Saturday Quiz – September 20, 2014 – 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:

This week the OECD revised its real GDP growth forecasts for the Euro area and now expects it to grow by 0.8 per cent in 2014 and 1.1 per cent in 2015. They also predicted that the Euro area unemployment rate would fall from 11.7 per cent in 2014 to 11.4 per cent in 2015. Additionally, they suggested that average annual growth in labour productivity was running at just over 1 per cent per annum (GDP per hours worked). If average weekly hours worked remains constant over 2015, then the implication of the OECD forecasts is that they think the Euro area labour force 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 2015 1.1 per cent compared to 0.8 per cent in 2014. The 2014 data is largely irrelevant for what will happen in 2015.
• Labour productivity growth (that is, growth in real output per person employed) to be 1 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 2014 to 11.4 per cent in 2015 – 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 2015 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 blogs may be of further interest to you:

• What do the IMF growth projections mean?
• US Federal Reserve chairman loses his independence

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 may be of further interest to you:

• Stock-flow consistent macro models

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 become more indebted as a consequence which means that austerity amounts to swapping public for private debt.

The answer is False.

The point is 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.

So this is a question about the sectoral balances – the government fiscal balance, the external balance and the private domestic balance – that have to always add to zero because they are derived as an accounting identity from the national accounts. The balances reflect the underlying economic behaviour in each sector which is interdependent – given this is a macroeconomic system we are considering.

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:

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.

You can also write this as:

(S – I) + (T – G) = (X – M)

Which gives an easier interpretation (especially in relation to this question).

The sectoral balances derived are:

• The private domestic balance (S – I) – positive if in surplus, negative if in deficit.
• The fiscal balance (T – G) – positive if in surplus, negative 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.

Using this version of the sectoral balance framework:

(S – I) + (T – G) = (X – M)

So the domestic balance (left-hand side) – which is the sum of the private domestic sector and the government sector equals the external balance.

For the left-hand side of the equation to be positive (that is, in surplus overall) and the individual sectoral components to be in surplus overall, the right-hand side has to be positive (that is, an external surplus) and of sufficient magnitude.

This is also a basic rule derived from the national accounts and has to apply at all times.

The following graph and accompanying 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).

For the question to be true we should never see the government surplus (T – G > 0) and the private domestic surplus (S – I > 0) simultaneously occurring – which in the terms of the graph will be the green and navy bars being above the zero line together.

You see that in the first four periods that never occurs which tells you that when there is an external deficit (X – M < 0) the private domestic and government sectors 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 5 that we see the condition satisfied (see red circle).

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.

Going back to the sequence, if the private domestic sector tried to push for higher saving overall (say in Period 6), national income would fall (because overall spending fell) and the government surplus would vanish as the automatic stabilisers responded with lower tax revenue and higher welfare payments.

Periods 7 and 8 show what happens when the private domestic sector runs deficits with an external surplus. The combination of the external surplus and the private domestic deficit adding to demand drives the automatic stabilisers to push the government fiscal balance into further surplus as economic activity is high. But this growth scenario is unsustainable because it implies an increasing level of indebtedness overall for the private domestic sector which has finite limits. Eventually, that sector will seek to stabilise its balance sheet (which means households and firms will start to save overall). That would reduce domestic income and the fiscal balance would move back into deficit (or a smaller surplus) depending on the size of the external surplus.

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 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!