The Weekend Quiz – April 7-8, 2018 – 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 fiscal 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) + CAD

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

Conversely, government surpluses (G – T < 0) and current account deficits (CAD < 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) – CAD] = (G – T)

where the term on the left-hand side [(S – I) – CAD] 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 graph with accompanying data table lets you see the evolution of the balances expressed in terms of percent of GDP. In each period I just held the fiscal 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 fiscal balance. But we will just assume there is no change for simplicity. It doesn’t violate the logic.

To aid interpretation remember that (I-S) > 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 deficit because imports are greater than exports.

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 “earning” and that puts a drag on aggregate demand and constrains the ability of the economy to grow. So the question is what are 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 blogs may be of further interest to you:

Question 2:

The only difference between quantitative easing and a discretionary fiscal injection is which branch of government is responsible for the stimulus.

The answer is False.

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

So 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.

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.

There is thus no stimulus as a result of that operation unless the changes in yields stimulate investment or other interest rate sensitive spending.

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.

In contrast, a fiscal injection is a direct stimulus, with government spending adding dollars directly into the spending stream. Tax cuts work slightly differently because some of the stimulus is lost to increased saving.

The following blogs may be of further interest to you:

Question 3:

While continuous national governments deficits are possible if the non-government sector desires to save, they do imply continuously rising public debt levels as a percentage of GDP.

The answer is False.

While Modern Monetary Theory (MMT) places no particular importance in the public debt to GDP ratio for a sovereign government, given that insolvency is not an issue, the mainstream debate is dominated by the concept. The unnecessary practice of fiat currency-issuing governments of issuing public debt $-for-$ to match public net spending (deficits) ensures that the debt levels will always rise when there are deficits.

But the rising debt levels do not necessarily have to rise at the same rate as GDP grows. The question is about the debt ratio not the level of debt per se.

Rising deficits often are associated with declining economic activity (especially if there is no evidence of accelerating inflation) which suggests that the debt/GDP ratio may be rising because the denominator is also likely to be falling or rising below trend.

Further, historical experience tells us that when economic growth resumes after a major recession, during which the public debt ratio can rise sharply, the latter always declines again.

It is this endogenous nature of the ratio that suggests it is far more important to focus on the underlying economic problems which the public debt ratio just mirrors.

Mainstream economics starts with the flawed analogy between the household and the sovereign government such that any excess in government spending over taxation receipts has to be “financed” in two ways: (a) by borrowing from the public; and/or (b) by “printing money”.

Neither characterisation is remotely representative of what happens in the real world in terms of the operations that define transactions between the government and non-government sector.

Further, the basic analogy is flawed at its most elemental level. The household must work out the financing before it can spend. The household cannot spend first. The government can spend first and ultimately does not have to worry about financing such expenditure.

However, in mainstream (dream) land, the framework for analysing these so-called “financing” choices is called the government budget constraint (GBC). The GBC says that the fiscal deficit in year t is equal to the change in government debt over year t plus the change in high powered money over year t. So in mathematical terms it is written as:


which you can read in English as saying that Budget deficit = Government spending + Government interest payments – Tax receipts must equal (be “financed” by) a change in Bonds (B) and/or a change in high powered money (H). The triangle sign (delta) is just shorthand for the change in a variable.

However, this is merely an accounting statement. In a stock-flow consistent macroeconomics, this statement will always hold. That is, it has to be true if all the transactions between the government and non-government sector have been correctly added and subtracted.

So in terms of MMT, the previous equation is just an ex post accounting identity that has to be true by definition and has no real economic importance.

But for the mainstream economist, the equation represents an ex ante (before the fact) financial constraint that the government is bound by. The difference between these two conceptions is very significant and the second (mainstream) interpretation cannot be correct if governments issue fiat currency (unless they place voluntary constraints on themselves and act as if it is a financial constraint).

Further, in mainstream economics, money creation is erroneously depicted as the government asking the central bank to buy treasury bonds which the central bank in return then prints money. The government then spends this money.

This is called debt monetisation and you can find out why this is typically not a viable option for a central bank by reading the Deficits 101 suite – Deficit spending 101 – Part 1Deficit spending 101 – Part 2Deficit spending 101 – Part 3.

Anyway, the mainstream claims that if governments increase the money growth rate (they erroneously call this “printing money”) the extra spending will cause accelerating inflation because there will be “too much money chasing too few goods”! Of-course, we know that proposition to be generally preposterous because economies that are constrained by deficient demand (defined as demand below the full employment level) respond to nominal demand increases by expanding real output rather than prices. There is an extensive literature pointing to this result.

So when governments are expanding deficits to offset a collapse in private spending, there is plenty of spare capacity available to ensure output rather than inflation increases.

But not to be daunted by the “facts”, the mainstream claim that because inflation is inevitable if “printing money” occurs, it is unwise to use this option to “finance” net public spending.

Hence they say as a better (but still poor) solution, governments should use debt issuance to “finance” their deficits. Thy also claim this is a poor option because in the short-term it is alleged to increase interest rates and in the longer-term is results in higher future tax rates because the debt has to be “paid back”.

Neither proposition bears scrutiny – you can read these blogs – Will we really pay higher taxes? and Will we really pay higher interest rates? – for further discussion on these points.

The mainstream textbooks are full of elaborate models of debt pay-back, debt stabilisation etc which all claim (falsely) to “prove” that the legacy of past deficits is higher debt and to stabilise the debt, the government must eliminate the deficit which means it must then run a primary surplus equal to interest payments on the existing debt.

A primary fiscal balance is the difference between government spending (excluding interest rate servicing) and taxation revenue.

The standard mainstream framework, which even the so-called progressives (deficit-doves) use, focuses on the ratio of debt to GDP rather than the level of debt per se. The following equation captures the approach:

So the change in the debt ratio is the sum of two terms on the right-hand side: (a) the difference between the real interest rate (r) and the GDP growth rate (g) times the initial debt ratio; and (b) the ratio of the primary deficit (G-T) to GDP.

The real interest rate is the difference between the nominal interest rate and the inflation rate.

This standard mainstream framework is used to highlight the dangers of running deficits. But even progressives (not me) use it in a perverse way to justify deficits in a downturn balanced by surpluses in the upturn.

Many mainstream economists and a fair number of so-called progressive economists say that governments should as some point in the business cycle run primary surpluses (taxation revenue in excess of non-interest government spending) to start reducing the debt ratio back to “safe” territory.

Almost all the media commentators that you read on this topic take it for granted that the only way to reduce the public debt ratio is to run primary surpluses. That is what the whole “credible exit strategy” rhetoric is about and what is driving the austerity push around the world at present.

So the question is whether continuous national governments deficits imply continuously rising public debt levels as a percentage of GDP. While MMT advocates running fiscal deficits when they are necessary to fill a spending gap left by non-government saving, it does not tell us that a currency-issuing government running a deficit can never reduce the debt ratio.

The standard formula above can easily demonstrate that a nation running a primary deficit can reduce its public debt ratio over time.

Furthermore, depending on contributions from the external sector, a nation running a deficit will more likely create the conditions for a reduction in the public debt ratio than a nation that introduces an austerity plan aimed at running primary surpluses.

Here is why that is the case. A growing economy can absorb more debt and keep the debt ratio constant or falling. From the formula above, if the primary fiscal balance is zero, public debt increases at a rate r but the public debt ratio increases at rg.

The orthodox economists use this analysis to argue that permanent deficits are bad because the financial markets will “penalise” a government living on debt. If the public debt ratio is “too high” (whatever that is or means), markets “lose faith” in the government.

To make matters simple, assume a public debt ratio at the start of the period of 100 per cent (so B/Y(-1) = 1) and a current real interest rate (r) of 3 per cent. Assume that GDP is growing (g) at 2 per cent. This would require a primary surplus of 1 per cent of GDP to stabilise the debt ratio (check it for yourself).

Now what if the financial markets want a risk premium on domestic bonds? Also assume the central bank is worried about inflation and pushes nominal interest rates up so that the real rate (r) rises to 6 per cent. Also assume that the primary surplus and the rising interest rates drive g to 0 per cent (GDP growth falls to zero).

So now the the fiscal austerity (primary surplus) has to rise to 6 per cent of GDP to stabilise debt. The sharp fiscal contraction would lead to recession and as the popularity of the government wanes the uncertainty drives further interest rate rises (via the “markets”). It becomes even harder to stabilise debt as r rises and g falls.

But consider the following example captured in Year 1 in the Table below. Assume, as before that B/Y(-1) = 1 (that is, the public debt ratio at the start of the period is 100 per cent). The (-1) just signals the value inherited in the current period.

It is a highly stylised example truncated into a two-period adjustment to demonstrate the point. But if the fiscal deficit is a large percentage of GDP then it might take some years to start reducing the public debt ratio as GDP growth ensures.

Assume that the real rate of interest is 0 (so the nominal interest rate equals the inflation rate).

Assume that the rate of real GDP growth is minus 2 per cent (that is, the nation is in recession) and the automatic stabilisers push the primary fiscal balance into deficit equal to 1 per cent of GDP. As a consequence, the public debt ratio will rise by 3 per cent.

At the start of Year 2, the public debt ratio is 1.03 as a consequence.

The government reacts to the recession in the correct manner and increases its discretionary net spending to take the deficit in Year 2 to 2 per cent of GDP (noting a positive number in this instance is a deficit).

The central bank maintains its zero interest rate policy and the inflation rate also remains at zero.

The increasing deficit stimulates economic growth in Year 2 such that real GDP grows by 3 per cent. In this case the public debt ratio falls by 1.02 per cent.

So even with an increasing (or unchanged) deficit, real GDP growth can reduce the public debt ratio, which is what has happened many times in past history following economic slowdowns.

The best way to reduce the public debt ratio is to stop issuing debt. A sovereign government doesn’t have to issue debt if the central bank is happy to keep its target interest rate at zero or pay interest on excess reserves.

The discussion also demonstrates why tightening monetary policy makes it harder for the government to reduce the public debt ratio – which, of-course, is one of the more subtle mainstream ways to force the government to run surpluses.

The following blog may be of further interest to you:

That is enough for today!

(c) Copyright 2018 William Mitchell. All Rights Reserved.

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    5 Responses to The Weekend Quiz – April 7-8, 2018 – answers and discussion

    1. Thorleif says:

      Dear Bill,

      As a MMT-soldier I think the weakest argument lies within the problems related to inflation. As far as I read so far MMT sees inflation-risk more as an endogen variable, i.e government buying up more resources than there are available. Looking back at the inflation-years in 60 and 70´s I think Europe imported it´s inflation from the US mainly. Even if that´s not completely the whole truth I think the trigger of inflation impulses came through the external sector. Then local internal system-infrastructures continued to manifest inflation until the ending of the dollar-gold peg(Bretton Wood) and the end of the oil-embargo(against the US) period had it´s final impacts(incl US FED raising it´s fundrate to 20%(1980) and later the Plaza agreements(1985).

      (todays disinflation is also more of a external sector-factor due to globalisation and outsourcing)

      So coming back to the question about inflation related to MMT I could see problems if nominal rates of a growing government debt(net financial assets)climbs high enough(say 10% instead of todays 2,8% on a UST 10ybond) to represent a too big piece of the government budget and thereby cause the government to fund it´s netinterest money with new debts(net financial assets) just to avoid austarity! You could maybe say that if inflation picks up slowly and real GDP-growth tags along there would not be any big problems. But the real problem with high cost-inflation is the multiplicator effects. It will finally show up as very negative for aggregate demand and therefore a stagnating real GDP-growth(stagflation).

      Maybe I missed something here but how would MMT respond to a scenario when the external sector is producing high inflation? Today there is already an environment with currency-competition.

    2. Thorleif says:

      Maybe I should notice upon the question above that permanent centralbank buying of high-yielded GB´s to fund the payment of netinterest-expenditures by the Treasury is not the expected answer! Or is it? Monetizing budget netinterest on government debts?

    3. Rob Rawlings says:

      For Q1;

      If I understand correctly:
      1: net exports net exports is in surplus = private dis-savings
      2: net exports are positive = private savings

      If 2 is bigger that 1 then the private domestic sector will save overall, if not they won’t. But as the questions say CAN not WILL I think the answer should be true.

    4. Rob Rawlings says:

      (Re posting as I see I somehow mangled it the first time, please ignore the first attempt)

      For Q1;

      If I understand correctly:
      1: fiscal balance is in surplus = private dis-savings
      2: net exports are positive = private savings

      If 2 is bigger that 1 then the private domestic sector will save overall, if not they won’t. But as the questions say CAN not WILL I think the answer should be true.

    5. Thorleif says:

      Rob; I would like to agree with you but…..

      Q1 says “…… long as net exports are positive”

      If answer would be “true” Q1 should instead say i.e “…… long as net exports are positive ENOUGH”

      See the Table above at column: “period 4”.

      Private sector can not save UNLESS net exports are bigger than the fiscal surplus as you correctly state. But the question was not put in that way. That is why the answer in “False” I guess.

      (UNLESS = ENOUGH). “Positive” is not good enough!

      Best wishes

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