Applied econometrics.

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(a) A university student is interested in estimating the long run relationship between the unemployment rate and inflation rate for her dissertation. She collects annual time series data for the U.S. over the period 1948-1996 on these series. unem : civilian unemployment rates (in %) inf: Consumer Price Index inflation rate The student wants to run an OLS regression of unem on inf but recalls from her econometrics lectures on time series models that she first needs to test for the presence of unit roots in the variables. She therefore runs a unit root test on each variable in STATA and reports the following results: For the variable unem: Augmented Dickey-Fuller test for unit root Number of obs 47 Interpolated dickey-Fuller Test 1% critical 5% critical 10% critical Statistic value Value Value z(t) -2.645 -3.600 -2.938 -2.604 Mackinnon approximate p-value for z(t) = 0.0840 D.unem Coef. Std. Err. t P>|t [95% conf. Interval] unem L1. LD. _cons -.2731795 .1344323 1.565748 .1032785 .1431926 .6149026 -2.65 0.94 2.55 0.011 0.353 0.014 -.4813237 -.1541534 .3264935 -.0650353 .423018 2.805003 For the variable inf: Augmented Dickey-Fuller test for unit root Number of obs = 42 Test Statistic Interpolated Dickey-Fuller 1% Critical 5% Critical 10% critical value Value Value z(t) -1.748 -3.634 -2.952 -2.610 Mackinnon approximate p-value for z(t) = 0.4065 D.inf Coef. Std. Err. t P> [t] [95% Conf. Interval] inf L1. LD. L2D. L3D. L4D. L5D. LOD. _cons .1670728 .4962153 .4383845 . 1575737 -.1312285 .1500116 .0747213 .7616877 .0955753 .1704279 .1858146 . 1592154 .1486957 .1184822 .1167642 .468607 -1.75 2.91 -2.36 0.99 -0.88 1.27 0.64 1.63 0.089 0.006 0.024 0.329 0.384 0.214 0.527 0.113 3613052 .149864 -.8160051 -.165991 -.4334145 -.0907732 . 1625721 ..1906363 .0271597 .8425665 -.0607639 .4811383 . 1709574 .3907964 .3120146 1.714012 The appropriate critical values of the Dickey-Fuller test are: -3.58 and -2.93 corresponding to significance levels of 1% and 5% respectively. (i) Explain why it is important test for unit roots in time series data and carefully describe how to implement the Dickey-Fuller test in practice. Based on the above output, what conclusion can you draw about the presence of unit roots in each of the two variables? (ii) The student decides to run an OLS regression of unem on inf and obtains the following results: (ii) The student decides to run an OLS regression of unem on inf and obtains the following results: Source SS df MS 35) = = Model Residual .315129674 3.71391647 1 35 .315129674 .106111899 Number of obs = FC 1, Prob > F R-squared Adj R-squared = Root MSE 37 2.97 0.0937 0.0782 0.0519 .32575 = Total 4.02904615 36 .111917949 = Ingdp Coef. Std. Err. t P>|t| [95% conf. Interval] ifi _cons 0299486 8.183698 .0173786 .0967682 1.72 84.57 0.094 0.000 -.0053318 7.987248 065229 8.380148 She shows the results to her supervisor, who suggests that she should carry out the Engle-Granger Cointegration Test on the two series. Explain how this test is run. (iii) After carrying out the Engle-Granger Cointegration Test, the student finds that the two series are not cointegrated. Further tests on these series also reveal that they are both I(1). Based on this, advise the student on how she should proceed about estimating the long run relationship between unem and inf. (b) Discuss how you can test for the existence of the ARCH effects. (a) A university student is interested in estimating the long run relationship between the unemployment rate and inflation rate for her dissertation. She collects annual time series data for the U.S. over the period 1948-1996 on these series. unem : civilian unemployment rates (in %) inf: Consumer Price Index inflation rate The student wants to run an OLS regression of unem on inf but recalls from her econometrics lectures on time series models that she first needs to test for the presence of unit roots in the variables. She therefore runs a unit root test on each variable in STATA and reports the following results: For the variable unem: Augmented Dickey-Fuller test for unit root Number of obs 47 Interpolated dickey-Fuller Test 1% critical 5% critical 10% critical Statistic value Value Value z(t) -2.645 -3.600 -2.938 -2.604 Mackinnon approximate p-value for z(t) = 0.0840 D.unem Coef. Std. Err. t P>|t [95% conf. Interval] unem L1. LD. _cons -.2731795 .1344323 1.565748 .1032785 .1431926 .6149026 -2.65 0.94 2.55 0.011 0.353 0.014 -.4813237 -.1541534 .3264935 -.0650353 .423018 2.805003 For the variable inf: Augmented Dickey-Fuller test for unit root Number of obs = 42 Test Statistic Interpolated Dickey-Fuller 1% Critical 5% Critical 10% critical value Value Value z(t) -1.748 -3.634 -2.952 -2.610 Mackinnon approximate p-value for z(t) = 0.4065 D.inf Coef. Std. Err. t P> [t] [95% Conf. Interval] inf L1. LD. L2D. L3D. L4D. L5D. LOD. _cons .1670728 .4962153 .4383845 . 1575737 -.1312285 .1500116 .0747213 .7616877 .0955753 .1704279 .1858146 . 1592154 .1486957 .1184822 .1167642 .468607 -1.75 2.91 -2.36 0.99 -0.88 1.27 0.64 1.63 0.089 0.006 0.024 0.329 0.384 0.214 0.527 0.113 3613052 .149864 -.8160051 -.165991 -.4334145 -.0907732 . 1625721 ..1906363 .0271597 .8425665 -.0607639 .4811383 . 1709574 .3907964 .3120146 1.714012 The appropriate critical values of the Dickey-Fuller test are: -3.58 and -2.93 corresponding to significance levels of 1% and 5% respectively. (i) Explain why it is important test for unit roots in time series data and carefully describe how to implement the Dickey-Fuller test in practice. Based on the above output, what conclusion can you draw about the presence of unit roots in each of the two variables? (ii) The student decides to run an OLS regression of unem on inf and obtains the following results: (ii) The student decides to run an OLS regression of unem on inf and obtains the following results: Source SS df MS 35) = = Model Residual .315129674 3.71391647 1 35 .315129674 .106111899 Number of obs = FC 1, Prob > F R-squared Adj R-squared = Root MSE 37 2.97 0.0937 0.0782 0.0519 .32575 = Total 4.02904615 36 .111917949 = Ingdp Coef. Std. Err. t P>|t| [95% conf. Interval] ifi _cons 0299486 8.183698 .0173786 .0967682 1.72 84.57 0.094 0.000 -.0053318 7.987248 065229 8.380148 She shows the results to her supervisor, who suggests that she should carry out the Engle-Granger Cointegration Test on the two series. Explain how this test is run. (iii) After carrying out the Engle-Granger Cointegration Test, the student finds that the two series are not cointegrated. Further tests on these series also reveal that they are both I(1). Based on this, advise the student on how she should proceed about estimating the long run relationship between unem and inf. (b) Discuss how you can test for the existence of the ARCH effects