Accelerator Effect - Accelerator Models

Accelerator 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 (Kd) and the existing stock of capital goods left over from the past (K_-1):

I_n = x(Kd - K_-1)

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

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