c$)$ Econometrician Ms$.$ Noisy run the regression with true model $(1)$ but she could not find data on $f_{1,t}$ and $f_{2,t}$ and can only found data on $f_{1,t}^{*}$ and $f_{2,t}^{*}$ which are data on $f_{1,t}$ and $f_{2,t}$ with measurement error

$f_{i,t}^{*}=f_{i,t}+{}_{i,t},i=1,2$

where ${}_{1,t}$ and ${}_{2,t}$ are white noises, independent of each other and independent with ${}_t$ at all leads and lags. Could Ms$.$ Noisy get unbiased estimators of ${}_1$ and ${}_2$ in model $(1)?$ Can she get consistent estimators?