Business Cycle Theory pp 36-64 | Cite as
Shock-Dependent Business Cycle Theories
Abstract
A business cycle model is called shock-dependent if, for reasonable values of the parameters, the generation of cycles relies on an impetus which is not explained in itself by the model. Although most of the models in this chapter are generally able to display steady and explosive oscillations as well, economic reasoning restricts their valid parameter regimes such that only damped oscillations around stable equilibria are allowed. In order to exhibit permanent fluctuations these models generally require the existence of ongoing exogenous forces which disturb the equilibrating tendencies of the model. Only as an exception and for certain parameter constellations can these models generate permanent oscillations with just one initial exogenous disturbance.
Keywords
Business Cycle Capital Stock Complex Root Exogenous Shock Monotonic BehaviorPreview
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Reference
- 1.Introductions to the mathematics of difference and differential equations can be found in Allen (1965,1967), Dernburg/Dernburg (1969), and Baumol (1958), who also elaborate on several of the older models presented here. The more mathematically interested reader is referred to Coddington/Levinson (1955) and Boyce/ DiPrima (1977).Google Scholar
- 2.The acceleration principle is due to Clark (1917.Google Scholar
- 3.Note that investors have to know the consumption function of consumers in order to know the current period’s consumption demand in advance. It can alternatively be assumed that the entire consumption demand is effective before investment decisions are made.Google Scholar
- 4.Compare Allen (1963), pp. 187 ff.Google Scholar
- 5.See e.g. Dernburg/Dernburg (1969), pp. 216 f.Google Scholar
- 6.See Allen (1963), p. 188.Google Scholar
- 7.Dernburg/Dernburg (1969), p. 144f.Google Scholar
- 8.DeMoivre’s theorem states that (r (cos B + i sin B))“ = r” (cos nO + i sin n8). See e.g. Goldberg (1958), p. 139.Google Scholar
- 9.In Laidler’s original contribution all variables are measured in natural logarithms.Google Scholar
- 10.In order to allow for a direct comparison with previous result, the following presentation is in antilog terms.Google Scholar
- 11.Alternatively, it can be assumed that the absolute value of the (negative) net investment is always smaller than a predetermined depreciation level.Google Scholar
- 12.In order to avoid confusion, it is useful to assume that Pi is exogenous government investment.Google Scholar
- 13.As was mentioned by Hicks (1950, p.102, footnote), the assumption of constant depreciation actually does not allow to draw the path Y as a parallel straight line in Fig. 3.7. Hicks assumed that this influence of a constant amount of depreciation can be neglected, however.Google Scholar
- 14.For a discussion of this type of non-linearities see Baumol (1958), pp. 281 ff.Google Scholar
- 15.Note that the dynamics of the model rely conceptually on disequilibria, whereas the models of Samuelson and Hicks are pure equilibrium business cycle models.Google Scholar
- 16.See e.g. Samuelson (1947), Math. App. B.Google Scholar
- 17.See e.g. Allen (1967), p. 331 and Goldberg (1958), pp. 141 f.Google Scholar
- 18.The following presentation of the 1935-model is basically adopted from Allen (1967), pp. 369 ff.Google Scholar
- 19.Compare Allen (1963), p. 255 f.Google Scholar
- 20.See Allen (1963), pp. 256 ff. for details on the calculations.Google Scholar