Among the earliest empirical investment models was the acceleration principle, or accelerator. In modern textbooks, the accelerator model survives as a theory of inventory investment, as discussed on page 481 of Mankiw’s text. The accelerator is a simple model that incorporates the kind of feedback from current output to investment that Keynes saw occurring through the effect of current output on investors’ expectations. The accelerator model begins with an assumption that firms’ desired capital-output ratio is roughly constant. This implies that the desired capital stock for any period ‘t’ is proportional to the level of output in t, Kt* = sYt, where s (the lower-case Greek letter sigma) is the desired capital-output ratio. Suppose that firms invest in period t in order to bring their capital stocks to the desired level Kt + 1* in period t + 1. Then, if depreciation is zero for simplicity, It = Kt + 1* - Kt. But since Kt = Kt*, that means that It = s (Yt + 1 - Yt ).
Thus, the simplest accelerator model predicts that investment is proportional to the increase in output in the coming period. Firms, of course, do not observe future output with certainty, so the Yt + 1 term must be interpreted as an expectation. The dependence of investment on expectations is both realistic and central to Keynes’s ideas. However, since we cannot observe expectations of firms about future output, this feature of the accelerator model posed problems for those who wished to implement it. The most common way of resolving this difficulty was to assume that firms expect the change in output in the coming period to be equal to the change in the current period. In mathematical terms, they assume that Et (Yt + 1 - Yt ) = Yt - Yt - 1.

Simply stated, The accelerator effect in economics refers to a positive effect on private fixed investment of the growth of the market economy (measured e.g. by a change in Gross Domestic Product). Rising GDP (an economic boom or prosperity) implies that businesses in general see rising profits, increased sales and cash flow, and greater use of existing capacity. This usually implies that profit expectations and business confidence rise, encouraging businesses to build more factories and other buildings and to install more machinery. (This expenditure is called fixed investment.) This may lead to further growth of the economy through the stimulation of consumer incomes and purchases, i.e., via the multiplier effect.

The accelerator effect also goes the other way: falling GDP (a recession) hurts business profits, sales, cash flow, use of capacity and expectations. This in turn discourages fixed investment, worsening a recession by the multiplier effect. The accelerator effect fits the behavior of an economy best when either the economy is moving away from full employment or when it is already below that level of production. This is because high levels of aggregate demand hit against the limits set by the existing labour force, the existing stock of capital goods, the availability of natural resources, and the technical ability of an economy to convert inputs into products .While modern theorists who are accustomed to using rational expectations will find fault with this myopic theory of expectations, it reflects quite reasonably what Keynes thought was happening in the 1930s—that firms observed a rise or decline in output and extrapolated that change into the future in determining their investment spending. Since the capital-output ratio in most economies is larger than one (often three or more in advanced economies), moderate expected changes in output are capable of triggering relatively large changes in investment in the accelerator model. This is one of the reasons that this theory gained great popularity after the Great Depression as a model of investment.