Investment Multiplier

The investment multiplier is the ratio of the change in national income to the change in investment that causes it. It is a special case of the general multiplier, and it captures the idea that an initial increase in investment raises income, part of which is spent on consumption, generating further income and further spending, so that the total effect exceeds the initial change. The concept was central to the Keynesian analysis of how fluctuations in investment, which is volatile, are amplified into fluctuations in output and employment.

Derivation

In the simplest Keynesian model, a closed economy with no government and no taxation, the multiplier equals one divided by one minus the marginal propensity to consume. If households spend eighty per cent of any additional income, the multiplier is five, so that an increase in investment of one unit raises national income by five units. The logic is that the initial spending becomes income for others, of which a fraction is spent, becoming income again, and so on in a converging geometric series.

The multiplier can be expressed in terms of the saving function as well, since one minus the marginal propensity to consume is the marginal propensity to save, so that the multiplier is the reciprocal of the marginal propensity to save. This formulation emphasises that the size of the multiplier depends on how much of any additional income leaks into saving, and that higher saving rates, which are usually desirable for growth, reduce the short-run multiplier.

The process

The process through which the multiplier operates can be traced in rounds. An increase in investment raises the income of those who supply the capital goods, who spend part of their income, raising the income of others, who spend part, and so on. Each round adds less than the previous one, because part of each increment is saved, and the series converges to the multiplier times the initial change. The process takes time, and the full effect is realised only after the rounds have worked through the economy.

Leakages reduce the multiplier. Saving, taxation, and imports all divert part of any increase in income away from domestic consumption, so that the rounds decay more quickly and the multiplier is smaller. In an open economy with taxes, the multiplier is smaller than in the simple closed-economy case, and its size depends on the marginal propensities to save, to pay taxes, and to import. The composition of investment also matters, since investment that uses domestic inputs has a larger effect than investment that relies on imports.

Relation to the accelerator

The investment multiplier is often combined with the accelerator, which relates investment to changes in output, in the multiplier-accelerator model. In that model, an initial increase in investment raises income, which induces further investment through the accelerator, generating further income and further investment. The interaction can amplify shocks and, under certain parameter values, produce cycles that persist even without new shocks.

The interaction illustrates both the power and the instability of investment-led growth. Because investment responds to changes in output, and because the multiplier magnifies changes in investment, the economy can be subject to self-reinforcing expansions and contractions. The model helps to explain the volatility of investment and the cyclical behaviour of economies, and it was an important step in the development of business cycle theory.

Criticisms and limitations

The simple multiplier has been criticised on several grounds. It assumes that resources are unemployed and that increases in demand can raise output without raising prices, which is not true at full employment. It ignores the effect of higher demand on interest rates, which may rise and crowd out investment, reducing the multiplier. It also ignores the role of expectations, since firms may not invest if they doubt that demand will persist, and households may save rather than spend if they fear for the future.

The empirical evidence suggests that the multiplier is smaller than the simple model implies, and that it varies with the state of the economy. In deep recessions with slack capacity and accommodative monetary policy, the multiplier is larger; in expansions, it is smaller. The concept nonetheless remains central to macroeconomics, because it explains how changes in investment and other autonomous spending are amplified into larger changes in output and employment, and because it informs the design of stabilisation policy.

Open economy and government

Extending the multiplier to include government and foreign trade modifies its size. Government spending adds directly to demand, while taxes reduce the income available for consumption and imports leak spending abroad. The multiplier in an open economy with taxes is therefore smaller than in the simple model, and its size depends on the marginal propensities to tax, to save, and to import. The composition of the spending also matters, since spending on domestic goods and services has a larger effect than spending on imports.

The presence of an automatic stabiliser further modifies the process. Progressive taxes and unemployment benefits reduce the fraction of any change in income that is spent, damping the multiplier. This damping is desirable for stability, since it reduces the amplitude of fluctuations, but it also means that discretionary measures have smaller effects than they would otherwise, and it changes the calculation of the fiscal cost of stimulus.

Empirical estimates

Estimates of the investment multiplier and of the broader fiscal multiplier vary widely. Studies using macroeconomic models find values typically in the range of one half to one and a half in normal conditions, with larger values when interest rates are near their lower bound. Evidence from historical episodes and from cross-country data supports larger multipliers during deep recessions, consistent with the view that the multiplier is state-dependent.

The variation reflects differences in method and in context. Narrative approaches, which identify exogenous changes in spending, tend to find different results from approaches that use timing restrictions, and the estimates depend on the sample and on the measure of the fiscal change. The consensus that emerges is that the multiplier is positive, that it is larger when there is slack and when monetary policy is accommodative, and that it is smaller in open economies and during expansions.

Critiques and modern developments

The simple multiplier has been criticised for ignoring the effect of expectations, of interest rates, and of the supply side. If households anticipate higher future taxes, they may save rather than spend, reducing the effect. If the central bank raises rates in response, the effect is offset. If the economy is at full capacity, additional demand raises prices rather than output. These considerations mean that the multiplier is not a fixed constant but a contingent parameter.

Modern research incorporates these considerations. Models with forward-looking households, with financial frictions, and with a monetary policy rule produce multipliers that vary with the state of the economy and with the policy mix. The empirical literature uses these models to interpret the evidence and to forecast the effects of policy, and it emphasises the uncertainty surrounding the estimates. The investment multiplier remains a central concept, but it is now understood as one whose value depends on circumstances.

See also

• Fiscal Multiplier
• Accelerator Model
• Marginal Propensity to Consume
• Keynesian Multiplier
• Autonomous Investment