Before revision:  We show that the CMME fully characterizes the original conditional moment restrictions, leading to consistency in both hypothesis testing and parameter estimation . The proposed test also has an analytic expression that is easy to compute as well as closed-form asymptotic distributions.
After revision:  We show that the CMME fully characterizes the original conditional moment restrictions, leading to consistency in both hypothesis testing and parameter estimation , but also has an analytic expression that is easy to compute as well as closed-form asymptotic distributions.