Short & Simple 19 – Sectoral Balances in a Closed, Demand-Determined Economy

We have seen that the ‘income-expenditure model’ combines key macro identities (introduced in parts 7 and 15) with particular behavioral assumptions to provide a theory of income determination (considered in parts 16 and 18). The behavioral assumptions relate to causation. The causation envisaged in the income-expenditure model has implications for the sectoral balances, some of which are the focus of the present post.

Recall that total leakages must equal total injections:

S + T = G + I

In a closed economy, the leakages are saving (S) and taxes (T). The injections are government spending (G) and private investment (I).

If we take all variables to the left-hand side and group them appropriately, we have:

(S – I) + (T – G) = 0

Or, in words:

Non-Government Balance + Government Balance = 0

As it stands, this is just an identity. But we can apply the behavioral assumptions of the income-expenditure model to consider various scenarios.

To do this, it will be helpful to derive a saving function by making use of the definition that saving is disposable income minus private consumption. In part 18 we defined tax and consumption functions:

T = tY

CP = C0 + c(Y – tY) = C0 + cY – ctY

Plugging these into our definition of saving (S = Y – T – CP) and rearranging enables us to express planned saving as a function of income:

S = Y – tY – (C0 + cY – ctY)

Upon rearrangement, and noting that the marginal propensity to save equals one minus the marginal propensity to consume (that is, s = 1 – c):

S = s(1 – t)Y – C0

The saving function enables us to consider the effects of changes in income on the non-government financial balance (NGB = S – I):

NGB = s(1 – t)Y – C0 – I

Likewise, we can consider the effects of changes in income on the government balance (GB) by taking account of the impact on tax revenue (using our definition T = tY).

GB = tY – G

We can consider an example by putting some numbers to the various parameters and exogenous variables. The parameters of the model are the marginal propensities to consume, tax and save. The exogenous variables are the components of spending that are autonomous of income, namely government spending, private investment and autonomous private consumption.

Let’s suppose, initially, that c = 0.8, t = 0.25 and s = 1 – c = 0.2. Using the formula for the multiplier:

The value of the marginal propensity to leak (α = 1 – c + ct) says that forty percent (or 0.4) of extra income will leak to taxes and saving. The other sixty percent will go to induced private consumption. The value of the expenditure multiplier says that a given increase in autonomous spending (A) will cause total income to rise by two-and-a-half times the change in A.

Suppose, initially, that government spending (G) is 25, private investment (I) is 10 and autonomous private consumption (C0) is 5. We know from previous parts of the series that the economy will tend to converge to a level of output determined by the size of the expenditure multiplier (2.5) and the sum of autonomous expenditures (A = C + I + G = 40):

Y = kA = 2.5(40) = 100

With this information, we can work out the corresponding sectoral financial balances:

NGB = s(1 – t)Y – C0 – I = 0.2(1 – 0.25)(100) – 5 – 10 = 0

GB = tY – G = 0.25(100) – 25 = 0

Both sectors happen to have a zero balance. Non-government is spending an amount equal to its disposable income. Government is taxing out of the economy the same amount it is spending into it.

This is the initial situation. If anything happens to a parameter or exogenous variable, the above outcomes will be modified. In the remainder of this post, we consider a number of scenarios. At the start of each scenario we assume the initial situation described above. That is, changes in one scenario do not carry over to the next scenario. We re-set each time. For convenience of reference, here is a summary of the initial situation:

G = 25, I = 10, C0 = 5, c = 0.8, t = 0.25, s = 0.2

This means that:

A = 40, α = 0.4, k = 1/α = 2.5, Y = kA = 100


NGB = 0 = GB

Increase in private investment. Starting from the initial situation, suppose that private investment doubles from 10 to 20, with no other changes to the exogenous variables or parameters. This will cause income to rise by two-and-a-half times the rise in private investment. The higher income will result in more taxes and saving (though not as much extra saving as private investment). The overall effect will be for the government to move into surplus and the non-government into deficit. The results are shown below:

ΔY = k.ΔA = 2.5(10) = 25

Y = kA = 2.5(50) = 125

NGB = s(1 – t)Y – C0 – I = 0.2(1 – 0.25)(125) – 5 – 20 = -6.25

GB = tY – G = 0.25(125) – 25 = 6.25

The increase in private investment pushes non-government into deficit because the higher income does not leak only to saving, but also to taxes.

Increase in government spending. Starting again from the initial situation, suppose government spending increases by 10 (to 35), with no other exogenous changes. This will cause income, taxes and saving to rise. However, taxes will not rise by as much as government spending because some of the leakage will go to saving rather than taxes. The change in income and the new level of income will be the same as in the previous example. The sectoral balances become:

NGB = s(1 – t)Y – C0 – I = 0.2(1 – 0.25)(125) – 5 – 20 = 6.25

GB = tY – G = 0.25(125) – 25 = -6.25

The government balance has moved into deficit, enabling non-government to maintain a financial surplus over the period. The higher income has enabled more saving.

A higher rate of taxation. Again starting from the initial situation, suppose now that the marginal propensity to tax is increased from 0.25 up to 0.375. The effect of this will be to increase the marginal propensity to leak (α) from 0.4 to 0.5. This shrinks the expenditure multiplier (k) from 2.5 down to 2. The autonomous spending of A = 40 now tends to generate, via the multiplier process, a level of income of only Y = kA = 80. This has ramifications for the sectoral financial balances:

NGB = s(1 – t)Y – C0 – I = 0.2(1 – 0.375)(80) – 5 – 10 = -5

GB = tY – G = 0.375(80) – 25 = 5

The higher tax rates cause the government balance to move into surplus and weaken the economy, which is now generating lower income. Non-government is pushed into financial deficit because the weaker income and higher taxes impact negatively on saving. Note that since total injections have not changed, total leakages also remain the same. It is just that more of the leakage goes to taxes rather than saving as a result of the policy change.

A higher marginal propensity to save. Reverting one more time to the initial situation in which income is 100 and the multiplier is 2.5, suppose the marginal propensity to save is increased from one-fifth to one-third. This will cause the marginal propensity to leak (α) to increase from 0.4 to 0.5 and the multiplier (k) to shrink from 2.5 to 2. Income will tend to fall from 100 to 80 and the sectoral financial balances will once again be affected:

NGB = s(1 – t)Y – C0 – I = 0.33(1 – 0.25)(80) – 5 – 10 = 5

GB = tY – G = 0.25(80) – 25 = -5

This time it is the government that moves into deficit and the non-government that moves into financial surplus. Total leakages are the same as in the initial situation (total leakage is 35 in each case, equal to total injections). Saving has increased from 10 to 15 whereas taxes have fallen from 25 to 20. The reduction in income hits both taxes and saving, but households are now saving a higher fraction of a lower income.


11 thoughts on “Short & Simple 19 – Sectoral Balances in a Closed, Demand-Determined Economy

  1. Hi Peter,
    Maybe you can help me with this?
    I have been trying to put into a spreadsheet the sectoral equation
    private savings (ps) = govt spending (govt ‘-‘ mean surplus) + external surplus (ca), both in $ terms and in GDP terms, using data from ABS so I can see it for myself
    [ABS 5302.0 for ca
    ABS 5512.0 for gs
    ABS 5206.0 for gdp]

    I first got govt spending and external surplus from ABS using their excel downloads, and then using the above equation worked out private savings which came out as follows:
    /ca /%gdp /govt /%gdp /ps /%gdp /gdp

    According to this table, other than 2011, we have had net dissavings, yet when I then go to the ABS catalogue 5232.0 I find the following for the end of 2016

    Gross disposable income 1701.6 billion
    Final consumption expenditure 970.0 billion
    Consumption of fixed capital 111.0 billion
    Net savings 620.6 billion

    Closing net worth 9409.2 billion

    I am obviously missing something here because these numbers are not adding up. Are you able to point me to the actual ABS statistics that I should be using for the above sectoral equation?


  2. Hi Dean. It seems easiest just to use ABS catalogue 5232.0. The net lending/borrowing term for each sector is what we are calling the sectoral financial balances.

    As an example, look at this page for the quarter ending March 2017:

    5232.0 – Australian National Accounts: Finance and Wealth, Mar 2017

    The table at the top gives info on “financing resources” (saving) and “uses of financing” (investment plus net lending/borrowing) for (i) households, non-financial corporations and financial corporations (which sum to what we are calling the ‘domestic-private sector’), (ii) general government (our ‘government sector’) and (iii) the rest of the world (‘foreign sector’). If you add up the net lending/borrowing for each sector, the sum is roughly zero (-0.1 billion). The difference should be made up by the net errors & omissions. If you add those up, they come to 0.2 billion. Rounding errors are presumably the culprit.

    If you scroll down the page to the second graph, you’ll see the net lending/borrowing historical record of the various domestic sectors (private and government). These are what we are calling the sectoral balances, though they are broken down into more sectors. To complete the picture, the rest of the world could be added in. Also, for simplicity, we are consolidating households, non-financial corporations and financial corporations into the domestic-private sector.

  3. Now, what I would like to see, is economists compelled to publish their Super asset class allocations …. 🙂 !

  4. wow Peter,
    Thank you so much. I spent two whole days trawling over ABS spreadsheets trying to come up with this and there it was all along!!

    And yes, now it makes sense and I can see it (sectoral balances).

    Now that I have that part in the bag, I wanted to ask another question on a slightly different note. I overlayed the household savings ratio (“ratio”) graph over the top of the $A and noticed that since we floated the $A the two have correlated, with the $A being more volatile but over time keeping near enough to the ratio.

    I am trying to work out why this might be the case. Do you see any reasons as to why this might be the case?

  5. i’m going to throw another Q out there for anyone to tackle. I see this as something that may potentially be grounds for policy change.

    On other blogs I have been trying to get a question answered, but in all cases instead of it being answered, the merit of the question itself is attacked as if it offends readers. I admit I tried playing devils advocate when asking this question because most to whom I ask it do not believe that inside money (demand deposits) has a direct liability to the Govt (even though all demand deposits carry the liability to convert to currency on demand). I purposely have created the distinction between outside and inside money based on this belief they all have so that it is obvious that outside money is ‘not’ something the private sector created. In other words I am playing the devils advocate and saying, for the purposes of my question, the govt will not spend inside money on non-economic purposes.

    The question is simply this: If the govt spent outside money on non-economic purposes, and when that money finally made its way back in taxes it was destroyed, would this cause economic loss to the tax-payer?

    Economic loss means that which can be seen on a balance sheet.

    Non-economic purposes means any purpose which is not aimed at improving the tax-payers ability to earn more money. For example, any spending which creates jobs and/or invests in job creation is economic (such as improving roads). Any spending which only serves to purchase goods/services from the private sector for final consumption is non-economic.

    Outside money, for the purposes of this question, simply means money created by the CB in exchange for bonds direct from the Treasury (I know this is prohibited now, but for the purposes of this question we shall ignore this).

    So, elaborating on the question, if the govt gave a bond to the CB in exchange for credits, spent these credits toward buying goods and services from the private sector, but for non-economic purposes (an example might be providing medicine to the aged), and that money was then destroyed when it finally made its way back in taxes, would the tax-payer in general suffer economic loss other than the tax they would normally pay anyway?

    I am unable to see how they can.

    For starters, the private sector is going to pay taxes on the sale of their goods/services anyway, irrespective of who buys them or for what purpose they were bought. If anything, the spending would actually benefit the supplier because if the govt had not stepped in and bought them the supplier may not have sold them at all. But more to the point (and because most tax-payers believe they fund govt spending), if the govt deliberately created this outside money for spending on non-economic purposes, then the tax-payer will have to prove that they still funded this particular spending, which even based on old out-dated beliefs, can’t be proven – can it?

  6. Dean, inside and outside money are terms already in use. Money is always someone’s liability. Inside money is money is a liability of commercial banks. Outside money is a liability of the government, chiefly of a central bank in a modern monetary production economy, although some Treasuries also issue liabilities in the form of notes and coin.

    Governments issue currency and create outside money by spending liabilities they create. They destroy these liabilties by imposing liabilities on nongovernment that can only be satisfied by liabilities that the government alone issues. The liabilities imposed on nongovernment include taxes, tariffs, fees and fines.

    Governments spend by directing central banks as the governments’ bank to credit commercial banks’ accounts at the central bank and to direct these banks to credit the corresponding customer accounts. It is a wash for banks. They receive an asset (credit in their reserve account at the central bank as a liability of the cb) and they incur corresponding bank liability when they credit a customer’s deposit account. Note there are two sets of books involved, the government’s at the central bank and the books of the commercial banks. This is the interface between government and nongovernment.

    Customers only receive a government liability when they demand cash at the window. The bank gets the cash, which is a government liability, by exchanging bank reserves that also a government liability for vault cash at the central bank. When vault cash is passed through the window it become cash in circulation.

    When taxes are paid, a bank debits the customer’s deposit account and the bank’s reserve account is debited at the central bank when the payment is made in the name of the customer.

    Banks create inside money by extending credit, which increases borrowers’ deposit accounts. Borrowers’ deposit accounts are debited as borrowers repay principal and interest.

    These are the two circuits of money creation-destruction. Inside money is endogenous while outside money involves the interface between government and nongovernment through the central bank.

    So you got it basically right as far as I can see.

    MMT economist Eric Tymoigne has a great course on this available at New Economic Perspectives, setting forth the details.

    As far as economic loss in addition to taxes, the private sector loses real resources when they are transferred to public use. This involves a redistribution of the available real resources of a society. This is the chief economic effect. Spending and taxation also affect nongovernment finances, which redistributes financial resources and also has economic implications, e.g., affecting demand. For instance, social security makes real resources available to pensioners that they might otherwise not be able to access.

    Obviously, if government transfers real resources to public use that involves infrastructure, R&D, education, etc. it will likely have a positive economic effect on the society, although it may not benefit all equally.

    People tend to obsess on “money” but the actual value of money is as a claim on real resources.

  7. “As far as economic loss in addition to taxes, the private sector loses real resources when they are transferred to public use. This involves a redistribution of the available real resources of a society. This is the chief economic effect. ”

    “People tend to obsess on “money” but the actual value of money is as a claim on real resources.”

    Ok I see. So in short, any transfer of real resources to the govt is going to be treated with suspicion and only tempered if the purpose can be seen to promote economic growth (in general that is)?

    Well that’s fair enough and not surprising really.

    I’m working on formulating a theory which suggests that once an economy becomes developed, true economic growth will only occur from that point onwards if there is also an economic contraction within the same economy. I know it sounds contradictory on face value, but it’s like ying and yang. A portion of the community will contract from an economic perspective (purposely) which will free up the rest to expand because the inherent cost in ownership and exchange (those events which are taxed) will be reduced. This will enable the producers to produce far higher quality goods and services which last longer and thus reduce the drain on resources (and hence temper the suspicion).

    My problem is I have such a bloody hard time explaining anything

  8. Economics is about the production, distribution and consumption of real goods.

    Conventional economics thinks about this in terms of a barter-exchange economy in which money is neutral and doesn’t affect the circuit in the long run.

    Keynes pointed out that money is not neutral and money & banking and finance have economic effects in the long run was well as the short run.

    In my view this is the place to start thinking about it.

    The next consideration is the assumption of conventional economics that this happens naturally in a market system in which market forces are operating freely. The assumed result in spontaneous natural order that is Pareto optimal, meaning that no one can improve position without making someone else worse off. The reason this doesn’t happen is that competition is imperfect.

    Both Marx and Keynes objected that the process is historical rather than natural, and humans have a degree of control over their social, political and economic systems based on choices including policy choices. These choice are not completely free choices, since they occur in specific contexts that limit choice owing to existing conditions and path dependence, for example. Moreover, social systems are non-ergodic and so uncertainty is an important factor.

    This is more or less the context of the debate about economic, policy, etc. One needs to understand the current state of the debate and then decide where to take a stand in it.

    Post Keynesianism and MMT are in the Keynesian tradition rather than the conventional neoclassical (marginalist) tradition regarding the effect of money, and in the Marxian-Keynesian historical tradition rather than the natural laws of economic tradition.

    Then the issue is how to best use money, banking and finance to produce and distribute goods optimally for the needs of a society and then its wants to the degree possible, using available resources, human and natural, to do so along with technology to increase productivity. A further challenge is doing this most effectively and efficiently to grow economically at least as fast as population growth, and to increase productivity to enhance the standard of living as much as possible.

    Finally, economics is not an end it itself. An economy is the material life-support system of a society. Society as a network of networks of people (families, which econ calls households) is foundational. The objective is achieving an ideal society (positive values over negative) iteratively and incrementally to avoid utopian thinking and magical thinking.

    Importantly, different societies are different culturally and historically and have different ideals and aspirations. There is no one size fits all approach. Thinking abstractly about this doesn’t go all that far in getting to the goal in specific geographical and historical cases. A lot of contemporary issues and pseudoproblsems arise from thinking in terms of one shoe fits all when that is patently false.

  9. Tom,
    That is an interesting definition of ecomomics. It is slightly different to the legal one which stipulates that it must be treated as a commodity before it is deemed an economic resource. As you say in your last paragraph societies have different cultures and ideals and aspirations. Some people both historically and presently do not wish to treat resources as commodities. So I cant take either stance as you suggest sorry. But anyway, this is good for a bit of wholesome debate but if the last couple of months has taught me anything it is that whatever stance I take is really irrelevant unless I can prove it has merit from a legal perspective

  10. Dean, in economics, the definition of commodity is a good produced for sale. Goods produced for personal use and not for sale are not considered commodities under this definition.

  11. “Dean, in economics, the definition of commodity is a good produced for sale. Goods produced for personal use and not for sale are not considered commodities under this definition.”


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