$4\mathrm{.}5$ Assume the correct GDP equation is given by equation $(6)$ below, where $Ln$ indicates the variable has been log$-$transformed.

$Ln{Y}_{it}=c+{}_{1}Ln{K}_{it}+{}_{2}Ln{L}_{it}+{}_{3}Ln{H}_{it}+{}_4{P}_{it}+u_{it}$dots

a$)$ Estimate a pooled OLS model and determine if there are random and time effects

$(4)$

Estimate a random effects model to answer the following questions below.

b$)$ Interpret estimated coefficients ${}_1,{}_2,{}_3$ and ${}_4$

c$)$ Compute the generalised feasible least estimator and comment on this estimator.

d$)$ Determine whether consumer price inflation and population are redundant in this model. $(6)$