Problem

The dataset Phillips.dta contains information on the civilian unemployment rate and the cpi inflation rate.  The data is available from 1948 through 2010, and was downloaded via FRED.

Part 1

a) import the dataset and let STATA know it is time series with the command tsset year.

b) Estimate an AR(1) model for the unemployment rate.  (That is, regress unemp on a single lag of unemp.)  Do this for observations of the year>=1951. You should use the "lag operator" in STATA to do this (L.unemp). 

c) Calculate the BIC with the command estat ic. 

d) Repeat b) and c) for an AR(2) and AR(3).

e) Use the BIC to determine what is the optimal lag length (q) for unemployment in this AR(q)?

f) What is the predicted unemployment rate for 2011 according to the AR(1) model?  (Use the coefficients and the data to calculate the expected value for 2011.)  What is it for the AR(2) and AR(3) models?

g) The actual unemployment rate in 2011 was 9.0.  What is the difference between the predicted values and actual for the AR(1), AR(2) and AR(3) models.

Part 2)

a) Add the lag of the cpi_inf rate to the AR(2) regression.  Continue to execute with year>=1951. Is the lag inflation statistically significant?

b) Predict the unemployment rate 2011 in using the ADL model from 2a.  Compare it to the actual level.

c) The inflation adjusted Phillips curve proposes that the unemployment rate falls when we encounter unexpected inflation.  Let's propose that the expected value of inflation for time t is the actual value of inflation for time t-1.  This means the difference between actual inflation and expected inflation for time t will be inf_t-inf_t-1.  Create a variable called d_inf  that equals the change in inflation.  Us the syntax D.cpi_inf to help you do this.  While you're at it, also create d_unemp that equals the change in unemployment.

d) Regress unemp on d_inf.  Report the coefficient and p-value.  Is it of the expected sign?

Part 3)

a) At a level of α=.05, do unemp and cpi_inf have unit roots?  Execute Dickey-Fuller tests for each as we did in class.  Note that the critical value for a 5% test for a dataset of our size is approximately -2.92.

b) It appears you cannot reject a unit root for unemp.  Let's try an Augmented Dickey-Fuller test for unemployment.  That is, include a lag of the change in unemployment in your Dickey-Fuller regression (we created this above, it's called d_unemp).  Can you reject a unit root now?