The Keynesian Multiplier Demystified

The Faults and Fallacies Behind The Idea of Benevolent Investment

The term Voodoo Economics weas originally coined by George H.W. Bush during the Reagan administration to deride the theory of “tricke-down economics”, meaning: as investors use their liquid assets to invest (build factories, fund startup companies etc), more people get employed, net income increases and overall wealth improves. As the Reagan administration has shown with courageous tax cuts, wealth does trickle down from investors to company leaders to employees all the way down to the poorest individuals, and everybody benefits. Seeing Reaganomics work, George H.W. Bush withdrew the term Voodoo Economics.

In this new age of socialism, we hear of a new wondrous phenomenon that may again deserve the term Voodoo Economics. It is called the Keynesian Multiplier and stipulates that for each dollar spent by the government, GDP increases by more than one dollar. One famous proponent, Paul Krugman, maintains that government spending must increase even further to bootstrap the economy. True enough, if government spending of an amount of G increases the GDP by m × G where m > 1, then we should tax all we can (ideally 100 percent), spend everything through the government, and enjoy an exponentially increasing GDP with a year-to-year increase of mk where k is the number of years after the introduction of Krugmanomics. Too good to be true? If it sounds so, it probably is. Let us analyze why.

In the seminal work of macroenomics, General Theory of Employment, Interest and Money by John M. Keynes, the idea of government spending as a tool to maintain full employment was introduced. The premise behind it is based on the relation of institutional aggregate spending and its effect on the economy. This idea usually becomes particularly popular during recessions or any other time a country’s GDP (Gross Domestic Product) is decreasing or stagnating. The GDP is the economic output of a nation, that is, the value of all goods and products produced in a country. It is most commonly calculated on an annual basis, and some macroeconomists see it as a leading indicator when spending by the government must be increased in order to offset any losses in GDP. To better illustrate this notion, let us look at Equation 1:

Input = ∑ Output (1)

where ∑ Input is the aggregate value of spending and ∑ Output is the value of products on which money was spent — this is the GDP. The sum of all inputs includes consumer and government spending, investments, and the difference between exports and imports. In recession periods, the input side of the equation decreases predominantly because consumer spending and investment are cut back. Consequently, the output side, the GDP, decreases as well (less products are bought and therefore less is produced). With it, GNP (Gross National Product) per capita — this is the net income of the citizens — decreases as well. Two familiar side effects of a recession include rising unemployment rate and decreasing consumption spending in a self-sustaining spiral.

Let us rewrite Equation 1 with more detail so that we arrive at Equation 2,

(G + C + I + ΔE) = ∑ Output (2)

where G is government spending, C is consumer spending, I is investment spending, and ΔE is the difference between exports and imports.

In a recession, consumer spending is the dominant factor that creates an imbalance. Let us denote reduced consumer spending with CR which reduces the left-hand side and consequently the right-hand side of the equation. Proponents of Keynesian Economics find recessions an urgent and opportune moment to agitate for increased government spending to compensate for any sustained negative variations in consumer spending CR. We denote the additional government spending S and the increase in output resulting from the additional spending ∑ OS. Under consideration of these two additional factors, Equation 2 expands into Equation 3:

(G + CR + I + ΔE + S) = ∑ Output + ∑ OS (3)

Keynesian economists now claim that additional government spending S causes a higher output ∑ OS than the monetary value injected into the economy. This effect is described by Equation 4 with m being the Keynesian multiplier that indicates how much more the output increases than justified by the additional spending S:

m × S = ∑ OS (4)

On what evidence is this claim based? The idea of the spending multiplier was initially introduced by Keynes and further quantitatively developed by John R. Hicks in his work on the IS/LM model (Investment Saving / Liquidity Preference Money Supply model). For a simple explanation of the spending multiplier, let us look at a government spending chain in the following figure. The assumption is that the government buys goods (in this example for $1.00), and those $1.00 are now in the hands of private entities. With those $1.00 they can now buy something – this is called the marginal propensity to consume or MPC. As the first recipients of the government funds spend their money, the second round of recipients also start spending.

Marginal Propensity to Consume (MPC)

This chain is infinite, but converges to a finite value m provided that |MPC|<1:

m = $1.00 + MPC + MPC2 + MPC3 + … = 1 / ( 1 – MPC ) (5)

To be more specific, MPC is defined as the additional consumer spending due to government spending as a percentage of income. For example if an individual has an income of $100 and the government provides $1, then

MPC = $1 / $101 (6)

We can see from Equations 5 and 6 that the Keynesian multiplier m is a number of unity or larger value. Under this theory, m=1 when MPC=0, in other words, government spending does not hurt in the worst case. As MPC increases, m grows rapidly, reaching infinity for MPC=1. A few examples demonstrate the significance of the multiplier. If the government spends 50 cents on every dollar made by private entities, the government spending multiplier is m=2 according to Equation 4. If the government spends 75 cents on every dollar, we get m=4. If the government spends 90 cents on every dollar, we get m=10. To stay with the last example, if the government spends 90 percent of the GNP, the nation’s GDP would increase ten-fold as a consequence of government spending, according to this theory. These examples show that the theory must be flawed.

We will now have to take a close look at the fallacies of this theory. Superficially, Keynesian spending sounds good: the goverment injects money into the economy, private entities have more money to spend and demand increases. As a consequence, production increases, in turn increasing demand – particularly of investment goods.

The problem with this theory lies in the failure to take into account both the source and the processing of the government’s largesse.

In detail:

  • In a recession, injection of government money in fact temporarily increases demand. However, much of this demand is related to basic goods. This demand can easily be covered by imports from other countries (China, India) which provide low-cost goods. This money is consequently lost for the chain in Equation 4, and the Keynesian multiplier does not take into account low-cost imports. With rising imports ΔE decreases in Equation 3 and offsets government spending S. An indirect consequence of this type of low-cost spending is the increase in trade balance deficit which weakens the national currency. A weakening of the national currency (the dollar) makes commodity imports, such as oil or metals, more expensive and leads to a backlash in prices.
  • The government injection of money into the economy leads to a spontaneous increase of demand. Supply follows with a lag, and in the meantime, prices increase. This price increase – inflation – is not considered in Keynesian theory as it necessarily decreases MPC: Equation 5 does not consider inflationary price increases which make negative values of MPC possible, with the consequence of a government mutiplier m dropping below unity.
  • Unfortunately, a government that causes a large deficit is interested in stoking an inflation. Let’s take a debt of one trillion as an example, just for the math. With a 2% inflation, its value in ten years is 820 billion – still a sizable chunk. With a 12% inflation (we have had almost 15% in the Seventies), the 10-year devaluation gets the value of the debt down to 320 billion. Down by two thirds! This is a good solution for the government. Clearly, inflation means that you can buy less with your money and your MPC is reduced (see previous bullet).
  • In a recession, the government typically borrows money at an interest. Primary and interest need to be serviced – the borrowed money has to be repaid at a later point in time. The money to service primary and interest has to come from somewhere – usually increased taxes.
  • To borrow money, the U.S. government sells treasury bonds, and private investors are eager to buy them because of the stability of U.S. government which has never defaulted on them. When private investors invest money in treasury bonds that means the same amount of money isn’t going to be invested into private enterprise, thereby depriving industry of resources to expand their operations and hire more people (and therefore lower unemployment).
  • Since government spending is directed spending, it is very likely to be spent on inefficient, unsustainable or temporary projects (“pork barrel projects”), thus rendering its usefulness to be short lived.
  • Government spending is also controlled by the influence of the constituents and lobbying groups. This effect is called “The Capture”. The concept of the Capture was first espoused by George Stigler in Economic Theory of Regulation, where various interest groups use regulation and the power of government to benefit their own interest. Examples of those interest groups are government sponsored enterprises to promote housing ownership, senior citizen groups’ lobbies against reform of entitlement programs, unions, and subsidized alternative energy firms.

The strongest and most intuitive argument can be made that every dollar that the government spends has to be taken away from the private sector of the economy – either by up-front taxation (direct or hidden, such as in a cap-and-trade scheme) – or at a later time when public debt has to be repaid with interest. This money is missing for investment and consumption activities. In fact, this argument can be illustrated with the Broken Window Fallacy. To quote from “ECONOMICS IN ONE LESSON” by Henry Hazlitt,

A young hoodlum, say, heaves a brick through the window of a baker’s shop. The shopkeeper runs out furious, but the boy is gone. A crowd gathers, and begins to stare with quiet satisfaction at the gaping hole in the window and the shattered glass over the bread and pies. After a while the crowd feels the need for philosophic reflection. And several of its members are almost certain to remind each other or the baker that, after all, the misfortune has its bright side. It will make business for some glazier. As they begin to think of this they elaborate upon it. How much does a new plate glass window cost? Two hundred and fifty dollars? That will be quite a sum. After all, if windows were never broken, what would happen to the glass business? Then, of course, the thing is endless. The glazier will have $250 more to spend with other merchants, and these in turn will have $250 more to spend with still other merchants, and so ad infinitum. The smashed window will go on providing money and employment in ever-widening circles. The logical conclusion from all this would be, if the crowd drew it, that the little hoodlum who threw the brick, far from being a public menace, was a public benefactor.

The analogy to government spending is clear. What is really happening, though? The baker, who is now forced to spend $250 to repair his window, has to scratch his plan to buy a new kneading machine. With this kneading machine, he was planning to make his production more efficient and lower the price of his bread. Not only will the baker now be unable to realize his plans, but the manufacturer of the kneading machine will not get those $250 that are now in the hands of the glazier. While one stream of spending (via the glazier) has been established, another stream (via the kneading machine manufacturer) failed to get established. In other words, The glazier’s gain of business is merely the manufacturer’s loss of business. It is obvious that nothing has been gained.

The situation is even worse, though. The baker had already paid for the glass pane when the shop was built. Now he will have to pay again because circumstances force him to change his priorities. In the end, the baker has gained nothing, but he is now lacking $250 that would have been used for an investment to make bread cheaper – the obvious benefit for his customers now fails to materialize.

We can further illustrate the point by exaggerating: if the hoodlum who smashed the window and forced the baker to pay the glazier (in our analogy, the government that takes away money and decides where it will be spent) causes the generation of money and employment in ever-widening circles, why don’t we torch our houses and have them rebuilt? It would create employment for builders, lumber manufacturers, drywall manufacturers and so on. Right? Of course not. By torching our houses, we destroy economic goods. Labor and materials to replace the houses are now missing elsewhere. Lumber and other building materials become more expensive. Scarcities ensue. The unfortunate but intuitive fact is that the destruction of goods does not make a people wealthier but poorer.

What about the government, then? The government spends money following political expediency. Political pet projects are seldom aimed at creating sustainable jobs. Yes, the government creates jobs. However, those jobs are normally not productive in terms of the GDP. You cannot eat government forms, not can you build a house or a car with government forms. It is important to consider a job’s contribution to the gross domestic product or, in other words, to the people’s wealth. A private company is forced to keep their administrative overhead low to remain competitive (few paper-pushers). Conversely, the government is under no compulsion to reduce its administrative costs (many paper-pushers). A good example for a political pet project is the San Francisco salt marsh harvest mouse (see this document, page 3, a public spending program that was appropriately ridiculed). While proponents of the salt marsh project claim job creation, the jobs are temporary and cease to exist when the pork money runs out. Moreover, the jobs do not create tangible economic output as opposed to, say, jobs in companies tha produce bread, steel, drywalls, or computers. Paper pushers or pet projects – none of them contribute to the GDP. However, to pay for them, money needs to be taken away elsewhere – higher taxation. This is money taken away from productive branches of the industry. In our baker example, the baker, forced to pay higher taxes, is now missing the money for a crucial investment to make bread cheaper. In the economy, employers are missing the money for investment or new employment. And the spending multiplier – irrespective of how fancy the equation is – does not take the transfer of funds from productive parts of the economy to unproductive parts into account.

To conclude: the main fallacy of the spending multiplier lies in the assessment of MPC. The multitude of factors that influences the propensity to consume is not taken into account. While government spending may have a small and transient positive effect on consumer spending (thus increasing MPC), there are numerous factors that reduce MPC. Among those factors are taxation and inflation (less money available for consumption), unemployment, and insecurity over the economic development. All these factors have the power to cause negative marginal propensity to consume and therefore a multiplier that is less than unity.

It is illogical that money taken away from the economy and then given back to the economy by the government should have any positive effect (m>1) on GDP. Rather, history proves that m<1 and government spending hurts the economy.


Akerlof George A. , Shiller Robert J. Animal Spirits (2009)
Hicks John R. Econometrica: Journal of the Econometric Society, 1937 Mr. Keynes and the “Classics”; A Suggested Interpretation.