The Weekend Quiz – February 8-9, 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:

For workers to get a rising share of national income their nominal wages have to grow faster than inflation.

The answer is False.

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:


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 post – 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.

Question 2:

Modern Monetary Theory implies that higher levels of taxation are not necessary for the government to spend more in real terms.

The answer is False.

Modern Monetary Theory (MMT) shows that taxpayers do fund anything and sovereign governments are never revenue-constrained because they are the monopoly issuers of the currency in use. Therefore, the government can spend whatever it likes irrespective of the level of taxation. Therefore if you didn’t really think beyond that you would conclude that the answer was True. And you would be wrong.

That logic while correct for the most part ignores the underlying role of taxation.

In a fiat monetary system the currency has no intrinsic worth. Further the government has no intrinsic financial constraint. Once we realise that government spending is not revenue-constrained then we have to analyse the functions of taxation in a different light. The starting point of this new understanding is that taxation functions to promote offers from private individuals to government of goods and services in return for the necessary funds to extinguish the tax liabilities.

In this way, it is clear that the imposition of taxes creates unemployment (people seeking paid work) in the non-government sector and allows a transfer of real goods and services from the non-government to the government sector, which in turn, facilitates the government’s economic and social program.

The crucial point is that the funds necessary to pay the tax liabilities are provided to the non-government sector by government spending. Accordingly, government spending provides the paid work which eliminates the unemployment created by the taxes.

This train of logic also explains why mass unemployment arises. It is the introduction of State Money (government taxing and spending) into a non-monetary economics that raises the spectre of involuntary unemployment. For aggregate output to be sold, total spending must equal total income (whether actual income generated in production is fully spent or not each period). Involuntary unemployment is idle labour offered for sale with no buyers at current prices (wages).

Unemployment occurs when the private sector, in aggregate, desires to earn the monetary unit of account, but doesn’t desire to spend all it earns, other things equal. As a result, involuntary inventory accumulation among sellers of goods and services translates into decreased output and employment. In this situation, nominal (or real) wage cuts per se do not clear the labour market, unless those cuts somehow eliminate the private sector desire to net save, and thereby increase spending.

The purpose of State Money is for the government to move real resources from private to public domain. It does so by first levying a tax, which creates a notional demand for its currency of issue. To obtain funds needed to pay taxes and net save, non-government agents offer real goods and services for sale in exchange for the needed units of the currency. This includes, of-course, the offer of labour by the unemployed. The obvious conclusion is that unemployment occurs when net government spending is too low to accommodate the need to pay taxes and the desire to net save.

This analysis also sets the limits on government spending. It is clear that government spending has to be sufficient to allow taxes to be paid. In addition, net government spending is required to meet the private desire to save (accumulate net financial assets). From the previous paragraph it is also clear that if the Government doesn’t spend enough to cover taxes and desire to save the manifestation of this deficiency will be unemployment.

Keynesians have used the term demand-deficient unemployment. In our conception, the basis of this deficiency is at all times inadequate net government spending, given the private spending decisions in force at any particular time.

Accordingly, the concept of fiscal sustainability does not entertain notions that the continuous deficits required to finance non-government net saving desires in the currency of issue will ultimately require high taxes. Taxes in the future might be higher or lower or unchanged. These movements have nothing to do with “funding” government spending.

To understand how taxes are used to attenuate demand please read this blog post – Functional finance and Modern Monetary Theory.

So to make the point clear – the taxes do not fund the spending. But they do free up space for the spending to occur in a non-inflationary environment.

You might say that the answer is only false when the economy is at full employment where there are no free resources.

In that context, taxation has to take those resources off the non-government sector in order for the government to spend more. That is a true statement.

But it doesn’t negate the overall falsity of the main proposition.

Further, you might say that governments can spend whenever they like. That is also true but if it just kept spending the growth in nominal demand would outstrip real capacity and inflation would certainly result.

So in that regard, this would not be a sensible strategy and is excluded as a reasonable proposition.

In addition, that angle is covered by the ‘real terms’ component of the question.

So on balance the sensible answer is false.

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

Question 3:

After a deep recession, governments wanting to reduce their unemployment rates should use expansionary fiscal policy such that real GDP growth equals the sum of the labour productivity growth and the labour force growth rate.

The answer is False.

To see why, we might usefully construct a scenario that will explicate the options available to a government.

Assume that:

  • Labour productivity growth (that is, growth in real output per person employed) is growing at 2 per cent per annum. So as this grows less employment in required per unit of output.
  • The labour force is growing by 1.5 per cent per annum. Growth in the labour force adds to the employment that has to be generated for unemployment to stay constant (or fall).
  • 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.
  • At the recession trough, the unemployment rate is 10 per cent and the real GDP growth rate is zero

We can use this scenario to explore different outcomes.

So the question asks whether through government stimulus, the unemployment rate will fall below 10 per cent if GDP growth rises to 3.5 per cent per annum.

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.

That is important.

What we are seeking is a reduction in the unemployment rate not a maintenance of its current level.

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 3.5 per cent per annum and if policy only aspires to keep real GDP growth at that annual growth rate, then the unemployment rate will not change.

As the stimulus sets in real GDP growth will start to increase towards 3.5 per cent (that being the governments growth goal).

But for as long as the growth rate is below 3.5 per cent the unemployment rate will continue to rise because real output growth is not strong enough to both absorb the new entrants into the labour market and offset the employment losses arising from labour productivity growth.

Once growth hits 3.5 per cent per annum, then the change in the unemployment rate becomes zero and the level stabilises.

So, clearly, to mop up the damage of the recession, growth has to, initially, exceed the required rate, and then once the desired unemployment rate is achieved, then the government has to seek the required growth rate to stabilise the unemployment rate at that level.

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

That is enough for today!

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

This Post Has 5 Comments

  1. Question 2:
    Modern Monetary Theory implies that higher levels of taxation are not necessary for the government to spend more in real terms.
    The answer is False.

    Well I have been studying MMT for quite a few years now and the idea that government requires more taxation in order to spend more in real terms, at least initially, is completely alien to everything Bill has taught me. And I will note there is no time period mentioned in the question. So the correct answer is ‘True’, perhaps with an asterisk to explain that long term expansion of government spending will usually require increased taxation to maintain the value of the currency.

    But I can imagine several scenarios where both increases in real government spending and changes in government regulations other than what is called ‘taxes’ would allow an increase in government spending without increases in taxation or inflation even in a long run situation.

    So I am going to retract my previously deleted comment about me getting dumber and just argue that there is a problem with the question. Which doesn’t mean I’m not getting dumber- just that I won’t and should not admit it at this point based on this question and answer.

  2. Bill, did the US federal government need to raise taxes before it began to spend money in response to Pearl Harbor- or did they just have wait to increase real spending until they managed to raise taxes through legislation first? And that was back when they were still on a type of gold standard. I know you have an aversion to ever accepting I might be right about anything- but come on professor. It is possible I could be right about something once in a while- you taught me pretty well after all.

    More recently, Obama cut taxes in the great recession and at the same time increased federal government spending. That wasn’t a ‘real’ increase in spending? It certainly wasn’t accompanied by rising inflation pressures.

  3. I also struggle to fit your explanation of quesiton 2, into my current understanding of MMT.

    The way I see it is that tax is there to drive the value of the currency, and to regulate inflation.

    Let’s say the government decides to apply an addition 30% tax on the wealth of billionares. This money is pulled back from the riches savings. However since this money was locked away in bank accounts, and real resources were not being used, how has this wealth tax enabled the government to acquire more resources?

  4. @Tony + @Jerry

    The way I interpret Bill’s answer to 2. is that the increased tax rates increases the requirement of real resource transfer from the non-govt sector to the government sector, based on the principles of tax liabilities creating unemployment in the non-govt sector. Therefore higher taxes must increase the availability of those resources for the govt sector to utilise whilst savings desires remain constant. It’s not about the money, it’s about the real resources.

    @Bill – Am I on the right track here?

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