# Saturday Quiz – December 26, 2015 – 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:

A hallmark of the neo-liberal period has been the declining share of wages in national income which in part meant that economic growth became more dependent on credit to maintain growth in consumption spending. Increasing the wage share will require that real wages grow in the coming years.

A faster rate of real wages growth is not even a necessary condition much less a sufficient condition for a rising wage share.

Abstracting from the share of national income going to government, we can divide national income into the proportion going to workers (the “wage share”) and the proportion going to capital (the “profits share”). For the profit share to fall, the wage share has to rise (given the proportion going to government is relatively constant over time).

The wage share in nominal GDP is expressed as the total wage bill as a percentage of nominal GDP. Economists differentiate between nominal GDP (\$GDP), which is total output produced at market prices and real GDP (GDP), which is the actual physical equivalent of the nominal GDP. We will come back to that distinction soon.

To compute the wage share we need to consider total labour costs in production and the flow of production (\$GDP) each period.

Employment (L) is a stock and is measured in persons (averaged over some period like a month or a quarter or a year.

The wage bill is a flow and is the product of total employment (L) and the average wage (w) prevailing at any point in time. Stocks (L) become flows if it is multiplied by a flow variable (W). So the wage bill is the total labour costs in production per period.

So the wage bill = W.L

The wage share is just the total labour costs expressed as a proportion of \$GDP – (W.L)/\$GDP in nominal terms, usually expressed as a percentage. We can actually break this down further.

Labour productivity (LP) is the units of real GDP per person employed per period. Using the symbols already defined this can be written as:

LP = GDP/L

so it tells us what real output (GDP) each labour unit that is added to production produces on average.

We can also define another term that is regularly used in the media – the real wage – which is the purchasing power equivalent on the nominal wage that workers get paid each period. To compute the real wage we need to consider two variables: (a) the nominal wage (W) and the aggregate price level (P).

We might consider the aggregate price level to be measured by the consumer price index (CPI) although there are huge debates about that. But in a sense, this macroeconomic price level doesn’t exist but represents some abstract measure of the general movement in all prices in the economy.

Macroeconomics is hard to learn because it involves these abstract variables that are never observed – like the price level, like “the interest rate” etc. They are just stylisations of the general tendency of all the different prices and interest rates.

Now the nominal wage (W) – that is paid by employers to workers is determined in the labour market – by the contract of employment between the worker and the employer. The price level (P) is determined in the goods market – by the interaction of total supply of output and aggregate demand for that output although there are complex models of firm price setting that use cost-plus mark-up formulas with demand just determining volume sold. We shouldn’t get into those debates here.

The inflation rate is just the continuous growth in the price level (P). A once-off adjustment in the price level is not considered by economists to constitute inflation.

So the real wage (w) tells us what volume of real goods and services the nominal wage (W) will be able to command and is obviously influenced by the level of W and the price level. For a given W, the lower is P the greater the purchasing power of the nominal wage and so the higher is the real wage (w).

We write the real wage (w) as W/P. So if W = 10 and P = 1, then the real wage (w) = 10 meaning that the current wage will buy 10 units of real output. If P rose to 2 then w = 5, meaning the real wage was now cut by one-half.

So the proposition in the question – that nominal wages grow faster than inflation – tells us that the real wage is rising.

Nominal GDP (\$GDP) can be written as P.GDP, where the P values the real physical output.

Now if you put of these concepts together you get an interesting framework. To help you follow the logic here are the terms developed and be careful not to confuse \$GDP (nominal) with GDP (real):

• Wage share = (W.L)/\$GDP
• Nominal GDP: \$GDP = P.GDP
• Labour productivity: LP = GDP/L
• Real wage: w = W/P

By substituting the expression for Nominal GDP into the wage share measure we get:

Wage share = (W.L)/P.GDP

In this area of economics, we often look for alternative way to write this expression – it maintains the equivalence (that is, obeys all the rules of algebra) but presents the expression (in this case the wage share) in a different “view”.

So we can write as an equivalent:

Wage share – (W/P).(L/GDP)

Now if you note that (L/GDP) is the inverse (reciprocal) of the labour productivity term (GDP/L). We can use another rule of algebra (reversing the invert and multiply rule) to rewrite this expression again in a more interpretable fashion.

So an equivalent but more convenient measure of the wage share is:

Wage share = (W/P)/(GDP/L) – that is, the real wage (W/P) divided by labour productivity (GDP/L).

I won’t show this but I could also express this in growth terms such that if the growth in the real wage equals labour productivity growth the wage share is constant. The algebra is simple but we have done enough of that already.

That journey might have seemed difficult to non-economists (or those not well-versed in algebra) but it produces a very easy to understand formula for the wage share.

Two other points to note. The wage share is also equivalent to the real unit labour cost (RULC) measures that Treasuries and central banks use to describe trends in costs within the economy. Please read my blog – Saturday Quiz – May 15, 2010 – answers and discussion – for more discussion on this point.

Now it becomes obvious that if the nominal wage (W) grows faster than the price level (P) then the real wage is growing. But that doesn’t automatically lead to a growing wage share. So the blanket proposition stated in the question is false.

If the real wage is growing at the same rate as labour productivity, then both terms in the wage share ratio are equal and so the wage share is constant.

If the real wage is growing but labour productivity is growing faster, then the wage share will fall.

Only if the real wage is growing faster than labour productivity, will the wage share rise.

The wage share was constant for a long time during the Post Second World period and this constancy was so marked that Kaldor (the Cambridge economist) termed it one of the great “stylised” facts. So real wages grew in line with productivity growth which was the source of increasing living standards for workers.

The productivity growth provided the “room” in the distribution system for workers to enjoy a greater command over real production and thus higher living standards without threatening inflation.

Since the mid-1980s, the neo-liberal assault on workers’ rights (trade union attacks; deregulation; privatisation; persistently high unemployment) has seen this nexus between real wages and labour productivity growth broken. So while real wages have been stagnant or growing modestly, this growth has been dwarfed by labour productivity growth.

So the question is false because you have to consider labour productivity growth in addition to real wages growth before you can make conclusions about the movements in factor shares in national income.

The following blog may be of further interest to you:

Question 2:

In a stock-flow consistent macroeconomics, the sectoral balance stocks all sum to zero.

The sectoral balances relate to flows.

All expenditure aggregates – such as government spending, private consumption, private investment, exports (minus imports) 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:

Question 3:

A rising household saving ratio combined with an stable external deficit that is draining aggregate spending, doesn’t necessarily mean that the fiscal deficit has to rise to maintain current output growth.

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 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).

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).

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) + 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 fiscal 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 over-indebted 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:

1. Bill,

“The answer (Q2) is False. The sectoral balances relate to flows.”

I did have some problem with Q2. I understand that stocks are like water in the bath whereas flows are flows in and out of the bath. But stocks are, mathematically, just the integrals of all the flows from time = -∞ until now. Or, of course, the flows are just the differentials (wrt time) of the stocks. So it is quite possible, mathematically, for both the stocks and flows to sum to zero. So, yes, the sector balances refer to flows but is that sufficient reason for the answer to be false?

If we just consider a very simple example of the creation of a new currency in a closed economy – no exports or imports. Say every year the Government spent 100 units and Received Back 90 in taxation. The Govt deficit and the non Govt surplus in any particular year are both 10. But, the stocks accumulate and in the second year debts and assets are both 20, and in the third year they are both 30 etc. But they (if we convert all deficits/debts to negative surpluses/assets) still sum to zero.

Am I missing something here?

Best wishes for the New Year

PM

2. Steve says:

This is all valid analysis but not complete if the economy/productive system itself is cost inflationary by cost accounting convention (all costs must go into price) and the costs of depreciation as well as many other incidental costs that inevitably arise throughout the productive process are additional to total financing. Then the only way to not re-initiate and overcome this cost inflationary systemic nature, especially as innovation and AI increasingly destroy individual demand, is to supplement individual incomes with a direct payment not associated with employment which again, being an aspect of the system, will re-initiate its cost inflationary nature.

The fundamental trend of capitalism is upward as Minsky correctly observed. In a profit making system this applies to the intersections of intent to succeed, perception of abundant demand and price. Thus prices will inevitably tend to inflate, regardless of competition….or lack thereof. This is why a macro-economic policy of a retail discount to prices by merchants (which is reciprocally rebated back to retail merchants by an independent governmental monetary agency) would be necessary to eliminate any inflation…and if we’re really smart, create price deflation thus reversing the trend of Financial domination of the individual and every other business model in the economy with a trend toward the monetary empowerment of the individual and the lifting of an unnecessary and oppressive onerousness for every other business model save finance.

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