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The Weekend Quiz – June 6-7, 2020 – answers and discussion

Here are the answers with discussion for this Weekend’s Quiz. The information provided should help you work out why you missed a question or three! If you haven’t already done the Quiz from yesterday then have a go at it before you read the answers. I hope this helps you develop an understanding of modern monetary theory (MMT) and its application to macroeconomic thinking. Comments as usual welcome, especially if I have made an error.

Question 1:

The private domestic sector can save overall even if the government fiscal balance is in surplus as long as net exports are positive.

The answer is False.

This is a question about the relative magnitude of the sectoral balances – the government budget balance, the external balance and the private domestic balance. The balances taken together always add to zero because they are derived as an accounting identity from the national accounts. The balances reflect the underlying economic behaviour in each sector which is interdependent – given this is a macroeconomic system we are considering.

To refresh your memory the sectoral balances are derived as follows. The basic income-expenditure model in macroeconomics can be viewed in (at least) two ways: (a) from the perspective of the sources of spending; and (b) from the perspective of the uses of the income produced. Bringing these two perspectives (of the same thing) together generates the sectoral balances.

From the sources perspective we write:

GDP = C + I + G + (X – M)

which says that total national income (GDP) is the sum of total final consumption spending (C), total private investment (I), total government spending (G) and net exports (X – M).

Expression (1) tells us that total income in the economy per period will be exactly equal to total spending from all sources of expenditure.

We also have to acknowledge that financial balances of the sectors are impacted by net government taxes (T) which includes all taxes and transfer and interest payments (the latter are not counted independently in the expenditure Expression (1)).

Further, as noted above the trade account is only one aspect of the financial flows between the domestic economy and the external sector. we have to include net external income flows (FNI).

Adding in the net external income flows (FNI) to Expression (2) for GDP we get the familiar gross national product or gross national income measure (GNP):

(2) GNP = C + I + G + (X – M) + FNI

To render this approach into the sectoral balances form, we subtract total taxes and transfers (T) from both sides of Expression (3) to get:

(3) GNP – T = C + I + G + (X – M) + FNI – T

Now we can collect the terms by arranging them according to the three sectoral balances:

(4) (GNP – C – T) – I = (G – T) + (X – M + FNI)

The the terms in Expression (4) are relatively easy to understand now.

The term (GNP – C – T) represents total income less the amount consumed less the amount paid to government in taxes (taking into account transfers coming the other way). In other words, it represents private domestic saving.

The left-hand side of Equation (4), (GNP – C – T) – I, thus is the overall saving of the private domestic sector, which is distinct from total household saving denoted by the term (GNP – C – T).

In other words, the left-hand side of Equation (4) is the private domestic financial balance and if it is positive then the sector is spending less than its total income and if it is negative the sector is spending more than it total income.

The term (G – T) is the government financial balance and is in deficit if government spending (G) is greater than government tax revenue minus transfers (T), and in surplus if the balance is negative.

Finally, the other right-hand side term (X – M + FNI) is the external financial balance, commonly known as the current account balance (CAD). It is in surplus if positive and deficit if negative.

In English we could say that:

The private financial balance equals the sum of the government financial balance plus the current account balance.

We can re-write Expression (6) in this way to get the sectoral balances equation:

(5) (S – I) = (G – T) + CAB

which is interpreted as meaning that government sector deficits (G – T > 0) and current account surpluses (CAB > 0) generate national income and net financial assets for the private domestic sector.

Conversely, government surpluses (G – T < 0) and current account deficits (CAB < 0) reduce national income and undermine the capacity of the private domestic sector to add financial assets.

Expression (5) can also be written as:

(6) [(S – I) – CAB] = (G – T)

where the term on the left-hand side [(S – I) – CAB] is the non-government sector financial balance and is of equal and opposite sign to the government financial balance.

This is the familiar MMT statement that a government sector deficit (surplus) is equal dollar-for-dollar to the non-government sector surplus (deficit).

The sectoral balances equation says that total private savings (S) minus private investment (I) has to equal the public deficit (spending, G minus taxes, T) plus net exports (exports (X) minus imports (M)) plus net income transfers.

All these relationships (equations) hold as a matter of accounting and not matters of opinion.

The following Table lets you see the evolution of the balances expressed in terms of percent of GDP. In each period I just held the budget balance at a constant surplus (2 per cent of GDP) (green bars). This is is artificial because as economic activity changes the automatic stabilisers would lead to endogenous changes in the budget balance. But we will just assume there is no change for simplicity. It doesn’t violate the logic.

To aid interpretation remember that (S – I) < 0 means that the private domestic sector is spending more than they are earning; that (G – T) < 0 means that the government is running a surplus because T > G; and (X – M) > 0 means the external position is in surplus because imports are less than than exports (disregarding net income flows).

  Period 1 Period 2 Period 3 Period 4 Period 5 Period 6
External Balance (X – M) 0 1 2 3 4 5
Fiscal Balance (G – T) -2 -2 -2 -2 -2 -2
Private Domestic Balance (S – I) -2 -1 0 1 2 3

If the nation is running an external surplus it means that the contribution to aggregate demand from the external sector is positive – that is net addition to spending, which would increase output and national income.

The external deficit also means that foreigners are decreasing financial claims denominated in the local currency. Given that exports represent a real cost and imports a real benefit, the motivation for a nation running a net exports surplus (the exporting nation in this case) must be to accumulate financial claims (assets) denominated in the currency of the nation running the external deficit.

A fiscal surplus also means the government is spending less than it is taking out of the economy and that puts a drag on aggregate demand and constrains the ability of the economy to grow.

So the question relates to the relative magnitudes of the external add and the fiscal subtract from income?

In Period 1, there is an external balance (X – M = 0) and then for each subsequent period the external balance goes into surplus incrementing by 1 per cent of GDP each period (light-blue bars).

You can see that in the first two periods, private domestic saving is negative, then as the demand injection from the external surplus offsets the fiscal drag arising from the fiscal surplus, the private domestic sector breakeven (spending as much as they earn, so I – S = 0).

Then the demand add overall arising from the net positions of the external and public sectors is positive and the income growth would allow the private sector to save. That is increasingly so as the net demand add increases with the increasing external surplus.

The following blog posts may be of further interest to you:

Question 2:

When the central bank purchases government bonds in the secondary bond market, it has the equivalent impact on financial assets in the non-government sector as if a fiscal deficit, which increased reserves by the same amount would hav

The answer is False.

Quantitative easing then involves the central bank buying assets from the private sector – government bonds and high quality corporate debt.

What the central bank is doing is swapping financial assets with the banks – they sell their financial assets and receive back in return extra reserves.

In other words, the central bank is buying one type of financial asset (private holdings of bonds, company paper) and exchanging it for another (reserve balances at the central bank).

The net financial assets in the private sector are in fact unchanged although the portfolio composition of those assets is altered (maturity substitution) which changes yields and returns.

In terms of changing portfolio compositions, quantitative easing increases central bank demand for “long maturity” assets held in the private sector which reduces interest rates at the longer end of the yield curve.

These are traditionally thought of as the investment rates. This might increase aggregate demand given the cost of investment funds is likely to drop.

But on the other hand, the lower rates reduce the interest-income of savers who will reduce consumption (demand) accordingly.

How these opposing effects balance out is unclear but the evidence suggests there is not very much impact at all.

However, fiscal policy adds net financial assets to the non-government sector by way of contradistinction to QE. It might add the same amount of reserves but they reflect new financial assets in the non-government sector.

The following blog posts may be of further interest to you:

Question 3:

While continuous national governments deficits are possible if the non-government sector desires to save overall, they do imply continuously rising public debt levels under current institutional arrangements.

The answer is True.

The trap was to confuse levels with ratios. If I had have asked whether the public debt ratio (as a per cent of GDP) continuously rose with on-going national deficits, then the answer would be false.

That is because the debt levels might not rise more quickly than the denominator (GDP).

But if there is an institutional arrangement in place to match fiscal deficits each period with new debt issuance then it is a trivial response – True.

The following blog post may be of further interest to you:

That is enough for today!

(c) Copyright 2020 William Mitchell. All Rights Reserved.

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    This Post Has 9 Comments
    1. On Q1, in Bill’s answer he has a chart where for every year net exports are positive. In year 4,5 and 6 the private sector saves despite a government surplus as next exports exceed the surplus. I am therefor confused at to why it is false to say ‘The private domestic sector can save overall even if the government fiscal balance is in surplus as long as net exports are positive.’ as this exactly the case in year 4,5 and 6. (it the CAN was a WILL, is could see why it would be false).

    2. @Rob Rawlings

      Dear Rob,

      The condition does not always hold due to the ‘relative’ magnitude.

      In year 2 and 3, private domestic sector ‘cannot’ save overall even the government is in surplus and the net exports are positive, because that positive is not big enough to offset the government surplus’s size to allow this to happen (it is the relative magnitude, as bill explained).

      The WILL or the CAN does not make a difference because of this accounting rule stated by the MMT sectoral balances equation.

      I got this question wrong also because i go by the general sectoral balances logic, but not by the exact equation, nor per period calculation.

      Or, maybe you simply forgot to look left when writing the comments…

      Have a nice day!

    3. @Vorapot

      Thanks for the reply!

      To continue to beat a dead horse:

      If its true to say ‘The private domestic sector will save overall even if the government fiscal balance is in surplus as long as net exports are positive and greater than the government fiscal balance ‘

      then surely as a matter of logic it is true to say

      ‘The private domestic sector can save overall even if the government fiscal balance is in surplus as long as net exports are positive’. ( there are some condition where it will save, which is all that is requited by the ‘can’)

      but false to say

      ‘The private domestic sector will save overall even if the government fiscal balance is in surplus as long as net exports are positive’. (there are some condition where it won’t save, which violates the ‘will’)

    4. Rob, sometimes Bill uses the word ‘can’ to mean ‘must always be able to’ . Of course using that meaning of the word would mean that no baseball player can hit a home run. Which is unfortunately true at the moment. But ordinarily in June there would be plenty of home runs in major league baseball, even if no player could hit one every time he was at bat.

      I have gotten many answers ‘wrong’ because of this different understanding of what ‘can’ means. I just adjust my score and award myself the answer at this point.

    5. Hi Jerry,

      You are right of course and I was just being a bit pedantic.

      Even though I am not an MMTer I do like the weekly quiz and can live with its occasional eccentricities.

    6. @Rob

      Dear Rob,

      I ponder over your comments a bit more, and I have to say, after all, I agree with you.

      The main point, like you said, is the ‘possibility’ of a word that can allow that condition to happen, in fact, it does not exist.

      I can see that this issue can sometimes be a ‘problem’, say, in an examination in front of a committee where passing or failing is at stake.

      And if i am one of the committee members, I cannot really fail that candidate.

      Thank for sharing the idea, it is very sharp!

      Have a nice day.

    7. The distinction is not between CAN and WILL but between EX POST and EX ANTE.

      And the tiny little word IF also seems to be neglected.

    8. @Henry Rech

      Dear Henry,

      That is precisely the point!

      The EX POST and EX ANTE can only always confirm that all conditions of the WILL is completely possible, but only partially for the CAN.

      I am not sure about your second sentence, what it means. But I think it is irrelevant.

      Have a nice day!

      BTW, many thanks for the providing the right link to one of my comments sometimes ago!


    9. “I am not sure about your second sentence, what it means. But I think it is irrelevant.”

      Every time the SBE is used it is supported by statements like “If the external balance is zero then the gov deficit will ……”

      With an “if” statement, any situation can be conjured up to support any point that is desired to be put.

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