Adaptive expectations are an assumption included in economic models to simplify the analysis. His main postulate is that agents base their projections on historical data.

This approach contrasts with rational expectations where it is assumed that people take advantage of all available information when formulating their estimates.

In other words, according to adaptive expectations, agents only consider the past. However, if the individuals were rational, they would also include in their analysis the events announced for the future, for example, if the Government ordered the validity of a measure from next year.

The origin of adaptive expectations is in 1956. That year Philip Cagan proposed a model where consumers estimate inflation based on historical data.  The aforementioned meant an advance regarding exogenous expectations. According to this hypothesis, the agents formulate their projections only based on external variables, alien to the personal experiences of each user. However, with the adaptive expectations approach, a key concept was introduced: Agents learn from their mistakes, as we will explain below.

Adaptive expectations as a result of learning

Adaptive expectations can be expressed mathematically as the result of a learning process. Thus, the expected value of a variable is constructed based on the mistakes made in the past at the time of projecting it, as we observe in the following formula:

O tra way of expressing this equation is:

From the above it can be interpreted that the expected evolution of X into the future depends on the error recorded when estimating its present value.

For example, let’s imagine that we are going to project inflation next year. Then, we must take into account the price increase we expected for this year and the data actually recorded.

Now, let’s find a general formula, considering that the above is repeated in several periods:

Then, we replace in the first equation:

In the previous equation, the older the historical data of the variable, the less weight it will have on the estimate. This, because  lambda  is a coefficient less than 1.