# The Weekend Quiz – September 26-27, 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.

**Question 1:**

Imagine we forecast real GDP growth for a nation to grow by 0.8 per cent in 2021 and 1.1 per cent in 2022. We also predict that the unemployment rate would fall from 11.7 per cent in 2021 to 11.4 per cent in 2022. Additionally, average annual growth in labour productivity has been running at just over 1 per cent per annum (GDP per hours worked). If average weekly hours worked remains constant over 2022, then the implication of our forecasts is that we think the labour force of this nation in 2022 will:

(a) grow by 0.2 per cent

(b) shrink by 0.2 per cent

(c) grow by 0.1 per cent

(d) shrink by 0.1 per cent

The answer is **Option (b) shrink by 0.2 per cent**.

The facts were:

- Real GDP growth projection for 2022 is 1.1 per cent compared to 0.8 per cent in 2021. The 2021 data is largely irrelevant for what will happen in 2021.
- Labour productivity growth (that is, growth in real output per person employed) to be 1.0 per cent per annum. So as this grows less employment is required per unit of output.
- The average working week is 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 unemployment rate falls from 11.7 per cent in 2021 to 11.4 per cent in 2022 – that is, 0.3 percentage points.

We need a method of relating the projections of real GDP growth into labour market outcomes. 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.

There is some algebra we could use to show this but a simple story will suffice to get to the point we want.

Arthur Okun originally said that when the US real GDP fell by 3 percentage points in relation to its trend rate, the unemployment rate would rise by 1 percentage point. On the other hand, if real GDP grew by 3 percentage points, then the unemployment rate would fall by 1 percentage point.

The question then is what determines that outcome.

Clearly, real output is the product of how many workers are employed, the hours they work per period and how productive each worker hour is.

So if a worker produces 10 units of output per hour worked and works for 40 hours per week, he/she will produce 400 units of real output. Multiply that up to the economy level and we can calculate real GDP.

So when real GDP is rising it is likely the there will be growth in the labour force (number of people willing to work), hour worked per person, and/or labout productivity (output per hour worked).

In fact, Okun estimated that when real GDP rose by 3 percentage points relative to trend, there would be a 0.5 percentage point increase in labour force participation, 0.5 percentage point increase in hours worked per person, and a 1 per cent increase in labour productivity. The difference was the decline in the unemployment rate (or the rise in the employment rate).

This observation led economists (who derived the relationship using algebra) to come up with an approximate ‘rule of thumb’ for assessing how much the unemployment rate will change when real GDP changes.

The rule of thumb relates the growth in output to the labour-force and labour productivity growth rates.

The approximate rule of thumb is as follows: 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 labour 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, we know that the change in the unemployment rate is expected to be -0.3 percentage points.

We know that the difference between forecast real GDP growth (1.1 per cent) and labour productivity growth (1 per cent) is 0.1 percentage points. So if the labour force was constant then the unemployment rate would fall by 0.1 percentage points over the next year.

For the unemployment rate to fall by -0.3 percentage points then the actual real GDP growth rate must be 0.3 percentage points higher than the required real GDP growth (which is the sum of the labour productivity and labour force growth).

That means that the forecasted labour force must be shrinking by -0.2 percentage points over 2022 for the forecasts to be consistent.

So while the 1 per cent labour productivity growth is reducing the need for jobs and pushing up unemployent, the contraction in the labour force more than offsets that given the real GDP growth. As a consequence, the unemployment rate would fall.

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

**Question 2:**

If the stock of aggregate demand growth outstrips the capacity of the productive sector to respond by producing extra real goods and services then inflation is inevitable.

The answer is **False**.

Spending definitely equals income and too much spending relative to the real capacity of the economy to absorb it will create inflation. But those facts do not relate to the point of the question, which is, in fact, a very easy test of the difference between flows and stocks.

All expenditure aggregates – such as government spending and investment spending are flows. They add up to total expenditure or aggregate demand which is also a flow rather than a stock. Aggregate demand (a flow) in any period and it jointly determines the flow of income and output in the same period (that is, GDP) (in partnership with aggregate supply).

So while flows can add to stock – for example, the flow of saving adds to wealth or the flow of investment adds to the stock of capital – flows can also be added together to form a “larger” flow.

For example, if you wanted to work out annual GDP from the quarterly national accounts you would **sum** the individual quarterly observations for the 12-month period of interest. Conversely, employment is a stock so if you wanted to create an annual employment time series you would **average** the individual quarterly observations for the 12-month period of interest.

The question thus tests the precision of language as they relate to economic concepts. Too often the language is loose and the concepts become confused as a result.

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

**Question 3:**

National accounting shows us that a government surplus equals a non-government deficit. If a government is successful in achieving a fiscal surplus then the private domestic sector will ultimately become more indebted as a consequence, which means that austerity amounts to swapping public for private debt.

The answer is **False**.

The use of the word ‘ultimately’ was to lead you astray and get you thinking about running down savings rather than entering into new debt contracts. That is, the private domestic sector can, for a time, fund their deficits by using prior saving or selling assets. Eventually, it must borrow to continue running deficits as a sector.

But the real point of the question is to highlight the fact that the non-government sector is not equivalent to the private domestic sector in the sectoral balance framework. We have to include the impact of the external sector.

To refresh your memory the sectoral 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:

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 taxes and 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 taxes and transfers (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) + CAB

which is interpreted as meaning that government sector deficits (G – T > 0) and current account surpluses (CAB > 0) generate national income and net financial assets for the private domestic sector.

Conversely, government surpluses (G – T < 0) and current account deficits (CAB < 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) – CAB] = (G – T)

where the term on the left-hand side [(S – I) – CAB] 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.

The following table shows a 8-period sequence where for the first four years the nation is running an external deficit (2 per cent of GDP) and for the last four year the external sector is in surplus (2 per cent of GDP).

Sectoral Balance | Period 1 | Period 2 | Period 3 | Period 4 | Period 5 | Period 6 | Period 7 | Period 8 |

External Balance (X – M) | -2 | -2 | -2 | -2 | 2 | 2 | 2 | 2 |

Fiscal Balance (G – T) | 4 | 3 | 1 | 0 | 0 | -1 | -3 | -4 |

Private Domestic Balance (S – I) | 2 | 1 | -1 | -2 | 2 | 1 | -1 | -2 |

For the question to be true we should never see the government surplus (G – T < 0) and the private domestic surplus (S – I > 0) simultaneously occurring.

You see that in the first four periods that coincidence never occurs.

Period 1: External deficit (2), public deficit (4), private domestic surplus (2).

Period 2: External deficit (2), public deficit (3), private domestic surplus (1).

Period 3: External deficit (2), public deficit (1), private domestic deficit (1).

Period 4: External deficit (2), public balance (0), private domestic deficit (2).

Period 5: External surplus (2), public balance (0), private domestic surplus (2).

Period 6: External surplus (2), public surplus (1), private domestic surplus (1) – condition holds.

Period 7: External surplus (2), public surplus (3), private domestic deficit (1).

Period 8: External surplus (2), public surplus (4), private domestic deficit (2).

Which tells you that when there is an external deficit (X – M < 0) the private domestic sector and government sector **cannot** simultaneously run surpluses, no matter how hard they might try. The income adjustments will always force one or both of the sectors into deficit.

The sum of the private domestic surplus and government surplus has to equal the external surplus. So that condition defines the situations when the private domestic sector and the government sector can simultaneously pay back debt.

It is only in Period 6 that we see the condition satisfied.

That is because the private and government balances (both surpluses) exactly equal the external surplus.

So if the government was able to pursue an austerity program with a burgeoning external sector then the private domestic sector would be able to save overall and reduce its debt levels. The reality is that this situation is unlikely to occur when all governments are pursuing austerity because the widespread contraction in spending undermines import spending and hence export income.

So what is the economics that underpin these different situations?

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 external deficit also means that foreigners are increasing financial claims denominated in the local currency. Given that exports represent a real cost and imports a real benefit, the motivation for a nation running a net exports surplus (the exporting nation in this case) must be to accumulate financial claims (assets) denominated in the currency of the nation running the external deficit.

A fiscal surplus also means the government is spending less than it is “earning” and that puts a drag on aggregate demand and constrains the ability of the economy to grow.

In these circumstances, for income to be stable, the private domestic sector has to spend more than they earn.

You can see this by going back to the aggregate demand relations above. For those who like simple algebra we can manipulate the aggregate demand model to see this more clearly.

Y = GDP = C + I + G + (X – M)

which says that the total national income (Y or GDP) is the sum of total final consumption spending (C), total private investment (I), total government spending (G) and net exports (X – M).

So if the G is spending less than it is “earning” and the external sector is adding less income (X) than it is absorbing spending (M), then the other spending components must be greater than total income.

Only when the government fiscal deficit supports aggregate demand at income levels which permit the private sector to save out of that income will the latter achieve its desired outcome. At this point, income and employment growth are maximised and private debt levels will be stable.

The following blog posts 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!

That is enough for today!

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