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:

Response Generalization

The process by which a learned response is applied to similar stimuli beyond the original conditioned stimulus.

Conditioned Stimulus

an originally neutral stimulus that, after association with an unconditioned stimulus, comes to trigger a conditioned response.

Little Albert

A famous psychology experiment conducted by John B. Watson and Rosalie Rayner, involving classical conditioning to induce a fear response in an infant named Albert.

White Rat

Typically refers to albino rats used as subjects in scientific research, especially in psychological experiments on conditioning and behavior.