Goodbye to "Rational Expectations"

Consider an economic model in which the agents within the model act on decisions based on their understanding of the model. For ease of exposition, assume the models within the heads of the agents all have the same form, and that that form matches the actual model. The agents must estimate the parameters of the model.

Suppose the agents have made some estimate of the model parameter. Their decisions result in the parameters being set in the actual model. And the agents use the data generated from the actual model to make their estimates. A rational expectations equilibrium is said to result when the agents' estimates match the model parameters. A rational expectations equilibrium can be thought of as a fixed point of a function from the agents' estimated parameters to the actual parameters.

Rational estimations is often applied to models of economic time series considered as stochastic processes. An important parameter for a stochastic process is the population mean at a given point in time. One can conceptually describe two types of sample means for a stochastic process:

• At a single point in time across many realizations of a stochastic process
• Across time samples for a single realization of a stochastic process

If and only if a stochastic process is ergodic, these two types of sample means converge as the number of realizations and the number of time samples increase.

Some stochastic processes observed in real world economies are non-stationary, for example, if they have a component growing at a constant rate. Non-stationary is sufficient for non-ergodicity, but not necessary. (For an example of a non-ergodic stationary process, consider a Spherically Invariant Random Process (SIRP).) Hence, some real-world processes are non-ergodic.

Agents only have access to a single realization of some processes. They therefore cannot form a sample spatial average for such a process. They only can take statistics, such as a time average, for a time series. And, if that process is non-ergodic, such a sample average will have no tendency to converge to the true model parameter, which is an average across the population of all realizations.

So much for "rational expectations".

Reference

• Paul Davidson (1982-1983). "Rational Expectations: A Fallacious Foundation for Studying Crucial Decision-Making Processes", Journal of Post Keynesian Economics, 5 (Winter): 182-197.