Accelerator Model
The accelerator model is a theory of investment that holds that the level of investment depends on the rate of change of output, rather than on the level of output itself. When output grows, firms must expand capacity, and investment rises; when growth slows or output falls, investment declines sharply. The model, associated with the early work of John Maurice Clark and later developed in the flexible accelerator framework, helps to explain the pronounced volatility of investment over the business cycle.
The simple accelerator
In the simplest form, the model assumes that firms wish to maintain a fixed ratio of capital to output, called the capital-output ratio. If demand for a firm's product rises, the firm must increase its capital stock in proportion to the higher level of output. Investment is therefore equal to the capital-output ratio multiplied by the change in output. This relationship implies that a small change in the growth rate of output can cause a large change in investment.
The model has striking implications. If output stops growing but remains at a high level, investment falls to zero, because no new capital is needed. If output declines, investment becomes negative, as firms allow capital to depreciate without replacing it. This sensitivity of investment to the rate of change of output explains why investment is the most volatile component of gross domestic product and why swings in demand can have amplified effects on capital spending.
The flexible accelerator
The simple accelerator assumes that firms adjust the capital stock instantaneously to the desired level, which is unrealistic. The flexible accelerator, also called the stock adjustment model, recognises that adjustment takes time because of delivery lags, planning, and adjustment costs. Investment in each period is a fraction of the gap between the desired and actual capital stock. The speed of adjustment depends on the costs of adjusting capital relative to the costs of being away from the desired level.
The flexible accelerator generates a gradual response of investment to changes in output, smoothing the volatility predicted by the simple model. It also incorporates the replacement of depreciated capital, so that investment includes a component to maintain the existing stock in addition to the component that expands it. This refinement improves the empirical fit of the model and provides a more realistic description of investment behaviour.
Determinants and extensions
The accelerator model emphasises output and its growth as the primary determinant of investment, but investment also depends on the cost of capital, including interest rates, taxes, and the relative price of capital goods; on profitability and cash flow; and on expectations and uncertainty. Extensions of the model incorporate these factors, often through the user cost of capital or through the Q theory of investment, which relates investment to the ratio of market value to replacement cost.
Expectations are central. Because investment projects are long-lived, firms must forecast future demand, and uncertainty about the future can delay or reduce investment. The accelerator model has been extended to incorporate expectations and to allow for the irreversibility of investment, which creates an option value to waiting. These extensions help to explain why investment is sensitive to uncertainty and why policy credibility matters for capital spending.
Policy implications
The accelerator model has important policy implications. Because investment responds to the rate of change of output, policies that stabilise demand can also stabilise investment. Conversely, policies that cause sharp fluctuations in demand, such as abrupt fiscal consolidation during a downturn, can trigger large falls in investment that magnify the slowdown. The model thus supports the case for countercyclical policy and for gradualism in fiscal adjustment.
The model also helps to explain the accelerator effect in business cycles, in which an initial change in demand sets off a chain of investment responses that amplify the original disturbance. Understanding this mechanism is important for forecasting and for designing policy that avoids destabilising swings in capital spending, and it informs the analysis of how shocks propagate through the economy.
The multiplier-accelerator interaction
The accelerator model is often combined with the multiplier to produce a theory of business cycles. In the multiplier-accelerator model, an initial change in autonomous spending raises income through the multiplier, which in turn raises investment through the accelerator, generating further income and further investment. The interaction can amplify shocks and, under certain parameter values, generate cyclical fluctuations that persist even without new shocks.
The model shows how the interaction of consumption and investment decisions can produce endogenous cycles, an important insight in the development of business-cycle theory. Depending on the values of the marginal propensity to consume and the capital-output ratio, the system may converge to equilibrium, oscillate with periods of expansion and contraction, or diverge. The framework helped to explain why economies experience recurring cycles and why small disturbances can have large effects.
Empirical evidence
Empirical tests of the accelerator model have produced mixed results. The relationship between investment and changes in output is robustly positive in the data, supporting the model's central prediction. However, the simple accelerator overstates the volatility of investment, and the fit improves substantially when the model is extended to include adjustment costs, the cost of capital, and cash flow. Investment also responds to expectations about the future, which the simple model ignores.
Modern investment theory integrates the accelerator with the Q theory, recognising that investment depends on both the level of demand and the valuation of capital relative to its replacement cost. Research using firm-level data finds that output growth, profitability, and financial constraints all influence investment, and that the response varies across firms, industries, and time periods. These findings refine the accelerator without discarding its core insight.
Cyclical and structural implications
The accelerator model has implications for understanding both cyclical and structural change. Cyclically, it explains why investment collapses during recessions and surges during recoveries, amplifying the business cycle. Structurally, it implies that steady growth requires continuing investment, since firms must expand capital to keep pace with demand. An economy that stops growing will also stop investing, and if growth resumes, investment will rebound.
These implications matter for policy. A slowdown in growth can trigger a disproportionate decline in investment, which reduces the capital stock and lowers future potential output, an effect that reinforces the slowdown. Policies that support demand stability and that reduce uncertainty can help to sustain investment, while structural policies that improve the business environment and the availability of finance can lower the cost of capital and support capital formation.