You want to determine whether or not the unemployment rate for the United States has a stochastic trend using the Augmented Dickey Fuller Test (ADF). You estimate a model where the SIC suggests using 4 lags, while the AIC suggests 3 lags.

a) Which of the information criterion will you use for your choice of the optimal lag length? Be sure to include a brief discussion of parsimony here.

b) After estimating the appropriate model, the t-statistic calculated (at the 5% level) on the lag level unemployment rate is (–2.186) (using a constant, but not a trend). You know that the ADF t-critical value is: -2.57. What is your decision regarding the stationarity of the stochastic trend of the unemployment rate series in the United States?

c) You decide to re-estimate the model using the difference in United States unemployment rates. Write out the new model specification in symbols.

d) The t-statistic calculated (at the 5% level) on the lag difference unemployment rate turns out to be (-4.791). What is your conclusion now regarding the stationarity of the stochastic trend of the unemployment rate series in the United States?

e) Which model specification would you choose to forecast? Why?