Recent Posts

Sunday, January 15, 2017

Central Banks In SFC Models

Central banks are often a feature of economic models, including stock-flow consistent (SFC) models. The role of the central bank is to supply money, which pays no interest, while the Treasury (fiscal arm of the central government) supplies interest-bearing instruments (typically Treasury bills). However, this level of detail is largely irrelevant to the model outcome; private sector money and treasury bill holdings are determined by the policy rate of interest (which equals the interest rate on Treasury bills), and the central bank operations are forced to conform to the desired portfolio holdings.

Model PC

Central banks appear in the second group of models in Godley and Lavoie's Monetary Economics, in Chapter 4. The model is referred to as Model PC -- Portfolio Choice.

Within the model, there are two financial assets: money,* and government bills.
  • The central bank is the monopoly supplier of money, which does not pay interest. Money is held within the private sector. (In this case, the business sector is assumed to not have financial asset holdings, so this is just the household sector.) The amount of money outstanding is the monetary base.
  • The Treasury is the monopoly supplier of Treasury bills, which pay interest. Treasury bills are held by the central bank and the private sector (household sector).
The only operations the central bank takes is to buy and sell Treasury bills (which creates and destroys money, respectively), and to pay a dividend to the Treasury. Since the liabilities of the central bank only consist of money, which pays no interest, it generates a profit based on the interest received on its Treasury bill holdings. These profits are used to pay the dividend to the Treasury.

This structure follows the pattern of the other markets in the SFC models I have implemented in the Python sfc_models framework (link to description). In the implemented market logic, it is assumed that there is a monopoly supplier of each commodity. (The household sector is a monopoly supplier of labour, and the business sector is a monopoly supplier of goods.) This allows for a demand-led solution of the system of equations:supply is simply assumed to meet demand. This is unrealistic for the product markets (goods and labour); the modelling framework needs to incorporate things such as inventories and supply constraints. However, for these financial assets, there are no limitations on supply: the central bank can issue as much money as it wishes in order to keep interest rates near target,

Targeting The Monetary Base or Interest Rates?

Within the model, the solution is calculated one time period at a time. Even if we allow for expectations within the model, the model entities need to have well-defined supply and demand functions at a given time point, which allows us to calculate the solution. Therefore, even if we believe that the central bank needs to have a reaction function that determines the future path of interest rates (or the size of the monetary base), we still need to pin down its value in the current time point.

The question then arises: does the central bank set the level of interest rates, or the size of the monetary base? Within the context of Model PC, either stance is legitimate. There is a well-defined portfolio allocation function that determines the weighting of money within the household's portfolio; if we fix the interest rate, that weighting is fixed (and vice-versa). Since the level of household financial assets are partly determined by the current period's income, there is a small technical difference between targeting the absolute size of the monetary base in a period and fixing an interest rate.

This would suggest that the money supply is exogenous -- it can be set by the central bank. As I discuss in "Primer: Endogenous Versus Exogenous Money," this equivalence does not apply in the real world. Central banks need to set an interest rate, and monetary base may or may not react in a smooth manner to interest rate changes.

The convention within Monetary Economics is to treat the interest rate as exogenous. We could specify the interest rate as a reaction function, but in order to be realistic, it would need to be based on data that are previously available. This means that the interest rate is "effectively exogenous" with respect to the current time period, which makes calculations easier. 

Treasury Bills Versus Deposits

The convention used in Monetary Economics is for the Treasury to issue interest-bearing deposits, rather than Treasury bills issued at a discount. The deposit convention is easier to work with, but it has one side effect: the price of a deposit is par, and so we cannot imagine price changes to the instrument. However, if the interest rate for a period is fixed (which it normally is), this distinction does not matter.

This may offend economists who like hand-waving stories about how changes at the margin change prices. However, such marginal price changes make no sense in an economic model where the time scale is discrete (for example, quarterly accounting periods), and all trading is assumed to occur at a single price within the period. I am in the camp that believes that it is better to have a mathematical model that we solve using real mathematics, than having a construct with which we can use to make up fairy stories.

Do We Need The Central Bank?

As I added the central bank to my existing modelling framework (in which the central bank did not appear), I could tell when my changes were done correctly: the figures of economic series I had in the code were completely unchanged. If something changed, it meant that I did something incorrectly.

The reason for the lack of importance of the central bank is that its actions are entirely driven by the portfolio allocation of the private sector (household sector). The monetary base equals money holdings, and the total size of bill and money holdings is determined by the fiscal deficit.

The only added degree of freedom within the model is the equity position of the central bank. If it does not pay a dividend to the Treasury, its bill holdings steadily increase from the retained profits. This means that the total amount of Treasury bills outstanding steady increases (while the amount held by the private sector converges to a steady state).

Once we set the dividend policy of the central bank, that degree of freedom disappears. If we take a realistic possibility -- all profits are paid as dividends, there is no degree of freedom.

If we consolidated the central bank with the rest of the central government, the intra-governmental debts would be cancelled out, and even the dividend policy does not matter. This gives a formal example of my arguments in Understanding Government Finance: we can safely consolidate the central bank for analytical purposes, except in the case where default is a possibility. 

From the perspective of building a model, it does not appear to make sense to incorporate the central bank within the set of equations. We can solve the system on a consolidated basis, and then back out the actions of the central bank as a set of ornamental series. I added code for the central bank within the Python sfc_models module, but it is unclear whether it was worth the effort for modelling a closed economy. Central banks might be more useful to incorporate within an open economy with a currency peg system (in which case, the central bank buys and sells some asset in order to balance the currency market at the pegged currency level). However, I have not yet attempted to build such models within the sfc_models framework, and it is unclear whether or not we could just achieve the same effect with a consolidated government sector.

Concluding Remarks

Central banks act as monopoly suppliers of (government) money in SFC models (much like mainstream economic models). Whether or not they are needed appears to be a question of taste; in most cases (other than trying to model the euro area, for example), the system of equations could be simplified by consolidating the central bank with the rest of the central government, and the central bank balance sheet backed out of the final set of equations. 


* Yes, money is in the model. Since it is just another financial asset along side Treasury bills, I do not have objections.

(c) Brian Romanchuk 2017


  1. "Central banks act as monopoly suppliers of (government) money"

    I see it the other way around. Central banks act to force the commercial banks to lend to them at a particular rate of interest using a particular denomination. That then means somebody in the system ends up with a deposit in that denomination based upon the payment instructions.

    Arguably central banks have an unlimited overdraft at a proscribed variable rate at the commercial banks with whom they have a relationship. And in return the commercial banks get a banking licence.

    1. I don't understand that Neil. What mechanisms do the Central Banks use to force commercial banks to lend to them? The license itself?

    2. Neil, this is still a simple model without banks, so I woud have to think about that.

    3. "What mechanisms do the Central Banks use to force commercial banks to lend to them? "

      They accept cash as a deposit.

      Cash is you lending to the state - a state IOU. That's why it is an asset in your hands and a 'credit' in the state's terms.

      So when you pay that into a bank, the bank takes the state's IOU as an asset (i.e. lends to the state) and 'credits' you a bank deposit (the bank's own IOU to you).

      If you think of state payments as the state giving somebody cash and them depositing the cash in the bank, you see how the lending to the state builds up.

      What we call 'Reserves' are really just a type of commercial bank loan to the state central bank.

      It's always worth remembering that banks are backwards. Loans to them are a source of income and an asset to be cherished.

    4. It is a little easier to think of financial assets as the investment allocations of each bank:

      1. Reserves
      2. Treasuries
      3. Loans

      and in this view each bank makes a loan to the government when it holds reserves or Treasuries in its investment portfolio.

      However the aggregate Bank sector does not have a choice of the level of its investment in reserves at the central bank. When the nonbanks have clean balance sheets the aggregate Bank uses a small fixed pool of reserves and Treasuries to grow the loan portfolio. When the nonbank sector gets saturated and cannot take up any more loans, either from banks or among nonbanks, the debt-deflation process can occur which will force the central bank to provide more reserves to banks and the federal government to provide more Treasuries if necessary to prevent a debt-deflation.

      The market (bank and nonbank) sector tries to minimize investments in State IOUs during a market sector expansion and it tries to convert market sector IOUs to State IOUs during a market sector contraction.

      The central bank can provide reserves to banks in two ways via bank borrowing or via non-borrowed reserves. The non-borrowed reserves are forced investments of the aggregate Bank caused when the central bank purchases securities from the aggregate nonbank sector. I am not sure the concept of an unlimited overdraft is the proper view of the mechanism for providing non-borrowed reserves or even of providing borrowed reserves. I need to think about it. In any event I think the circular nature of IOUs under quadruple entry accounting causes too much confusion in discussions and the mechanics of debit and credit in the context of financial deals and investment motives provides more clarity on the games being played.

    5. Neil Wilson, I can understand that cash currency can be considered a liability of the state. But banks are not forced by the government to accept any and all cash deposits in return for their own liability- a positive customer account balance in a checking or savings account. They generally seem willing to do that as a service to their existing customers, but they don't have to, so they aren't being forced. I guess they are forced to accept payment in the government currency to extinguish a customer's loan liability to that bank. At least if they were forced to go to court to enforce collection on that debt.

      As an aside, any deposits I am likely to ever have in a commercial bank here in the US will continue to be a liability of sorts of the government, because of FDIC rules.

      Anyways, I find this topic fascinating and am much awaiting Brian's book on the subject of banning money from economics. To the point of asking for updates on his progress quite frequently. I cant imagine I will agree with it given its title, but I am looking forwards to reading it.

  2. Another informative post Brian,

    I would agree that it's not generally necessary to represent central banks in sfc models. It's useful to look at models like those in G&L to understand how the central bank fits in, but if the purpose of the model is to look at some other aspect, then including the central bank adds unnecessary complexity.

    Where we don't want to show the central bank, it's worth noting that, instead of consolidating it into the government sector, we can consolidate it with the private sector (more correctly the non-government sector) or, if we have such a break-down, simply with other monetary financial institutions. This tends to be my preferred approach.

    1. Hi,

      I would have to think about that consolidation. The issue I see is seigneurage revenue; it might not be obvious why monetary financial institutions have to pay that dividend to the government.

    2. As a starting point, it is worth noting that central banks are included with other monetary financial institutions, and not with the government, for the purposes of national accounting. Remitted profits of central banks are then just part of the dividend receipts of government, which will also include dividends from other equity investments held by the government.

      If we have an empirically realistic model that is structured in line with the national accounts, then it's going to be useful to follow this convention. In most theoretical models we are generally assuming the government holds no financial assets except central bank equity, so it may be more convenient to consolidate the central bank with the government. If we do not, you are right that we have to think about how to deal with central bank profits arising from the spread between bonds and cash. I generally deal with this by assuming that cash holdings are small enough to be ignored.

  3. The 18 page paper under the following link begins with a discussion of the public role of the monetary authority and the principal-agent problems in which the government may make a more credible commitment to price stability by authorizing an independent central bank:

    Grouping the central bank with the financial sector unfortunately tends to obscure or distort some features of political-economic reality and probably does not improve one's understanding of how political power is used by the central bank and government when private markets fail to generate price stability via market mechanisms.




