EXPECTATIONS, LEARNING AND THE KALMAN FILTER

Abstract

Summary Our final comments can be relatively brief. In assessing the empirical importance of expectations variables in macroeconomic behavioural equations, a variety of “expectations models” should be used. To date, the Muth‐rational expectations approach has dominated the empirical literature. A major drawback, however, is the lack of an explicit optimal learning process by agents. We have attempted to remedy this by bringing together various diverse strands in the expectations, statistics and engineering literature to formalize models that embody “optimal information extraction” by agents faced with a stochastic environment. The Khan filter provides a unified method of approaching these problems and in this paper we presented the Kalman filter in terms of the usual least squares approach familiar to applied economists. Relatively inexpensive econometric software which utilizes recursive estimation techniques has recently become available. It is hoped that this paper has provided a framework favourable to its use by applied economists particularly in investigating the role of expectations variables in economic models.

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