The Decision Fiscal Property Holdings Inwards Sfc Models

This article discusses how I systematically generate the systems of equations that determines financial property holdings inside the Python sfc_models framework for Stock-Flow Consistent (SFC) models. It should last noted that despite the generality of the title, I am only discussing how I attacked the work (the results of my technique is consistent with the literature that I induce got studied). The existing literature relies on the derivation of organisation equations past times hand, in addition to then the modelling techniques used past times others are less constrained than the algorithmic equation generation I use.

(This article is technical, in addition to aimed at those with an involvement inwards SFC models, or to a greater extent than generally, an involvement inwards how to laid upward a mathematical macro model. It volition presumably brand its means into an upcoming majority on SFC modelling inwards Python.)

Two-Step Process: Income, Then Portfolio

One difficulty of macro modelling is that for the same economical model, nosotros tin generate a spectacular number of equations that depict the relationships betwixt sectors. In social club to algorithmic generate the systems of equations, I ask to last able to develop rules that pivot downward the laid of equations that are to last included.

It should last noted that my technique does generate redundant equations. However, the redundant equations by in addition to large look to last variables that are descriptive, in addition to produce non outcome the balance of the equations. For example, the primary financial deficit appears equally an equation inwards about models, but since no sector bases its behavior on the primary deficit, the extra equation does non effort difficulties for the solution technique.

Financial assets pose a detail problem, equally they exhibit upward inwards many ways.

1. The alter inwards the full value of financial property holdings is determined internet cash flow. The internet cash current is normally equal to income (that is, including the outcome of upper-case missive of the alphabet gains), but nosotros may ask to add together flows that produce non touching on income. (For example, consumption spending past times the trace solid sector does non subtract from trace solid income.) Income is driven past times by flows inwards the existent economic scheme (wage income, goods purchases) in addition to transfers (dividends, taxes).
2.  The full value of financial assets held is equal to the total of the values of the holdings of detail instruments.
3. Instruments are issued past times detail sectors (for example, the Treasury/central authorities issues Treasury bills), in addition to this issuance is used to finance purchases of goods or other financial assets.
4. The render of whatever property has to equal its demand.

The approach currently used inside the sfc_models parcel is straightforward.

1. The novel degree of a sector's financial property holdings is equal to the previous period's financial property holdings summation the total of the period's cash current terms. (At present, in that place is no ask to rail upper-case missive of the alphabet gains, since none of the modelled instruments generate them. However, Treasury bills generate involvement that enters equally a cash current term.) Examples are discussed below.
2. The degree of holdings of whatever detail financial musical instrument for a menstruum is equal to a weighting term times the full financial property holding. For example, inwards a model where the only financial assets are coin (with a 0% charge per unit of measurement of interest) in addition to Treasury bills (which pay the policy rate), the trace solid in addition to trace organisation sectors volition allocate their portfolios betwixt coin in addition to bills based on the charge per unit of measurement of interest. The total of the weightings has to last 1 (or else in that place volition effectively last a ghost musical instrument created that catches the missing wealth).*
3. The render of whatever financial property is assumed to last equal to the total of the holdings inwards all sectors.

The get-go pace is the most complex, in addition to it mightiness last unclear what the cash current price refer to. Some unproblematic examples (based on the simplest SFC models, such equally models SIM in addition to PC from Godley in addition to Lavoie) would include:

1. For a trace solid sector that only receives wages, pays taxes, in addition to buys goods -- trace solid consumption. The equation is:
   (new financial assets) = (old financial assets) + (wages) - (taxes) - (consumption). 
2. A authorities that purchases goods in addition to imposes taxes, in addition to pays involvement on Treasury bills:
   (new financial assets) = (old financial assets) + (taxes) - (government consumption) - (interest cost).
   Since financial assets inwards these models are typically authorities liabilities, it should last noted that the financial property holdings for the authorities are typically negative.
3. For a trace organisation sector (in which nosotros ignore trace organisation taxation in addition to investment),
   (new financial assets) = (old financial assets) + (total goods sales) - (wages) - (dividends).

These examples illustrate that these equations are mainly driven past times the nominal cash flows inside the existent economy, such equally the full wage bill, goods consumption, taxes, in addition to interest. They produce non evidence how sectors enhance cash, such equally the split betwixt debt in addition to currency issuance past times the government.

It should last noted that the equations generated past times the technique are solved simultaneously, in addition to then the steps inwards a higher house produce non tell us virtually the behavior of the solution. For example, nosotros could induce got the trace solid sector's consumption depending upon coin holdings, in addition to then the "real economy" variables are non determined earlier the portfolio allotment step. (However, the run a hazard is that such an information loop mightiness effort a lack of convergence of the organisation of equations.)

Consequences

The description taken inside the framework is demand driven; the supplier of a financial musical instrument has no pick but to render the amount demanded.

For example, in that place is no endeavour to impose the governmental budget constraint (in which spending is "financed" past times taxes, or the issuance of bills or money). We tin dorsum out the constraint from the organisation of equations, but it is purely the termination of the accounting adding upward properly. The full alter inwards the government's financial seat is driven past times a wide financial deficit (with adjustments needed for the monetisation of assets, etc.), in addition to the levels of detail liabilities (money, debt) is driven alone past times someone sector portfolio allocation. (I am including the external sector nether the "private sector," which mightiness last awkward when thinking virtually existent the world data. By my Definition here, the Chinese fundamental banking concern is inwards the someone sector, at to the lowest degree inwards the context of its reserve holdings inwards the United States.)

(If nosotros process the fundamental banking concern equally beingness distinct from the balance of the government, the moving-picture exhibit mightiness look to last slightly different, but nosotros yet destination upward with roughly the outcome. I volition beak over this inwards a follow upward article.)

Although having the render of financial assets beingness driven alone past times the demand for holdings is reasonable for authorities liabilities (which is only what I induce got attempted to model), it may experience odd for financial assets issued past times the someone sector. It would imply that someone sector credit creation is driven alone past times credit rationing alongside the holders of financial assets, which does seem similar a reasonable modelling assumption. However, nether this assumption, it is nearly impossible to capture odd positive feedback loops where a sector lends to itself. This happens a lot inwards the existent world, such equally the trace solid sector is lending to itself equally business office of existent estate transactions. 

Concluding Remarks

In social club to systematically generate the equations of a SFC model, nosotros ask to adopt a relatively fixed perspective inwards social club to create upward one's hear which equations are included. The most natural approach is to induce got a demand-driven view, in addition to assume that render volition e'er accommodate to come across demand.

Once again, if someone sets upward the equations past times hand, they are costless to last to a greater extent than flexible. However, such an approach relies on the powerfulness of the researcher to pick in addition to direct a coherent laid of constraints.

Footnote:

* At the fourth dimension of writing, the organisation does non straight back upward portfolio weightings; the equations are generated at inside the sector code. Making portfolio weightings to a greater extent than systematic is a convenient characteristic that volition last added equally the projection develops.

(c) Brian Romanchuk 2017