The Weekend Quiz – July 11-12, 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.

Here are the answers with discussion for yesterday’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:

Larger fiscal deficits as a percentage of GDP reduce the local productive resources that are available to the private sector.

The answer is True.

It is clear that at any point in time, there are finite real resources available for production. New resources can be discovered, produced and the old stock spread better via education and productivity growth. The aim of production is to use these real resources to produce goods and services that people want either via private or public provision.

So by definition any sectoral claim (via spending) on the real resources reduces the availability for other users. There is always an opportunity cost involved in real terms when one component of spending increases relative to another.

Unless you subscribe to the extreme end of mainstream economics which espouses concepts such as 100 per cent crowding out via financial markets and/or Ricardian equivalence consumption effects, you will conclude that rising net public spending as percentage of GDP will add to aggregate demand and as long as the economy can produce more real goods and services in response, this increase in public demand will be met with increased public access to real goods and services.

You might also wonder whether it matters if the economy is already at full capacity. Under these conditions a rising public share of GDP must squeeze real usage by the non-government sector which might also drive inflation as the economy tries to siphon of the incompatible nominal demands on final real output.

You might say that the deficits might rise as a percentage of GDP as a result of a decline in private spending triggering the automatic stabilisers which would suggest many idle resources. That is clearly possible but doesn’t alter the fact that the public claims on the total resources available have risen.

Under these circumstances the opportunity costs involved are very low because of the excess capacity. The question really seeks to detect whether you have been able to distinguish between the financial crowding out myth that is found in all the mainstream macroeconomics textbooks and concepts of real crowding out.

The normal presentation of the crowding out hypothesis which is a central plank in the mainstream economics attack on government fiscal intervention is more accurately called “financial crowding out”.

At the heart of this conception is the theory of loanable funds, which is a aggregate construction of the way financial markets are meant to work in mainstream macroeconomic thinking. The original conception was designed to explain how aggregate demand could never fall short of aggregate supply because interest rate adjustments would always bring investment and saving into equality.

At the heart of this erroneous hypothesis is a flawed viewed of financial markets. The so-called loanable funds market is constructed by the mainstream economists as serving to mediate saving and investment via interest rate variations.

This is pre-Keynesian thinking and was a central part of the so-called classical model where perfectly flexible prices delivered self-adjusting, market-clearing aggregate markets at all times. If consumption fell, then saving would rise and this would not lead to an oversupply of goods because investment (capital goods production) would rise in proportion with saving. So while the composition of output might change (workers would be shifted between the consumption goods sector to the capital goods sector), a full employment equilibrium was always maintained as long as price flexibility was not impeded. The interest rate became the vehicle to mediate saving and investment to ensure that there was never any gluts.

So saving (supply of funds) is conceived of as a positive function of the real interest rate because rising rates increase the opportunity cost of current consumption and thus encourage saving. Investment (demand for funds) declines with the interest rate because the costs of funds to invest in (houses, factories, equipment etc) rises.

Changes in the interest rate thus create continuous equilibrium such that aggregate demand always equals aggregate supply and the composition of final demand (between consumption and investment) changes as interest rates adjust.

According to this theory, if there is a rising fiscal deficit then there is increased demand is placed on the scarce savings (via the alleged need to borrow by the government) and this pushes interest rates to “clear” the loanable funds market. This chokes off investment spending.

So allegedly, when the government borrows to “finance” its fiscal deficit, it crowds out private borrowers who are trying to finance investment. The mainstream economists conceive of this as the government reducing national saving (by running a fiscal deficit) and pushing up interest rates which damage private investment.

The analysis relies on layers of myths which have permeated the public space to become almost self-evident truths.

This trilogy of blog posts will help you understand this if you are new to my blog

1. Deficit spending 101 – Part 1 (February 21, 2009).

2. Deficit spending 101 – Part 2 (February 23, 2009)

3. Deficit spending 101 – Part 3 (March 2, 2009).

The basic flaws in the mainstream story are that governments just borrow back the net financial assets that they create when they spend. Its a wash! It is true that the private sector might wish to spread these financial assets across different portfolios. But then the implication is that the private spending component of total demand will rise and there will be a reduced need for net public spending.

Further, they assume that savings are finite and the government spending is financially constrained which means it has to seek “funding” in order to progress their fiscal plans. But government spending by stimulating income also stimulates saving.

The flawed notion of financial crowding out has to be distinguished from other forms of crowding out which are possible. In particular, MMT recognises the need to avoid or manage real crowding out which arises from there being insufficient real resources being available to satisfy all the nominal demands for such resources at any point in time.

In these situation, the competing demands will drive inflation pressures and ultimately demand contraction is required to resolve the conflict and to bring the nominal demand growth into line with the growth in real output capacity.

The idea of real crowding out also invokes and emphasis on political issues. If there is full capacity utilisation and the government wants to increase its share of full employment output then it has to crowd the private sector out in real terms to accomplish that. It can achieve this aim via tax policy (as an example). But ultimately this trade-off would be a political choice – rather than financial.

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

• When a huge pack of lies is barely enough
• Saturday Quiz – April 17, 2010 – answers and discussion

Question 2:

A national government that issues its own currency and freely floats it on foreign markets never faces a risk of insolvency.

The answer is False.

The answer would be true if the sentence had appended the description “issues its own currency and freely floats it on foreign markets” with and only ever borrows in its own currency. The national government can always service its debts so long as these are denominated in domestic currency.

So the answer is false because if a government borrows in foreign currencies in addition to its own currency then it can clearly face a situation where its cannot get sufficient foreign currency to meet its obligations.

It also makes no significant difference for solvency whether the debt is held domestically or by foreign holders because it is serviced in the same manner in either case – by crediting bank accounts.

The situation changes when the government issues debt in a foreign-currency. Given it does not issue that currency then it is in the same situation as a private holder of foreign-currency denominated debt.

Private sector debt obligations have to be serviced out of income, asset sales, or by further borrowing. This is why long-term servicing is enhanced by productive investments and by keeping the interest rate below the overall growth rate.

Private sector debts are always subject to default risk – and should they be used to fund unwise investments, or if the interest rate is too high, private bankruptcies are the “market solution”.

Only if the domestic government intervenes to take on the private sector debts does this then become a government problem. Again, however, so long as the debts are in domestic currency (and even if they are not, government can impose this condition before it takes over private debts), government can always service all domestic currency debt.

The solvency risk the private sector faces on all debt is inherited by the national government if it takes on foreign-currency denominated debt. In those circumstances it must have foreign exchange reserves to allow it to make the necessary repayments to the creditors. In times when the economy is strong and foreigners are demanding the exports of the nation, then getting access to foreign reserves is not an issue.

But when the external sector weakens the economy may find it hard accumulating foreign currency reserves and once it exhausts its stock, the risk of national government insolvency becomes real.

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

• Modern monetary theory in an open economy
• Debt is not debt
• The deficit and debt debate
• Debt and deficits again!

Question 3:

Assume the government increases spending by $100 billion from now and maintains that injection for three years. Economists estimate the spending multiplier to be 1.6 and the impact is immediate and exhausted in each year; imports rise by 20 cents for every dollar generated in the economy; and the current tax rate is equal to 20 per cent. They also estimate that the tax multiplier (impact of tax changes on income) to be equal to 1. Which of the following statements is correct?

(a) The cumulative impact of this fiscal expansion on nominal GDP is $480 billion and the private sector saves 24 cents out of every extra dollar generated.

(b) The cumulative impact of this fiscal expansion on nominal GDP is $480 billion and the private sector saves 28 cents out of every extra dollar generated.

(c) The cumulative impact of this fiscal expansion on nominal GDP is $384 billion and the private sector saves 24 cents out of every extra dollar generated.

(d) The cumulative impact of this fiscal expansion on nominal GDP is $384 billion and the private sector saves 28 cents out of every extra dollar generated.

The answer was Option (b) $480 billion and 28 cents.

The question involves two parts: (a) working out what is relevant to the answer; and (b) reverse engineering some of the relevant data to get the marginal propensity to consume (and hence the saving propensity).

To work out the cumulative impact you need to understand the concept of the spending multiplier which is the easier part of the question.

In Year 1, government spending rises by $100 billion, which leads to a total increase in GDP of $160 billion via the spending multiplier. The multiplier process is explained in the following way. Government spending, say, on some equipment or construction, leads to firms in those areas responding by increasing real output. In doing so they pay out extra wages and other payments which then provide the workers (consumers) with extra disposable income (once taxes are paid).

Higher consumption is thus induced by the initial injection of government spending. Some of the higher income is saved and some is lost to the local economy via import spending. So when the workers spend their higher wages (which for some might be the difference between no wage as an unemployed person and a positive wage), broadly throughout the economy, this stimulates further induced spending and so on, with each successive round of spending being smaller than the last because of the leakages to taxation, saving and imports.

Eventually, the process exhausts and the total rise in GDP is the “multiplied” effect of the initial government injection. In this question we adopt the simplifying (and unrealistic) assumption that all induced effects are exhausted within the same year. In reality, multiplier effects of a given injection usually are estimated to go beyond 4 quarters.

So this process goes on for 3 years so the $300 billion cumulative injection leads to a cumulative increase in GDP of $480 billion.

It is true that total tax revenue rises by $96 billion over the three years but this is just an automatic stabiliser effect. There was no change in the tax structure (that is, tax rates) posited in the question.

That means that the tax multiplier, whatever value it might have been, is irrelevant to this example.

Some might have decided to subtract the $96 billion from the $480 billion to get answer (c) or (d) on the presumption that there was a tax effect. But the automatic stabiliser effect of the tax system is already built into the expenditure multiplier.

So answers (c) and (d) were there to lure you into thinking the tax parameters were important for the first part of the solution.

However, the second part of the question required you to reverse engineer the multiplier. In mathematics the general rule is that you can only solve for unknown parameters if you have as many equations as unknowns. So if you have y = 2x. You cannot solve for y because you don’t know what x is. If I tell you x = 2 then you have one equation (y = 2x) and one unknown (y) so it becomes trivial y = 4.

Similar reasoning applies in this question.

The expenditure multiplier is defined as the change in real income that results from a dollar change in exogenous aggregate demand (so one of G, I or X). We could complicate this by having autonomous consumption as well but the principle is not altered.

Consumption and Saving

So the starting point is to define the consumption relationship. The most simple is a proportional relationship to disposable income (Yd). So we might write it as C = c*Yd – where little c is the marginal propensity to consume (MPC) or the fraction of every dollar of disposable income consumed. The marginal propensity to consume is just equal to 1 minus the marginal propensity to save.

The * sign denotes multiplication. You can do this example in an spreadsheet if you like.

Taxes

Our tax relationship is already defined above – so T = tY. The little t is the marginal tax rate which in this case is the proportional rate – 0.2 in the question. Note here taxes are taken out of total income (Y) which then defines disposable income.

So Yd = (1-t) times Y or Yd = (1-0.3)*Y = 0.2*Y

Imports

If imports (M) are 20 per cent of total income (Y) then the relationship is M = m*Y where little m is the marginal propensity to import or the economy will increase imports by 20 cents for every real GDP dollar produced.

Multiplier

If you understand all that then the explanation of the multiplier follows logically. Imagine that government spending went up by $100 and the change in real national income is $160. Then the multiplier is the ratio (denoted k) of the

Change in Total Income to the Change in government spending.

Thus k = $160/$100 = 1.60

That is the value assumed in the question. This says that for every dollar the government spends total real GDP will rise by $1.60 after taking into account the leakages from taxation, saving and imports.

When we conduct this thought experiment we are assuming the other autonomous expenditure components (I and X) are unchanged.

But the important point is to understand why the process generates a multiplier value of 1.60.

The formula for the spending multiplier is given as (see blogs listed below for a complete explanation):

k = 1/(1 – c*(1-t) + m)

where c is the MPC, t is the tax rate so c(1-t) is the extra spending per dollar of disposable income and m is the MPM. The * denotes multiplication as before.

This formula is derived as follows:

The national income identity is:

GDP = Y = C + I + G + (X – M)

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

A simple model of these expenditure components taking the information above is:

GDP = Y = c*Yd + I + G + X – m*Y

Yd = (1 – t)*Y

We consider (in this model for simplicity) that the expenditure components I, G and X are autonomous and do not depend on the level of income (GDP) in any particular period. So we can aggregate them as all autonomous expenditure A.

Thus:

GDP = Y = c*(1- t)*Y -m*Y + A

While I am not trying to test one’s ability to do algebra, and in that sense the answer can be worked out conceptually, to get the multiplier formula we re-arrange the previous equation as follows:

Y – c*(1-t)*Y + m*Y – A

Then collect the like terms and simplify:

Y[1- c*(1-t) + m] = A

So a change in A will generate a change in Y according to this formula:

Change in Y = k = 1/(1 – c*(1-t) + m)*Change in A

or if k = 1/(1 – c*(1-t) + m)

Change in Y = k*Change in A.

So in the question you have one equation (the multiplier) and one unknown (c). This is because of the 3 behaviorial parameters (c, t and m) two are known (t and m) and you also know the value of the left-hand side of the equation (1.5). So in effect you can solve for c:

k = 1/(1 – c*(1-t) + m)

Thus k*[1 – c*(1-t) + m] = 1

Thus k – c*k*(1-t) + k*m = 1

Thus k + k*m -1 = c*k*(1-t)

Thus c = (k + k*m – 1)/(k*(1-t))

Then you plug in the values of the knowns and the result is:

c = (1.6 + 0.32 – 1)/(1.6*0.8)

c = 0.92/1.28 = 0.71875

So the MPS (marginal propensity to save) = (1 – c) = approximately 28 cents.

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

• Spending multipliers
• Pushing the fantasy barrow
• Saturday Quiz – October 2, 2010 – answers and discussion

That is enough for today!

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