(Requires Appendix Material) the Long-Run, Stationary State Solution of An \operatorname

(Requires Appendix material) The long-run, stationary state solution of an $\operatorname { AD } ( p , q )$ model, which can be written as $A ( L ) Y _ { t } = \beta _ { 0 } + c ( L ) X _ { t - 1 } + u _ { t }$ , where $a _ { 0 } = 1$ , and $a _ { j } = - \beta _ { j }$ , $c _ { j } = \delta _ { j }$ , can be found by setting $L = 1$ in the two lag polynomials. Explain. Derive the long-run solution for the estimated $\operatorname { ADL } ( 4,4 )$ of the change in the inflation rate on unemployment: $$\begin{array} { l } \widehat { \Delta I n f } _ { t } = 1.32 - .36 \Delta \operatorname { Inf } f _ { t - 1 } - 0.34 \Delta \operatorname { Inf } _ { t - 2 } + .07 \Delta \operatorname { Inf } t _ { t - 3 } - .03 \Delta \operatorname { Inf } f _ { t - 4 } \\\\- 2.68 \text { Unemp } _ { t - 1 } + 3.43 \text { Unemp } _ { t - 2 } - 1.04 \text { Unemp } _ { t - 3 } + .07 \text { Unemp } _ { t - 4 }\end{array}$$ Assume that the inflation rate is constant in the long-run and calculate the resulting
unemployment rate.What does the solution represent? Is it reasonable to assume that this
long-run solution is constant over the estimation period 1962-1999? If not, how could
you detect the instability?