If you’ve ever taken a macroeconomics course, there should be a distant memory of economic multipliers filed under “useless things I learned in college” somewhere in a dusty cabinet of your mind. It was probably presented to you as how one billion dollars of government spending magically turns into five billion dollars of economic activity.

Unfortunately, this is one of those topics that is easy to grasp in concept, but not in detail. Many people who have a basic knowledge of economics are fooled into thinking they can speak it fluently. I often hear people talking about economic multipliers in the same way a person visiting Mexico asks for directions: “hay un gato en mis pantalones“. Sure, it’s the right language, but it doesn’t mean what you think.

 Economic Multipliers – the Basics

The idea is pretty simple. Let’s imagine a rich person moving to Alaska with a billion dollars in the bank. If we assume the economy was already balanced without this rich guy, his luxurious lifestyle will cause the economy to adjust. He might hire a personal chef, a housekeeper, a gardener, a boat captain, a pilot, and a personal assistant (we call these direct jobs).

Assuming he didn’t move those people to Alaska with him, he will hire them out of the labor pool. This does one of two things. Either it creates employment for people who were looking for jobs, or it creates competition for the people with the skills he is looking for. In either case, in means higher total wages in the economy.

His presence also does something else. His chef is going to buy groceries from the local store, his housekeeper is going to buy cleaning supplies, his gardener will spend money at Home Depot, the boat captain and pilot are going to get fuel from a local distributor, and the personal assistant is going to take his clothes to the local dry cleaner. All of these purchases are increases in activity at the local businesses. That increased business might cause the business owners to adjust by hiring more people (we call these indirect jobs).

But wait, there’s more. His 6 employees (and anyone at the local businesses that got hired because this billionaire moved to town) now have more income. That means they can afford more things. They can go to the movies, or out to eat, or can buy a new TV. When they do, the movie theater, restaurant, and Wal-Mart all get a little busier. So they hire more people to manage more business (we call these induced jobs).

Economic Multipliers – Intermediate

With a basic understanding of how injections of new money create jobs, and how those jobs create more jobs, and how those jobs create even more jobs, we can dive a little deeper.

The first thing we must establish is the concept of equilibrium. Imagine a pond with its surface perfectly smooth. That pond’s surface is in a state of equilibrium. If you throw a pebble into the pond, you create a disruption. You can see a small wave push out in all directions. Water also rushes in to fill that voided space. When it does, a small portion of which pushes out of the water and falls back in. This creates another, smaller ripple. This process continues, in smaller and smaller amounts, until the balance is restored.

The economy works in the same way. There is a natural state of balance that an economic system can support. When something comes in and disturbs that balance, the system adjusts until an equilibrium is restored.

In the example above, the billionaire doesn’t keep creating more and more jobs each month. The system adjusts to his being there and reaches a new, higher equilibrium.

This is a more important point that first realized. When he moves to town, he creates jobs. If he moves away, he destroys jobs. His living in town establishes a new status quo from which we measure.

Injections vs Growth

What if rather than moving to town, he just came for an extravagant vacation. He spends a million dollars on restaurants, bars, souvenirs, sightseeing, etc. over the course of the summer. That injection of cash creates a temporary increase in business.  But that increase does not establish a new equilibrium; it is just a pebble in the pond.

Once the money cycles through the economy, it returns to normal. If we wanted the economy to do as well next year as this year, we would need him to come back again. It hard to say that his vacation “grew the economy.”

In order to have economic growth, a new equilibrium level of activity must be reached. In order for the multipliers to kick in, the growth must be sustained. (Don’t get this confused with stimulating a depressed economy, which is a very different topic). 

Likewise, shifts within the economy do not get the benefit of multiplier effects. When someone closes a business and goes to work on an oil rig, you can’t count the multiplier effects of a “new oil job”.

Technically, you could say that the loss of the business has negative multipliers and the gain of an oil job has positive multipliers, which cancel each other out. But, if you look at the economic data, you will see no change.

This is the biggest mistake people tend to make when talking about multipliers. They count the gains and ignore the losses. (Try adding up all the jobs people claim as indirect and induced jobs from their industries. You’ll find that there are more jobs than people. I show you why next).

Economic Multipliers – Advanced

There are two more topics we need to address to fully understand what is going on: timing and propensities.

Timing

Probably the most challenging topic my economic students have is centered around understanding the difference between stocks and flows. It is natural to think about things in terms of their physical presence. We individually deal with money in terms of its finiteness. When we spend a dollar, it is gone in our minds. But from the macro perspective, it has not been consumed – merely changed hands. From a macroeconomic perspective, economic activity is a flow.

Understanding Flows

Imagine for a moment that you have a faucet in front of you. You turn it on and water begins to flow. How much water do you have? Don’t try to answer, that’s a trick question.

It depends on two things, the rate of the water flow and the time you keep it on. If it is flowing at one gallon per minute and you let in run for 5 minutes, then you observed 5 gallons of water flow down the drain. Open the valve to 2 gallon per minute and now you will witness 10 gallons in those 5 minutes.

What if I told you that there was a pump under the sink that was pushing the water back into the tank? And what if I told you that there are only 5 gallons of water in the system? Would that change your answer?

There are only 5 gallons of physical water, but you witnessed 10 gallons of water flow passed you. Let that water flow for an hour and all of a sudden the same 5 gallons of water generate 120 gallons of water flowing past your eyes.

Did turning up the value “create” 60 extra gallons of water? Leave that faucet on forever. Did you just create an infinite increase in the water supply?

This is why economic multipliers are so confusing. They convert what is easy to understand (the rate of flow), into an aggregate number (the total activity over time). But that total number doesn’t make a lot of sense.

Remember those 6 people the billionaire hired? Let’s say he keeps them employed for 10 years. Would it make sense to say he created 60 jobs?

Geometric Series

I know a lot of very smart people who get confused about this stuff. Let’s think about another example.

Let’s say I have a delicious cheesecake. I am going to eat this cheesecake over 5 days. So, I cut the cheesecake into five equal pieces and eat one each day. Two questions, how long will it take to eat the cheesecake and how much cheesecake will I eat?

Now, let’s change the rules a little. Rather than eating 20% of the whole cheesecake each day, I can only eat 20% of the remaining cheesecake each day. Same two questions: how long will it take to eat the cheesecake and how much cheesecake will I eat?

The answers are just as easy as before (as long as we ignore that the cheesecake will spoil and we assume we can split atoms). It will take infinity days to eat the whole cheesecake and I will have eaten exactly one whole cheesecake at the end of time (in reality you get to eat about 2/3rd of it before you throw it away. If it keeps for 3 weeks, you only have a crumb). Reality aside, the theory here is called a geometric series and it is where the economic multipliers come from.

Geometric Series in Economics

In an economic system, we know that all of the money that gets paid out in paychecks goes to either consumption, taxes, or savings. Some of that consumption happens within the economy, and some goes to purchases outside of the economy.

We also know that the money the business collects goes to either purchases, payments for labor, taxes, savings, or distributions to equity owners.

As money circulates around the economy – moving from payments for goods to payments for labor, then back again – some of that money gets diverted out of the economy (as savings, taxes, or purchases from outside). Let’s say 20% of the money gets diverted each year (taxes and savings tend to be based on percentages of income).

Calculating the Economic Multiplier

Let’s say the economy is circulating $100 billion per year. That means $20 billion per year is leaving the economy. If the economy is stable, then $20 billion must also flowing into the economy from outside each year.

Now let’s inject an extra $1 billion into the economy. So, in year 1, $100 billion of economic activity occurred within the economy, $20 billion flowed out and $21 billion flowed in. We would count the total GDP at $101 billion.

In year 2, the $101 billion would circulate in the economy, $20.2 would flow out and $20 would flow in (inflows are not based on a percentage of activity). So, we would count GDP as $100.8 billion.

Follow this same logic for 25 years and you end up with this table:

Circulating Flowing Out Flowing in Net GDP
Year 1  $  100.00  $    20.00  $    21.00  $     101.00
Year 2  $  101.00  $    20.20  $    20.00  $     100.80
Year 3  $  100.80  $    20.16  $    20.00  $     100.64
Year 4  $  100.64  $    20.13  $    20.00  $     100.51
Year 5  $  100.51  $    20.10  $    20.00  $     100.41
Year 6  $  100.41  $    20.08  $    20.00  $     100.33
Year 7  $  100.33  $    20.07  $    20.00  $     100.26
Year 8  $  100.26  $    20.05  $    20.00  $     100.21
Year 9  $  100.21  $    20.04  $    20.00  $     100.17
Year 10  $  100.17  $    20.03  $    20.00  $     100.13
Year 11  $  100.13  $    20.03  $    20.00  $     100.11
Year 12  $  100.11  $    20.02  $    20.00  $     100.09
Year 13  $  100.09  $    20.02  $    20.00  $     100.07
Year 14  $  100.07  $    20.01  $    20.00  $     100.05
Year 15  $  100.05  $    20.01  $    20.00  $     100.04
Year 16  $  100.04  $    20.01  $    20.00  $     100.04
Year 17  $  100.04  $    20.01  $    20.00  $     100.03
Year 18  $  100.03  $    20.01  $    20.00  $     100.02
Year 19  $  100.02  $    20.00  $    20.00  $     100.02
Year 20  $  100.02  $    20.00  $    20.00  $     100.01
Year 21  $  100.01  $    20.00  $    20.00  $     100.01
Year 22  $  100.01  $    20.00  $    20.00  $     100.01
Year 23  $  100.01  $    20.00  $    20.00  $     100.01
Year 24  $  100.01  $    20.00  $    20.00  $     100.01
Year 25  $  100.01  $    20.00  $    20.00  $     100.00

Add up the column to the right and you get $2,505 billion. If you take away that $1 billion dollar injection in year 1, you would have got $2,500 billion. Hence, that $1 billion injection was multiplied 5 times as is worked its way through the economy. (By the way, you can solve for that multiplier by taking 1 divided by the 20% we said was being diverted.)

This is what an economic multiplier is – the sum total of all of the increased flow of activity generated by an injection over time.

Closed System Multiplier

This point is probably most clear if we imagine that this was a closed economic system (with no diverting). In that case, the multiplier would be infinity and we would all scratch our collective heads about what someone was trying to sell us (“Mr. President, if you increase government spending by $1 billion is will create an infinite increase in economic activity”).

What would make more sense is to say that the injection keeps circulating in the economy each period, creating $1 billion per year in economic growth.

Try to translate that logic into the table above. “The $1 billion injection creates a decreasing amount of additional activity each year”?

Maybe “the injection creates a one time increase of $1 billion followed by economic decline each year”?

Those sure don’t sound as good. And that’s the problem. Economists understand (I hope) what we mean by an economic multiplier. But it doesn’t convey the same message when the public hears it.

Propensity

The way we typically think about economic multipliers is to look at what things are made and who uses them. These are literally called the “make table” and “use table” in the input-output models. Basically, we need to understand that if we encourage farmers to grow more food, how does that impact other sectors. Does that mean the farmers will buy more tractors and fertilizer? Will we need more truck drivers to deliver the increased food production? Will we need more supermarket cashiers?

The economic system is complex. Every change is met with corresponding adjustments throughout the system. What the input-output models try to do is understand the how an increase in one sector will ripple through the rest of the economy.

Problems with O-I Models

While this is probably the best tool we have right now, there are problems with this approach. First, it is a static model. It holds everything constant and allows the researcher to turn a knob. This is informative, but not a valid predictive tool.

The problem is that the real world is dynamic. When something changes, everything else reacts. The economy doesn’t sit idle as the shock ripples through it, it makes adjustments on it own. In complexity theory, this is called a “dancing landscape” and it is very difficult to model.

Second, input-output models need a huge amount of data to be useful (just 50 sectors create 2,450 direction sensitive relationships). So, the national average pairwise comparisons are probably valid. But they don’t necessarily reflect any local economy very well.

Marginal Propensity

Third, average numbers are only useful on average. But, what we are usually interested in is an incremental change. Let’s say a person spends their income in this way:

  • Rent = $1,200
  • Food = $500
  • Entertainment = $500
  • Bills = $800

Now let’s say we give this person another $500 per paycheck. Do you imagine they will spend it proportionally (increasing their rent by $200, their bills by $133 and their discretionary spending by $167)? Or might they stay in the same apartment and go out more often?  Maybe open an IRA or pay off a credit card?

Imagine that $500 was a one-time gift rather than a monthly increase. Might that change how they spend it?

The point is that the marginal propensities are not likely to be the same as the average relationships between sectors. So, the models are likely to produce results that don’t reflect actual behavior.

Wrap up

While economic multipliers are important, we must understand what they mean. Don’t confuse the multiplier with a projection of sustainable growth. It’s usually not even a description of what will happen in a single time period, much less in every time period going forward.

And realize that the models simply turn up the knob on one industry and see how it trickles through the economy. This is useful, but these numbers probably won’t show up in the real data. As I said before, the system is too complex and ignoring the corresponding negative impacts are the most common way that multipliers are misused.

In a later post, I will explore what the actual data looks like here in Alaska. But for now, just keep in mind that economic multipliers are not magic beans that will grow into a beanstalk to the clouds.

When you hear people talk about how one jobs creates 26 more, or how $1 billion of government spending creates $5 billion of activity, or how we can keep borrowing more money because the economic fairy will multiply our spending into so much activity that it will create the taxes to pay for itself, just step back and ask yourself “Did he just tell me that he has a cat in his pants?”

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