Douglas A. Ruby

Inflation

Rational Expectations

Macroeconomic Theory

The Adaptive Expectations model is based on the notion that economic agents develop forecasts of future inflation based on past actual rates adjusted for their own past expectations. Specifically, inflationary expectations are calculated by using a weighted average of past actual 'πt' and past expected inflation 'E[πt-1]':

E[πt] = θ πt-1 + (1-θ)E[ πt-1] where 0 < θ < 1
By algebraically rearranging this equation we have:
E[πt] = E[πt-1] + θ{ πt-1 - E[πt-1]}

where the term in the brackets represents the forecast error made by the economic agent in attempts to determine the previous rate of inflation. From this second equation current inflationary expectations are defined to be the sum of the rate previously expected and this forecast error. The rate by which economic agents adapt to accelerating inflation depends on the value of the weight 'θ' assigned to past expected inflation in developing current inflationary expectations. Note if this weight is equal to one then current inflationary expectations are exactly equal to the size of this forecast error.

Steady Inflation, Shock in Time Period-4
 (θ = 0.10) (θ = 0.50)

In the above tables, we see that in the absence of an acceleration of inflation the value of theta influences how quickly economic agents adjust to the shock in time period 4.

Accelerating Inflation, Shock in Time Period-4
 (θ =0.10) (θ =0.50)