# The Weekend Quiz – September 29-30, 2018 – 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:**

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

The answer is **False**.

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 fiscal balance you would be leaving an essential component of the private domestic balance out – private capital formation (investment).

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.

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 fiscal 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 deficit has to be large enough to offset the current account deficit.

Say, (X – M) = -20 (as above). Then a balanced fiscal position (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 fiscal 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.

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:**

If an economy is projected to grow in real terms by around 2.1 per cent over the next 12 months. 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 over the period. 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 period 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.

The following blogs may be of further interest to you:

- US opinion polls expose mainstream economic theory
- What if economists were personally liable for their advice
- What do the IMF growth projections mean?

**Question 3:**

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 spending 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

The answer is **$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.

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

That is enough for today!

(c) Copyright 2018 William Mitchell. All Rights Reserved.

Ahh, the tax rate is built into the expenditure multiplier already….now I get it…so the multiplier takes account of the leakages to tax imports and savings already. Now I get it! Love these quizes.

Thanks Bill

I got q2 correct but with your explanation i see how hours worked could be an important factor, which is something i missed.

Prof

I hope you are enjoying the conference? – I am, even though the camera work is slightly off the mark.

This is just a thought without much substance behind it at this time: but what about a crowd funded club, a foundation, or an incorporated (not for profit business) that should try to go institutional status. Or something around those lines.

That way you will demonstrate to any potential partner (University(s)) that you mean business and are in it for the long haul. Set up as a properly administered business with formal accounting it should give the members the benefit of being part of such an August group. And you four of Stephanie, Warren and Randy plus numerous other already have a substantial following, so properly marketed I can see it working very well for you.

You already have a perfect marketer: Steve Grumbine. With his unbridled enthusiasm, get up and go – MMT could not go wrong.

Finally ask for volunteers – I am sure there are heaps of followers out there who would like to get involved.