Generalized Method of Moments

When information on a set of parameters is given in the form of moments (expectations), equations containing this information are called the moment conditions. For example, if yt = x′tθ+ ut is considered and the statistician knows a priori that xt and ut are uncorrelated, then the corresponding moment conditions are Ext(yt – x′tθ) = 0. Alternatively, if it is believed that zt and ut are uncorrelated for some random variables zt, then the moment conditions would be Ezt(yt – x′tθ) = 0. In the above examples, the functions xt(yt – x′tθ) and zt(yt – xt′θ), whose ...