Q1

[1] In a 1991 article in the Journal of Money, Credit, and Banking, R.W. Hafer and Dennis Jansen reported the results of unit root tests on long quarterly time series of several U.S. macroeconomic variables: real M1, real M2, real output, the commercial paper rate, and the corporate bond rate. To conduct these unit root tests, the authors estimated augmented Dickey- Fuller (ADF) test specifications of the following form: AY, = B. + SY,- + 7,AY_1 + 1249,-2 + u,. = + t1 - The table below reproduces a sample of their results. The number reported for each variable is the calculated t ratio for testing the null hypothesis that S = 0. = Sample 1915-1988 Real M1 -0.49 Real M2 -1.03 Commercial Real Output Paper Rate -0.32 -1.17 Corporate Bond Rate -0.92 The Dickey-Fuller critical values are -2.57 at the 0.10 level, -2.86 at the 0.05 level, and -3.43 at the 0.01 level. For each variable, what would you conclude about the presence of a unit root? [1] In a 1991 article in the Journal of Money, Credit, and Banking, R.W. Hafer and Dennis Jansen reported the results of unit root tests on long quarterly time series of several U.S. macroeconomic variables: real M1, real M2, real output, the commercial paper rate, and the corporate bond rate. To conduct these unit root tests, the authors estimated augmented Dickey- Fuller (ADF) test specifications of the following form: AY, = B. + SY,- + 7,AY_1 + 1249,-2 + u,. = + t1 - The table below reproduces a sample of their results. The number reported for each variable is the calculated t ratio for testing the null hypothesis that S = 0. = Sample 1915-1988 Real M1 -0.49 Real M2 -1.03 Commercial Real Output Paper Rate -0.32 -1.17 Corporate Bond Rate -0.92 The Dickey-Fuller critical values are -2.57 at the 0.10 level, -2.86 at the 0.05 level, and -3.43 at the 0.01 level. For each variable, what would you conclude about the presence of a unit root