You Have Decided to Use the Dickey Fuller (DF)test on the United

Essay

You have decided to use the Dickey Fuller (DF)test on the United States aggregate unemployment rate (sample period 1962:I - 1995:IV). As a result, you estimate the following AR(1)model $\widehat { \Delta \text { UmteUs } }$ _t = 0.114 - 0.024 UrateUS_t-1, R² = 0.0118, SER = 0.3417
(0.121)(0.019)
You recall that your textbook mentioned that this form of the AR(1)is convenient because it allows for you to test for the presence of a unit root by using the t- statistic of the slope. Being adventurous, you decide to estimate the original form of the AR(1)instead, which results in the following output $\widehat { \text { UmteUs } }$ _t = 0.114 - 0.976 UrateUS_t-1, R² = 0.9510, SER = 0.3417
(0.121)(0.019)
You are surprised to find the constant, the standard errors of the two coefficients, and the SER unchanged, while the regression R² increased substantially. Explain this increase in the regression R². Why should you have been able to predict the change in the slope coefficient and the constancy of the standard errors of the two coefficients and the SER?