# Unbiasedness of MoM estimator

Why is the method of moments estimator $$g(\bar{Y})$$ of $$\theta$$ only unbiased if $$g(\mu)$$ is a linear function of $$\mu$$? (Note: It is assumed that $$\theta=g(\mu)$$ for some function $$g$$ and $$\bar{Y}$$ is a consistent and unbiased estimator of $$\mu$$)

I'm working in Appendix C (p.685) in the 6th edition of Wooldridge's Introductory Econometrics. Many thanks in advance for helping me develop an intuition.

• $E[g(\bar{Y})] \neq \theta$, in general, when $g$ is nonlinear. – Michael Feb 15 at 22:38
• Though not necessary, to add just a little more to Michael's comment, $E[g(\bar{Y})] \ne g(E[\bar{Y}]) = g(\mu) = \theta$ in general if $g$ is nonlinear. – chan1142 Feb 16 at 5:26