Saturday Quiz – August 8, 2015 – answers and discussion

Here are the answers with discussion for yesterday’s quiz. The information provided should help you understand the reasoning behind the answers. 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 then the private domestic sector cannot save overall if the government runs a balanced fiscal outcome.

The answer is True.

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

First, you need to understand the basic relationship between the sectoral flows and the balances that are derived from them. The flows are derived from the National Accounting relationship between aggregate spending and income. So:

(1) Y = C + I + G + (X – M)

where Y is GDP (income), C is consumption spending, I is investment spending, G is government spending, X is exports and M is imports (so X – M = net exports).

Another perspective on the national income accounting is to note that households can use total income (Y) for the following uses:

(2) Y = C + S + T

where S is total saving and T is total taxation (the other variables are as previously defined).

You than then bring the two perspectives together (because they are both just “views” of Y) to write:

(3) C + S + T = Y = C + I + G + (X – M)

You can then drop the C (common on both sides) and you get:

(4) S + T = I + G + (X – M)

Then you can convert this into the familiar sectoral balances accounting relations which allow us to understand the influence of fiscal policy over private sector indebtedness.

So we can re-arrange Equation (4) to get the accounting identity for the three sectoral balances – private domestic, government fiscal balance and external:

(S – I) = (G – T) + (X – M)

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)), where net exports represent the net savings of non-residents.

Another way of saying this is that total private savings (S) is equal to private investment (I) plus the public deficit (spending, G minus taxes, T) plus net exports (exports (X) minus imports (M)), where net exports represent the net savings of non-residents.

All these relationships (equations) hold as a matter of accounting.

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. The government would be undermining any desire by the private domestic sector to spend less than they earn by not providing the fiscal stimulus necessary to increase national output and income.

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 the fiscal balance into deficit 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!