative generalized method of moments (GMM) teststhat are analytically solvable in many econometric models, yieldingin particular analytical GMM tests for asset pricing modelswith time-varying risk premiums. We also provide simulationevidence showing that the proposed tests have good finite sampleproperties and that their asymptotic distribution is reliablefor the sample size commonly used. We apply our tests to studythe number of latent factors in the predictable variations ofthe returns on portfolios grouped by industries. Using datafrom October 1941 to September 1986 and two sets of instrumentalvariables, we find that the tests reject a one factor modelbut not a two-factor one.