Accelerator effect

The acceleration effect is the phenomenon that a variable moves toward its desired value faster and faster with respect to time. Usually, the variable is the capital stock. In Keynesian models, fixed capital is not in consideration, so the accelerator coefficient becomes the reciprocal of the multiplier and the capital decision degenerates to investment decision. In more general theory, where the capital decision determines the desired level of capital stock (which includes fixed capital and working capital), and the investment decision determines the change of capital stock in a sequences of periods, the acceleration effect emerges as only the current period gap affects the current investment, so do the previous gaps. The Aftalion-Clark accelerator v has such a form ${\displaystyle I_{t}=\mu v\sum _{i=1}^{\infty }\left(1-\mu \right)^{i}\left(Y_{t-i}-Y_{t-i-1}\right)}$, while the Keynesian multiplier m has such a form ${\displaystyle Y_{t}=mI_{t}={\frac {1}{1-MPC}}I_{t}}$ where MPC is the marginal propensity to consume. The idea of the accelerator has been very well explained by Hayek.

As the acceleration effect dictates that the increase of income accelerates capital accumulation, and the decrease of income accelerates capital depletion (in a simple model), this might cause the system to become unstable or cyclical, and hence many kinds of business cycle models are of this kind (the multiplier-accelerator cycle models).

The accelerator effect is shown in the simple accelerator model. This model assumes that the stock of capital goods (K) is proportional to the level of production (Y):

K = k×Y

This implies that if k (the capital-output ratio) is constant, an increase in Y requires an increase in K. That is, net investment, I_n equals:

I_n = k×ΔY

Suppose that k = 2 (usually, k is assumed to be in (0,1)). This equation implies that if Y rises by 10, then net investment will equal 10×2 = 20, as suggested by the accelerator effect. If Y then rises by only 5, the equation implies that the level of investment will be 5×2 = 10. This means that the simple accelerator model implies that fixed investment will fall if the growth of production slows. An actual fall in production is not needed to cause investment to fall. However, such a fall in output will result if slowing growth of production causes investment to fall, since that reduces aggregate demand. Thus, the simple accelerator model implies an endogenous explanation of the business-cycle downturn, the transition to a recession.

Modern economists have described the accelerator effect in terms of the more sophisticated flexible accelerator model of investment. Businesses are described as engaging in net investment in fixed capital goods in order to close the gap between the desired stock of capital goods (K^d) and the existing stock of capital goods left over from the past (K₋₁):

${\displaystyle I_{n}=x(K^{d}-K_{-1})}$

where x is a coefficient representing the speed of adjustment (1 ≥ x ≥ 0).

${\displaystyle I_{t}=\mu v\sum _{i=1}^{\infty }\left(1-\mu \right)^{i}\left(Y_{t-i}-Y_{t-i-1}\right)}$

The desired stock of capital goods is determined by such variables as the expected profit rate, the expected level of output, the interest rate (the cost of finance), and technology. Because the expected level of output plays a role, this model exhibits behavior described by the accelerator effect but less extreme than that of the simple accelerator. Because the existing capital stock grows over time due to past net investment, a slowing of the growth of output (GDP) can cause the gap between the desired K and the existing K to narrow, close, or even become negative, causing current net investment to fall.

Obviously, ceteris paribus, an actual fall in output depresses the desired stock of capital goods and thus net investment. Similarly, a rise in output causes a rise in investment. Finally, if the desired capital stock is less than the actual stock, then net investment may be depressed for a long time.

In the neoclassical accelerator model of Jorgenson, the desired capital stock is derived from the aggregate production function assuming profit maximization and perfect competition. In Jorgenson's original model (1963),[2] there is no acceleration effect, since the investment is instantaneous, so the capital stock can jump.

• Multiplier (economics)
• Spending multiplier
• Financial accelerator

• Knox, A. D. (1970). "The Acceleration Principle and the Theory of Investment: A Survey". In Shapiro, Edward (ed.). Macroeconomics: Selected Readings. New York: Harcourt, Brace & World. pp. 49–74. ISBN 0-15-551207-2.