Suppose we impose the constraint that $\mathrm{E}\left[{\mathbf{w}}_i\right]=\mathbf{g}(\theta )$, where $\dim [\mathbf{w}]>\dim [\theta ]$.

(a) Obtain the objective function for the GMM estimator.

(b) Obtain the objective function for the minimum distance estimator (see Section 6.7) with $\pi =\mathrm{E}\left[{\mathbf{w}}_i\right]$ and $\hat{\pi }=\overline{\mathbf{w}}$.

(c) Show that MD and GMM are equivalent in this example.