Fiscal multiplier

In economics, the multiplier effect or spending multiplier is the idea that an initial amount of spending (usually by the government) leads to increased consumption spending and so results in an increase in national income greater than the initial amount of spending. In other words, an initial change in aggregate demand causes a change in aggregate output for the economy that is a multiple of the initial change.

However, multiplier values less than one have been empirically measured, suggesting that government spending crowds out private investments and spending that would have otherwise happened.

The existence of a multiplier effect was initially proposed by Ralph George Hawtrey 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.

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.^[1]

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
• Δy is change in income (equivalent to GDP)
• Δa_T is change in lump-sum tax rate
• Δb_T is change in income tax rate
• ΔG is change in government spending
• ΔT is change in aggregate taxes
• ΔI is change in investment
• ΔX is change in exports

Standard Lump-sum Tax Equation

Note: only Δa_T is here because if this is a change in lump-sum tax rate then Δb_T is implied to be 0.

Standard Income Tax Equation

Note: only Δb_T is here because if this is a change in income tax rate then Δa_T is implied to be 0.

Standard Government Spending Equation

Standard Investment Equation

Standard Exports Equation

Balanced-Budget Government Spending Equation

Δy = ΔG * 1

Δy = ΔT * 1

Estimated values

United States of America

American Economist Paul Samuelson credits Alvin Hansen for the inspiration behind his seminal 1939 contributions to the theory. The original Samuelson multiplier-accelerator model (or, as he belatedly baptised it, the "Hansen-Samuelson" model) relies on a multiplier mechanism which is based on a simple Keynesian consumption function with a Robertsonian lag:

Ct = c0 + cYt-1

so present consumption is a function of past income (with c as the marginal propensity to consume). Investment, in turn, is assumed to be composed of three parts:

It = I0 + I(r) + b (Ct - Ct-1)

The first part is autonomous investment, the second is investment induced by interest rates and the final part is investment induced by changes in consumption demand (the "acceleration" principle). It is assumed that 0 < b . As we are concentrating on the income-expenditure side, let us assume Ir = 0 (or alternatively, constant interest), so that:

It = I0 + b (Ct - Ct-1)

Now, assuming away government and foreign sector, aggregate demand at time t is:

Ytd = Ct + It = c0 + I0 + cYt-1 + b (Ct - Ct-1)

assuming goods market equilibrium (so Yt = Ytd), then in equilibrium:

Yt = c0 + I0 + cYt-1 + b (Ct - Ct-1)

But we know the values of Ct and Ct-1 are merely Ct = c0 + cYt-1 and Ct-1 = c0 + cYt-2 respectively, then substituting these in:

Yt = c0 + I0 + cYt-1 + b (c0 + cYt-1 - c0 - cYt-2)

or, rearranging and rewriting as a second order linear difference equation:

Yt - (1 + b )cYt-1 + b cYt-2 = (c0 + I0)

The solution to this system then becomes elementary. The equilibrium level of Y (call it Yp, the particular solution) is easily solved by letting Yt = Yt-1 = Yt-2 = Yp, or:

(1 - c - b c + b c)Yp = (c0 + I0)

so:

Yp = (c0 + I0)/(1-c)

The complementary function, Yc is also easy to determine. Namely, we know that it will have the form Yc = A1r1t + A2r2t where A1 and A2 are arbitrary constants to be defined and where r1 and r2 are the two eigenvalues (characteristic roots) of the following characteristic equation:

r2 - (1+b )cr + b c = 0

Thus, the entire solution is written as Y = Yc + Yp

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.^[2]

Notably, such multipliers ignore the important long run effects on equilibrium output that tax cuts create.

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).

The above table is for the fourth quarter under which a permanent change in policy is in force.^[3] The "money supply constant" values correspond more realistically to current central bank policies (if interest rates are kept independent of fiscal expansion, inflation increases relative to the no-expansion scenario).

Some economists believe that the multiplier could be less than one. Robert Barro has done research in this area.^[4].

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 less likely to occur in a recession, where savings rates are traditionally higher and capital is not being fully utilized in the private market.

See also

• Multiplier (economics)
• Keynesian economics
• Fiscal policy

References