Question

1. The price index from 2016 to 2018 is : 200, 210, 220. Derive a forecast for 2019 on the basis of adaptive expectations using 0.2, 0.3 and 0.5 as weights in 2016, 2017 and 2018 respectively.
2. The optimal forecast for 2019 is 225 using all available information. What is the expected price index in 2019 based on rational expectations?
3. The actual value in 2019 is 223. Based on this, Paul concluded that the expected value in (b) derived using rational expectations was wrong. Do you agree? Why?

Answer 1

a)

The theory of adaptive expectation states that people build their expectation about future prices according to experience. The price level expected is a linear combination of past prices. In this case, the price index for the year 2019 is calculated by

Here PI is price index, and W is the weight of the respective year. The table below gives the calculations.

Table 1

Year	Price Index	Weights	PI×W
2016	200	0.2	40
2017	210	0.3	63
2018	220	0.5	110
2019	∑(PI×W)		213

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b)

The theory of rational expectation tells that people form theor expectation about future price from current policy actions and recent data. Under rational expectation the actual price level is expected price level.

Then if the optimal forecast for 2019 price is 225, the expected price level will be 225 as well.

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c)

The actual price level is result of current policy changes and data. The expected price level may differ from actual price level is reality. That does not implies the expected level is wrong. Any mismatch under rational expectation is corrected quickly and the agents make their decisions accordingly.