The NGC Model, Banking and the Creation of Money

Nick Rowe is a prolific and creative author to whom we all owe thanks. Today he gives us a model that we can use to create a new vision of the creation of money.

Nick writes

You decide to make a new monetary system from scratch. You give everyone a chequing account on your computer, with an initial balance of 0 units. If Andy buys bananas from Betty and pays her 100 units, Betty now has a positive balance and Andy now has a negative balance.

Nick may disagree but I think his model first presupposes a monetary system and then calls our attention to a nearly complete monetary event. The focus of this post will be on the events that had to occur before Nick's model begins. It is these background-events that are interesting and offer us additional insight into the creation of money.

Establish a Frame of Reference

These background events need a frame of reference to make them plausible, easily described, and comparable to actual macroeconomic events. The framework we will use is the National Gift Certificate Model (NGC) which treats money as an analog of the well known gift-certificate.

The possibility of a NGC model of money creation first appears in a comment to Nick's post:

Using the NGC example, the issuing store prepares to sell a gift certificate by printing the certificate. Then the store has a choice: recognize the increase in inventory and expense of production immediately OR wait until actual sale and then recognize the event. The first choice makes sense if the intended use of the gift-certificates is to pay for goods and services; the second choice makes sense if the intended use is to sell the gift-certificate for money in the future.
In either case, the actual creation of money or NGC is not visible to the usual measuring tools available to the public. The actual issuance of new money is more visible but identical to using old money; issuance is just another exchange of goods and services for money/NGC.

It is obvious that any store offering gift certificates can do some accounting behind the curtains as just described. We need to notice that the store is providing not only accounting services behind the curtains--it is providing banking services. With the issuance of a gift certificate, the store is providing a certificate with future value (like a check written on a bank). The store is also providing storage for future value that will be claimed when the gift certificate is presented for redemption (store products will be available in the future which is comparable to bank money that will be available when a check is written).

A Model of Money Creation

We have not yet created money. An analog with newly created money comes from the observation that a gift certificate can be issued by a store in payment of goods and services received. This event can be compared directly with a barter transaction in which goods are traded for goods. The only difference is that this is a partially delayed transaction: the services are delivered first; payment is made later when the gift certificate is redeemed. The creation of a money certificate is easily compared to the creation of this delayed-payment* gift-certificate.

To see the comparison, we look at the creation of money by a bank when a bank makes a loan. The bank creates a deposit in the borrowers name and will ask the borrower to sign a promise to repay the amount borrowed (and a small charge in repayment for the bank's services). This action creates an increase in the money supply and is widely recognized as a creation of money.

If you are like me, you don't immediately see these two events (the store's certificate and bank's new deposit) as being nearly identical. To see this clearly, we need to go behind the curtain. The bank can perform the identical steps just completed by a store preparing to offer gift-certificates as payment. Whether either store or bank actually does these steps in preparation or not, the important take-away is that observably identical results are obtained.

There are two behind-the-curtain tasks that both banks and gift-certificate issuing stores perform:

1.  Prepare a certificate that will be delivered to the customer. A store will prepare a gift-certificate. A bank will open an account with a positive balance in place. In both cases, before delivery to the customer, the name on the instrument will be the name of the issuing entity (or blank).

2. Make a record that the certificate/account has been backed by an asset. A store will reserve goods/value owned by the store.  A bank will create a bond signed by the bank and promising to repay the amount on deposit.  (Yes, this is a bank lending to itself but no problem, the actions are entirely within the bank, hidden behind a curtain.)

With the instruments in place and funded, a store or bank is ready to pay a bill or service a new customer.

When a bank borrower actually comes through the door, he is asked to sign a loan agreement. If he does, the account is signed over to the borrower. The bank's loan document is now secondly backed by the borrowers signed repayment commitment.

We can see that money has been created ad nihilum. Or has it? When the borrower reduces the deposit by spending money the deposit represents, other banks will receive money.  In the fiat monetary system, the bank transferring funds must transfer money that all banks will accept. There has to be a problem if all banks are lending money created by assigning accounts and backing them with bank guarantees.

The Dilution Problem

There is a problem. The observed money supply rapidly increases which effectively dilutes the base money supply that was first used to begin the repeated-lending-sequence. In the modern fiat monetary system, this expansion is controlled by the central bank.

The control process is simple. The central bank creates a block of money using the bank money creating process previously described. This would be considered as "base money". Base money is then distributed to private banks, usually through the sponsoring government when government pays for goods and services. Once received, private banks are allowed to re-loan the new deposits. Control of the loan process is maintained by the central bank with a requirement that a "tax" be collected on deposits in every private bank. This "tax" drains original funds at a rate proportionate to the "tax rate",  amount, and number of loan events. After several events, the entire original money issue will be returned to the central bank, allowing the central bank to know when the original base money supply has been completely loaned-to-limit. (This sequence is partially described in the Federal Reserve document "Reserve Maintenance Manual").

We have seen how the NGC model can be used to understand the creation of money.

Another Look at Nick's illustration--Motive

We now have the opportunity to examine Nick's illustration from a new perspective. We can see that behind the curtain, some entity must have prepared the green entry that Betty would receive in trade. Some entity would have prepared the red entry that Andy received. Further, Andy would have been given the red entry along with the green entry that he later traded to Betty. The entity behind the curtain can be assumed to have authorized all of this activity.

Why would any entity carry out all this activity? One logical possibility is that Andy thought that bananas were worth more than the 100 units and the added obligation-to-repay that he incurred. At the same time, the sponsoring entity could have thought that Andy's obligation to repay 100 units in the future (together with service charges)  was worth more than the 100 units that the entity would render temporarily unavailable. We can safely believe that Nick's illustration has described a three-way mutually advantageous trade.

Nick inconveniently omitted the events that occurred behind the curtain.

The Value of Money

It does not seem logical to extend the creation of money into the value of money. We can safely believe that Betty willingly traded 100 units for bananas but we don't know how many bananas she traded. We only safely observe that 100 units have been found.

Conclusion

The NGC model provides a powerful analogy to processes found in the broader monetary system. This descriptive path-of-creation for money is yet another example in the use of the model.

Thanks

Thanks to Nick Rowe, whose cryptic yet tantalizing posts on macroeconomics repeatedly inspire many amateurs and professionals.

*[11/10/2016 update] The combined words "delayed-payment" were inserted to call attention to the important fact that the comparison of money to a gift-certificate depends upon the store FIRST receiving goods or services THEN providing a gift-certificate in acknowledgement. The gift-certificate is evidence of an obligation for the store, only payable by trade within the store. We could think of the certificate as being Delayed Evidence of a Barter Transaction (DEBT).

Comment on National Gift Certificates as a Money Analog

Antti Jokinen and I continued to exchange comments for a short time on Nick Rowe's blog. The comments resulted in what I thought were some good guidance for future development. I will re-post the comments here in an effort to consolidate the record.

The comments repeated here follow the original posting of my article "National-Gift-Certificates as an Analog to Money".

Antti begins:
Roger: First, thanks for all the acknowledgements! Very kind of you. I might be repeating myself, but here are some comments on your post:

From the point-of-view of the HOLDER of a NGC, the USBS metaphor works quite well. But from the point-of-view of the ISSUER, I can't make it work. To start with, you should define what kind of money you are talking about: only fiat money, or also "bank money"? Then, you must decide how a NGC can be redeemed: say, by buying goods for sale in any store in the US, or just by paying taxes (latter is what Randall Wray suggests, having in mind fiat money). "(private) Bank money", deposit, can disappear when you use it to buy something from any store in the US. Fiat money doesn't, so in that case you'd only trade the (fiat-money-as-a) NGC with a non-issuer (This begs a question: How can a commercial bank deposit disappear when you buy something from a non-issuer?).

If we only talk about fiat money, and by this we mean "central bank IOUs" (not my terminology), then we face a problem Wray/MMT seem to face, too: If fiat money is a "CB/government IOU", then why does it disappear when a private entity behind the MBSs on Fed's balance sheet makes a mortgage payment? Does the government not only allow its IOUs to be used in tax payments, but in mortgage payments too?

As you see, I see problems on the "issuer side" both when it comes to your NGC interpretation and when it comes to interpretation of money as an IOU. I think those problems are very, very hard to solve if we stay within those frameworks.

Posted by: Antti Jokinen | November 03, 2016 at 04:09 PM

Antti (Nov. 3, 04:09 PM);

Thanks for reading my post and commenting.

You will be surprised when I say that all of these issues are easily incorporated into the analogy. The difficult part is to explain in a comprehensive way. I begin with a brief background:

Fiat money is nothing more than circulating paper printed by the government. Period. It is given legitimacy by taking care that a bond is issued at the same time circulating paper (or electronic equivalent in every case) is printed. Therefore, it is possible for the central bank to meet with the Treasure (two people from two departments) and exchange products: The CB delivers currency and the Treasure issues a promise to pay it back. Period.

The duration of this distributed paper will depend upon the tax rate charged. Assume that a tax is charged at each transaction (income tax, sales tax, VAT tax). After each tax, less currency remains in circulation.

If there is no tax on a transaction (such as on the expense side for income-tax-on-business-profits), there is no reduction in outstanding currency. This enables the duration of any issued paper to be VERY long.

Banks do not issue money. They only have the character of increasing the amount in measured circulation. Take gold as the example. If gold is the money in use, it is very difficult to increase the amount of gold in-hand. It is easy to write a gold certificate and lend it (as if it were gold in-hand) without telling the owner of the original gold. If this is done repeatedly, the amount of gold on deposit will remain unchanged but the amount of gold CLAIMED will increase. The role of central bank reserves comes into play here to control this process.

With this background complete (in a very sketchy fashion), we need to deal with each of your gaps from the issuers standpoint. We group concerns:

1. Money disappears that can be identified as originating with a bank. This occurs when a loan is paid away. Until the loan is paid, the money issued can circulate between users including government (both as a user and destroyer of money).

2. Money disappears that can be identified as originating with government. Taxes are the mechanism already described.

3. I don't understand the MBS mortgage question so I will skip that (perhaps to my peril).

4. It remains to tie fiat money to NGCs.

It is easy to see that government can allow everything-mentioned-so-far to occur. Not everyone will agree with me but I think everything described already occurs on a routine basis. The question then, is whether a private store that issued gift certificates could put in place each of these processes and procedures? I think this has happened already, visible and embodied in the form of company stores and company towns. The early development of America had several examples of small communities that were basically owned by one entity. In come cases, the community used company money which was the equivalent of paying bills with gift certificates.

This was not a good deal for the workers. The company had control of the interaction of company currency and the greater currency of the central government.

There is no question that private stores can issue gift certificates. It certainly seems possible for the private use of gift certificates to expand to include borrowing, banking and complete use in trade exchange. This expanded use of gift-certificates creates what I would like to call "A National Gift Certificate Economy", even if is limited in size to be no more than a company town.

I have attempted to tie fiat money to NGCs. Is the analogy making more sense now?

Posted by: Roger Sparks | November 03, 2016 at 06:34 PM

Antti: I should revise one line to introduce the actual issuance of fiat money. Issuance does not occur when the money is created (creation is all within the confines of government). Issuance occurs when government spends the newly created money.

The line "The duration of this distributed paper will depend upon the tax rate charged." would be much more informative if it read " After issuance (by government paying it's obligations), the duration of this newly distributed paper will depend upon the tax rate charged. "

Posted by: Roger Sparks | November 03, 2016 at 11:52 PM

Roger: The example of a company town is a good one. There the issuer of the money/LGC (Local Gift Certificate) owns the store(s) where the money/LGC can be presented for redemption; it is redeemed for GOODS by the issuer. Almost everyone has to regularly buy something from the issuer's store, which makes the money also acceptable in transactions where the issuer is not one of the parties. What bugs me is how to explain that you get something from the government for your NGC when you use it to pay taxes? In that case its more like a Stay-out-of-jail card than a gift-certificate. This is where Lonergan and Wray disagreed, and I'm arguing Lonergan's case which I believe has some merits. The big question is: If you hold money (or NGC), who owes you and what?

About your definition of "fiat money": You talk only about paper, but we have to include bank reserves, right? All "high-powered money".

Posted by: Antti Jokinen | November 04, 2016 at 10:52 AM

Antti (Nov. 4 10:52 AM): Antti writes "What bugs me is how to explain that you get something from the government for your NGC when you use it to pay taxes?".

I can't argue an explanation here. The best I can do is to suggest a philosophy. I would suggest that tax on land (we pay annual property taxes in America) and trying to get something from government in exchange for my NGC are the same. One rational philosophy is that both are a payment of "rent". Using land as the example, the American land owner is more-accurately sub-leasing the ground from the government who is the REAL OWNER. This basic philosophy underlays the entire NGC-USBS framework.

Following this philosophy, we could claim that a tax on each exchange of money is a payment of rent for the privilege of using money. Wild?!

Now I would like to change the focus to fiat money, banks, and government.

As I thought about my previous reply, particularly about the timing of issuance, I began to place more importance on this observation: both banks and government create money in a private fashion, which means "behind closed doors". Let me elaborate: Both banks and in the CB-Treasury-trade create money in a "back-room", low visibility, event where they prepare to issue money.

Using the NGC example, the issuing store prepares to sell a gift certificate by printing the certificate. Then the store has a choice: recognize the increase in inventory and expense of production immediately OR wait until actual sale and then recognize the event. The first choice makes sense if the intended use of the gift-certificates is to pay for goods and services; the second choice makes sense if the intended use is to sell the gift-certificate for money in the future.

In either case, the actual creation of money or NGC is not visible to the usual measuring tools available to the public. The actual issuance of new money is more visible but identical to using old money; issuance is just another exchange of goods and services for money/NGC.

Turning now to central bank reserves, I think this FED maintenance manual is helpful:
https://www.federalreserve.gov/monetarypolicy/reservereq-reserve-maintenance-manual.htm

I understand the manual to require a reserve deposit at the central bank that increases proportionately to the increase in bank deposits. In other words, it acts like a tax paid in positive money. What is positive money? I think it is money issued by the government but how do you separate it from bank issued money? Well, if positive money is taxed at each reissue/new-loan, the positive money will eventually all be back at the CB. This gives the CB a lot of control.

Posted by: Roger Sparks | November 04, 2016 at 12:28 PM

These comments, while they seem somewhat disjointed, contain some very important insight. Particularly important is the thought that the store issuing a gift-certificate has two choices of when to "book" the process. Which choice is picked would likely depend upon the purpose to which the gift-certificate placed.

Thanks to both Nick and Antti for their roles in advancing the theory of macroeconomics.

National-Gift-Certificates as an Analog to Money

I will begin this post by thanking Antti Jokinen for engaging in a very thoughtful discussion about the merits of comparing money to a gift certificate. While at first glance, the two instruments seem very different, upon closer inspection and appropriate scaling, the two instruments compare very well. Antti's skepticism coupled (with encouragement) helped bring the parallels and differences into focus.

This post is a response to Antti's comment "The problem I see with your approach is how to explain why we would call a piece of paper a "gift-certificate", when it entitles the holder of it to nothing else than being relieved of his tax obligation (or fines or other charges collected by the government). I do see some sense behind that kind of thinking, but there are many people who don't."

Yes, we need an explanation. We think we know what money is (or do we?) and a gift-certificate seems to have many differences from money.

I first wrote about the similarity of money and gift-certificates in my post "Money is Like a National Gift Certificate". That post was prompted by my observation that a hardware store gift certificate was a lot like money in many ways.

When I walked into that hardware store with my gift-certificate in hand, I wondered why I just didn't go over the the clerk and request she change it into money. It certainly would have been easier than walking around the store, looking for something that I wanted only marginally. Of course, the store wanted the sale, not the possibility that they would retire the certificate and I leave the store with THEIR money. (There might be a clue here)

Paper money is harder to characterize than a gift-certificate but let's look for some DIFFERENCES and characterize them:

1. The size of the acceptability footprint is hugely different. Money is nation wide but a gift-certificate is only store wide; but both have boundaries of acceptance.

2. The denomination is hugely different. Money can be any value if a check, a fixed value if a gift-certificate; but both have EXACT values on the traded instrument.

3. The source of the instruments is hugely different. Money can be created legally only by government, a gift-certificate is created by private entity; but both are created by unique human entities.

4. The range of items available for purchase is HUGELY HUGELY different. Money can buy anything, a gift-certificate can only buy things in the store;  but both can only buy things identified as being for sale.

The ownership of items for sale is hugely, hugely different. The issuer of money does not own the items that might be purchased using money while the issuer of a gift-certificate owns/controls the items that can be traded in exchange; but exchange is observed to occur. (This ownership difference may be related to government's ability to collect tax at each exchange (sales tax or VAT tax).

Now let's look at the many identical features of money and gift-certificates:

Both disappear (retired, or if you prefer, "recycled") when they are received by the issuing entity.
Both can be traded before being presented to the issuing entity.
Both have unlimited durability while (at the same time) both can be lost or destroyed by intentional action.
Both can (or could) be borrowed by either the issuing entity or third parties.
Both are usually created (issued) AFTER the issuer has received some physical good or service.
Both can be created (issued) as a gift without exchange of any physical good or service.

We began this post with the challenge of explaining how money could be considered as being a National-Gift-Certificate (NGC). While the differences between money and a gift-certificate are several, the differences disappear when the differences are scaled and adjusted for character of ownership. We need to scale the gift-certificate up and into a "National-gift certificate". After the scale-up is done, it is reasonable to argue that a National-Gift-Certificate is an analog for money.

In an early comment, Antti suggested that the footprint for a United States monetary system could be described as the "United States as a Big Store (USBS)". This is an excellent description that I have used several times since.

If we think of the United States as a Big Store, we can compare the value of money to the contents of that store. Of course only the items on sale could be purchased but the same condition is a restriction in a store issuing a gift-certificates. The value of USBS money would be dependent upon the ability of money holders to buy freely what ever they wanted and their desire to purchase.

We conclude by opining that we can not call money a "gift-certificate", the differences are too great. We need to call money a "National-gift-certificate" which is a scaled up, souped-up version of the familiar gift-certificate.

Thanks again to Antti. Your participation in this discussion is much appreciated.

Money is Like a National Gift Certificate

For my birthday, my son and daughter-in-law gave me a hardware store gift card. They could not have thought of a more welcome gift for this mechanically tuned writer. A hardware store is a trove of fascinating gadgets crying for exploration. Usually though, my pocket book is a throttle on my enthusiasm. Their gift gave me a chance to have a tool usually out of reach due to budget discipline.

As I searched the store looking for a digital caliper*, I could not help but think that the gift card was so very much like the green money we use every day. Of course, being a gift card, it was also very much like my credit card except that the bill was prepaid. My goodness, I could think of many parallels between gift cards and money!

Let's explore some of  the parallels.

Money is a store of value. That was the first parallel that came to mind. My gift card had been prepaid with money for a fixed amount. It could be used at any time. It was certainly nice that I could carefully decide what to get. (I wanted to get something that would last so that I could remember their generosity every time I used the gift.) There was no need to hurry the purchase.

Green money has that same character. There is no need to spend it quickly. The ability to store value by building one's monetary inventory is a great feature of a stable monetary environment. You know, it's even possible that a nice little nest-egg could be a great help in buying something like a house when a down payment is needed.

A I continued to think on this, I could't help but think that green money is limited to use in a single store just like my gift card was limited to use in just one store. Another parallel! Of course the accepting store for green money is the entire United States, not a single small hardware store--but the principal is the same. Green money has limited use in non-dollar economies just like my hardware store gift card would have limited value in a grocery store. There would be a discount applied to either if I used them in a less-than-hospitable environment.

The more I thought about it, the more I realized that money really is nothing more than a super-charged gift certificate. It can be exchanged for anything that is for sale in the currency zone. Nice! Money has a huge exchange footprint!

And there are more parallels.  A gift certificate is paper like money. A gift card  is more like a debit card and linked bank deposit--electronic in accounting but limited in size.

How about the relationship between gift cards, debit cards, and a credit card? Well, gift cards and debit cards are prepaid while the credit card is a pre-qualified loan.

With all of these parallels, I began looking for differences. The first difference found was in the way a gift certificate is created and the way that money is created. A gift certificate is created when someone uses money to purchase it. Someone must first acquire that money and then purchase the certificate from a store willing to promise future delivery of store merchandise in exchange for the return of the certificate. No one seems to even consider the possibility of borrowing or lending a gift certificate but I guess it could be done if the gift certificate lender was willing to accept the risk of failure to repay.

Turning to the creation of money, modern money is created when banks lend. The process is simple. In exchange for a promise to repay, a bank will create a limited deposit in a transferable account. This may be a case of a bank lending to itself as when a central bank creates a loan to a sponsoring government, or it may be a case of a bank lending to a customer without deducting or limiting any other accounts existing in the bank. Either way, a tally of all the bank deposit accounts will show an increase directly equal to the amount of new loans created. New money has been created.

But here we see a striking difference between gift certificates and money. The person spending money on a gift certificate has first earned the money used to buy the certificate. On the other hand, during the creation of money, the first spender does not first earn the new green money he is spending. This is a HUGE difference between the two monetary instruments. The difference has profound effects on the long term psychology of the persons creating either of the two instruments.

First, consider the psychology of the store owner creating a gift certificate. He would be very reluctant to create the certificate unless he received something in return. After all, if he created a lot of gift certificates and gave them away, it would be equivalent to giving away the merchandise in his store. Good advertising but a sure path to business ruin.

The creation of money is far less personal. The creation of money by bank lending is a mechanical decision by an administrator. Lending by private banks is generally based on construction of goods of offsetting value. This would generally be viewed as a reasonable exchange that would preserve or improve the financial condition of the transacting parties. The lending of money by central banks to their sponsoring governments is not so easily characterized.

If we think of a central bank as creating a national gift certificate, the creation of money by a central bank lending to the sponsoring government is an act of giving away the merchandise in the store.

Walking out of the store with my new digital calipers in hand, I came back to the day-to-day world. I would use this digital tool and remember the source of the gift. That has happened many times.

The insights into money are just beginning. The clear parallels between money and gift certificates are striking, the sharp differences in work-required-before-spending sobering. I fully expect to explore these parallels further in future posts.

* A digital caliper is a tool long desired. It approaches being a luxury item.

When Central Banks Buy Equities

Yesterday, the BOJ (Bank of Japan) announced further stimulus in the form of purchase of stock ETFs. Of course, ETFs are each aggregated owners of stocks, rather random in composure, and freely exchanged on the market. What is the effect of this action from a mechanical money perspective?

The mechanical money perspective treats money as physical object. Money becomes property, freely exchanged for other property of any nature. Money is always owned by someone or some entity.

The first question to ask is "Where does the BOJ get money for these purchases of ETFs?". The answer: The BOJ can 'print' all the money it desires. It does not need previously earned resources, it does not need to ask the government of Japan for a grant or gift. It can just 'print' the money needed to buy ETFs.

We can ask "From whom does the BOJ buy these ETFs?". Apparently they are to be purchased from the open market at times selected by the BOJ. This has several implications: First, the purchases are between willing buyer and willing seller. We can make a general observation that the seller has a motive to sell and the buyer has a goal and expectation. The two exchange participants have different goals. The goal of the BOJ is to increase the amount of monetary property available to the economy (to put a charitable motive forth for some decision maker acting on the behalf of the BOJ).

From the mechanical money perspective, this sequence of events is easy to analyze. The sellers of ETFs walk away with more money than they expected because a buyer with NEW MONEY appeared. The price of ETFs would close (in the daily market) HIGHER than market conditions would otherwise have supported. It is also clear that the money supply would necessarily increase if money supply is measured in a mechanical fashion.

How is money supply measured in a "mechanical fashion" ? We could begin by considering that the seller began the exchange with no money but walks away with cash. If we measured his bank account (or the accounts of his agent), we would necessarily see an increase. There would be no corresponding decrease in deposits anyplace in the system if the purchaser was the BOJ.

We would hope that the BOJ would at least keep track of the creation of new money later used to buy ETFs. It could easily do this by recording a liability for cash spent for equity. The balance sheet of the BOJ would show an increase in total size.

What would be the future mechanics of central bank purchases of equity? What would the seller do with the sale proceeds, knowing that a central bank was the purchaser? What would the attitude of the market become under these conditions?

I can only speak for myself. I see a market distortion that inserts an unpredictable element into pricing. The unpredictable risk is obviously to the high side, requiring a negative factor to compensate. If I wanted to buy an ETF, I am competing with a central bank who is spending unearned money. How can I possibly compete with that kind of competition? I see a conundrum for the forward looking investor.

An Alternative SIM Equation

Wynne Godley and Marc Lavoie's book "Monetary Economics" provides an excellent introduction to SFC analysis. Chapter 3 introduces model SIM (for simplest) and introduces the reader to a system of equations suitable for entry into a spreadsheet. Unfortunately, the system introduced is interlaced with the premise that people have a tendency to spend part of their income [1] . While undoubtedly true, this premise leads the reader down a difficult path. This path leads to the arithmetic of diminishing series which requires enabling the iteration capabilities of the spreadsheet and complicated, interactive calculations.

The possibility that an alternate path may exist is inferred from the knowledge that a diminishing series (such as we have here) will converge to a limit. The fact that a limit does exist should give us confidence that any path found can be coequal with series-based-pathways .

A Monetary Relationship

A relationship between taxes, value exchanged and money is easily found. Ask yourself "If I have money, say $ \\{$100} $, how much can I and all the people I trade with buy before the government takes the $ \\{$100} $ away with taxes?"

We can answer that question easily. Assume a tax rate of 20% (like the income tax) that is extracted at each exchange. We set up an equation in the form of unknown amount times tax rate equals $ \\{$100} $ . We can write that in a conventional format by letting X = the unknown amount and θ = the tax rate . We would write

(1)     $ \theta X = 100 $

The reader can see that if θ is 20%, X will be $ \\{$500} $ .

We can relate this to the general economy. Government is the source of much of the money that powers our economy. When government pays wages, the wages count toward the Gross National Product (GDP). Government typical collects taxes on those wages in the form of an income tax collected before the worker actually holds those wages in his hands. (The tax collected does not have to be an "income tax" but the concept is easier to accept when we use familiar terms and conditions.) If we let T represent any tax repetitively collected at each transaction, we can write

(2)    $ GDP = \frac{T}{θ} $

Equation 2 gives us a simple, intuitive way to relate GDP, taxes and a tax rate. It also provides a relationship to the money supply.

The Money Supply

We began this analysis by assuming we had $ \\{$100} $. This is a supply of money. We continued with another supply of money, $ \\{$500} $ which the government used to pay wages and collect taxes. Now we notice something peculiar. Government needed $ \\{$500} $ to pay the wages and taxes, but we only needed $ \\{$100} $ to generate $ \\{$500} $ in GDP. This is a multiplier effect found when translating between wealth and GDP. This effect is a result of the durable nature of money which can be reused until removed from circulation by taxation.

We have assumed that government used it's money supply to pay wages. What happened to the money once it left government hands? It became wealth held by the private sector [2]. The money supply, at least what is left after taxation, is then all held by the private sector as wealth. We will assign this wealth the general term H (following G&L who considered this to be High-powered-money), a term we will frequently use for the remainder of this analysis. We assign the term G to mean government expenses (such as paying wages) and we can write

(3)    $ G = T + H $

We previously said that government expenses are counted as GDP. This will be important later as we develop the analysis. For now, we will modify Equation 3 to add GDP and write

(4)    $ \\{part GDP} = G = T + H $

In Equation 4, we can foresee a logical extension to use GDP as a substitute for the T and H terms. This extension opens the door to building a simple equation that can be used to build a simple spreadsheet model.

[In Equation 4, we have both parts of the flow-of-funds method of measuring economies. The G represents the expense or spending method while the T and H represent the income method. The two methods should give the identical result but practical data collection considerations will typically result in small differences in reported numbers.]

We will write the government  and private GDP contribution equations as

(5)    $  \theta GDP = T $

(6)    $ GDP (1 - \theta) = H $

where GDP is recognized as just being part of the entire GDP.

We can combine Equations 4,5 and 6 to write

(7)    $ G =  \theta GDP + GDP (1 - \theta)  $

Further Spending Within the Period

Equation 7 describes a single transaction and the wealth distribution following the transaction. There is no reason to think that the economy stops here. Instead, the economy can be expected to move ahead and people will spend their newly earned money. Re-spending will expose the income to additional taxes and can be expected to increase the reported GDP as well as the taxes collected by government. We have a situation where we need to develop an equation using a parameter controlling the expected reuse of money by the private sector during the time period under consideration. G&L use the concept of "propensity to spend" [1] but here we use the concept of "propensity to save". We will label propensity to save as $ \alpha_4 $ .

 [Both "propensity to spend" and "propensity to save" are terms related to the expected behavior of people as they act in the market economy. As such, they can be expected to change from period to period. Later in this analysis, we will examine the USA flow-of-funds data and attempt to relate this term to actual data.]

We will assume that the propensity to save acts the same as a government tax. Part of each transaction is set aside by the private sector for the duration of the period under consideration. (Equation 4 will now be considered to describe an earlier time in the economy) Using the term $ \alpha_4 $, we write

(8)    $ G =  \theta GDP  + GDP (1 - \theta) \alpha_4  $

Equation 8 only includes government spending as the initial economic driver. We need to add provision for past wealth, held over from previous periods, which will also be an economic driver. We will assign wealth from a previous period the label $ H_{-1} $ and use the term $ \alpha_2 $ to modify H to conform with various descriptions of money supply. We will leave the term $ \alpha_4 $ unchanged but recognize that it may vary as previously described. Increasing the money supply is expected to increase GDP.

With the addition of $ \alpha_2 H_{-1} $, we write

(9)    $ G + \alpha_2 H_{-1} =  \theta GDP  + GDP (1 - \theta) \alpha_4  $

Equation 9 can be rearranged to write

(10)     $ GDP = \frac{G + \alpha_2 H_{-1}}{ \theta + (1 - \theta) \alpha_4} $

which is the result we are seeking.

Find   $ \alpha_4 $ from flow-of-funds Data

If we allow $ \alpha_2 = 1 - \alpha_4 $ , Equation 10 can be rearranged to write

(11)    $ \alpha_4 = \frac{G + H_{-1} - T}{GDP - T + H_{-1}} $

Using Equation 11, we build Figure 2 which is the chart of $ \alpha_4 $ since 1947.

Figure 2. Chart of term $ \alpha_4 $ since 1947.  $ \alpha_2 = 1 - \alpha_4 $

Conclusion

Equation 10 represents a considerable divergence from the SIM_0 model. The focus is upon wealth, not consumption.

In limited testing, using equivalent factors, both the SIM_0 model and SIM_MECH_0 give similar results. This is a requirement if the initial premise (two pathways to the same result) is to be fulfilled.

The existence of two SFC methods, both giving substantially identical results allows crosschecking of methodology, there-by bolstering the validity of the model.

I would like to acknowledge the contributions of Tom Brown to this post. He asked a number of questions, made many suggestions for improved appearance and raised the standard for consistent mathematics. His electrical circuit  representation of the SIM model gives us confidence that a wealth memory effect is important.

[1] In their book "Monetary Economics", page 66, G*L make a subtle choice in definition of terms. They choose to consider household consumption rather than household wealth. This leads them to write $ C_d = \alpha_1 YD + \alpha_2 H_{-1} $ where $ C_d $ is household consumption. In this analysis, making the same G&L choice, we would write $ C_d =(1-  \alpha_4 ) YD + \alpha_2 H_{-1} $ Our emphasis is on wealth, not consumption.

[2] The private sector is the counter-party to most government exchange examples. Government to government exchanges become important when both governments have the ability to create money. The ability to create money is powerful economic tool usually carefully controlled by government.

A Master Equation for SIM Models Using the GDP Object DRAFT

DRAFT

There seems to be a path from the barter economy to the money economy.  The SIM spreadsheet model is a simple emulation of a stable money beginning but we need a better path from start to monetary stability, Lets's see if we can find that path and equations for building a SIM style of model.

The Barter Economy

First, we will build an economy measured in transactions and described by GDP (Gross Domestic Product). This is a barter economy without money. We label GDP as GDPt (using the sub t as a identifier). There is a private sector (PSt) and a government sector (Gt). Government is allowed to levy tax to enable spending. The tax is applied at a rate of TRt on a period basis.

We can write three equations that will describe this eonomy:

(1)     Gt + PSt = GDPt
(2)     GDPt*TRt = Gt
(3)     GDPt*(1-TRt) = PSt

With these three equations and an assigned (or discovered) value of TRt, we can describe this economy in a spreadsheet environment. Years can be represented by columns marching across the page. These three equations are a simple measurement with no memory between periods (There is no need for memory because transactions are events.)

Introducing Money

Modern economies are money based, not transaction based. How can we introduce money into this spreadsheet model?

Figure 1. A barter economy can be converted into a money economy. The GDP curves are considered to be square or rectangular hyperbolas, with the property xy =1.                        

From Figure 1, we can see that GDP can be represented by transactions or money. How would we make and display the transition from transactions to money?

Unlike transactions, money has a characteristic of duration. Money is an object with a lifespan. The three transaction equations will need to be supplemented with additional terms and equations that record the money carried between periods.

We will define money that is held from one measurement period into a second period as wealth (H). Wealth from a previous period will be labeled H-1.

Wealth held in more than one period must be dynamic. There must be a method of creation, holding, and destruction. Money can be created by borrowing [Exactly how is an ongoing debate among economist and philosophers.] In this simple model we will assume that government can borrow from itself, spend this borrowed money into existence, and finally destroy money with taxation. While the money is in existence, the private sector will be allowed to store money as wealth.

There is no way to know when the private sector will spend it's stored wealth. There is no way to know how much money the private sector will save from each period. We do know that the private sector cannot save more than that part of GDP left after government extracts it's share. The private sector gets a remainder. This sequential nature of events will be important later when we design equations.

We are ready to write equations that describe the entry of money into a transaction economy. We will use three assumptions to simplify the equation construction:

1.  Government will have no savings.
2.  Government will spend new money into existence unless it has tax money to spend. This is similar to government beginning a new program and using money it borrows from itself to fund the program.
3.  Equations 1, 2 and 3 are still valid but they are missing wealth terms. We  add the necessary wealth terms and drop the sub t label-modifier.

We will take an empirical approach. Because we cannot hope to predict the actions of people, we will build in adjustable parameters that can be calibrated to reasonable values discovered by measurements of existing actual economies. What we need is a mathematical system that repeats at every replication with some memory of the past. We are ready to begin.

Building the Dynamic Money Equation

If government spends (G) and collects taxes (T) at rate (TR), we can write

(4)     GDP*TR = G = T

For the private sector share of GDP,  write

(5)     GDP*(1-Tr) = PS

Here is a critical point. These equations describe a stable economy.  If we stopped this analysis using only equations 4 and 5, we would be assuming that government recovered the entire initial amount spent. [In equation 4, we wrote that the tax collected equals the amount initially spent. This describes a stable economy, not a dynamic economy with wealth remaining at the end of the period.] The GDP for any period can only be as big as allowed by the remaining wealth circulating completely expanded in the economy.

The act of saving money from the present period will be treated as second tax.   This savings rate tax (α1) will be applied to the private sector share of annual GDP (AGDP) to fund the annual amount saved H. We can write

(6) AGDP*(1-TR)*α1 = H

We assume that government will tax the annual GDP so we write

(7) AGDP*TR = AT

where AT is the annual tax collected by government.

We assume that the amount saved added to the amount collected in taxes equals the amount spent by government added to the amount spent from savings during the period. We can write

(8) H + AT = G + H-1.

We can combine equations 6, 7, and 8 to write

(9) AGDP*(1-TR)*α1 + AGDP*TR = G + H-1.

Rearrange equation 9 to write the master equation for period GDP

(10) AGDP = (G + H-1) / ((1-TR)*α1 + TR).

Now we can examine equation 10 to see that if we assign values to terms G, TR, and α1, we have defined AGDP. The values for these three parameters will be discovered by empirical methods.

Tie to the SIM Model

Wynne Godley and Marc Lavoie in their book "Monetary Economics (2007) , chapter 3, describe an economic model SIM. Several versions of these models are available on the Internet. The parameters used in this post can be directly converted to the SIM parameters.

TR -> θ || G -> G || α1->α1 || α2->α2 || H->H || AGDP->Y

We have not yet used the term α2. We used the term H-1 (wealth) to provide the memory between periods. Empirically, we find that there is no need for all of the wealth saved in one period to be used in a second period. We use the factor α2 ( Propensity to consume wealth) to modify the amount of wealth used in a later period. Therefore, we can write (for example)

H-0 = α2*H-1
$H_0 = \alpha_2 H_{-1}$

and use H-0 as the starting wealth in the next replication. Term α2 is also empirically determined.

Using the Equation in a Spreadsheet

We can use equation 10 to build a spreadsheet model of an economy without using spreadsheet iteration. This makes the model much easier to understand. Each of the three empirical parameters can be adjusted to create a unique model. The wealth carried between periods can be adjusted by changing term α2. 

Spreadsheet columns can represent time periods. Each period can be adjusted to introduce "jump" changes in later periods. [Later adjustments require a second empirical entry table and decision logic in the spreadsheet column structure. This is easy to do but tedious in construction]

Conclusion

We have found one possible path from the barter economy to a simulated monetary economy. This is a very simple model but flexible to allow inclusion of additional parameters. The ability to construct a mathematically satisfying simple model encourages further use and development of this mechanical method and theory.

DRAFT

For Tom: The GDP Object

DRAFT


[4/3/2016 1:30 update
Tom comments that the drawing shows a "square hyperbola", also known as a "rectangular hyperbola". This is a hyperbola with the relation xy = 1. This is useful in creating a model economy. We can assign one axis to represent money, the second axis to represent transactions. Assuming every transaction can be represented by money, the sum of all transactions multiplied by the sum of all money values will form a square hyperbola if every-possible-combination-that-forms-the-same-constant-value is plotted. This gives us the "GDP Object". 

The GDP Object will be useful in writing a SIM style of spreadsheet model that avoids iteration but yields similar results. This results in easier to understand equations. (I hope!)
(This concept and the enabling equations have not yet passed peer review.)]]

[4/2/2016 10:00 AM update    
"The GDP Object" may not be the best way to characterize the nature of GDP.

GDP (Gross Domestic Product) can be related to at least three different concepts:

1)   A measure of economic activity. It can be considered as the sum of all transactions with a price value. Here, GDP is a defined measurement. If government expenditures are also known, an average tax rate can be calculated.

2)   A theoretical limit. Money supplied by government can be taxed every time it is received. If only one issue is made, money disappears from the private sector and returns to government. Eventually, the entire issue is recovered. Limit GDP is the maximum possible GDP if the tax rate is known.

3)  A  PERIOD theoretical limit. The theoretical limit can be divided into time periods. Each time period will have a different GDP limit based on a period common tax rate and rate for parallel money collectors, and a period-unique beginning money supply.

A characterization of GDP as an "object" nears becoming misdirection. Perhaps we should characterize GDP as a "limiture" (where we combine the words "limit" and "measure"), giving GDP an unique characterization.]

This is for Tom. It is quick and dirty. I am bogged down with detail in another attempt to present the same material.

Figure 1. The GDP Object is the value on the GDP curve at any point in money-transaction space. 

GDP can be considered a limit defined by G and T as in

GDP = G/T

where T is a dimensionless pure number. G is money and GDP is money. GDP is constant when G and T are defined. Now GDP is an object.

Find GDP for a period

We can use T with a time period dimension to find the GDP expansion for that period. We can count on T being less than one because it takes an infinite time period with infinite transactions to find the GDP limit by series expansion.

If we assume that we have TWO taxing authorities, one authority can be government using the assigned tax rate FOR A PERIOD. The second authority will be assigned a tax rate that captures the remainder of the potential GDP FOR A PERIOD. The remaining GDP potentially available for capture is GDP*(1-T) .

This gives us two equations that capture the entire GDP expansion to limit.

Convert into a series of annual events 

We can convert GDP to annual events (AGDP) by considering every step is a division between two taxing authorities. The primary authority will receive the Annual Tax (AT) share and the second authority (savers) will receive the remainder (AR). Write this in two equations.

(1) AGDP*Tr = AT

 and

(2) AGDP*(1-Tr)*Rr = AR

where Rr is the Remainder "tax" rate.

Notice that the sequence of events is important here. Tax is removed from GDP before a remainder can be calculated.

We know that the sum of the two tax divisions is the original injection by government (G):

(3) AT + AR = G

Substitute  1 and 2 into 3 to get

(4) AGDP*Tr + AGDP*(1-Tr)*Rr = G

Simplify 5 to get

(5) AGDP*( Tr + (1-Tr)*Rr) = G

Now we can define parameter Rr just as we defined the government tax rate. AGDP is constant for the period just as GDP is the constant GDP Object. Once we know AGDP, we can find wealth and every other term as you did using Linear System Analysis.

We can next add wealth to the next period by assuming that wealth is also all spent to create a new GDP Object.  It now becomes repetition to complete the table for as many years as desired.

At this point, I think we may be in correlation with Linear System Analysis

Does this make sense now?

DRAFT

The Durable Goods Model and Debt

You probably have never heard of the Durable Goods Model of economic activity. That is because it is a new model proposed by Nick Rowe (without a formal name).

Introduction

The concept underlying the model is very simple: What happens if all the goods produced have some durability? What happens if some goods only have durability of days (such as a haircut) and others (such as a concrete sidewalk) have a durability of many years?

In his post, Nick's focus is on the math and he is seeking help. Reader Keshav offered a solution. Reader Roger Sparks (me) offered improvements in his initial base equality formulation. As I write, comment seems to have ended with the basic concept largely unexplored.

This post is an attempt to explore one of the nuances of a Durable Goods Model.  Nick points out that Keynesian models treat the economy using goods that are instantly consumed. If goods are  not instantly consumed, the dynamics of the model are changed in several ways, often subtle ways. The focus here will be on the effect of debt.

Debt in the Durable Goods Model

Debt in Keynesian models is treated as a simple monetary exchange. In other words, debt may-as-well-be money. Debt cannot be simply money in the Durable Goods Model. An illustration (Figure 1.) helps in understanding why not.

Figure 1. The remaining value of many items constructed in one period. A single sidewalk bought with debt demonstrates the subtlety of correct accounting in the Durable Goods Model.

Debt is a commitment to perform in a specified fashion in the future. In the Durable Goods Model, this is an important detail to remember when we measure economic activity such as GDP. GDP is a measure of economic activity within one period. As a result of measuring year-by-year, the entire activity initiated by a single durable event is captured by GDP over several years. In Figure 1, this is demonstrated with the construction of a concrete sidewalk. Built with debt, this project will show in the period of construction indirectly by counting the secondary effects of reusing the money borrowed (while the cost of the sidewalk may not be counted directly, the money used would be counted when re-spent). The sidewalk will be counted again in GDP when the owner of the sidewalk debt is repaid (because the borrower must have activity countable-by-GDP to earn the payment). The overall GDP effect in the Durable Goods Model is to count the economic activity initiated by the single debt event two times.

This double counting occurs unrecognized in standard Keynesian models as described by Nick. The Keynesian equality described by Nick only includes economic events in one time period. Unlike the Durable Goods Model, there is no carryover between measurement periods that would carry information about debt commitments. 

An intersection with macro-economics and politics

Economics is often accused as becoming politics in disguise. What does the Durable Goods Model reveal about social behavior that might affect a political view?

We can use the construction of a sidewalk as a social example. The future owner of a sidewalk may construct it himself. This would be viewed economically as a single transaction, to be recorded as an increment to GDP. This would be no different from purchasing a steak dinner or buying a pair of shoes. Two sectors have come together to make an exchange valued in money. Both sectors have performed an economic activity that ultimately resulted in the existence of a sidewalk, steak dinner, or pair of shoes.

Now consider the case of a sidewalk that was constructed using debt. The sidewalk would be built by a builder, not by the sidewalk owner. The builder would have a lien on the property for work performed, He would trade his ownership of the lien  for a promise by the property owner to repay the value of the loan, usually with interest. The builder and all of his suppliers would report this GDP countable activity the same way as if the sidewalk owner was the actual builder. 

Up to this point in the debt based analysis, there is no difference in the activity of sidewalk construction and GDP-reporting between debt and cash. The difference lays in the future. From the macro-economic view of society, the builder has improved the well being of society with the construction a sidewalk. The builder has spent his time and resources to improve the well-being of someone other than himself. He has done this in exchange for a promise to repay this generosity, presumably by performing future well-being activity for  others. This sets up the predestination of expected future economic activity.

The "predestination of expected future economic activity" can viewed as a promise by the borrower to generate (in the future) an amount of economic activity equal to the amount of money borrowed. If interest on the borrowing is promised, the future economic activity is promised to be greater than the amount borrowed. This promise could be the logical basis for using the interest rate on borrowed money as an indicator of future economic growth.

The "predestination of expected future economic activity" can be short-circuited by hints of refusal of future debt repayment. The promise of inflation (as a method of avoiding debt repayment) can have the same short-circuiting effect.

From the point-of-view of macro-economics and the broader society, the removal or decline in predestined economic commitment will have a discouraging effect on the enthusiasm of builders who build for the longer term. The removal will have little effect on those who focus their decisions on the near term with little view towards long term effects. This shift in focus from long term to short term may explain the observed mediocre effectiveness of central bank's monetary stimulation.

Conclusion

The Nick Rowe' Durable Goods Model is an attempt to model the observable fact that much of one year's production has economic impact on future years. The effects can be subtle, the mathematics more difficult, and a complete model is not yet described. The concept seems to have the potential of rich reward in terms of understanding economic systems.

A Cash-In-Advance Model Comparing Consumers and Suppliers

John Handley presents a simple Cash-In-Advance model which I think can be the genesis for presenting a clear contrast in the inflation effect between consumers and suppliers.

The heart of John's model is

(1)       K*Pt = Pt+1 

where K is a proportioning factor relating price at measurement one (Pt) and price at measurement plus one (Pt+1).  K can be composed of any factor or a multitude of factors.

John sets K = Rt where Rt is the current "gross nominal interest rate" (his definition) expressed as one plus the current interest rate (example 1 + .05 = 1.05). With this assignment, John  shows us how a future price can be found based on an increase attributed to interest accumulation.

We can use equation 1 to  compare consumers and suppliers using factors that cause a price difference between the beginning and end of a period (which requires two measurements). Interest on money is a very simple example that readers can use and agree upon.

The Cash-In-Advance model is based on the concept that cash must be in hand before trade can occur. In the simple form, it does not need a definition for money; it is only required that money be a fact of commerce.

In the coming comparison, we assume that both the customer and supplier have all the cash they need to complete a purchase. The purchase price is only part of the available cash held by each party. We are looking for motivation to complete a purchase now and motivation to complete the purchase of the same item in the future.

Everyone is a consumer which makes it easy to tell the consumers story. Allowing that the consumer has cash, he has a choice of buying now or buying in the future. If he delays his purchase until past the second measuring point, he can increase his cash holding by the amount of interest received.

Here is a vital point for this analysis. The supplier has the ability to delay construction of a product. A delay would allow the supplier to increase his cash (which would otherwise be used to build a product) position in the identical fashion as the consumer.

Any interest received from money-in-hand will provide the identical incentive to both customers and suppliers, with both having equal incentive to delay commerce. For both consumer and supplier, we have

(2)     Pt+1 = Rt*Pt              (for both consumers and suppliers)

If interest provides both economic sectors equal incentive to delay commerce, what about inflation from any cause? Inflation (which here is simply a price increase found at the next price measurement) could be caused by multiple factors. We will assume that both interest (Rt) and a general term for inflation (Ft) will be the cause of an increase in price at the second measurement.

Before we write the equation(s), we must notice that inflation may affect the consumer unequally with the supplier. From the point of view of the consumer, inflation will act as a negative interest rate.  On-the-other-hand, the supplier is often the beneficiary of inflation (but not necessarily) so, in general, inflation will act the same as interest. We see that we must write two equations to express the effects of inflation, one for the consumer and one for the supplier. We write

(3)      Pt+1 = (Rt - Ft) * Pt                (for the consumer)

(4)      Pt+1 = (Rt + Ft) * Pt               (for the supplier)

We might be tempted to say "Eureka! The cause for the slow response to the QE programs!".  Slow down. Suppliers have much more than inflation to balance when making product building decisions.

We close with the observation that Cash-In-Advance models are capable of providing insight into the motivation of both customers and suppliers. It is easy to see that motivation for one sector may be disincentive for a second sector.

New Debt Initates a Cash Flow Pattern

[Edited 1/12/2016. Replaced Figure One with improved graphics and text.]

Nick Edmonds has an interesting post on "Sticky Prices, Unexpected Inflation and Ricardian Equivalence". 

Ricardian Equivalence is a theorem that includes the concept that people must change their spending assumptions when new government spending occurs. It is claimed that the this change occurs coincident with the announcement of new spending. 

Here is a quote from the post:

"To look at this, I need to make some of the standard assumptions for Ricardian Equivalence to apply, so I'm going to assume homogenous households with infinite horizons and no issues like liquidity constraints. Under this assumption, the long-run government budget constraint is binding. This says that the present value of taxes cannot be less than the value of current debt plus the present value of government spending.


The usual way to interpret this is to suppose that any change in tax now must be offset by a change in tax at some future time. So, for example, if there is a one-off tax reduction today, then this will need to be financed by issuing debt. That additional debt, plus the interest, must be repaid at some point and this requires future taxes."

I doubt the Ricardian Equivalence theorem because I see new debt as initiating a cash flow pattern that looks like the outline in Figure One. This outline is similar to the outline projected by Edmonds but broken into components. I think the breakdown of components speaks directly to the Ricardian Equivalence Theorem.

Figure One: New debt results in a cash flow pattern

New debt (by any party) initiates a series of events.

When a party takes on new debt (not refunding old debt), it can be safely assumed that the purpose is to initiate new spending. This new spending is depicted in Figure One as a green area. This spending will show up on the GDP calculation as an increase in economic activity.

The party taking on the obligation of debt repayment will probably agree to a constant rate of debt repayment and interest payments. In Figure One, this constant payment stream is represented by the purple area. It will result in increased taxes paid to government to the extent that only after tax income can be used for debt and interest payments.

[For any one debt pattern, the amount of money represented by the purple area will be bigger than the amount of money represented by the green area by the amount of interest paid.]

The red area of Figure One is of particular interest: This area represents reuse of the money placed into motion by the creation and spending of the original debt. The size of this area is dependent upon the rate of money destruction. The easiest way to see this is to realize that, each year, some of the new money is likely to be used to repay older monetary debts, thus destroying money. Money is created when new debt is assumed; money is destroyed when debt is repaid.

We can argue that not all loans create new money as in "only bank loans can create new money", or perhaps "only government loans create money". [It is generally agreed that private loans do not create money. Private loans only accelerate the rotation of money through more hands.] It is not important for this discussion to agree on how money is created and destroyed; we only need to agree that it is possible to create and destroy money.

We close this discussion by looking at the future spending implications of Figure One.

If we are part of the red area (we are secondary beneficiaries of the new spending) we will consider this sudden influx of spending to be a temporary event unless we know this to be a consistent pattern of the borrower. We have little choice except to accept the jobs and income offered, and to pay the taxes extracted. We only know that the pattern we see will continue until it does not.

If we are part of the green or purple area, we are a decision maker. We had a choice of creating the debt or not. We have the choice of making the payments and interest by doing hard work, by imposing new taxes, by borrowing additional funding next year, or by simply not honoring the obligation. 

Ricardian Equivalence anticipates hard work or new taxes. Modern governments around the world more likely choose borrowing-additional-funding-next-year.