Consider the quadratic regression model \(y=\alpha+\beta x^{*}+\gamma x^{* 2}+\varepsilon\), where the regressor \(x^{*}=x+v\), with \(x\) observed and \(v\) a measurement error. Assume that \(\left(x^{*}, \varepsilon, v\right.\) ) are mutually uncorrelated and normally distributed and that all variables have zero mean.

(a) Compare the bias of the least-squares estimator of \(\beta\) and \(\gamma\).

(b) Is the model identified? Compare the latter result with that from the bivariate linear errors-in-variable model.