# Saturday Quiz – October 13, 2012 – 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:

In the wake of a rising household saving ratio, a nation with an external deficit will move towards recession unless government net spending increases.

This question tests one’s basic understanding of the sectoral balances that can be derived from the National Accounts. The secret to getting the correct answer is to realise that the household saving ratio is not the overall sectoral balance for the private domestic sector.

In other words, if you just compared the household saving ratio with the external deficit and the budget balance you would be leaving an essential component of the private domestic balance out – private capital formation (investment).

To understand that, in macroeconomics we have a way of looking at the national accounts (the expenditure and income data) which allows us to highlight the various sectors – the government sector and the non-government sector (and the important sub-sectors within the non-government sector).

So we start by focusing on the final expenditure components of consumption (C), investment (I), government spending (G), and net exports (exports minus imports) (NX).

The basic aggregate demand equation in terms of the sources of spending is:

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).

In terms of the uses that national income (GDP) can be put too, we say:

GDP = C + S + T

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

So if we equate these two ideas sources of GDP and uses of GDP, we get:

C + S + T = C + I + G + (X – M)

Which we then can simplify by cancelling out the C from both sides and re-arranging (shifting things around but still satisfying the rules of algebra) into what we call the sectoral balances view of the national accounts.

There are three sectoral balances derived – the Budget Deficit (G – T), the Current Account balance (X – M) and the private domestic balance (S – I).

These balances are usually expressed as a per cent of GDP but we just keep them in \$ values here:

(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.

You can then manipulate these balances to tell stories about what is going on in a country.

For example, when an external deficit (X – M < 0) and a public surplus (G – T < 0) coincide, there must be a private deficit. So if X = 10 and M = 20, X - M = -10 (a current account deficit). Also if G = 20 and T = 30, G - T = -10 (a budget surplus). So the right-hand side of the sectoral balances equation will equal (20 - 30) + (10 - 20) = -20. As a matter of accounting then (S - I) = -20 which means that the domestic private sector is spending more than they are earning because I > S by 20 (whatever \$ units we like). So the fiscal drag from the public sector is coinciding with an influx of net savings from the external sector. While private spending can persist for a time under these conditions using the net savings of the external sector, the private sector becomes increasingly indebted in the process. It is an unsustainable growth path.

So if a nation usually has a current account deficit (X – M < 0) then if the private domestic sector is to net save (S - I) > 0, then the public budget deficit has to be large enough to offset the current account deficit. Say, (X – M) = -20 (as above). Then a balanced budget (G – T = 0) will force the domestic private sector to spend more than they are earning (S – I) = -20. But a government deficit of 25 (for example, G = 55 and T = 30) will give a right-hand solution of (55 – 30) + (10 – 20) = 15. The domestic private sector can net save.

So by only focusing on the household saving ratio in the question, I was only referring to one component of the private domestic balance. Clearly in the case of the question, if private investment is strong enough to offset the household desire to increase saving (and withdraw from consumption) then no spending gap arises.

In the present situation in most countries, households have reduced the growth in consumption (as they have tried to repair overindebted balance sheets) at the same time that private investment has fallen dramatically.

As a consequence a major spending gap emerged that could only be filled in the short- to medium-term by government deficits if output growth was to remain intact. The reality is that the budget deficits were not large enough and so income adjustments (negative) occurred and this brought the sectoral balances in line at lower levels of economic activity.

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Question 2:

The IMF recently downgraded their real GDP growth estimates. The US economy is now projected to grow in real terms by around 2.1 per cent in 2013. Real GDP per employed person is estimated to grow by 1.1 per cent over the same period and there is also the expectation that average weekly hours worked will remain more or less constant in 2013. Which of the following labour force growth rates would provide the basis for an expectation that the unemployment rate will be lower at the end of 2013 than at the beginning?

(a) 3.1 per cent

(b) 2.1 per cent

(c) 0.9 per cent

(d) Cannot tell because we don’t know what the participation rate is likely to be.

The answer is Option (c) 0.9 per cent.

The facts were:

• Real GDP growth is projected to grow at 2.1 per cent in 2013
• Labour productivity growth (that is, growth in real output per person employed) is expected to grow at 1.1 per cent in 2013. So as this grows less employment in required per unit of output.
• The average working week is expected to be 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.

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.

Take the following output accounting statement:

(1) Y = LP*(1-UR)LH

where Y is real GDP, LP is labour productivity in persons (that is, real output per unit of labour), H is the average number of hours worked per period, UR is the aggregate unemployment rate, and L is the labour-force. So (1-UR) is the employment rate, by definition.

Equation (1) just tells us the obvious – that total output produced in a period is equal to total labour input [(1-UR)LH] times the amount of output each unit of labour input produces (LP).

Using some simple calculus you can convert Equation (1) into an approximate dynamic equation expressing percentage growth rates, which in turn, provides a simple benchmark to estimate, for given labour-force and labour productivity growth rates, the increase in output required to achieve a desired unemployment rate.

Accordingly, with small letters indicating percentage growth rates and assuming that the average number of hours worked per period is more or less constant, we get:

(2) y = lp + (1 – ur) + lf

Re-arranging Equation (2) to express it in a way that allows us to achieve our aim (re-arranging just means taking and adding things to both sides of the equation):

(3) ur = 1 + lp + lf – y

Equation (3) provides the approximate rule of thumb – 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.

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 2.1 per cent which means that the sum of labour productivity growth and labour force growth has to be less than 2.1 per cent in 2011 for the unemployment rate to fall.

So the correct answer is that if the labour force grew by 0.9 per cent in 2013, there would be a small decrease in the unemployment rate over the course of that year.

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Question 3:

EMU member nations would eliminate their exposure to solvency risk if they exited the Eurozone and re-established their currency sovereignty – that is, issued their own floating currency.

The answer would be true if the sentence had added – “and only issues debt in its own currency”.

A national government that issues its own floating currency can always service its debts so long as these are denominated in domestic currency.

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.

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Question 4:

Economists use two multipliers to estimate the impact on GDP of an expansion in government spending associated with rising tax rates. The spending multiplier indicates the extent to which GDP rises as a result of the extra aggregate demand arising from the increased government spending. The tax multiplier indicates the impact of rising tax rates on GDP as labour supply is reduced because of the disincentives associated with taxation. The net effect on GDP is the sum of these two impacts.

Mainstream economics analysis does posit that rising marginal tax rates distort the labour supply choice – by increasing the hourly cost of work and providing greater incenctives for workers to choose more leisure. This allegation forms the basis of their case for substantial tax cuts and proportional tax systems; and, as a consequence, reduced budget deficits.

As an aside there is no empirical evidence to support this claim. Most of the credible studies find very little evidence of a negative tax elasticity within normal ranges that these variables shift. The most significant tax effect is found at the intersection of the welfare system and the wage system where workers who work an extra hour while on benefits often face 100 per cent marginal taxes (loss of benefit equal to earnings). But that is another story again.

However, in terms of this question, the trick was in understanding what the tax multiplier is trying to conceptualise.

First, it is a macroeconomic rather than a microeconomic concept. Households are assumed to pay some tax out of gross income and the tax rate (keeping it simple) specifies that proportion. In reality, there are a myriad of tax rates but the total effect can be summarised by a single (weighted-average!) tax rate.

Households consume out of disposable income. Assume the overall propensity to consume is 0.80 – which means that overall consumers will spend 80 cents for every extra dollar of disposable income received.

So, if the tax rate rises, then disposable income falls. If nothing else changes, then this fall in disposable income will lead to a reduction in consumption (equal to the propensity to consume times the fall in disposable income). The resulting fall in GDP is defined as the tax multiplier.

Similarly, when tax rates falls and increase disposable income, the reverse occurs.

You should not confuse the hypothesised tax multiplier effect with the increase in tax revenue that occurs as a result of the automatic stabilisers. This effect occurs with no discretionary change in the tax regime. It is a common mistake to assume that because tax revenue is rising that tax policy is becoming contractionary.

Further, at the individual level, as GDP growth recovers most people will not be paying higher taxes at all while others will be paying a substantial increase – why? Because they move from unemployment (zero taxes paid) to earning an income (some taxes paid).

The IMF recently admitted they had made serious errors in their modelling and grossly underestimated the size of spending multipliers. Economists use two multipliers to estimate the impact on GDP of an expansion in government spending associated with rising tax rates. The spending multiplier indicates the extent to which GDP rises as a result of the extra aggregate demand arising from the increased government spending. The tax multiplier indicates the impact of rising tax rates on GDP as labour supply is reduced because of the disincentives associated with taxation. The net effect on GDP is the sum of these two impacts. Assume that the government increases spending by \$100 billion at the start of each year and maintains this policy for the next three years from now. Economists estimate the spending multiplier to be 1.5 and the impact is exhausted within each year (all induced consumption is completed within 12 months). The tax multiplier is estimated to be equal to 1 and the current tax rate is equal to 30 per cent (so tax revenue rises by 30 cents for every extra dollar of GDP produced ). What is the cumulative impact of this fiscal expansion on GDP after three years?

(a) \$135 billion

(b) \$150 billion

(c) \$315 billion

(d) \$450 billion

In Year 1, government spending rises by \$100 billion, which leads to a total increase in GDP of \$150 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 \$450 billion.

It is true that total tax revenue rises by \$135 billion 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 \$135 billion from the \$450 billion to get answer (c) 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.

Some might have just computed \$135 billion and said (a). Clearly, not correct.

Some might have thought it was a total injection of \$100 billion and multiplied that by 1.5 to get answer (b). Clearly, not correct.