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

question 11

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 $\begin{aligned}{\widehat{\Delta \text { UrateUS }_{t}}}{=} & 0.114-0.024 \text { UrateUS }_{\mathrm{t}-1}, R^{2}=0.0118, \text { SER }=0.3417 \\& (0.121)(0.019)\end{aligned}$
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 $\begin{aligned}{\widehat{\Delta \text { UrateUS }_{t}}}{=} & 0.114-0.024 \text { UrateUS }_{\mathrm{t}-1}, R^{2}=0.0118, \text { SER }=0.3417 \\& (0.121)(0.019)\end{aligned}$

You are surprised to find the constant, the standard errors of the two coefficients, and the SER unchanged, while the regression $\mathrm { R } ^ { 2 }$ increased substantially. Explain this increase in the regression $\mathrm { R } ^ { 2 }$ . 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:

Mass Production

Manufactures a large number of uniform products with an assembly‐line system.

Service Delivery

The act of providing a service to customers, including all activities and processes that contribute to the service's effectiveness and quality.

Continuous-Process Production

A manufacturing method where the production process is uninterrupted to ensure efficient and scalable production of goods.

Automated Production

The use of automation technologies to perform manufacturing tasks and processes, reducing the need for human labor and increasing efficiency.