Primer: Coin As Well As Debt Inwards Sfc Models

How coin as well as debt are described inwards unproblematic economical models colours economists' interpretation of existent dry reason monetary systems. My feeling is that coin is somewhat superfluous inwards these models, but it is necessary to empathise why that is the case. This article explains how coin as well as regime debt (Treasury bills) operate inwards the minute simplest Stock-Flow Consistent (SFC) model inwards the textbook Monetary Economics by Godley as well as Lavoie -- model PC (Portfolio Choice; constitute inwards chapter 4).

If the reader is familiar amongst mainstream models -- similar Dynamic Stochastic General Equilibrium models (DSGE) -- the handling of coin as well as debt is mostly similar to model PC. There are a number of convention differences, which agency that the formulae facial expression different, but they quite frequently imply the same behaviour. The existent differences demo upwards inwards the philosophy of the solution of the model, which genuinely should non bear on how coin as well as debt operate every bit instruments. In interests of brevity, I volition defer the intelligence of the differences to later. However, agreement how coin as well as debt piece of work inside a SFC model -- which tin give notice survive cleanly solved -- volition prepare readers' agreement of the to a greater extent than poorly-defined DSGE models.

Comparison To Model SIM

Model PC is constitute inwards Chapter iv of Monetary Economics: An Integrated Approach to Credit, Money, Income, Production as well as Wealth, by Wynne Godley as well as Marc Lavoie. This text has boot the bucket the criterion for learning nigh SFC models. It is a textbook, as well as hence it may survive imposing to readers who are less mathematically inclined. This article (and similar ones) aims to give a non-technical overview to the topic; either every bit an assist to agreement the text, or at to the lowest degree to innovate the basic concepts. The text itself contains a lot of information, which my summaries cannot promise to cover.

For those of you lot without the text, the models are available online at the sfc-models site: http://models.sfc-models.net/  Shown below is a screenshot of the Excel spreadsheet version of model PC. You may survive able to relate the variables inside the spreadsheet to my diagram (although my labelling mightiness survive slightly different).

Screenshot: Excel spreadsheet (partial) of Model PC from sfc-models.net 

The number of equations is impressive for what is genuinely a fairly unproblematic model.

I described Model SIM inwards the article Finding The Solution In H5N1 Simple SFC Model, in which I explained how to abide by the solution easily for the inaugural of all fourth dimension menstruation if nosotros brand the supposition that the taxation charge per unit of measurement is zero. H5N1 minute article, Techniques For Finding SFC Model Solutions, discusses how the model tin give notice survive solved amongst a non-zero taxation rate, as well as for multiple periods. (Essentially, nosotros remove to work numerical solution techniques, similar the Excel spreadsheet shown above.)

Flows inside model SIM

We start of amongst the flows inwards the SIM model, every bit shown above. (Note that this diagram adds taxes, different the diagram shown inwards the previous article.) This model only has "money" -- which bears no involvement -- every bit a financial asset. It is denoted H inside the equations, every bit it is what is referred to inwards economist jargon every bit high powered money.

Note that Government Expenditures (denoted G) is an exogenous variable that drives the system; all other variables are determined yesteryear it (and the previous stock of regime coin held from the previous period). The regime mostly uses deficit financing, issuing coin (which it creates at no existent cost) inwards consequence. If coin were gold-backed, nosotros would remove to rail the government's gilt holdings inside the model, every bit that would boundary the powerfulness to number money.

I accept labelled the regime every bit "Consolidated Government." This entity includes the Treasury (fiscal agency) as well as the key bank. Within model SIM, it makes fiddling sense to dis-aggregate the consolidated government, but that changes when nosotros movement to model PC.

As discussed inwards the previous article, the describe of piece of work organisation sector has the apparently magical powerfulness to hire precisely plenty workers hence that full revenues equals its wage bill. Since the describe of piece of work organisation sector is ever simply breaking even, it pays no tax. This is unrealistic (perhaps other than the taxation part), but relaxing this supposition greatly increases the model complexity -- otherwise, nosotros remove to allow for the describe of piece of work organisation sector to accept a mismatch production as well as sales. That possibility implies the remove to rail inventory, as well as describe of piece of work organisation sector holdings of money. The number of "state variables" inside the model starts to explode. Although nosotros tin give notice solve those to a greater extent than complex models numerically, intuition is harder to come upwards by.

(It should survive noted that after models innovate expectation errors yesteryear households as well as businesses, at the cost of added complexity. That magical forecasting powerfulness inside models SIM as well as PC are non full general properties of SFC models.)

With the describe of piece of work organisation sector lead locked down, the diagram makes it clear that at that spot is only i conclusion to survive made inside the model -- how volition the menage sector allocate its income betwixt consumption as well as saving? Once that conclusion is reached, all other lead is determined yesteryear the income flows. The conclusion itself is reached via a consumption function.

The diagram inwards a higher house illustrates the flows inside Model PC. There are 3 functional differences.

1. The regime pays involvement upon Treasury bills (which are only held yesteryear households exterior the consolidated government).
2. The menage sector at nowadays faces 2 decisions, which are marked. It inaugural of all needs to determine how much to swallow out of its income (wages addition interest), as well as it hence needs to determine upon its portfolio allotment betwixt coin as well as Treasury bills. (Note that the allotment conclusion covers the entire portfolio, as well as non simply cash inflows for the period.)
3. The involvement charge per unit of measurement on Treasury bills acts every bit a novel external (exogenous) variable.

I volition hash out how model PC behaves inwards after articles. In particular, the effect of involvement charge per unit of measurement changes mightiness non survive intuitive. The explanation is constitute inwards the text, but the reader may experiment amongst the numerical models to essay its behaviour.

The residuum of this article discusses how coin is handled inwards SFC models inwards general, which mostly follows the designing of model PC. 

New Financial Assets

Within the SFC model framework, it is straightforward to add together novel property classes, at the cost of increasing model complexity. The conclusion procedure is similar -- the menage inaugural of all decides the degree of consumption, as well as hence the property weightings inwards the portfolio.

The number amongst adding novel assets is how to model their prices. Is it possible to reverberate the lead of the equity marketplace inside a simplified model? The opportunity is that pocket-size behavioural differences tin give notice termination inwards completely different outcomes.

Treasury Bill Pricing Conventions

The supposition is that the Treasury issues bills that mature i model fourth dimension menstruation inwards the future. That is, if the model fourth dimension pace represents 3 months, the Treasury issues 3-month Treasury bills. The entire stock of Treasury bills is rolled over every accounting period; at that spot are no long-term securities which remove to survive tracked. (That supposition is relaxed inwards after chapters of Monetary Economics.) 

This agency that nosotros cannot endeavour to convert to a higher model frequency without creating complications. Instead of tracking the stock of Treasury bills at the "end of the accounting period," where nosotros assume that they are i menstruation away from maturity, nosotros would remove to rail the marketplace value of Treasury bills during fractional periods of their maturities. If nosotros allow involvement rates to vary at each fourth dimension step, this would create uppercase gains/loss on Treasury bills. This would highly complicate the model (being somewhat equivalent to introducing bonds). Moving to a lower frequency -- quarterly to annual, say -- is less of a problem, every bit the "interest rate" corresponds to the annual average. (Although it raises concerns amongst regards to model behaviour.)

This simplification tin give notice survive defended upon the dry reason of marketplace efficiency -- on average, a bond portfolio should accept the same render every bit a Treasury pecker portfolio (modulo opportunity premia). However, this efficiency declaration is plainly violated if nosotros experience a bond bull marketplace (which is precisely what happened). As a result, nosotros accept to promise that the effect of uppercase gains on bond portfolios are non plenty to greatly bear on economical behaviour. (This complication creates a wedge betwixt what nosotros tin give notice promise to model, as well as real-world economical data, every bit governments accept an entire bend of bonds outstanding.)

Monetary Economics also uses a "bank deposit" involvement charge per unit of measurement convention, instead of a "discount" pricing convention that is the characteristic of real-world Treasury bills. This simplifies the accounting, as well as but has no effect on the model solution. (DSGE models work the to a greater extent than complex discount convention.)

The deposit convention says that the involvement payment made inwards a menstruation is equal to the previous period's "Treasury bill" holdings times the previous period's involvement rate. Since at that spot is a dependence upon the previous period's values, nosotros remove to survive careful nigh the fourth dimension menstruation inside formulae.

Time Period Issues

There are a number of economically equivalent ways of defining how involvement payments occur -- the only departure betwixt them is that nosotros may remove to shift unopen to fourth dimension serial yesteryear i menstruation inwards guild to align model solutions. The difficulty is that nosotros are using abstract accounting periods, as well as at that spot is an fuzzily-defined notion of the "beginning of period" as well as "end of period" values. The only way to eliminate this fuzziness is to somehow construct a model that tracks every transaction, which is good beyond our modelling capabilities.

(The logic inside this department may survive hard to follow. This is an inherent job amongst model accounting; abstract "accounting periods" practice non completely align amongst real-world behaviour. I believe that it is necessary to piece of work amongst the variables, as well as run across how they relate, inwards guild to appreciate this issue.)

As an illustration of how fourth dimension conventions matter, imagine that nosotros accept a model menage that receives $100 inwards reward inwards fourth dimension menstruation 0 (and has no other financial assets "at the starting fourth dimension of the period"). Furthermore, the one-period involvement charge per unit of measurement is laid at 1%. It hence wishes to purchase a Treasury pecker inwards menstruation 0, as well as hence work the proceeds to purchase $101 inwards goods (1% interest).

• The convention of Monetary Economics is that it bought $100 inwards Treasury bills (market value) during menstruation 0, as well as hence has $101 available to purchase goods inwards menstruation 1. 
• Another possible convention is that it buys the Treasury pecker "at the halt of Period 0", as well as hence it receives the $101 "at the halt of Period 1", which agency that it tin give notice only purchase the goods during Period 2. This convention enforces to a greater extent than of a delay inside the system, as well as perchance is to a greater extent than realistic. But it raises the interrogation whether the menage could sell the Treasury pecker during menstruation 1 inwards guild to brand purchases at that fourth dimension point.
• A fairly nonsensical convention would survive that the menage buys the bills during the period, hence they mature at the halt of the period, as well as it purchases $101 inwards goods at the menstruation end. I believe that it would survive possible to acquire the model accounting to work, but it would require the powerfulness to allow Treasury pecker trading inside the model period. (The menage would accept to purchase an existing Treasury pecker from a holder at the starting fourth dimension of the period, which matures at the halt of the period.) New Treasury bills would accept to survive auctioned at the "end of the period."

Government Budget Constraint

Within the mainstream literature, at that spot is a fair amount of mysticism nigh the "governmental budget constraint." With SFC models, the dubious "inter-temporal" factor disappears (the status on interplanetary space fourth dimension horizons), as well as all that matters is the single-period accounting constraint.

All this constraints says is that regime accounting properly follows the rules of double-entry accounting. This is non peculiarly interesting, other than yesteryear comparing to unopen to older mainstream models where the accounting was non done correctly.

Consolidation And The Portfolio Allocation Decision

Within model PC, the menage decisions are hierarchical.

1. The menage sector inaugural of all decides on the degree of consumption for the period. (This is based on starting wealth, involvement as well as wage income.) The residuum is saved, which increases the value of its portfolio of financial assets (money as well as Treasury bills).
2. The portfolio is allocated betwixt coin as well as Treasury bills. Since coin does non pay interest, it is less attractive attractive every bit involvement rates climb. Hence, the allotment role depends upon the degree of involvement rates.

This raises an obvious number -- how tin give notice the menage sector alter its portfolio allocation? The describe of piece of work organisation sector holds no financial assets, as well as at that spot are no other non-government sectors. (The unusual sector has non all the same been introduced.) Therefore, yesteryear procedure of elimination, the portfolio allotment conclusion yesteryear households must be accommodated yesteryear the consolidated regime sector. That is, the consolidated regime must accommodate the coin as well as Treasury pecker outstanding amounts to check the whims of the menage sector.

The machinery that allows this is the key bank. It holds Treasury bills every bit assets, as well as issues coin every bit a liability. Since coin pays no interest, as well as at that spot is no possibility of uppercase gains/losses on Treasury bills inside the model, the key banking concern earns a steady turn a profit from involvement payments on its portfolio. The key banking concern is hence assumed to pay the profits at nowadays dorsum to the Treasury, hence that the full involvement cost for the regime is simply the involvement paid on Treasury bills owned yesteryear the non-government.

Determination Of Interest Rates And The Monetary Base

Within the SFC model, the degree of involvement rates is fixed yesteryear the key banking concern (and is external to the model). The amount of coin held is exclusively determined yesteryear the portfolio preference of households. This corresponds to "normal" key banking concern behaviour, where the policy commission sets the degree of involvement rates, as well as the coin render is determined yesteryear someone sector behaviour; the key banking concern has to engage inwards "open marketplace operations" to maintain the overnight charge per unit of measurement close target.

Alternatively, if the portfolio allotment role is obliging, the key banking concern could target the amount of coin inwards the system. The key banking concern adjusts the involvement charge per unit of measurement until the coin render hits target. Within the context of this model, at that spot is no way of distinguishing the targeting regime. This ambiguity has been exploited yesteryear unopen to economists who are fixated on the coin supply.

In the existent world, the size of the coin render is driven yesteryear to a greater extent than complicated factors. For example, inwards the United States, banks remove to concord reserves against for sure types of deposits. The interchangeability of involvement rates as well as the coin render starts to intermission down.

If the involvement charge per unit of measurement is zero, at that spot is cypher that distinguishes a Treasury pecker from coin inside the model. In such a case, the key banking concern tin give notice force the allotment dorsum as well as forth how it wants, without it mattering for the someone sector. (In the existent world, at that spot mightiness survive pocket-size fry institutional differences betwixt the instruments.)

It should survive noted that what is discussed inwards this department has been the object of considerable contention -- "endogenous money" versus "exogenous money." The i reward of delving into models such every bit this is that nosotros tin give notice run across that much of the fighting is a waste product of time.

No QE

Within this model, the notion of Quantitative Easing (QE) makes fiddling sense. (Quantitative Easing inwards the purchase of bonds yesteryear the key bank, inwards guild to increment the size of the monetary base.) The only property it tin give notice purchase are Treasury bills, which are the only musical instrument bearing a charge per unit of measurement of interest. The only way the key banking concern tin give notice increment the monetary base of operations is via lowering involvement rates, until it hits 0%. At which point, it is gratis to force the money/bills allotment around, but that has no effect on households -- it has precisely the same involvement income regardless of allocation, which is zero.

Broadly speaking, QE does non brand sense inwards the existent dry reason either. Since real-world QE operations involve the purchase of bonds, it is possible that at that spot would survive unopen to effect on the economy. That would require the work of a to a greater extent than complex model (with to a greater extent than financial assets) to judge.

Concluding Remarks

This article is an introduction to the topic. There are many interesting issues that are opened upwards in i lawsuit nosotros empathise how coin plant inside a SFC model. These include:

• How practice real-world monetary systems relate to the model conventions?
• How does the handling of coin as well as debt differ betwixt a SFC model as well as a DSGE model?
• What are the effects of involvement charge per unit of measurement changes inside the SFC model?
• The endogenous/exogenous coin debate.
• What's upwards amongst "helicopter drops"?
• Should nosotros fifty-fifty model coin inside an economical model? (In my view, the answer is "no," which should horrify most monetarists.)

I promise to comprehend unopen to of these topics inwards after articles.

 (c) Brian Romanchuk 2015