You Have Collected Quarterly Canadian Data on the Unemployment and the Inflation

Essay

You have collected quarterly Canadian data on the unemployment and the inflation rate from 1962:I to 2001:IV. You want to re-estimate the $\operatorname { ADL } ( 3,1 )$ formulation of the Phillips curve using a $\mathrm { GARCH } ( 1,1 )$ specification. The results are as follows:
$$\begin{aligned}\widehat { \Delta \operatorname { Inf } f _ { t } } = & 1.17 - .56 \Delta \operatorname { Inf } f _ { t - 1 } - .47 \Delta \operatorname { Inf } f _ { t - 2 } - .31 \Delta \operatorname { Inf } _ { t - 3 } - .13 \text { Unemp } _ { t - 1 } \\& ( .48 ) ( .08 )\quad\quad\quad\quad \quad(.10)\quad\quad\quad\quad\quad(.09)\quad\quad\quad\quad(.06)\\\hat { \sigma } _ { t } ^ { 2 } = & .86 + .27 u _ { t - 1 } ^ { 2 } + .53 \sigma _ { t - 1 } ^ { 2 } . \\& ( .40 ) ( .11 )\quad\quad(.15)\end{aligned}$$ (a) Test the two coefficients for $u _ { t - 1 } ^ { 2 }$ and $\sigma _ { t - 1 } ^ { 2 }$ in the GARCH model individually for statistical significance.