Fiscal multiplier

This article is about the effect of spending on national income. For the multiplier effect in banking, see Fractional-reserve banking.

In economics, the fiscal multiplier is the ratio of a change in national income to the change in government spending that causes it. More generally, the exogenous spending multiplier is the ratio of a change in national income to any autonomous change in spending (private investment spending, consumer spending, government spending, or spending by foreigners on the country's exports) that causes it. When this multiplier exceeds one, the enhanced effect on national income is called the multiplier effect. The mechanism that can give rise to a multiplier effect is that an initial incremental amount of spending can lead to increased consumption spending, increasing income further and hence further increasing consumption, etc., resulting in an overall increase in national income greater than the initial incremental amount of spending. In other words, an initial change in aggregate demand may cause a change in aggregate output (and hence the aggregate income that it generates) that is a multiple of the initial change.

However, multiplier values less than one have been empirically measured, suggesting that certain types of government spending crowd out private investment or consumer spending that would have otherwise taken place. This crowding out can occur because the initial increase in spending may cause an increase in interest rates or in the price level.

The existence of a multiplier effect was initially proposed by Richard Kahn in 1930 and published in 1931. It is particularly associated with Keynesian economics. Some other schools of economic thought reject or downplay the importance of multiplier effects, particularly in terms of the long run. The multiplier effect has been used as an argument for the efficacy of government spending or taxation relief to stimulate aggregate demand.

Net Government Spending

The other important aspect of the multiplier, is that to the extent that government spending generates new consumption, it also generates "new" tax revenues. For example, when money is spent in a shop, purchases taxes such as VAT are paid on the expenditure, and the shopkeeper earns a higher income, and thus pays more income taxes. Therefore, although the government spends $1, it is likely that it receives back a significant proportion of the $1 in due course, making the net expenditure much less than $1. Indeed, in theory, it is possible, if the initial expenditure is targeted well, that the government could receive back more than the initial $1 expended.

Examples

For example: a company spends $1 million to build a factory. The money does not disappear, but rather becomes wages to builders, revenue to suppliers etc. The builders will have higher disposable income as a result, consumption rises as well, and hence aggregate demand will also rise. Suppose further that recipients of the new spending by the builder in turn spend their new income, this will raise consumption and demand further, and so on.

The increase in the gross domestic product is the sum of the increases in net income of everyone affected. If the builder receives $1 million and pays out $800,000 to sub contractors, he has a net income of $200,000 and a corresponding increase in disposable income (the amount remaining after taxes).

This process proceeds down the line through subcontractors and their employees, each experiencing an increase in disposable income to the degree the new work they perform does not displace other work they are already performing. Each participant who experiences an increase in disposable income then spends some portion of it on final (consumer) goods, according to his or her marginal propensity to consume, which causes the cycle to repeat an arbitrary number of times, limited only by the spare capacity available.

Another example: when tourists visit somewhere they need to buy the plane ticket, catch a taxi from the airport to the hotel, book in at the hotel, eat at the restaurant and go to the movies or tourist destination. The taxi driver needs petrol (gasoline) for his cab, the hotel needs to hire the staff, the restaurant needs attendants and chefs, and the movies and tourist destinations need staff and cleaners.

Applications

The multiplier effect is a tool used by governments to attempt to stimulate aggregate demand. This can be done in a period of recession or economic uncertainty. The money invested by a government creates more jobs, which in turn will mean more spending and so on.

The idea is that the net increase in disposable income by all parties throughout the economy will be greater than the original investment. When that is the case, the government can increase the gross domestic product by an amount that is greater than an increase in the amount it spends relative to the amount it collects in taxes.

The difference is the fiscal stimulus. The net fiscal stimulus may be increased by raising spending above the level of tax revenues, reducing taxes below the level of government spending, or any combination of the two that results in the government taxing less than it spends.

The resulting deficit spending must be financed from government reserves (if any) or net borrowing from private or foreign investors. If the money is borrowed, it must eventually be paid back with interest, such that the long term effect on the economy depends on the trade off between the immediate increase to the GDP and the long term cost of servicing the resulting government debt.

It must be noted that the extent of the multiplier effect is dependent upon the marginal propensity to consume and marginal propensity to import. Also that the multiplier can work in reverse as well, so an initial fall in spending can trigger further falls in aggregate output.

The concept of the economic multiplier on a macroeconomic scale can be extended to any economic region. For example, building a new factory may lead to new employment for locals, which may have knock-on economic effects for the city or region.

Various types of fiscal multipliers

The following values are theoretical values based on simplified models, and the empirical values corresponding to the reality have been found to be lower (see below).

Note: In the following examples the multiplier is the right-hand-side equation without the first component.

• y is original output (GDP)
• $b_{C}$ is marginal propensity of consumption (MPC)
• $b_{T}$ is original income tax rate
• $b_{M}$ is marginal propensity to import
• $\Delta y$ is change in income (equivalent to GDP)
• $\Delta a_{T}$ is change in lump-sum tax rate
• $\Delta b_{T}$ is change in income tax rate
• $\Delta G$ is change in government spending
• $\Delta T$ is change in aggregate taxes
• $\Delta I$ is change in investment
• $\Delta X$ is change in exports

Standard Income Tax Equation

$\Delta y=\Delta T*{\frac {-C*y}{(1-C)(1-T)+M}}$

Note: only $\Delta b_{T}$ is here because if this is a change in income tax rate then $\Delta a_{T}$ is implied to be 0.

Standard Government Spending Equation

$\Delta y=\Delta G*{\frac {1}{(1-b_{C})(1-b_{T})+b_{M}}}$ or K

Standard Investment Equation

$\Delta y=\Delta I*{\frac {1}{(1-b_{C})(1-b_{T})+b_{M}}}$

Standard Exports Equation

$\Delta y=\Delta X*{\frac {1}{(1-b_{C})(1-b_{T})+b_{M}}}$ or K

Balanced-Budget Government Spending Equation

$\Delta y=\Delta G*1$

$\Delta y=\Delta T*1$

Estimated values

United States of America

In congressional testimony given in July 2008, Mark Zandi, chief economist for Moody's Economy.com, provided estimates of the one year multiplier effect for several fiscal policy options. The multipliers showed that increased government spending would have more of a multiplier effect than tax cuts. The most effective policy, a temporary increase in food stamps, had an estimated multiplier of 1.73. Making the Bush tax cuts permanent, had the second lowest multiplier, 0.23. A payroll tax holiday had the largest multiplier for tax cuts, 1.29. Refundable lump-sum tax rebates, the policy used in the Economic Stimulus Act of 2008, had the second largest multiplier for a tax cut, 1.26.

Robert J. Barro estimated that government spending has a multiplier of around 0.8, meaning for $1.00 spent, the economy gets $0.80. In addition, the spending must be repaid in the future most likely with tax increases which he assumes to have a multiplier of -1.1. This results in a further decrease in GDP and concludes that government spending actually has more cost than benefit.

According to Otto Eckstein, estimation has found "textbook" values of multipliers are overstated. The following tables has assumptions about monetary policy along the left hand side. Along the top is whether the multiplier value is for a change in government spending (ΔG) or a tax cut (-ΔT).

Monetary Policy Assumption	ΔY/ΔG	ΔY/(-ΔT)
Interest Rate Constant	1.93	1.19
Money Supply Constant	0.6	0.26

The above table is for the fourth quarter under which a permanent change in policy is in force.

Europe

Italian economists have estimated multiplier values ranging from 1.4 up to 2.0 when dynamic effects are accounted for. The economists used mafia influence as an instrumental variable to help estimate the effect of central funds given to local councils.

Crowding out

Fiscal activity does not always lead to increased economic activity because deficit spending used to finance spending or tax cuts can crowd out financing for other economic activity. Of course, this phenomenon is argued to be less likely to occur in a recession, where savings rates are traditionally higher and capital is not being fully utilized in the private market.

Marginal Propensity to Consume, targeting the Multiplier and "benevolent" consumption

As has been discussed, the Multiplier relies on the MPC (Marginal Propensity to Consume). The use of the term MPC here, is a reference to the MPC of a country (or similar economic unit) as a whole, and the theory and the mathematical formulae apply to this use of the term. However, individuals have an MPC, and furthermore MPC is not homogeneous across society. Even if it was, the nature of the consumption is not homogeneous. Some consumption may be seen as more benevolent (to the economy) than others. Therefore spending could be targeted where it would do most benefit, and thus generate the highest (closest to 1) MPC. This has traditionally been regarded as construction or other major projects (which also bring a direct benefit in the form of the finished product).

Clearly, some sectors of society are likely to have a much higher MPC than others. Someone with above average wealth or income or both may have a very low (short term, at least) MPC of nearly zero - saving most of any extra income.

But a pensioner, for example, will have an MPC of 1 or even greater than 1. This is because a pensioner is quite likely to spend every penny of any extra income. Further, if the extra income is seen as regular extra income, and guaranteed into the future, the pensioner may actually spend MORE than the extra £1. This would occur where the extra income stream gives confidence that the individual does not need to put aside as much in the form of savings, or perhaps can even dip into existing savings.

More importantly, this consumption is much more likely to occur in local small business - local shops, pubs and other leisure activities for example. These types of businesses are themselves likely to have a high MPC, and again the nature of their consumption is likely to be in the same, or next tier of businesses, and also of a benevolent nature.

Other individuals with a high, and benevolent, MPC would include almost anyone on a low income - students, parents with young children, and of course, the unemployed.

See also

• Multiplier (economics)
• Multiplier uncertainty
• Keynesian economics
• Fiscal policy
• Local multiplier effect