Precautionary Learning and Inflationary Biases

Recursive least squares learning is a central concept employed in selecting amongst competing outcomes of dynamic stochastic economic models. In employing least squares estimators, such learning relies on the assumption of a symmetric loss function defined over estimation errors. Within a statistical decision making context, this loss function can be understood as a second order approximation to a von-Neumann Morgenstern utility function. This paper considers instead the implications for adaptive learning of a third order approximation. The resulting asymmetry leads the estimator to put more weight on avoiding mistakes in one direction as opposed to the other. As a precaution against making a more costly mistake, a statistician biases his estimates in the less costly direction by an amount proportional to the variance of the estimate. We investigate how this precautionary bias will affect learning dynamics in a model of inflationary biases. In particular we find that it is possible to maintain a lower long run inflation rate than could be obtained in a time consistent rational expectations equilibrium.