Changes in the natural rate of unemployment

a. Repeat Problem 6 but now draw separate graphs for the period 1970 to 1990 and the period since 1990.

b. Do you find that the relation between inflation and unemployment is different in the two periods? If so, how has the natural rate of unemployment changed?

Data from problem 6

Suppose that the Phillips curve is given by \[
\pi_{t}-\pi_{t}^{e}=0.1-2 u_{t}
\]
where \[
\pi_{t}^{e}=\pi_{t-1}
\]
Suppose that inflation in year \(t-1\) is zero. In year \(t\), the central bank decides to keep the unemployment rate at \(4 \%\) forever.