Question: Assume that model 3 is the true model. You can do this using a computer package so do not worry about not estimating the standard errors. Report the coefficient results for each model (you can just list these, as always, do not include the raw output).

Y X2 X3

1 1 2

3 2 1

8 3 -3

Based on these data, estimate the following regressions:

\(\begin{aligned} & {{Y}_{1i}}={{\alpha }_{1}}+{{\alpha }_{2}}{{X}_{2i}}+{{\Pi }_{1i}} \\ & {{Y}_{2i}}={{\gamma }_{1}}+{{\gamma }_{3}}{{X}_{3i}}+{{\Pi }_{2i}} \\ & {{Y}_{3i}}={{\beta }_{1}}+{{\beta }_{2}}{{X}_{2i}}+{{\beta }_{3}}{{X}_{3}}_{i}+{{\Pi }_{3i}} \\ \end{aligned}\)

Estimate only the coefficients and not the standard errors.

a. Is \({{\alpha }_{2}}={{\beta }_{2}}\) ? Why or why not?

b. Is \({{\gamma }_{3}}={{\beta }_{3}}\) ? Why or why not?