Econometrics Question. Question 20. You have collected quarterly data on Canadia

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Econometrics Question.

Question 20. You have collected quarterly data on Canadian unemployment (UrateC) and inflation (InfC) from 1962 to 1999 with the aim to forecast Canadian inflation. (a) To get a better feel for the data, you first inspect the plots for the series. Inspecting the Canadian inflation rate plot and having calculated the first autocorrelation to be 0.79 for the sample period, you suspect that the Canadian inflation rate has a stochastic trend. What more formal methods do you have available to test for a unit root? (b) You run the following regression, where the numbers in parenthesis are homoskedasticity-only standard errors: 1nfC,-049-0.10 1nfCt-1-0.30 1nfCt-2-0.331 nfCt-3-0.21 1nfCH (0.28) (0.05) (0.09) (0.09) (0.09) [Hint: See page 557 and footnote 3 in Chapter 14.] you determine the number of lags? for the sample period 1962 Q1 to 1999:Q4·The results are as follows: Test for the presence of a stochastic trend. Should you have used heteroskedasticity-robust standard errors? Does the fact that you use quarterly data suggest including four lags in the above regression, or how shoulod (c) To forecast the Canadian inflation rate for 2000:Q1, you estimate an AR(1), AR(4), and an ADL(4,1) model 1nfC,-0.002-0.31 1nfG_1 (0.014) (0.10) (0.158) (o.10) (0.08) 1nfC,-1.28-0.51 1nfct-1-0.44A1nfct-2-0.30 1nfCt-3-0.02 1nfCH (0.57) (0.10) (0.09) (0.08) 0.07) In addition, you have the following information on inflation in Canada during the four quarters of 1999 and the first quarter of 2000: ment Rate (Urat flation (In irst 0.8 0.8 4.3 arter ate ation 1999:Q1 7.7 0.8 0.0 1999:Q3 7.7 999Q4 7 0.8 Q16.8 For each of the three models, calculate the predicted inflation rate for the period 2000:Q1 and the forecast error (d) For the last estimated model above, perform a test on whether or not Canadian unemployment rates Granger-causes the Canadian inflation rate. [Hint: There is only 1 lag of unemployment.]

Explanation / Answer

Answer:

(a) Unit Root Test

A unit root test indicates whether a time series variable is non-stationary and possess a unit root. The standard method that exists in econometrics for measuring unit root are:

(b) Please mention the Chapter 14 name for answering this part of the question.

According to the rule a data with quarterly frequency should have four lag. Hence employing four lag in the regression is okay. Apart from the rule one can check for the optimal lag length through lag selection criterion. The standard lag selection criterion are: Akaike Information Criterion (AIC) and Bayesian Information Criterion or Schwarz criterion (SBIC).

This question is incomplete. It requires the dataset that has been asked in the very begining. Without data it is difficult to calculate the rest of the question. The required theory is answered above.

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