The Weekend Quiz – May 27-28, 2017 – 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:

If a nation’s external sector is in balance (and thus making no contribution to real GDP growth) then the private domestic sector cannot save if the government runs a balanced fiscal outcome.

The answer is False.

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

To refresh your memory the 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:

(1) 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 tax revenue minus total 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 net taxes (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.

If you had answered True, you might have engaged the following logic, where all the statements are correct but missing the point.

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

Period 1, the fiscal balance is in surplus (T – G = 1) and the private balance is in deficit (S – I = -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 Period 3, the fiscal balance is in deficit (T – G = -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 (S – I = 1).

Period 2, is the case in point and the sectoral balances show that if the external sector is in balance and the government is able to achieve a fiscal balance, then the private domestic sector must also be in balance.

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.

So under the conditions specified in the question, the private domestic sector cannot save overall – that is, spend less than it earns.

In that case, the government would be undermining any desire on the part of the private domestic sector to spend less than its total income by not providing the fiscal stimulus necessary to increase national output and income so that private households/firms could save overall.

But the households and firms can still save a portion of their disposable income under these circumstances. The trick is in understanding that there is a difference between saving overall (so S > I or spending less than income) and saving (so S > 0).

You may wish to read the following blogs 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:

A tax increase, which aims to increase tax revenue at the current level of national income by $x, will have a smaller initial negative impact on aggregate demand than a government spending cut of $x?

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 doomsayers who have never predicted anything of empirical note! I am also ignoring the empirically-questionable mainstream claims that tax increases erode work incentives which force workers to supply less labour.

You may wish to read the following blogs for more information:

• Spending multipliers

Question 3:

If the external sector is accumulating financial claims on the local economy and the GDP growth rate is lower than the real interest rate, then the private domestic sector and the government sector can run surpluses without damaging employment growth.

The answer is False.

When the external sector is accumulating financial claims on the local economy it must mean the current account is in deficit – so the external balance is in deficit. Under these conditions it is impossible for both the private domestic sector and government sector to run surpluses. One of those two has to also be in deficit to satisfy the national accounting rules and income adjustments will always ensure that is the case.

The relationship between the rate of GDP growth and the real interest rate doesn’t alter this result and was included as superflous information to test the clarity of your understanding.

To understand this we need to begin with the national accounts which underpin the basic income-expenditure model that is at the heart of introductory macroeconomics. See the answer to Question 1 for the background conceptual development.

Consider the following graph and associated table of data which shows six states. All states have a constant external deficit equal to 2 per cent of GDP (light-blue columns).

State 1 show a government running a surplus equal to 2 per cent of GDP (green columns). As a consequence, the private domestic balance is in deficit of 4 per cent of GDP (royal-blue columns). This cannot be a sustainable growth strategy because eventually the private sector will collapse under the weight of its indebtedness and start to save. At that point the fiscal drag from the fiscal surpluses will reinforce the spending decline and the economy would go into recession.

State 2 shows that when the fiscal surplus moderates to 1 per cent of GDP the private domestic deficit is reduced.

State 3 is a fiscal balance and then the private domestic deficit is exactly equal to the external deficit. So the private sector spending more than they earn exactly funds the desire of the external sector to accumulate financial assets in the currency of issue in this country.

States 4 to 6 shows what happens when the fiscal balance goes into deficit – the private domestic sector (given the external deficit) can then start reducing its deficit and by State 5 it is in balance. Then by State 6 the private domestic sector is able to net save overall (that is, spend less than its income).

Note also that the government balance equals exactly $-for-$ (as a per cent of GDP) the non-government balance (the sum of the private domestic and external balances). This is also a basic rule derived from the national accounts.

Most countries currently run external deficits. The crisis was marked by households reducing consumption spending growth to try to manage their debt exposure and private investment retreating. The consequence was a major spending gap which pushed fiscal balancess into deficits via the automatic stabilisers.

The only way to get income growth going in this context and to allow the private sector surpluses to build was to increase the deficits beyond the impact of the automatic stabilisers. The reality is that this policy change hasn’t delivered large enough fiscal deficits (even with external deficits narrowing). The result has been large negative income adjustments which brought the sectoral balances into equality at significantly lower levels of economic activity.

The following blogs may be of further interest to you:

• Barnaby, better to walk before we run
• Stock-flow consistent macro models
• Norway and sectoral balances
• The OECD is at it again!

That is enough for today!

(c) Copyright 2017 William Mitchell. All Rights Reserved.