Redundancy of moment conditions

It is well known that adding moment conditions cannot decrease asymptotic efficiency. However, sometimes additional moment conditions are redundant, in the sense that they do not increase the asymptotic efficiency of estimation for some or all of the parameters of interest. This paper gives a general treatment of redundancy of moment conditions. It provides necessary and sufficient conditions for redundancy, in several equivalent forms. The paper also provides interesting results for the case that there are three (or more) sets of moment conditions.