How to Calculate Adaptive Expectations
Adaptive expectations set next period's expected inflation as the expectation people already held plus a fraction of the forecast error they just made.
The Adaptive Expectations formula
Calculator
Enter the expectation people held, the inflation rate that arrived and the adjustment weight to get the next forecast.
The rate people forecast before the period began, which is what wages were set on.
The rate that actually arrived. The gap between the two is the whole input to the update.
The share of the miss carried into the next forecast. Enter 0.5 to close half the gap each period.
Adding the weighted miss to the old forecast puts next period's expectation at 4%.
- Forecast error this period
- 4 percentage points
- Correction carried forward
- 2 percentage points
- Expectation after three updates
- 5.5%
- Gap still open after three updates
- 0.5 percentage points
- Where the forecast settles
- 6%
Actual inflation came in 4 percentage points away from what people expected, and that miss is the only new information the rule uses.
The weight lets 2 percentage points of the miss through, so the rest of the error is simply left uncorrected this round.
Holding actual inflation where it is, three rounds of the same rule lift the forecast to 5.5%.
People are still 0.5 percentage points below the rate they have been watching, and that lag is what keeps real wages squeezed.
With a positive weight and a steady inflation rate the forecast converges on the actual rate, so the lag is temporary rather than permanent.
How to calculate Adaptive Expectations, step by step
- 1Write down the expectation people held. Start from the inflation rate forecast before the period began, since that is the rate wage contracts and prices were set on.
- 2Subtract it from actual inflation. Actual minus expected is the forecast error, measured in percentage points. A positive error means inflation ran hotter than people planned for.
- 3Multiply the error by the adjustment weight. The weight a sits between 0 and 1 and says how much of the miss gets carried forward. A weight of 0.5 closes half the gap each period.
- 4Add the correction to the old expectation. The sum is the forecast for the next period. Repeat the step each period and the forecast walks toward whatever rate people keep observing.
- 5Read it onto the Phillips curve. A higher expected inflation rate shifts the short-run Phillips curve up and short-run aggregate supply left, which is where exam questions take this.
Worked example: Adaptive Expectations
People expected 2 percent inflation and the actual rate arrived at 6 percent, so the forecast error is 4 percentage points. At an adjustment weight of 0.5 they carry half the miss forward: expected inflation next period = 2 + 0.5 × 4 = 4 percent. If inflation holds at 6 percent, the forecast climbs to 5 percent, then to 5.5 percent, still 0.5 points short of a rate people have now watched for three periods running.
Adaptive Expectations questions
What does the adjustment weight mean?
It is the share of the latest forecast error folded into the next forecast. A weight of 1 sets next period's expectation equal to the rate just observed, while a weight near 0 leaves the forecast almost frozen at its old level.
Why do adaptive expectations lag a rising inflation rate?
Each forecast starts from the previous one and closes only part of the gap, so it trails behind whenever inflation keeps climbing. The errors then run in the same direction period after period, which makes them systematic rather than random.
How is this different from rational expectations?
Adaptive expectations look backward at inflation already observed, while rational expectations use everything known today, including announced policy. Under rational expectations the forecast error has no predictable pattern, so a stimulus people see coming does not raise real output.
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