On the consistency of backward-looking expectations: The case of the cobweb

In dynamic models of economic fluctuations backward-looking expectations with systematic forecasting errors are inconsistent with rational behaviour. In non-linear dynamic models exhibiting seemingly unpredictable, chaotic fluctuations, however, simple habitual ‘rule of thumb’ backward-looking expectation rules may yield non-zero but nevertheless non-systematic forecasting errors. In a chaotic model expectational forecasting errors may have zero autocorrelations at all lags. Even for rational agents patterns in these forecasting errors may be very difficult to detect, especially in the presence of (small) noise. Backward-looking expectations are then not necessarily inconsistent with rational behaviour. We investigate whether simple expectation schemes such as naive or adaptive expectations can be consistent with rational behaviour in the simplest of all non-linear dynamic economic models, the non-linear cobweb model.