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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.

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  • $\begingroup$ $E[g(\bar{Y})] \neq \theta$, in general, when $g$ is nonlinear. $\endgroup$ – Michael Feb 15 at 22:38
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    $\begingroup$ 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. $\endgroup$ – chan1142 Feb 16 at 5:26

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