If 【图片】 is an i.i.d. random sample of size 【图片】 from a Poisson distribution with the unknown parameter 【图片】, and we consider the GMM estimator of 【图片】. When we only use the first order moment 【图片】, the GMM estimator is denoted 【图片】. When we use both the first order moment 【图片】 and the second order moment 【图片】, the GMM estimator is denoted 【图片】. 【图片】 is asymptotically strictly more efficient than 【图片】.