## Mathematical expression of

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Mathematical expression of the theory The theory of adaptive expectations can be expressed in the following equation, where pe is the inflation rate next year than currently expected pe-1 is the inflation rate this year than was expected by the year past p is the current inflation rate, and is the coefficient of partial adjustment (less than or equal to one and greater than or equal to zero) pe pe-1 (p – pe-1) between 1 and 0, this means that current expectations of future inflation reflect past expectations and a period of “adjustment” error, in which current expectations are increased (or reduced) according to the gap between current inflation and previous expectations. NYC , This error term is also called “partial adjustment.” Rather than reflecting changes in expected inflation, this reflects the slow change in the ability of people to react to changes in its expectations.Alternatively, the adaptive expectations theory implies that current inflation expectations are equal to: pe (1 – ) ( j p-j) where the summation ( ) is over all j from 0 to p-j infinity equals the current inflation in the past j years. Thus, current expected inflation reflects a weighted average of all past inflation, where the weights become smaller each time we move further into the past. An alternative theory of how expectations are formed is the theory of rational expectations.