Consider the ADL model (Y_{t}=3.1+0.4 Y_{t-1}+2.0 X_{t}-0.8 X_{t-1}+widetilde{u}_{t}), where (X_{t}) is strictly exogenous. a. Derive the impact
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Consider the ADL model \(Y_{t}=3.1+0.4 Y_{t-1}+2.0 X_{t}-0.8 X_{t-1}+\widetilde{u}_{t}\), where \(X_{t}\) is strictly exogenous.
a. Derive the impact effect of \(X\) on \(Y\).
b. Derive the first five dynamic multipliers.
c. Derive the first five cumulative multipliers.
d. Derive the long-run cumulative dynamic multiplier.
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