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Aug 2, 2008

Econ 201: The Myth of the Economic Multiplier

$1000 Business Sales x 4 Economic Multiplier = $4000 Economic Benefit. No.

PBO's (politicians and business owners) often want to develop businesses using taxpayer money. The politicians may subsidize loans, give tax breaks, sell public land cheaply, buy private land for the project, build utility services and roads, and provide subsidies. The PBO's need justification for the public expense. A claimed economic multiplier helps them get the money.

I usually suspect the motivations of the PBO's. The politicians or their family members may own part of the business, be its suppliers, or sell the land used. The politicians may get contributions from the business owners and/or the unions that supply workers to the business. The business may receive contracts from the town at favored prices.

PBO's gain public support by giving an inflated "Economic Value" or "impact" for the project. This sounds good but has no meaning. Call the project X-Corp. The Economic Value of X-Corp is supposed to be its spending increased by an Economic Multiplier of about 4. If X-Corp spends $1 million per year, it is supposed to have an Economic Value of $4 million to the people of its town and state.

The Economic Multiplier comes from counting transactions. X-Corp pays dollars to its employees and to other businesses. Then these people and businesses re-spend the dollars to more employees and businesses, and so on, in a spreading wave of re-spending that makes everyone happier. The Economic Multiplier is supposed to estimate how much additional value is generated from this re-spending.

The PBO's might say that a 5% sales tax on the $1 million in X-Corp's sales, plus a 5% income tax on the $4 million in increased Economic Value, produces $.25 million ($250,000) in additional tax revenue, each year.

This looks like a big win for the public. The tax revenue over 10 years is worth up to $1,755,000 in public expense up front to get X-Corp going and produce that $4 million in economic benefit each year.

That would justify the public investment, if it were true.

Note that a single payment of $1,755,000 today is worth 10 yearly payments of $250,000, if similar investments earn 7% interest.
Two nagging thoughts.
  • When X-Corp sells $1 million in goods, does it really produce $4 million in benefits to the community? X-Corp collects the first million; who is getting the other $3 million? (They aren't)
  • If Bob pays his neighbor's son Jim $10 to mow his lawn, does this send $40 in value into the community? (No) Is Bob's situation different from X-Corp? (It isn't)

Transactions Overcount Benefits

Economic Value and the Economic Multiplier count transactions, which overcounts value.

Passing dinner rolls around a table shows what is going on. Don't laugh. The first person accepts 6 rolls from the waiter. He takes one roll and passes five to the next person, who passes 4 to the next, and so on.

The appearance of 6 rolls at the table is new value appearing in the dinner table economy. The wave of spending and re-spending sends value around the table. The Economic Value approach sees 6 rolls of spending, followed by a wave of 5+4+3+2+1 of re-spending, for a total of 21 rolls of Economic Value, and a 3.5 Economic Multiplier (3.5 x 6 = 21). But there are only 6 rolls. The re-spending distributes the rolls; it doesn't create more rolls. The real value of 6 rolls is overcounted by looking at the roll-passing transactions.

In the same way, X-Corp pays its employees and suppliers for the value they provide to X-Corp. The X-Corp employees and suppliers pay others for goods and services. The others pay still others for the goods and services received from them. And so on. The money, like the dinner rolls, distributes the value created by X-Corp to all of the people who are directly or indirectly providing goods and services to X-Corp and its employees. Money moves away from X-Corp in exchange for the resources (value) moving to X-Corp and finally to X-Corp's customers.

Many layers of suppliers do not increase the value created by X-Corp. That value is set by X-Corp's sales. That value does not increase as it is distributed among all of the people who somehow contribute to X-Corp's products. The Economic Multiplier is 1. In other words, there is no Economic Multiplier when we look at value rather than the many transactions that distribute value.

The True Value of X-Corp

Say X-Corp sells $1 million in goods each year. A 5% sales tax on the $1 million in sales, plus a 5% income tax on the $1 million in value that X-Corp distributes to its employees, suppliers, and owners (however indirectly) produces $.10 million ($100,000) in additional tax revenue, each year.
Note that $100,000 tax revenue per year for 10 years is worth $702,000 in public expense up front to get X-Corp going, and $1 million in benefit is distributed to X-Corp's workers and suppliers each year.
It sounds great when a PBO says: "Spending $1 million in public funds today to support X-Corp will generate $250,000 per year in increased tax revenues over the next 10 years (worth $1,755,000 today). There may be some continuing subsidies, which are well worth giving to X-Corp for the $4 million in economic benefits (4X multiplier) generated each year by the $1 million yearly sales by X-Corp."

The reality is not so good: "Spending $1 million in public funds today will generate $100,000 per year in increased tax revenues over the next 10 years (worth $702,000 today). There may be some continuing public subsidies, which we hope are worth the $1 million in income produced each year by the $1 million yearly sales of X-Corp."

More bad news. Any spending by X-Corp for supplies and services produced out of town does not give income to people in the town and it is not taxed by the town government. Any sales by X-Corp out of town do not contribute sales taxes to the town. This reduces the benefits coming back to the town from starting X-Corp, and reduces the amount of investment by the town that makes sense.

The Government is a Bad Investor

It is probably not good for the community when a government spends taxes to start up and subsidize X-Corp, regardless of the amount.
  • The PBO's are happy to overstate the economic value by 4 or 5 times to get the deal done. The PBO's must expect benefits for themselves that don't depend on any widely distributed public ones. Why should the PBO's look too deeply into the math? Why trust PBO's who are willing to fool us?
  • The town usually invests more into X-Corp than the increased tax receipts are worth. It is not an investment in the usual sense; the town does not own any part of X-Corp, although the town is providing resources to start it up and maybe keep it going.
  • There is no guarantee that X-Corp will last 10 years, but the town provides its support up-front. The PBO's may receive enough value that they don't suffer if the business fails in a few years.
  • Businesses started or operated with a government subsidy are not likely to be the most efficient. So, they are more likely to be driven out of business by competition, making the return in taxes worth less than expected.

Worse, subsidized and favored X-Corp may compete successfully with other unsubsidized businesses. The inefficient, tax supported X-Corp can replace another efficient, completely private, tax-paying company. This makes everyone worse off, other than the X-Corp PBO's.

New businesses should pay for the infrastructure improvements they need. This assures that the business is beneficial to the town. It rewards businessmen who organize all costs into their business plan without draining resources from the government. Government only has the money contributed by its citizens. Tax revenue shouldn't be distributed to businesses in the hope of making "everyone" wealthier.

Not Priming the Pump

An economy that uses money is vast, complicated, and wonderful. It is easy to think of it as magical, as if we can "tweak" the system to get more stuff from somewhere. In fact, work produces things of value, and the economy is a system for organizing work and distributing those things, using money as a placeholder in transactions.

That is all. No magic and no multipliers. The rules of the system are simple. People exchange goods and services as they wish. The complexity comes from the number of people involved, and the detailed organization of work that they create.

People use analogies to understand complex systems. False analogies are "Priming the pump" and "Jump-starting the economy." The idea is to add some money to an economy to get the transactions flowing and increase wealth more than the amount of money added. These are both closely related to the false idea of the Economic Multiplier.

Some water pumps cannot pump air when starting up if their valves are dry. They need a wet internal seal to pull the air out of the supply hose. Pouring in some water to "prime the pump" solves the problem. The pump moves the air, then moves the water it was designed for. The priming water is a stimulus that helps the pump to start up when there is air in the line.

A car battery can be too weak to start a car, but the car can run and recharge the battery (using its electric generator) if the car can somehow be started. The power from a good second battery "jump-starts" the car for driving, and provides a power stimulus only needed briefly at the start.

These are weird and false analogies when applied to an economy. An economy is a group of people exchanging goods and organizing work. There is no central pump. People don't forget how to transact business or spend money. They do not get out of the habit of working or become sluggish. Money does not create wealth by "flowing around". Money is a placeholder in transactions for the exchange of goods and services between people. A transaction recognizes something of value but does not create that value.

A PBO relies on the Multiplier when he talks about "stimulus" or such. He says that taxpayers will benefit when the government gives people public money, because the long term improvement in the economy will repay any expense. As usual, this is very convenient for the PBO, and wrong. The economy is not like a pump, engine, or thick syrup that needs to start flowing. There is no long-term improvement in the economy from the "priming", only a one time increase in work to create the goods in exchange for the new money.

Taxing Peter to Pay Paul

Government is supposed to collect and spend taxes for public goods, such as roads, police, education, and parks, that have some relation to benefiting the general public. PBO's use the Multiplier and glib analogies to ask for government subsidies as a public good. We would all now be rich from government spending if this were true.

Government "investments" and subsidies are actually transfers of money from taxpayers to PBO's. It makes taxpayers poorer to the same extent that it transfers goods to the PBO's and the public. This does not create wealth overall, and usually destroys wealth as bad deals and failed projects eat the real value of collected taxes or government borrowing.

Personal Experience Of Transactions

People like receiving money, and they usually like spending money. Transactions produce pleasure on both sides. These feelings make it seem like the Economic Multiplier should be true. It is hard to argue against feelings, and it may take more than the above analysis to convince you that the Economic Multiplier is hot air.

Jim is an employee. He keeps almost all of his pay for his benefit. This supports Jim's feeling that transactions create value. Transactions deliver opportunities to him when he is paid, and he receives value personally when he pays others.

Jim has some expenses that support his job and cannot be avoided, such as for commuting, more expensive lunches, and office clothing. He enjoys these, except for the small expense of commuting.

Bob sells office supplies to X-Corp. He buys the supplies from manufacturers, then packages and delivers them. When X-Corp pays Bob $1000, he keeps about $80 as his pay (8% profit), and transfers $920 to others. Bob divides the money among the people who produced $1000 of value: he, his employees, and his suppliers. Almost all of the money and goods that Bob receives and spends is distributed to others.

Bob pays income tax on the $80 that he earns, and the others pay income tax on the portion of the $920 that each one earns. So, the total tax paid to the government is based on $1000, once.

Economic Benefit/Impact and the Multiplier counts transactions as being value. This is almost correct for Jim, who collects almost all of the value of his transactions. It is wildly incorrect for Bob, who organizes the work of others. Most people are like Jim, so they tend to believe the Multiplier without thinking much about it.

Looking For The Multiplier

The presentation above gives a direct explanation. But, you might think that I missed something or used bad logic. We can examine the Multiplier in other ways.

The Spending Goes On And On

PBO's claim that when X-Corp spends $1000 it produces $4000 of Economic Benefit/Impact. If true, then this good effect is not limited to X-Corp. There is nothing that distinguishes between corporate and personal spending. Every amount spent would have the Multiplier effect.

So, when Bob's employer gives him $1000 it goes on to create $4000 in Economic Benefit. When Bob spends the $1000 for rent, it creates $4000 in Economic Benefit. Also, when his landlord re-spends the $1000 on mortgage and heat. You would have to believe that every dollar in circulation is going to produce $4 in Economic Benefit, every time it is spent. This is a dreamworld.

In the real world, Bob receives money in exchange for his work (the value he creates), and he spends that money to acquire goods (value that others create). Once. No Multiplier. There are no additional Economic Benefits lying around.

Trading Vegetables

Some examples at a small scale show the details of what happens in transactions, the use and effect of money, and how value is created and distributed. The complexity of an economy is produced by linking together millions of such chains of transactions.

1. Barter

Bob grows beans in his spare time. Tom grows tomatoes. They tire of eating just their own produce, so they meet to exchange 5 pounds of beans for 5 pounds of tomatoes. The Multiplier cannot apply here. The magic of money is not involved. Only Bob and Tom are affected by this trade. They are happier because of the trade, but no one else is happier. Bob and Tom get the benefit of this trade once, not 4 times.

2. Olive Oil

Bob's beans are not ready; he brings a bottle of olive oil. Tom gives tomatoes to Bob and takes the oil. Bob will come back in a few days with the beans in exchange for the oil. Tom can keep the oil if Bob doesn't deliver the beans. Bob brings the beans two days later and takes back the oil. The oil gave Tom some value to hold so that the exchange could be done in two parts. The value of the oil assured Tom that he wouldn't lose value on the trade.

3. Money

Bob's beans are not ready; he brings $10 instead of olive oil. We can say that Tom sells tomatoes to Bob for $10. Later, Bob sells beans to Tom for $10. Money is changing hands. Still, there is no Multiplier.

4. Three People

Pam joins the group, selling peppers.
                      Tom     Bob    Pam       
Bob buys tomatoes    $ 10    $-10   $
Tom buys peppers      - 5              5
Tom buys beans        - 5       5
Pam buys beans                  5    - 5
                     ----    ----   ----
                     $  0    $  0   $  0
Three people exchange vegetables. Money provides value for trades that are separated by time and divided into smaller amounts. It is confusing to describe these exchanges entirely in words. The table shows where the money went in exchange for the vegetables traded.

For example, Bob buys tomatoes from Tom for $10. The table shows that Bob spent $10 and Tom received $10.

The money balances each trade, so the people are even in value at each moment. Olive oil might be used instead of money, but it is less convenient, and not everyone would agree to holding olive oil in exchange.

Three people sell their vegetables, buy what they want, and end with the same cash they started with. This would be impractical without money as a way of completing individual transactions. They have a more interesting dinner as a result.

These exchanges traded $25 worth of vegetables. That value was created by growing the vegetables. The money revealed value, and helped to exchange value, but it did not create value. There is clearly no multiplier in this closed system.

5. Economy

Mike appears and buys vegetables for sale in town. He buys $60 of vegetables and sells them in town for $100.

Mike produces $100 of value for his customers, the value of his sales. The vegetables were worth $60 in the country; Mike added $40 in value by transporting them to willing customers.

Customers provided $100 in value (money) to Mike. Here is where the value went or is going to go:

1 Mike       34   Mike's profit (his pay)
2 ABC Gas     5   Mike's Delayed expense 
                   for gas, 25 mile trip
3 ABC Garage  1   Mike's Delayed expense
                   for tune-ups
4 Tom        20   Tomatoes
5 Bob        20   Beans
6 Pam        20   Peppers
           $100   Mike's sales to customers
The $100 in sales to customers is the total value available. The other transactions distribute it to all of the people who support Mike's efforts. Mike receives $40 and Tom, Bob, and Pam receive $60. Soon, Mike pays $5 for gas used on his trip. Later, this trip costs another $1 in related car maintenance.

A PBO talking about Economic Benefit would count $100 paid to Mike, plus $60 paid to the growers as $160 in economic benefit. This counts the $60 transfer payment twice. In a typical Economic Benefit analysis, transfer payments are counted many times to get the Multiplier of 4. This overcounts value and gives an inflated result.

This shows some of the complexity in an economy. The ABC Garage contributes a little value to Mike's business without knowing it. The growers know that Mike is selling their vegetables, but don't know or care much about the details. Mike saw that he could make some money when he compared the price for vegetables in the country to the sale price he expected in the city.

Discounted Value (optional reading)

Discounted Value is the value today of payments to be received in the future. I said above that 10 yearly payments of $100,000 is worth $702,000 today, at a 7% interest rate. The exact math is complicated, but the idea is easier.

What amount would you loan X-Corp in order to get back 10 payments of $100,000 over 10 years? $1 million is too much. You would just get back your money over time, without earning anything from the loan.

This is like calculating a home loan, except we want to know the loan amount that produces a payment of $100,000, rather than starting with a loan amount and calculating the payment.

We will start by being generous and then correct ourselves. Say we loan the full $1 million, and want to earn 7% interest. X-Corp has roughly one-half of the money on average during the 10 years of the loan. X-Corp starts with $1 million during the first year. In the last year, after making 9 payments, X-Corp has about $100,000 in loan outstanding. We can estimate the total interest at 7% x 10 years x $500,000 (half the loan) = $350,000. Our rough estimate of principal plus interest is $1,350,000, so the rough payment is $135,000 for 10 years.

The detailed calculation (not shown) gives a payment of $142,400. So, a $1 million loan at 7% yearly interest is paid back by $142,400 per year for 10 years.

We need to loan less money if the repayment is only $100,000 per year. $100,000 is 70.2% of $142,400. A loan of (70.2% x $1 million) = $702,000 is repaid by $100,000 per year.

So, the government can spend up to $702,000 to get X-Corp started, if it wants at least a 7% return on this investment, and if it expects $100,000 per year in increased taxes in repayment.


The Multiplier from The Concise Guide To Economics, by Jim Cox, 1997.

He sees the Multiplier as "theory run amok" and notes other mistakes in analyzing an economy. The description is direct and somewhat technical, but you can get the idea without understanding the mathematics.

-- --
With multiplier, poultry has $8-billion economic impact
from BNet, from The Mississippi Business Journal, by Becky Gillette, July 2, 2007,

It never hurts to puff up the importance of a business by using the Multiplier. Notice the word "impact" because no one is quite sure what the effect really is.

The farm gate value of poultry in Mississippi in round numbers is $2 billion," said Mississippi Farm Bureau president David Waide. "That is huge." Waide said the multiplier impact of the industry as dollars get turned over in the economy is approximately four times the farm gate value. That would give poultry an $8-billion impact on the state's economy.

-- --
Economic Multipliers and Local Economic Impact Analysis
by David Kay, Cornell Local Government Program, December 2002

This talks about the Multiplier with a scholarly tone. It says that the "direct effects" should be estimated carefully. Then, just Multiply to get the overall economic impact. That is it for explaining the Multiplier. Notice the use of "impact" again, because people don't know what the effect really is.

Headlines like these recent real-life examples are prized by project promoters and business boosters. They often appear when advocates for private sector projects are seeking public support. The dollar figures featured in the stories are large, even "huge". They signal to readers both economic importance and political significance.

An economic multiplier lies behind nearly all [dramatic development] headlines. Multipliers are typically used to turn large dollar impacts into even larger ones. They do this because they translate project-specific effects into economy-wide impacts.

The local spending impacts associated directly with a specific project or economic activity are the starting point of any impact analysis. Known or planned facility construction and operating expenditures are a typical example. Called "direct effects", they are nearly always the most important data to estimate well in any impact analysis. To estimate economy-wide impacts, numbers known as multipliers are literally multiplied by the direct effects.

-- --
The Tax Rebate Was a Flop.   Obama's Stimulus Plan Won't Work Either
August 6, 2008 - By Martin Feldstein
Mr. Feldstein is former chairman of the Council of Economic Advisers under President Reagan, a professor at Harvard, and contributor to The Wall Street Journal.

My analysis of the Multiplier conflicts with Mr. Feldstein. The US Government recently distributed $100 Billion dollars to stimulate the economy by increasing spending (transactions). It failed miserably. Partly because people were not inclined to spend it all. Partly because there is no Multiplier. The Government believes that "confidence", and "impact" are somehow the same as value. The government relies on a Multiplier to create more benefit than the dollars spent.

"Those of us who supported this fiscal package reasoned that the program would boost consumer confidence as well as available cash. We hoped the combination would cause households to spend a substantial fraction of the rebate dollars, leading to more production and employment.

An optimistic and influential study by economists at the Brookings Institution projected that each dollar of revenue loss would increase real GDP by more than a dollar if households spent at least 50 cents of every rebate dollar."

-- --
Keynesian Economics Is Wrong
04/10/09 by Daniel Mitchel (video 7:29)

Politicians claim that more government spending can stimulate an economy, an economic theory by Keynes in 1935. The Center for Freedom and Prosperity Foundation produced this video which examines both the theory and evidence. Allowing politicians to spend more money does not produce better economic performance.


Cameron Murray said...

Great post. I work for the government (in Australia) as an economist and find it hard to explain to people that multipliers are a load of rubbish. Keep up the good work

SteveH said...

I haven't heard much about frictional deficits but they would result from the government spending multiplier being on average less than one. The obverse is that when there is a surplus then the lost effect of the government spending multiplier plus the retirement of debt could be the reciprocal of the multiplier and that rate could be expressed as the net drag of that additional dollar of taxation. For a government spending multiplier of .9 then the net drag on the economy would be $.11 for each additional dollar of tax in surplus.

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