Saturday Quiz – July 30, 2011 – answers and discussion

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:

For the US private sector to reduce its overall overall debt levels, the government must run a deficit.

The answer is True.

This question requires an understanding of the sectoral balances that can be derived from the National Accounts. But it also requires some understanding of the behavioural relationships within and between these sectors which generate the outcomes that are captured in the National Accounts and summarised by the sectoral balances.

The first fact that is assumed by the question is that the US external sector is in deficit and will remain that way for the foreseeable future. If the external sector was in surplus then the answer may be different (depending on the relative size of the budget and the external balance).

Refreshing the balances (again) – we know that from an accounting sense, if the external sector overall is in deficit, then 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 accounting rules.

The important point is to understand what behaviour and economic adjustments drive these outcomes.

So here is the accounting (again). 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).

From the uses perspective, national income (GDP) can be used for:

GDP = C + S + T

which says that GDP (income) ultimately comes back to households who consume (C), save (S) or pay taxes (T) with it once all the distributions are made.

Equating these two perspectives we get:

C + S + T = GDP = C + I + G + (X – M)

So after simplification (but obeying the equation) we get the sectoral balances view of the national accounts.

(I – S) + (G – T) + (X – M) = 0

That is the three balances have to sum to zero. The sectoral balances derived are:

• The private domestic balance (I – S) – positive if in deficit, negative if in surplus.
• The Budget Deficit (G – T) – negative if in surplus, positive if in deficit.
• The Current Account balance (X – M) – positive if in surplus, negative if in deficit.

These balances are usually expressed as a per cent of GDP but that doesn’t alter the accounting rules that they sum to zero, it just means the balance to GDP ratios sum to zero.

A simplification is to add (I – S) + (X – M) and call it the non-government sector. Then you get the basic result that the government balance equals exactly $-for-$ (absolutely or 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 and has to apply at all times.

So what economic behaviour might lead to the outcome specified in the question?

If the nation is running an external deficit it means that the contribution to aggregate demand from the external sector is negative – that is net drain of spending – dragging output down. The reference to a “small” external deficit was to place doubt in your mind. In fact, it doesn’t matter how large the external deficit is for this question.

Assume, now that the private domestic sector (households and firms) seeks to reduce its overall debt holdings. That requires it to save overall – spend less than it is earning as a sector. Consistent with this aspiration, households may cut back on consumption spending and save more out of disposable income. The immediate impact is that aggregate demand will fall and inventories will start to increase beyond the desired level of the firms.

The firms will soon react to the increased inventory holding costs and will start to cut back production. How quickly this happens depends on a number of factors including the pace and magnitude of the initial demand contraction. But if the households persist in trying to save more and consumption continues to lag, then soon enough the economy starts to contract – output, employment and income all fall.

The initial contraction in consumption multiplies through the expenditure system as workers who are laid off also lose income and their spending declines. This leads to further contractions.

The declining income leads to a number of consequences. Net exports improve as imports fall (less income) but the question clearly assumes that the external sector remains in deficit. Total saving actually starts to decline as income falls as does induced consumption.

So the initial discretionary decline in consumption is supplemented by the induced consumption falls driven by the multiplier process.

The decline in income then stifles firms’ investment plans – they become pessimistic of the chances of realising the output derived from augmented capacity and so aggregate demand plunges further. Both these effects push the private domestic balance further towards and eventually into surplus

With the economy in decline, tax revenue falls and welfare payments rise which push the public budget balance towards and eventually into deficit via the automatic stabilisers.

If the private sector persists in trying to increase its saving ratio then the contracting income will clearly push the budget into deficit.

So we would have an external deficit, a private domestic surplus and a budget deficit.

The general point is that the government would be far better supporting this saving strategy by running a discretionary deficit and ensuring income and employment levels are high.

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!

Question 2:

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 budget 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 budget 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 budget 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 blogs will help you understand this if you are new to my blog – Deficit spending 101 – Part 1 – Deficit spending 101 – Part 2 – Deficit spending 101 – Part 3.

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 blogs 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 3:

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 blogs 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 4:

The US Federal Reserve could easily directly purchase Treasury debt to facilitate the US Government’s budget deficit with compromising its monetary policy settings because its short-term policy rate is already near zero.

The answer is False.

The Federal Reserve could easily directly purchase Treasury debt to facilitate the US Government’s budget deficit but not because its short-term policy rate is already so low.

They could also do the same with higher positive policy rates by ensuring they offer a support rate on the excess reserves.

So what is the explanation?

The central bank conducts what are called liquidity management operations for two reasons. First, it has to ensure that all private cheques (that are funded) clear and other interbank transactions occur smoothly as part of its role of maintaining financial stability. Second, it must maintain aggregate bank reserves at a level that is consistent with its target policy setting given the relationship between the two.

So operating factors link the level of reserves to the monetary policy setting under certain circumstances. These circumstances require that the return on “excess” reserves held by the banks is below the monetary policy target rate. In addition to setting a lending rate (discount rate), the central bank also sets a support rate which is paid on commercial bank reserves held by the central bank.

Commercial banks maintain accounts with the central bank which permit reserves to be managed and also the clearing system to operate smoothly. In addition to setting a lending rate (discount rate), the central bank also can set a support rate which is paid on commercial bank reserves held by the central bank (which might be zero).

Many countries (such as Australia, Canada and zones such as the European Monetary Union) maintain a default return on surplus reserve accounts (for example, the Reserve Bank of Australia pays a default return equal to 25 basis points less than the overnight rate on surplus Exchange Settlement accounts). Other countries like Japan and the US have typically not offered a return on reserves until the onset of the current crisis.

If the support rate is zero then persistent excess liquidity in the cash system (excess reserves) will instigate dynamic forces which would drive the short-term interest rate to zero unless the government sells bonds (or raises taxes). This support rate becomes the interest-rate floor for the economy.

The short-run or operational target interest rate, which represents the current monetary policy stance, is set by the central bank between the discount and support rate. This effectively creates a corridor or a spread within which the short-term interest rates can fluctuate with liquidity variability. It is this spread that the central bank manages in its daily operations.

In most nations, commercial banks by law have to maintain positive reserve balances at the central bank, accumulated over some specified period. At the end of each day commercial banks have to appraise the status of their reserve accounts. Those that are in deficit can borrow the required funds from the central bank at the discount rate.

Alternatively banks with excess reserves are faced with earning the support rate which is below the current market rate of interest on overnight funds if they do nothing. Clearly it is profitable for banks with excess funds to lend to banks with deficits at market rates. Competition between banks with excess reserves for custom puts downward pressure on the short-term interest rate (overnight funds rate) and depending on the state of overall liquidity may drive the interbank rate down below the operational target interest rate. When the system is in surplus overall this competition would drive the rate down to the support rate.

The main instrument of this liquidity management is through open market operations, that is, buying and selling government debt. When the competitive pressures in the overnight funds market drives the interbank rate below the desired target rate, the central bank drains liquidity by selling government debt. This open market intervention therefore will result in a higher value for the overnight rate. Importantly, we characterise the debt-issuance as a monetary policy operation designed to provide interest-rate maintenance. This is in stark contrast to orthodox theory which asserts that debt-issuance is an aspect of fiscal policy and is required to finance deficit spending.

So the fundamental principles that arise in a fiat monetary system are as follows.

• The central bank sets the short-term interest rate based on its policy aspirations.
• Government spending is independent of borrowing which the latter best thought of as coming after spending.
• Government spending provides the net financial assets (bank reserves) which ultimately represent the funds used by the non-government agents to purchase the debt.
• Budget deficits put downward pressure on interest rates contrary to the myths that appear in macroeconomic textbooks about ‘crowding out’.
• The “penalty for not borrowing” is that the interest rate will fall to the bottom of the “corridor” prevailing in the country which may be zero if the central bank does not offer a return on reserves.
• Government debt-issuance is a “monetary policy” operation rather than being intrinsic to fiscal policy, although in a modern monetary paradigm the distinctions between monetary and fiscal policy as traditionally defined are moot.

Accordingly, debt is issued as an interest-maintenance strategy by the central bank. It has no correspondence with any need to fund government spending. Debt might also be issued if the government wants the private sector to have less purchasing power.

Further, the idea that governments would simply get the central bank to “monetise” treasury debt (which is seen orthodox economists as the alternative “financing” method for government spending) is highly misleading. Debt monetisation is usually referred to as a process whereby the central bank buys government bonds directly from the treasury.

In other words, the federal government borrows money from the central bank rather than the public. Debt monetisation is the process usually implied when a government is said to be printing money. Debt monetisation, all else equal, is said to increase the money supply and can lead to severe inflation.

However, as long as the central bank has a mandate to maintain a target short-term interest rate, the size of its purchases and sales of government debt are not discretionary. Once the central bank sets a short-term interest rate target, its portfolio of government securities changes only because of the transactions that are required to support the target interest rate.

The central bank’s lack of control over the quantity of reserves underscores the impossibility of debt monetisation. The central bank is unable to monetise the federal debt by purchasing government securities at will because to do so would cause the short-term target rate to fall to zero or to the support rate. If the central bank purchased securities directly from the treasury and the treasury then spent the money, its expenditures would be excess reserves in the banking system. The central bank would be forced to sell an equal amount of securities to support the target interest rate.

The central bank would act only as an intermediary. The central bank would be buying securities from the treasury and selling them to the public. No monetisation would occur.

However, the central bank may agree to pay the short-term interest rate to banks who hold excess overnight reserves. This would eliminate the need by the commercial banks to access the interbank market to get rid of any excess reserves and would allow the central bank to maintain its target interest rate without issuing debt.

The following blogs may be of further interest to you:

• The consolidated government – treasury and central bank
• Saturday Quiz – May 1, 2010 – answers and discussion
• Understanding central bank operations
• Building bank reserves will not expand credit
• Building bank reserves is not inflationary
• Deficit spending 101 – Part 1
• Deficit spending 101 – Part 2
• Deficit spending 101 – Part 3

Question 5 Premium:

Premium Question: 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. They also estimate that the import propensity is 0.2 (meaning that 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 blogs for more information:

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