# The Weekend Quiz – July 10-11, 2021 – 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:

Over a given economic cycle (peak to peak), if a nation’s external sector is on average balanced and the government gap between its tax revenue and spending is, on average, equal to 1 per cent of GDP, then the private domestic sector’s spending-income balance will on average be in:

(a) Deficit of 1 per cent of GDP

(b) Surplus of 1 per cent of GDP

The answer is **Deficit of 1 per cent of GDP**.

Note the question stated that the “gap between its tax revenue and spending”, which in normal usage would mean we are calculating, T – G. That is, the fiscal surplus is on average equal to 1 per cent of GDP. It would not make sense to interpret it the other way around.

This is a question about sectoral balances. Skip the derivation if you are familiar with the framework.

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 (CAB). 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.

Consider the following Table which shows three situations where the external sector is in balance.

Period 1, is the case in point (that is, the situation specified in the question) with the fiscal balance in surplus, (G – T) = -1.

With the external balance equal to 0, the general rule that the government surplus (deficit) equals the non-government deficit (surplus) applies to the government and the private domestic sector. In other words, the private domestic sector must be spending more than it is earning (a deficit).

Hence the answer is that the private domestic sector is in deficit (S – I) = -1.

In Period 3, the fiscal balance is in deficit (G – T) = 1, and this provides some demand stimulus in the absence of any impact from the external sector, which allows the private domestic sector to save overall.

Period 2, the fiscal balance is in balance and so the private domestic sector must also be in balance (spending equals its earning).

The movements in income associated with the spending and revenue patterns will ensure these balances arise. The problem is that if the private domestic sector desires to save **overall** then this outcome will be unstable and would lead to changes in the other balances as national income changed in response to the decline in private spending.

Sectoral Balance | Interpretation of Result | Case A | Case B | Case C |

External Balance (X – M) | Deficit is negative | 0 | 0 | 0 |

Fiscal Balance (G – T) | Deficit is positive | -1 | 0 | 1 |

Private Domestic Balance (S – I) | Deficit is negative | -1 | 0 | 1 |

So under the conditions specified in the question, the private domestic sector cannot save.

The government would be undermining any desire to save by not providing the fiscal stimulus necessary to increase national output and income so that private households/firms could save.

You may wish to read the following blog posts for more information:

- Stock-flow consistent macro models
- Norway and sectoral balances
- The OECD is at it again!
- Barnaby, better to walk before we run
- Saturday Quiz – June 19, 2010 – answers and discussion

## Question 2:

Considering only the initial impact on national income (ignoring multiplier effects), fiscal austerity will have a greater negative effect on real GDP if it manifests as a spending cut of $x than if the government chose to raise a value added tax to generate $x revenue at the current level of national income.

The answer is **True**.

The question is only seeking an understanding of the **initial** drain on the spending stream rather than the fully exhausted multiplied contraction of national income that will result. It is clear that the tax increase increase will have two effects: (a) some initial demand drain; and (b) it reduces the value of the multiplier, other things equal.

We are only interested in the first effect rather than the total effect. But I will give you some insight also into what the two components of the tax result might imply overall when compared to the impact on demand motivated by an decrease in government spending.

To give you a concrete example which will consolidate the understanding of what happens, imagine that the marginal propensity to consume out of disposable income is 0.8 and there is only one tax rate set at 0.20. So for every extra dollar that the economy produces the government taxes 20 cents leaving 80 cents in disposable income. In turn, households then consume 0.8 of this 80 cents which means an injection of 64 cents goes into aggregate demand which them multiplies as the initial spending creates income which, in turn, generates more spending and so on.

__Government spending cut__

A cut in government spending (say of $1000) is what we call an exogenous withdrawal from the aggregate spending stream and this directly reduces aggregate demand by that amount. So it might be the cancellation of a long-standing order for $1000 worth of gadget X. The firm that produces gadget X thus reduces production of the good or service by the fall in orders ($1000) (if they deem the drop in sales to be permanent) and as a result incomes of the productive factors working for and/or used by the firm fall by $1000. So the initial fall in aggregate demand is $1000.

This initial fall in national output and income would then induce a further fall in consumption by 64 cents in the dollar so in Period 2, aggregate demand would decline by $640. Output and income fall further by the same amount to meet this drop in spending. In Period 3, aggregate demand falls by 0.8 x 0.8 x $640 and so on. The induced spending decrease gets smaller and smaller because some of each round of income drop is taxed away, some goes to a decline in imports and some manifests as a decline in saving.

__Tax-increase induced contraction__

The contraction coming from a tax-cut does not directly impact on the spending stream in the same way as the cut in government spending.

First, imagine the government worked out a tax rise cut that would reduce its initial fiscal deficit by the same amount as would have been the case if it had cut government spending (so in our example, $1000).

In other words, disposable income at each level of GDP falls initially by $1000. What happens next?

Some of the decline in disposable income manifests as lost saving (20 cents in each dollar that disposable income falls in the example being used). So the lost consumption is equal to the marginal propensity to consume out of disposable income times the drop in disposable income (which if the MPC is less than 1 will be lower than the $1000).

In this case the reduction in aggregate demand is $800 rather than $1000 in the case of the cut in government spending.

What happens next depends on the parameters of the macroeconomic system. The multiplied fall in national income may be higher or lower depending on these parameters. But it will never be the case that an initial fiscal equivalent tax rise will be more damaging to national income than a cut in government spending.

Note in answering this question I am disregarding all the nonsensical notions of Ricardian equivalence that abound among the mainstream economists. I am also ignoring the empirically-questionable mainstream claims that tax increases erode work incentives which force workers to supply less labour. In this case, I avoid those issues by imposing a value-added tax increase.

You may wish to read the following blog post for more information:

## Question 3:

During a recession, the government can always restore full employment if it uses expansionary fiscal policy to restore trend real GDP growth.

The answer is **False**.

To see why, we might usefully construct a scenario that will explicate the options available to a government:

- Trend real GDP growth rate is 3 per cent annum.
- Labour productivity growth (that is, growth in real output per person employed) is growing at 2 per cent per annum. So as this grows less employment in required per unit of output.
- The labour force is growing by 1.5 per cent per annum. Growth in the labour force adds to the employment that has to be generated for unemployment to stay constant (or fall).
- The average working week is constant in hours. So firms are not making hours adjustments up or down with their existing workforce. Hours adjustments alter the relationship between real GDP growth and persons employed.

We can use this scenario to explore the different outcomes.

The trend rate of real GDP growth doesn’t relate to the labour market in any direct way. The late Arthur Okun is famous (among other things) for estimating the relationship that links the percentage deviation in real GDP growth from potential to the percentage change in the unemployment rate – the so-called Okun’s Law.

The algebra underlying this law can be manipulated to estimate the evolution of the unemployment rate based on real output forecasts.

From Okun, we can relate the major output and labour force aggregates to form expectations about changes in the aggregate unemployment rate based on output growth rates. A series of accounting identities underpins Okun’s Law and helps us, in part, to understand why unemployment rates have risen.

The rule of thumb that Okun came up with was that if the unemployment rate is to remain constant, the rate of real output growth must equal the rate of growth in the labour force plus the growth rate in labour productivity, assuming no change in working hours per week.

It is an approximate relationship because cyclical movements in labour productivity (changes in hoarding) and the labour force participation rates can modify the relationships in the short-run. But it provides reasonable estimates of what happens when real output changes.

The sum of labour force and productivity growth rates is referred to as the required real GDP growth rate – required to keep the unemployment rate constant.

Remember that labour productivity growth (real GDP per person employed) reduces the need for labour for a given real GDP growth rate while labour force growth adds workers that have to be accommodated for by the real GDP growth (for a given productivity growth rate).

So in the example, the required real GDP growth rate is 3.5 per cent per annum and if policy only aspires to keep real GDP growth at its trend growth rate of 3 per cent annum, then the output gap that emerges is 0.5 per cent per annum.

The unemployment rate will rise by this much (give or take) and reflects the fact that real output growth is not strong enough to both absorb the new entrants into the labour market and offset the employment losses arising from labour productivity growth.

So the appropriate fiscal strategy does not relate to “trend output” but to the required real GDP growth rate given labour force and productivity growth.

The two growth rates might be consistent but then they need not be. That lack of concordance makes the proposition false.

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

That is enough for today!

(c) Copyright 2021 William Mitchell. All Rights Reserved.

Once in a while I am glad you are way over on the other side of the world.

“and the government gap between its tax revenue and spending is, on average, equal to 1 per cent of GDP”

In American English this means the government is either spending 1% of GDP more than it takes in tax, or 1% less than it takes in tax. It absolutely makes sense to interpret it either way. And the difference between them is kind of important when you try to answer Question 1.

“… the government gap between its tax revenue and spending is, on average, equal to 1 per cent of GDP …” In U.S. political discourse, the term “gap” would suggest “something lacking” or “something which needs to be filled.” That would imply an excess of government spending over tax revenue. So I agree with Jerry Brown that the wording is ambiguous.

… the government gap between its tax revenue and spending …

This is one of Bill’s tricky questions, because as Jerry and James point out “gap” is usually interpreted as something missing. However, in this case the sequence of government transactions is crucial: tax revenue preceding spending means that the gap between them is positive and hence there’s a budget surplus!

Conclusion: always be suspicious in dealing with Bill’s quizzes, especially if the answer appears obvious!

The term ‘gap’ implies a difference between. One can interpret that as a shortfall or a surplus from one side or the other. The question is ambiguous, but as I calculated it meant a government deficit – my answer was correct – the important thing is that we understand the sectoral balances.

In Q1 there should have been an option “c) Can’t tell from the given information.”

Q1 is a “depends on the numbers” question, like the one about whether an external surplus means the private sector can save despite government austerity. It all depends on who’s doing how much of what.

Jon,

In sectoral balances, given that the external sector is balanced, for the private sector to run a deficit the government must have a fiscal surplus. You might got the correct answer, but I’m afraid your reasoning is faulty if you calculated a government deficit.

Demetrios,

There is a gap between what I have spent and what I have saved.

Please tell me whether I am in surplus or deficit.

Thanks.

Jon,

A good point but not well put.

No gap between what you spent and what you saved would mean that you spent exactly half your earnings. That would mean a surplus, but possibly a zero surplus.

As it stands, c) can’t tell from the given information. :)

Dear All

I guess we are coming up language differences across the English-speaking world.

My education in English usage taught me that if I state the following – “… gap between its tax revenue and spending is …” then I am using the first named concept (tax revenue) as the deviation and the second concept (spending) as the benchmark.

So if the deviation is the number FROM the benchmark. If it is positive then it is a fiscal surplus in this context and vice versa.

We obviously use the language differently, given the comments that have followed the quiz.

I am happy though that the discussion reflects the willingness and capacity of commentators to think through the underlying issues.

best wishes

bill

Jon,

Ignoring semantics, if the external sector is balanced for convenience we can drop it from the sectoral balance identity. Consequently taking Bill’s answer as correct, that is the private domestic sector is in deficit, then there must be a SURPLUS in the government sector.

When you said “(t)he question is ambiguous, but as I calculated it meant a government ‘deficit’ – my answer was correct –“, this CANNOT happen. With only two sectors one must be the opposite of the other. Correct?