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

question 45

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?

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Definitions:

Debt Covenant

Agreements between a borrower and lender stating specific limitations or conditions about the borrower's actions.

Borrowing Costs

Expenses incurred by an entity for borrowing funds, including interest, amortization of discounts or premiums on debt, and other related costs.

Agency Theory

The theory that deals with problems caused by separating ownership from control in the modern corporation.

Fiduciary Duty

A legal obligation of one party to act in the best interest of another when entrusted with care of property, finances, or other responsibilities.