Go to the St. Louis Federal Reserve FRED database, and find data on the personal consumption expenditure price index (PCECTPI). Download the data, then calculate a series for inflation. For each quarter, take the percentage change in the price index from the previous quarter. Multiply by 100 to represent the change in percentage form, and multiply by 4 to “annualize” the quarterly inflation figure. Now, create a new series representing adaptive inflation expectations. For each quarter, calculate inflation expectations as the simple average of the previous four quarters of inflation.

a) How does expected inflation under the adaptive approach compare to actual inflation for the most recent quarter of data available?

b) For each quarter, calculate the error, that is, the difference between actual inflation and expected inflation. Then, calculate and report the average of the error over the most recent 2-year period, and over the most recent 5-year period.

c) If forecasters use rational expectations to form an “optimal” forecast, the implication is that forecasters will not make systematic errors. Thus, on average, the forecast errors should be close to zero. Comment on how your answers to part (b) would compare to a rational expectations forecast.