Central Banks Inwards Sfc Models

Central banks are oft a characteristic of economical models, including stock-flow consistent (SFC) models. The role of the primal banking venture is to render money, which pays no interest, piece the Treasury (fiscal arm of the primal government) supplies interest-bearing instruments (typically Treasury bills). However, this bird of item is largely irrelevant to the model outcome; someone sector coin in addition to treasury neb holdings are determined past times the policy charge per unit of measurement of involvement (which equals the involvement charge per unit of measurement on Treasury bills), in addition to the primal banking venture operations are forced to conform to the desired portfolio holdings.

Model PC

Central banks look inwards the minute grouping of models inwards Godley in addition to Lavoie's Monetary Economics, in Chapter 4. The model is referred to equally Model PC -- Portfolio Choice.

Within the model, in that location are 2 financial assets: money,* in addition to regime bills.

• The primal banking venture is the monopoly supplier of money, which does non pay interest. Money is held inside the someone sector. (In this case, the occupation organisation sector is assumed to non cause got financial property holdings, hence this is exactly the identify sector.) The amount of coin outstanding is the monetary base.
• The Treasury is the monopoly supplier of Treasury bills, which pay interest. Treasury bills are held past times the primal banking venture in addition to the someone sector (household sector).

The only operations the primal banking venture takes is to purchase in addition to sell Treasury bills (which creates in addition to destroys money, respectively), in addition to to pay a dividend to the Treasury. Since the liabilities of the primal banking venture only consist of money, which pays no interest, it generates a turn a profit based on the involvement received on its Treasury neb holdings. These profits are used to pay the dividend to the Treasury.

This construction follows the designing of the other markets inwards the SFC models I cause got implemented inwards the Python sfc_models framework (link to description). In the implemented marketplace seat logic, it is assumed that in that location is a monopoly supplier of each commodity. (The identify sector is a monopoly supplier of labour, in addition to the occupation organisation sector is a monopoly supplier of goods.) This allows for a demand-led solution of the arrangement of equations:supply is but assumed to run across demand. This is unrealistic for the production markets (goods in addition to labour); the modelling framework needs to contain things such equally inventories in addition to render constraints. However, for these financial assets, in that location are no limitations on supply: the primal banking venture tin number equally much coin equally it wishes inwards gild to croak on involvement rates close target,

Targeting The Monetary Base or Interest Rates?

Within the model, the solution is calculated 1 fourth dimension menstruum at a time. Even if nosotros allow for expectations inside the model, the model entities ask to cause got well-defined render in addition to demand functions at a given fourth dimension point, which allows us to calculate the solution. Therefore, fifty-fifty if nosotros believe that the primal banking venture needs to cause got a reaction business office that determines the hereafter path of involvement rates (or the size of the monetary base), nosotros withal ask to pivot downwardly its value inwards the electrical flow fourth dimension point.

The inquiry hence arises: does the primal banking venture laid the bird of involvement rates, or the size of the monetary base? Within the context of Model PC, either opinion is legitimate. There is a well-defined portfolio allotment business office that determines the weighting of coin inside the household's portfolio; if nosotros create the involvement rate, that weighting is fixed (and vice-versa). Since the bird of identify financial assets are partly determined past times the electrical flow period's income, in that location is a modest technical departure betwixt targeting the absolute size of the monetary base of operations inwards a menstruum in addition to fixing an involvement rate.

This would advise that the coin render is exogenous -- it tin locomote laid past times the primal bank. As I verbalise over inwards "Primer: Endogenous Versus Exogenous Money," this equivalence does non apply inwards the existent world. Central banks ask to laid an involvement rate, in addition to monetary base of operations may or may non react inwards a smoothen mode to involvement charge per unit of measurement changes.

The convention inside Monetary Economics is to process the involvement charge per unit of measurement equally exogenous. We could specify the involvement charge per unit of measurement equally a reaction function, but inwards gild to locomote realistic, it would ask to locomote based on information that are previously available. This agency that the involvement charge per unit of measurement is "effectively exogenous" amongst abide by to the electrical flow fourth dimension period, which makes calculations easier. 

Treasury Bills Versus Deposits

The convention used inwards Monetary Economics is for the Treasury to number interest-bearing deposits, rather than Treasury bills issued at a discount. The deposit convention is easier to piece of work with, but it has 1 side effect: the toll of a deposit is par, in addition to hence nosotros cannot imagine toll changes to the instrument. However, if the involvement charge per unit of measurement for a menstruum is fixed (which it ordinarily is), this distinction does non matter.

This may scandalise economists who similar hand-waving stories close how changes at the margin alter prices. However, such marginal toll changes brand no feel inwards an economical model where the fourth dimension scale is discrete (for example, quarterly accounting periods), in addition to all trading is assumed to occur at a unmarried toll inside the period. I am inwards the military camp that believes that it is meliorate to cause got a mathematical model that nosotros solve using existent mathematics, than having a build amongst which nosotros tin job to brand upward fairy stories.

Do We Need The Central Bank?

As I added the primal banking venture to my existing modelling framework (in which the primal banking venture did non appear), I could tell when my changes were done correctly: the figures of economical serial I had inwards the code were completely unchanged. If something changed, it meant that I did something incorrectly.

The argue for the lack of importance of the primal banking venture is that its actions are exclusively driven past times the portfolio allotment of the someone sector (household sector). The monetary base of operations equals coin holdings, in addition to the full size of neb in addition to coin holdings is determined past times the financial deficit.

The only added grade of liberty inside the model is the equity seat of the primal bank. If it does non pay a dividend to the Treasury, its neb holdings steadily increment from the retained profits. This agency that the full amount of Treasury bills outstanding steady increases (while the amount held past times the someone sector converges to a steady state).

Once nosotros laid the dividend policy of the primal bank, that grade of liberty disappears. If nosotros accept a realistic possibility -- all profits are paid equally dividends, in that location is no grade of freedom.

If we consolidated the primal banking venture amongst the repose of the primal government, the intra-governmental debts would locomote cancelled out, in addition to fifty-fifty the dividend policy does non matter. This gives a formal illustration of my arguments inwards Understanding Government Finance: nosotros tin safely consolidate the primal banking venture for analytical purposes, except inwards the instance where default is a possibility. 

From the perspective of edifice a model, it does non look to brand feel to contain the primal banking venture inside the laid of equations. We tin solve the arrangement on a consolidated basis, in addition to hence dorsum out the actions of the primal banking venture equally a laid of ornamental series. I added code for the primal banking venture inside the Python sfc_models module, but it is unclear whether it was worth the sweat for modelling a unopen economy. Central banks mightiness locomote to a greater extent than useful to contain inside an opened upward economic scheme amongst a currency peg arrangement (in which case, the primal banking venture buys in addition to sells exactly about property inwards gild to residual the currency marketplace seat at the pegged currency level). However, I cause got non yet attempted to build such models inside the sfc_models framework, in addition to it is unclear whether or non nosotros could exactly accomplish the same number amongst a consolidated regime sector.

Concluding Remarks

Central banks deed equally monopoly suppliers of (government) coin inwards SFC models (much similar mainstream economical models). Whether or non they are needed appears to locomote a inquiry of taste; inwards most cases (other than trying to model the euro area, for example), the arrangement of equations could locomote simplified past times consolidating the primal banking venture amongst the repose of the primal government, in addition to the primal banking venture residual canvas backed out of the concluding laid of equations. 

Footnote:

* Yes, coin is inwards the model. Since it is exactly just about other financial property along side Treasury bills, I practise non cause got objections.

(c) Brian Romanchuk 2017