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

Question 33

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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: 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: t = 1.17 - .56 ΔInft-1 - .47 ΔInft-2 - .31 ΔInft-3 - .13 Unempt-1 (.48)(.08)(.10)(.09)(.06) = .86 + .27 + .53 . (.40)(.11)(.15) (a)Test the two coefficients for and in the GARCH model individually for statistical significance. (b)Estimating the same equation by OLS results in t = 1.19 - .51 ΔInft-1 - .47 ΔInft-2 - .28 ΔInft-3 - .16Unempt-1 (.54)(.10)(.11)(.08)(.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,± )based on the GARCH(1,1)model. Describe what you see. t = 1.17 - .56 ΔInft-1 - .47 ΔInft-2 - .31 ΔInft-3 - .13 Unempt-1
(.48)(.08)(.10)(.09)(.06) 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: t = 1.17 - .56 ΔInft-1 - .47 ΔInft-2 - .31 ΔInft-3 - .13 Unempt-1 (.48)(.08)(.10)(.09)(.06) = .86 + .27 + .53 . (.40)(.11)(.15) (a)Test the two coefficients for and in the GARCH model individually for statistical significance. (b)Estimating the same equation by OLS results in t = 1.19 - .51 ΔInft-1 - .47 ΔInft-2 - .28 ΔInft-3 - .16Unempt-1 (.54)(.10)(.11)(.08)(.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,± )based on the GARCH(1,1)model. Describe what you see. = .86 + .27 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: t = 1.17 - .56 ΔInft-1 - .47 ΔInft-2 - .31 ΔInft-3 - .13 Unempt-1 (.48)(.08)(.10)(.09)(.06) = .86 + .27 + .53 . (.40)(.11)(.15) (a)Test the two coefficients for and in the GARCH model individually for statistical significance. (b)Estimating the same equation by OLS results in t = 1.19 - .51 ΔInft-1 - .47 ΔInft-2 - .28 ΔInft-3 - .16Unempt-1 (.54)(.10)(.11)(.08)(.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,± )based on the GARCH(1,1)model. Describe what you see. + .53 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: t = 1.17 - .56 ΔInft-1 - .47 ΔInft-2 - .31 ΔInft-3 - .13 Unempt-1 (.48)(.08)(.10)(.09)(.06) = .86 + .27 + .53 . (.40)(.11)(.15) (a)Test the two coefficients for and in the GARCH model individually for statistical significance. (b)Estimating the same equation by OLS results in t = 1.19 - .51 ΔInft-1 - .47 ΔInft-2 - .28 ΔInft-3 - .16Unempt-1 (.54)(.10)(.11)(.08)(.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,± )based on the GARCH(1,1)model. Describe what you see. .
(.40)(.11)(.15)
(a)Test the two coefficients for 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: t = 1.17 - .56 ΔInft-1 - .47 ΔInft-2 - .31 ΔInft-3 - .13 Unempt-1 (.48)(.08)(.10)(.09)(.06) = .86 + .27 + .53 . (.40)(.11)(.15) (a)Test the two coefficients for and in the GARCH model individually for statistical significance. (b)Estimating the same equation by OLS results in t = 1.19 - .51 ΔInft-1 - .47 ΔInft-2 - .28 ΔInft-3 - .16Unempt-1 (.54)(.10)(.11)(.08)(.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,± )based on the GARCH(1,1)model. Describe what you see. and 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: t = 1.17 - .56 ΔInft-1 - .47 ΔInft-2 - .31 ΔInft-3 - .13 Unempt-1 (.48)(.08)(.10)(.09)(.06) = .86 + .27 + .53 . (.40)(.11)(.15) (a)Test the two coefficients for and in the GARCH model individually for statistical significance. (b)Estimating the same equation by OLS results in t = 1.19 - .51 ΔInft-1 - .47 ΔInft-2 - .28 ΔInft-3 - .16Unempt-1 (.54)(.10)(.11)(.08)(.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,± )based on the GARCH(1,1)model. Describe what you see. in the GARCH model individually for statistical significance.
(b)Estimating the same equation by OLS results in 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: t = 1.17 - .56 ΔInft-1 - .47 ΔInft-2 - .31 ΔInft-3 - .13 Unempt-1 (.48)(.08)(.10)(.09)(.06) = .86 + .27 + .53 . (.40)(.11)(.15) (a)Test the two coefficients for and in the GARCH model individually for statistical significance. (b)Estimating the same equation by OLS results in t = 1.19 - .51 ΔInft-1 - .47 ΔInft-2 - .28 ΔInft-3 - .16Unempt-1 (.54)(.10)(.11)(.08)(.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,± )based on the GARCH(1,1)model. Describe what you see. t = 1.19 - .51 ΔInft-1 - .47 ΔInft-2 - .28 ΔInft-3 - .16Unempt-1
(.54)(.10)(.11)(.08)(.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,± 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: t = 1.17 - .56 ΔInft-1 - .47 ΔInft-2 - .31 ΔInft-3 - .13 Unempt-1 (.48)(.08)(.10)(.09)(.06) = .86 + .27 + .53 . (.40)(.11)(.15) (a)Test the two coefficients for and in the GARCH model individually for statistical significance. (b)Estimating the same equation by OLS results in t = 1.19 - .51 ΔInft-1 - .47 ΔInft-2 - .28 ΔInft-3 - .16Unempt-1 (.54)(.10)(.11)(.08)(.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,± )based on the GARCH(1,1)model. Describe what you see. )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: t = 1.17 - .56 ΔInft-1 - .47 ΔInft-2 - .31 ΔInft-3 - .13 Unempt-1 (.48)(.08)(.10)(.09)(.06) = .86 + .27 + .53 . (.40)(.11)(.15) (a)Test the two coefficients for and in the GARCH model individually for statistical significance. (b)Estimating the same equation by OLS results in t = 1.19 - .51 ΔInft-1 - .47 ΔInft-2 - .28 ΔInft-3 - .16Unempt-1 (.54)(.10)(.11)(.08)(.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,± )based on the GARCH(1,1)model. Describe what you see. Describe what you see.

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(a)The two t-statistics are 2.46 and 3.5...

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