Memoranda Spatio - Temporal Processes in Dynamic Logit Models

Chaos theory has recently caught the attention in the social sciences for its capability of capturing irregular motions which are endogenously produced in economie and social systems. However, in many cases major questions are arising concerning the real-world significance of critical parameter values leading to chaos, the testability of the models concerned and the validity of model specifications. This paper focusses the attention on this last issue, in particular on the compatibility between rationality and chaos in a social environment. Firstly, it will be shown that a population modelled by a dynamic structure of a logit type (i.e., a population maximising a dynamicstochastic micro utility function in a choice problem) can exhibit chaotic or complex movements in its choices. This finding reinforces previous contributions obtained in the rational expectations literature. However, it also questions the validity of the predictions of dynamic logit models in the presence of chaotic behaviour. Secondly, the importance of time lag effects and hence the influence of the past will be examined by considering a degenerated logit model with delays of two and three generations, thus confirming that lags in population dynamics may lead to erratic behaviour in population movement. These lessons from higher-order dynamics show that the values of the parameters in critical ranges play a fundamental role in chaotic regimes. Consequently much more emphasis has to be placed upon empirical validation of these models. 1