The concept and calculation of the Keynesian multiplier

The Keynesian multiplier explains how an initial increase in spending, such as government expenditure, leads to a proportionally larger rise in national income. This process occurs through successive rounds of spending, where one person's expenditure becomes another's income, stimulating further economic activity.

How the multiplier works

Economic activity unfolds in rounds:

• An initial injection (e.g., government spending on infrastructure) increases income for workers and suppliers.
• Recipients spend a portion of this new income on domestic goods and services, creating further income for others.
• This cycle continues, with each round adding to national income, though the amounts diminish due to withdrawals like saving, taxes, and imports.

The overall change in national income (ΔY) is given by:

$\mathrm{\Delta }Y=k\mathrm{\Delta }J$

Where:

• ΔY = Change in national income
• k = Multiplier
• ΔJ = Change in injections (e.g., government spending G, investment I, or exports X)

Formulas for the multiplier

The size of the multiplier depends on the proportion of additional income that leaks out of the economy through withdrawals.

$\text{Multiplier (k)}=\frac{1}{1-\text{MPCd}}$

Where:

• MPCd = Marginal propensity to consume domestically produced goods and services (proportion of additional income spent on domestic output)

Alternatively:

$\text{Multiplier (k)}=\frac{1}{\text{MPW}}$

Where:

• MPW = Marginal propensity to withdraw (sum of MPS + MPT + MPM)

The multiplier is larger when MPCd is higher (more spending stays in the economy) and withdrawals are smaller.

Worked example - Calculating the multiplier and change in national income

Suppose the government increases spending on public services by £60 million, and the marginal propensity to consume domestically (MPCd) is 0.8. Calculate the multiplier and the total increase in national income.

Step 1: Identify the values

• Change in government spending (ΔJ) = £60 million
• MPCd = 0.8

Step 2: Apply the multiplier formula

$\text{Multiplier (k)}=\frac{1}{1-0.8}=\frac{1}{0.2}=5$

Step 3: Calculate the change in national income

$\mathrm{\Delta }Y=5\times \pounds 60\text{ million}=\pounds 300\text{ million}$

Marginal propensities and their role in the multiplier

Marginal propensities describe how additional income is allocated between consumption, saving, taxation, and imports. These influence the multiplier by determining how much income remains in circulation.

Marginal propensity to consume (MPC)

The MPC is the proportion of additional income spent on domestic goods and services.

$\text{MPC}=\frac{\mathrm{\Delta }\text{Cd}}{\mathrm{\Delta }Y}$

Where:

• ΔCd = Change in consumption of domestic goods and services
• ΔY = Change in income

Marginal propensity to save (MPS)

The MPS is the proportion of additional income saved.

$\text{MPS}=\frac{\mathrm{\Delta }S}{\mathrm{\Delta }Y}$

Where:

• ΔS = Change in savings
• ΔY = Change in income

Marginal propensity to tax (MPT)

The MPT is the proportion of additional income paid in taxes.

$\text{MPT}=\frac{\mathrm{\Delta }T}{\mathrm{\Delta }Y}$

Where:

• ΔT = Change in taxes
• ΔY = Change in income

Marginal propensity to import (MPM)

The MPM is the proportion of additional income spent on imports.

$\text{MPM}=\frac{\mathrm{\Delta }M}{\mathrm{\Delta }Y}$

Where:

• ΔM = Change in imports
• ΔY = Change in income

Marginal propensity to withdraw (MPW)

The MPW is the total proportion of additional income withdrawn from the economy.

$\text{MPW}=\text{MPS}+\text{MPT}+\text{MPM}$

MPW equals (1 - MPCd), as income is either spent domestically or withdrawn.

Higher MPCd strengthens the multiplier, while higher withdrawals (e.g., greater MPS or MPM) weaken it.

Research studies on the multiplier effect

Several studies have estimated the multiplier in real-world scenarios, highlighting its variability and policy implications.

Study on the 2020 US stimulus response to Covid-19

• Method - C Bayer and colleagues analysed the $2 trillion US stimulus package introduced in March 2020.
• Results - The multiplier was estimated at up to 2, meaning national income could rise by twice the stimulus amount.
• Conclusions - This high multiplier reflected the severe economic downturn, where additional spending circulated effectively due to low withdrawals.

Study on the 2009 Obama Stimulus Plan

• Method - Christina Romer, Chair of the Council of Economic Advisers, evaluated the $787 billion stimulus.
• Results - The US multiplier was estimated at 1.6, predicting a GDP increase of about $1.26 trillion.
• Conclusions - The stimulus helped mitigate recession, though actual outcomes depended on economic conditions.

IMF analysis during the Greek debt crisis

• Method - The International Monetary Fund (IMF) initially forecasted multipliers for austerity measures.
• Results - The IMF underestimated the expenditure multiplier, leading to a deeper recession than predicted.
• Conclusions - As acknowledged by IMF chief economist Olivier Blanchard, higher-than-expected multipliers amplified the negative impact of spending cuts.

Automatic stabilisers and their economic impact

Automatic stabilisers are built-in fiscal mechanisms that help smooth economic fluctuations without needing new government action. They adjust automatically to changes in economic conditions, stabilising disposable income and demand.

Examples and functions of automatic stabilisers

• Progressive income taxes - Taxes where higher earners pay a larger proportion of their income. In booms, tax burdens rise faster, slowing disposable income growth and curbing inflation. In recessions, tax payments fall, supporting spending.
• Unemployment benefits - Payments to the jobless that increase during downturns, maintaining disposable income and preventing sharper falls in demand.

How automatic stabilisers operate

• In recessions - Falling incomes reduce tax liabilities, while rising unemployment boosts benefit payouts. This cushions disposable income, limiting the drop in aggregate demand.
• In booms - Rising incomes increase tax payments proportionally more, and lower unemployment reduces benefits. This tempers demand growth, reducing inflation risks.
• Advantages - They act immediately, unlike discretionary policies that require legislative approval. For example, during the US recession starting in 2008, automatic stabilisers expanded to nearly 2% of potential GDP before the Obama Stimulus was enacted five quarters later.

Proposals for enhanced stabilisers include automatic lump-sum payments triggered by unemployment rising more than 0.5% above the previous year's low.

The crowding-out effect and its implications

The crowding-out effect describes how increased government borrowing can reduce private sector activity, offsetting some benefits of fiscal stimulus. It is a key criticism of Keynesian policy from monetarist perspectives.

Mechanism of the crowding-out effect

• Government deficit spending raises demand for loanable funds, shifting the demand curve rightward.
• This increases interest rates (from r₁ to r₂), making borrowing more expensive.
• Higher rates discourage private investment, as firms delay or cancel projects.
• Consequently, aggregate demand may not rise as much as anticipated from the initial stimulus.

Factors influencing crowding out

• Economic conditions - Crowding out is less likely in deep recessions, where business confidence is low and investment is already subdued, regardless of interest rates.
• Size of the deflationary gap - In economies with significant spare capacity, the risk is lower, as increased government spending does not compete as intensely for resources.
• Criticisms of Keynesian policy - Monetarists argue that crowding out undermines the effectiveness of expansionary fiscal measures, potentially leading to limited net gains in output.