The economy is initially at the natural rate of unemployment, which is 5%, when the authorities decide to bring the unemployment rate down to 3% and hold it there forever. With theta equal to zero, this will yield a 6 % rate of inflation every year. Now suppose that in year (tplus 6), theta changes to 1. theta might increase in this way because

theta might increase in this way because inflation expectations adapt to persistently positive inflation.

Explanation:

Since every year inflation rate is 6%, rather then expected inflation according to formula, 3%

Thus inflationary expectations should incorporate the higher inflation rate, so adaptive expectations follow:

In year t + 6 : 10%

t + 7 : 14%

t + 8 : 18%