IAI Actuarial Core Principles · Economic Modelling · Rational expectations theory and the efficient markets hypothesis

Inflation is modelled as pi(t) = E[pi(t) | information at t-1] + e(t). If expectations are rational, which statement about the error e(t) is correct?

The error has zero conditional mean and is uncorrelated with any information available when the forecast was made. Rational expectations do not rule out errors, because unforeseen shocks occur. Systematic bias or correlation with past information would let agents improve their forecasts, which contradicts rationality.

Ae(t) is positively correlated with inflation in period t-1
Be(t) always has the same sign as the previous error
Ce(t) has zero conditional mean and is uncorrelated with information available at t-1Correct
De(t) must be zero in every period
e(t) is negative on average because agents are cautious

Explanation

With rational expectations, the forecast uses all information at t-1, so the error has zero mean given that information and is uncorrelated with it. Errors need not be zero in each period, since unforeseen shocks occur. Serial correlation or bias would imply that agents could improve their forecasts.

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