Solved

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

question 22

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 ADL(3,1)formulation of the Phillips curve using a GARCH(1,1)specification. The results are as follows: $\widehat{\Delta I n f}_{t}=1.17-.56 \Delta I n f_{t-1}-.47 \Delta I n f_{t-2}-.31 \Delta I n f_{t-3}-.13 \text { Unempt-1 }$
(.48) (.08) $\quad$ (.10) $\quad$ (.09) $\quad$ $(.06)$
$\hat{\sigma}_{t}^{2}=.86+.27 u_{t-1}^{2}+.53 \sigma_{t-1}^{2} .$
$(.40)(.11)$ $\quad$ (.15)
(a)Test the two coefficients for $u _ { t - 1 } ^ { 2 }$ and $\sigma _ { t - 1 } ^ { 2 }$ in the GARCH model individually for statistical significance.
(b)Estimating the same equation by OLS results in $\widehat{\Delta I n f}_{t}=1.19-.51 \Delta I n f_{t-1}-.47 \Delta I n f_{t-2}-.28 \Delta I n f_{t-3}-.16 U_{n e m p t-1}$
(.54) (.10) $\quad$ (.11) $\quad$ (.08) $\quad$ $(.07)$
Briefly compare the estimates. Which of the two methods do you prefer?
(c)Given your results from the test in (a), what can you say about the variance of the error terms in the Phillips Curve for Canada?
(d)The following figure plots the residuals along with bands of plus or minus one predicted standard deviation (that is, ± $\widehat{\sigma _ { t }}$ )based on the GARCH(1,1)model. $You have collected quarterly Canadian data on the unemployment and the inflation rate from 1962:I to 2001:IV. You want to re-estimate the ADL(3,1)formulation of the Phillips curve using a GARCH(1,1)specification. The results are as follows: \widehat{\Delta I n f}_{t}=1.17-.56 \Delta I n f_{t-1}-.47 \Delta I n f_{t-2}-.31 \Delta I n f_{t-3}-.13 \text { Unempt-1 } (.48) (.08) \quad (.10) \quad (.09) \quad (.06) \hat{\sigma}_{t}^{2}=.86+.27 u_{t-1}^{2}+.53 \sigma_{t-1}^{2} . (.40)(.11)\quad (.15) (a)Test the two coefficients for u _ { t - 1 } ^ { 2 } and \sigma _ { t - 1 } ^ { 2 } in the GARCH model individually for statistical significance. (b)Estimating the same equation by OLS results in \widehat{\Delta I n f}_{t}=1.19-.51 \Delta I n f_{t-1}-.47 \Delta I n f_{t-2}-.28 \Delta I n f_{t-3}-.16 U_{n e m p t-1} (.54) (.10) \quad (.11) \quad (.08) \quad (.07) Briefly compare the estimates. Which of the two methods do you prefer? (c)Given your results from the test in (a), what can you say about the variance of the error terms in the Phillips Curve for Canada? (d)The following figure plots the residuals along with bands of plus or minus one predicted standard deviation (that is, ± \widehat{\sigma _ { t }} )based on the GARCH(1,1)model. Describe what you see.$ Describe what you see.

Definitions:

Sociological Imagination

The ability to see the relationship between individual experiences and the larger society, recognizing how societal forces influence personal life choices and phenomena.

Social Structures

The complex pattern of relationships, institutions, and social roles that define a society and influence individuals' positions and interactions.

Personal Troubles

Private difficulties or problems that individuals face as part of their personal lives, often distinct from public issues or societal problems.

Macro-structures

Large-scale societal structures and systems that shape individuals' lives, influencing social relations and individual behaviors on a broad level.