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

Suppose actual inflation is π = E[π | I] + ε, where I is the information available when expectations are formed and ε is the forecast error. Which of the following is inconsistent with rational expectations?

A significant regression of the forecast error on last period's money growth contradicts rational expectations. Errors must be unpredictable from information already available, so any systematic link shows the information was not used efficiently. Non-zero error variance is entirely consistent with rational expectations.

  1. AE[ε] = 0
  2. Bε is uncorrelated with every variable in I
  3. CPast forecast errors in ε are serially uncorrelated
  4. DForecast errors have non-zero variance
  5. A regression of ε on last period's money growth (which is in I) gives a significantly positive coefficientCorrect

Explanation

Rational expectations require errors to be orthogonal to the information set, so any predictable relation between ε and variables in I implies information was not used efficiently. Non-zero variance is perfectly consistent, since errors still occur. Zero mean, no correlation with I and no serial correlation are all required properties.

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