0
$\begingroup$

$y_t$ is the dependent variable, $x_t$ and $z_t$ are explanatory variables, and $α$, $β$ and $γ$ are unknown parameters.

$y_t$ = $α$ + $β$$x^3_t$ + $γ$/$log$($x_t$) + $u_t$

$y_t$ = $α$ + $β$$x_t$ + $x_t$/$γ$ + $u_t$

$y_t$ =$√β$$√x_t$ + $u_t$

For the 3 regressions, how would I determine if they are "Identified" or not (basically is it possible to obtain a least squares estimator of the parameters). Furthermore if it can be estimated via linear OLS, how would I write the regressand and regressors for the linear regression to be used?

$\endgroup$
0
$\begingroup$

The first model is multilinear, define $z=x^3$ and $w=\frac{1}{\log(x)}$; so $y=\alpha+\beta z+\gamma w$

The second model is linear but it write $y=\alpha+(\beta+\frac{1}{\gamma})x=\alpha+\delta x$ and you only can reach the value of $\delta$ (no way to get separately $\beta$ and $\gamma$).

The third model is linear : define $z=\sqrt x$ and $\alpha=\sqrt{\beta}$ and the model write $y=\alpha z$.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.