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

question 9

Essay

(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?

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Definitions:

Atrial Natriuretic Hormone

A hormone secreted by the heart's atria that regulates blood pressure, blood volume, and the balance of fluids and electrolytes in the body.

Macula Densa Cells

Specialized cells in the kidney that monitor sodium chloride concentrations and regulate renal blood flow and glomerular filtration rate.

Filtrate

The liquid that passes through a filter, separating it from suspended solids or impurities.

Renin Secretion

The process by which the kidneys release the enzyme renin, a key regulator of blood pressure and electrolyte balance.