Multiplier Effect

The multiplier effect is the process by which an initial change in spending leads to a larger total change in national income. When a government, firm or foreign buyer spends money, the people who receive it spend part of it in turn, and the recipients of that spending do the same, so the first injection ripples through the economy. The ratio of the final change in output to the initial change in spending is called the multiplier.

The concept is most often applied to fiscal policy, where it is known as the fiscal multiplier: how much GDP rises for each extra unit of government spending or tax cut. It was introduced by the British economist Richard Kahn in 1931 and became a centrepiece of Keynesian economics after John Maynard Keynes's General Theory of 1936. It should not be confused with the money multiplier, which concerns how bank lending relates to the money supply.

Imagine a town that hires a builder to repair the school roof. The builder spends part of the payment at the local café and hardware store. The café owner then buys new chairs, and the hardware store pays its staff, who go out for dinner. One payment has turned into several rounds of income across the town.

Each round is smaller than the one before, because people save some of what they earn or spend it on goods from outside the town. The multiplier adds up all those rounds. The more people re-spend locally, the bigger the total; the more they save or buy from elsewhere, the faster the ripple fades.

In the simplest model, with no taxes or imports, the multiplier depends only on the marginal propensity to consume:

Here $k$ is the multiplier and MPC is the share of each extra unit of income that households spend. If the MPC is 0.8, then $k = \frac{1}{1 - 0.8} = 5$: an extra 100 of spending would eventually raise income by 500.

Real economies leak spending through taxes and imports, which gives a smaller figure:

• $c$ is the marginal propensity to consume out of after-tax income.
• $t$ is the marginal tax rate on income.
• $m$ is the marginal propensity to import.

With $c = 0.8$, $t = 0.25$ and $m = 0.2$, the denominator is $1 - 0.6 + 0.2 = 0.6$, so $k \approx 1.67$. The 100 of extra spending now raises income by about 167. Open economies with high tax rates therefore tend to have smaller multipliers than closed ones.

• Slack in the economy. Multipliers are larger in a recession, when idle workers and machines can be put to use, and smaller near full employment, when extra demand mostly raises prices.
• Central bank response. If the central bank raises interest rates to offset fiscal stimulus, the multiplier shrinks; at the zero lower bound, when rates cannot fall further and are not raised, it tends to be larger.
• Type of measure. Spending on goods, services and investment usually has a larger effect than tax cuts, and transfers to low-income households larger than tax cuts for high earners, because of differences in propensity to spend.
• Financing and expectations. Crowding out of private investment and Ricardian saving in anticipation of future taxes both reduce the effect.
• Exchange-rate regime. Under a fixed exchange rate, fiscal multipliers tend to be larger than under a floating rate, where higher rates can strengthen the currency and reduce exports.

Estimating multipliers is difficult because government spending often responds to the economy rather than the other way round. Researchers use military build-ups, regional variation and natural experiments to isolate cause and effect. Estimates for advanced economies commonly range from below 0.5 to around 2, with higher values found in downturns. When scoring the US American Recovery and Reinvestment Act of 2009, the Congressional Budget Office used ranges of roughly 0.5 to 2.5 for federal purchases of goods and services. A 2013 IMF working paper by Olivier Blanchard and Daniel Leigh concluded that during the early euro-crisis years multipliers had been substantially above the 0.5 that forecasters had assumed, so austerity programmes cut output more than expected.

The multiplier is used to estimate the effect of stimulus packages, budget cuts, new factories, tourism or remittances on a regional or national economy. It also works in reverse: a fall in spending, such as a collapse in exports, can shrink income by more than the initial loss. Critics note that simple multipliers ignore supply constraints, inflation, the long-run cost of debt and changes in confidence, and that local impact studies sometimes use inflated multipliers to promote projects. Classical and monetarist economists argue that, over time, the multiplier is close to zero once prices and interest rates adjust; Keynesians reply that in a deep slump the short run is what matters.

• IMF Working Paper: Growth Forecast Errors and Fiscal Multipliers
• Congressional Budget Office