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Content archived on 2024-04-16

Convergence of learning mechanisms in dynamic economic models


Research was carried out on the robustness of bubbles in linear rational expectations (RE) models. The research analysed E-stability (expectational stability) for the complete set of autoregressive moving average (ARMA) solutions to a class of linear RE models including a predetermined variable. It is argued that E-stability governs local convergence of adaptive real time learning rules. Possible differences between weak and strong E-stability are emphasized. It is shown that locally unique solutions can be strongly E-stable, while the continuum of ARMA solutions can form a weakly E-stable class. The relationship of E-stability to saddlepoint stability stochastic stationarity, process consistency and the 'minimal state variable' principle often used to define 'bubble' solutions is examined. Conditions are given under which these concepts coincide. However, it is shown that if the degree of feedback and feedforward in the model is sufficiently high then they become distinct. In particular, nonstationary 'bubble' solutions can be strongly E-stable even in models which are saddlepoint stable.
The results are applied to a rational expectations IS-LM-Lucas supply curve model with real balance effects and a monetary feedback rule.

Central work on the stability under learning of steady states and cycles has been completed. This includes an application to overlapping generations models.
Preliminary work on the stability under learning of 'sunspot solutions' and 'animal spirit' solutions has been finished and an application has been developed which incorporates a production externality, yielding social increasing returns to scale with multiple steady states and sunspot equilibria.
Research has also been carried out on the use of fiscal policy to eliminate inefficient sunspot solutions and on E-stability and adaptive learning.


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Houghton Street
United Kingdom

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