What is the difference between rational expectations and adaptive expectations?

Rational expectations is an economic theory that suggests individuals in an economy make their decisions based on available information, and they form expectations about the future using all relevant data and models. In other words, individuals are assumed to have access to all relevant information and have the ability to predict future economic outcomes optimally. This means that predictions of future economic variables (e.g., inflation) will be unbiased and consistent with the actual outcome, on average.

Adaptive expectations, on the other hand, is an alternative theory that assumes individuals in an economy make their predictions about future economic outcomes based on past experiences and trends. In this approach, individuals update their expectations as new information becomes available, but they do so with a certain degree of inertia. This means that their predictions are less precise and may not be consistent with actual economic outcomes, leading to systematic errors and discrepancies between predicted and actual variables.

Rational expectations and adaptive expectations differ mainly in how they predict future economic variables. Rational expectations rely on the assumption that individuals have access to all pertinent information and can optimally predict future outcomes, whereas adaptive expectations rely on past experiences and trends to form predictions, which may be less accurate.

Suppose we have an economy with two groups of people: one group that forms expectations rationally, and another group that forms expectations adaptively. Let's consider an event, such as a central bank announcing a new monetary policy leading to increased inflation in the coming year. The group with rational expectations would take this new information into account when predicting future inflation rates and would adjust their predictions accordingly. On the other hand, the group with adaptive expectations might not immediately change their predictions based on this new information, and they might underestimate the extent to which future inflation rates will rise. As a result, the adaptive expectations group may make less accurate predictions about the economy's future.

Both rational and adaptive expectations theories are used in various economic models and help policymakers analyze the potential consequences of economic policies. Rational expectations models are often employed when forecasting medium to long-term economic variables and determining optimal policy settings, while adaptive expectations models might be more suitable for analyzing short-term behavior and the dynamics of economic adjustment.