1. Standard GMM problem Consider the i.i.d. Normal stochastic process, {r, ) , with Er, = [ and E(1, - 1)? = 02. Let m = E(x, - #)' denote the /the moment about the mean. A property of the Normal distribution is that odd-ordered moments are zero, and even- ordered moments satisfy: /2k = (20! . Skewness of any distribution is defined as - 56 2. In the case of a Normal distribution, this is of course zero. Skewness is estimated as follows: (a) Set this estimator of skewness up as an exactly identified GMM estimator. Find the asymptotic distribution of ST. (b) Now suppose that the true value of the mean is known. Find the asymptotic distribution of ST. (Hint: to do each part of this question, you have to identify a different "GMM stochastic process", hi(0, w.) , having the property, Eh,(80, wx) = 0, where 60 is the true value of the parameters, and 0 = (#, o, s)' in the case of part a, while 0 = (o, s)' in the case of part b. When computing the matrices required by GMM, be sure to impose all the properties of the Normal distribution.)