ABSTRACT
It was indicated in Chapter 10 that the influence of erratic shocks prevents the damping of fluctuations in investment. That is, if a damped cycle is inherent in the equation: https://www.w3.org/1998/Math/MathML"> i t = a 1 + c i t − θ + μ Δ i t − θ − ω Δ t https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203708668/09397ff6-dfe3-4264-97b7-fa15b1e26590/content/math_140_B.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> then, when ϵ t is the erratic shock at time t, the equation: https://www.w3.org/1998/Math/MathML"> i t = a 1 + c i t + θ + μ Δ i t − θ − ω Δ t + ϵ t https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203708668/09397ff6-dfe3-4264-97b7-fa15b1e26590/content/math_141_B.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> will represent semi-regular undamped fluctuations. In the investigations made on the subject, it appeared, as stated above, that this cycle was fairly regular and of an amplitude appreciably greater than that of erratic shocks if the damping was mild. With heavier damping, the cycle generated became irregular and its amplitude of the same order of magnitude as that of the shocks. The above can be illustrated by the following example. The first variant of the business cycle model, obtained above from the United States data for the period 1929–1940, involves mildly damped fluctuations. The damping is about 1·5 per cent per annum and the period is 8·5 years. If we introduce erratic shocks in this model, it will be seen that fairly regular cyclical fluctuations are generated.
