2. Some accelerator-multiplier models 1. INTRODUCTION In spite of the inability of statistical studies to establish that a measurable accelerator coeﬃcient exists, many models of the business cycle have appeared in which the accelerator coeﬃcient is an institutional or engineering constant. In addition to such constant valued accelerator models, models of the business cycle have appeared in which the value of the accelerator coeﬃcient varies over the business cycle. In general the mechanism by which the change in the value of the accelerator coeﬃcient is brought about is not explicitly stated. Assumptions as to the existence of a ﬂoor or a ceiling to investment due to the technological limitations upon disinvestment and to the existence of a full employment ceiling (total or sectoral) are made. In addition, a third variety of accelerator business cycle model may be distinguished, one in which the model is subject to random shocks. In this chapter models from each of these classes will be taken up. Variants of such models will be constructed. We will see whether or not these models are consistent with the hypothesis that the business cycle of experience can be best analysed by assuming that the value of the accelerator coeﬃcient varies in a systematic manner over the business cycle, and that the systematic variation in the value of the accelerator coeﬃcient can be imputed to the economic phenomena associated with the diﬀerent levels and rates of changes in income. In this chapter we...
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