Research into the Phillips curve is concerned with providing empirical evidence of a tradeoff between inflation and unemployment. Can an economy experience lower unemployment if it is prepared to accept higher inflation? Figure 13.7 plots the changes in a measure of the unemployment rate \((D U)\) and the changes in a measure of inflation \((D P)\) for the United States for the sample period 1970M07 to 2009M06. A VAR model was estimated as follows:

a. Is there evidence of an inverse relationship between the change in the unemployment rate \((D U)\) and the change in the inflation rate \((D P)\) ?

b. What is the response of \(D U\) at time \(t+1\) following a unit shock to \(D U\) at time \(t\) ?

c. What is the response of \(D P\) at time \(t+1\) following a unit shock to \(D U\) at time \(t\) ?

d. What is the response of \(D U\) at time \(t+2\) ?

e. What is the response of \(D P\) at time \(t+2\) ?

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0.180DU-1-0.046DP-1 DU, (1) (3.905) (-0.909) DP = -0.098DU- +0.373DP-1 (1) (-2.522) (8.711)