# Saturday Quiz – October 16, 2010 – 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:

If the growth in wages (the money you get paid) keeps pace with inflation which is accelerating at the same rate as labour productivity is growing then the wage share in GDP remains constant.

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.

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) and the price level (P) are growing at the pace the real wage is constant. And 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.

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.

In this blog – The origins of the economic crisis – I provided these graphs. First, the movement real wages and labour productivity since 1979. Both series are indexed to 100 as at the September quarter 1978. So by September 2008, the real wage index had climbed to 116.7 (that is, around 15 per cent growth in just over 12 years) but the labour productivity index was 179.1.

This suggests from our discussion that the wage share should have fallen. That is what the next graph depicts – it shows how far the wage share has fallen in Australia over the last two decades. The trend has been common across the globe during the neo-liberal years and is one of the pre-conditions that explain our current economic crisis.

The following blogs may be of further interest to you:

Question 2:

Central bankers are talking about the possible need for more quantitative easing to ease the aggregate demand losses associated with the implementation of fiscal austerity programs. If calibrated correctly, QE can replace the net financial assets destroyed by the withdrawal of the fiscal injection.

Quantitative easing then involves the central bank buying assets from the private sector – government bonds and high quality corporate debt. So what the central bank is doing is swapping financial assets with the banks – they sell their financial assets and receive back in return extra reserves. So the central bank is buying one type of financial asset (private holdings of bonds, company paper) and exchanging it for another (reserve balances at the central bank). The net financial assets in the private sector are in fact unchanged although the portfolio composition of those assets is altered (maturity substitution) which changes yields and returns.

In terms of changing portfolio compositions, quantitative easing increases central bank demand for “long maturity” assets held in the private sector which reduces interest rates at the longer end of the yield curve. These are traditionally thought of as the investment rates. This might increase aggregate demand given the cost of investment funds is likely to drop. But on the other hand, the lower rates reduce the interest-income of savers who will reduce consumption (demand) accordingly.

How these opposing effects balance out is unclear but the evidence suggests there is not very much impact at all.

You should read the answer to Question 3 to reflect on how fiscal policy adds net financial assets to the non-government sector by way of contradistinction to QE.

The following blogs may be of further interest to you:

Question 3:

The expansionary impact of deficit spending on aggregate demand is lower when the government matches the deficit with debt-issuance because then excess reserves are drained and the purchasing power is taken out of the monetary system.

The mainstream macroeconomic textbooks all have a chapter on fiscal policy (and it is often written in the context of the so-called IS-LM model but not always).

The chapters always introduces the so-called Government Budget Constraint that alleges that governments have to “finance” all spending either through taxation; debt-issuance; or money creation. The writer fails to understand that government spending is performed in the same way irrespective of the accompanying monetary operations.

They claim that money creation (borrowing from central bank) is inflationary while the latter (private bond sales) is less so. These conclusions are based on their erroneous claim that “money creation” adds more to aggregate demand than bond sales, because the latter forces up interest rates which crowd out some private spending.

All these claims are without foundation in a fiat monetary system and an understanding of the banking operations that occur when governments spend and issue debt helps to show why.

So what would happen if a sovereign, currency-issuing government (with a flexible exchange rate) ran a budget deficit without issuing debt?

Like all government spending, the Treasury would credit the reserve accounts held by the commercial bank at the central bank. The commercial bank in question would be where the target of the spending had an account. So the commercial bank’s assets rise and its liabilities also increase because a deposit would be made.

The transactions are clear: The commercial bank’s assets rise and its liabilities also increase because a new deposit has been made. Further, the target of the fiscal initiative enjoys increased assets (bank deposit) and net worth (a liability/equity entry on their balance sheet). Taxation does the opposite and so a deficit (spending greater than taxation) means that reserves increase and private net worth increases.

This means that there are likely to be excess reserves in the “cash system” which then raises issues for the central bank about its liquidity management. The aim of the central bank is to “hit” a target interest rate and so it has to ensure that competitive forces in the interbank market do not compromise that target.

When there are excess reserves there is downward pressure on the overnight interest rate (as banks scurry to seek interest-earning opportunities), the central bank then has to sell government bonds to the banks to soak the excess up and maintain liquidity at a level consistent with the target. Some central banks offer a return on overnight reserves which reduces the need to sell debt as a liquidity management operation.

There is no sense that these debt sales have anything to do with “financing” government net spending. The sales are a monetary operation aimed at interest-rate maintenance. So M1 (deposits in the non-government sector) rise as a result of the deficit without a corresponding increase in liabilities. It is this result that leads to the conclusion that that deficits increase net financial assets in the non-government sector.

What would happen if there were bond sales? All that happens is that the banks reserves are reduced by the bond sales but this does not reduce the deposits created by the net spending. So net worth is not altered. What is changed is the composition of the asset portfolio held in the non-government sector.

The only difference between the Treasury “borrowing from the central bank” and issuing debt to the private sector is that the central bank has to use different operations to pursue its policy interest rate target. If it debt is not issued to match the deficit then it has to either pay interest on excess reserves (which most central banks are doing now anyway) or let the target rate fall to zero (the Japan solution).

There is no difference to the impact of the deficits on net worth in the non-government sector.

Mainstream economists would say that by draining the reserves, the central bank has reduced the ability of banks to lend which then, via the money multiplier, expands the money supply.

However, the reality is that:

• Building bank reserves does not increase the ability of the banks to lend.
• The money multiplier process so loved by the mainstream does not describe the way in which banks make loans.
• Inflation is caused by aggregate demand growing faster than real output capacity. The reserve position of the banks is not functionally related with that process.

So the banks are able to create as much credit as they can find credit-worthy customers to hold irrespective of the operations that accompany government net spending.

This doesn’t lead to the conclusion that deficits do not carry an inflation risk. All components of aggregate demand carry an inflation risk if they become excessive, which can only be defined in terms of the relation between spending and productive capacity.

It is totally fallacious to think that private placement of debt reduces the inflation risk. It does not.

Question 4:

The change in the net worth of the non-government sector when the government increases its net spending is invariant to government issuing debt which exactly matches (\$-for-\$) the increase in net public spending.

This answer is complementary to that provided for Question 3 and relies on the same understanding of reserve operations. So within a fiat monetary system we need to understand the banking operations that occur when governments spend and issue debt. That understanding allows us to appreciate what would happen if a sovereign, currency-issuing government (with a flexible exchange rate) ran a budget deficit without issuing debt?

Like all government spending, the Treasury would credit the reserve accounts held by the commercial bank at the central bank. The commercial bank in question would be where the target of the spending had an account. So the commercial bank’s assets rise and its liabilities also increase because a deposit would be made.

The transactions are clear: The commercial bank’s assets rise and its liabilities also increase because a new deposit has been made. Further, the target of the fiscal initiative enjoys increased assets (bank deposit) and net worth (a liability/equity entry on their balance sheet). Taxation does the opposite and so a deficit (spending greater than taxation) means that reserves increase and private net worth increases.

This means that there are likely to be excess reserves in the “cash system” which then raises issues for the central bank about its liquidity management as explained in the answer to Question 3. But at this stage, M1 (deposits in the non-government sector) rise as a result of the deficit without a corresponding increase in liabilities. In other words, budget deficits increase net financial assets in the non-government sector.

What would happen if there were bond sales? All that happens is that the banks reserves are reduced by the bond sales but this does not reduce the deposits created by the net spending. So net worth is not altered. What is changed is the composition of the asset portfolio held in the non-government sector.

The only difference between the Treasury “borrowing from the central bank” and issuing debt to the private sector is that the central bank has to use different operations to pursue its policy interest rate target. If it debt is not issued to match the deficit then it has to either pay interest on excess reserves (which most central banks are doing now anyway) or let the target rate fall to zero (the Japan solution).

There is no difference to the impact of the deficits on net worth in the non-government sector.

The government is attempting to stimulate the economy via an expansion in the budget deficit. The private market orientated advisors tell them to cut taxes and “privatise” the expansion whereas the more civic-minded advisers argue that there is a need for improved public infrastructure which requires increases in government spending. So imagine that the government is choosing between a tax cut that will reduce tax revenue at the current level of national income by \$x and a spending increase of \$x. Which policy option will have the greater initial impact on aggregate demand?

(a) Tax cut
(b) Spending increase
(c) Both will be equivalent
(d) There is not enough information to answer this question

The question is only seeking an understanding of the initial injection into the spending stream rather than the fully exhausted multiplied expansion of national income that will result. It is clear that the tax cut approach will have two effects: (a) some initial demand stimulus; and (b) it increases the value of the multiplier, other things equal.

We are only interested in the first effect rather than the total effect. But I will give you some insight also into what the two components of the tax result might imply overall when compared to the stimulus motivated by an increase in government spending.

To give you a concrete example which will consolidate the understanding of what happens, imagine that the marginal propensity to consume out of disposable income is 0.8 and there is only one tax rate set at 0.20. So for every extra dollar that the economy produces the government taxes 20 cents leaving 80 cents in disposable income. In turn, households then consume 0.8 of this 80 cents which means an injection of 64 cents goes into aggregate demand which them multiplies as the initial spending creates income which, in turn, generates more spending and so on.

Government spending increase

An increase in government spending (say of \$1000) is what we call an exogenous injection into the spending stream and stimulates aggregate demand by that amount. So it might be an order of \$1000 worth of gadget X which advances human welfare immeasurably! The firm that produces gadget X thus increases production of the good or service by the rise in orders (\$1000) and as a result incomes of the productive factors rises by \$1000. So the initial rise in aggregate demand is \$1000.

This initial increase in national output and income then stimulates (induces) further consumption by 64 cents in the dollar so in Period 2, aggregate demand increases by \$640. Output and income rises by the same amount to meet this increase in spending. In Period 3, aggregate demand rises by 0.8 x 0.8 x \$640 and so on. The induced spending increase gets smaller and smaller because some of each round of income increase is taxed away, some goes to imports and some is saved.

Tax-cut induced stimulus

The stimulus coming from a tax-cut does not directly impact on the spending stream in the same way as the rise in government spending.

First, imagine the government worked out a tax cut that would increase its initial budget deficit by the same amount as would have been the case if it had increased government spending (so in our example, \$1000).

In other words, disposable income at each level of GDP rises initially by \$1000. What happens next?

Some of the disposable income is saved (20 cents in each dollar that disposable income increases). So immediately some of the tax increase is lost from the spending stream.

In this case the injection into aggregate demand is \$800 rather than \$1000 in the case of the increase in government spending.

What happens next depends on the parameters of the macroeconomic system. The multiplied rise in national income may be higher or lower depending on these parameters. But it will never be the case that an initial budget equivalent tax cut will be more stimulatory than a government spending increase.

Note in answering this question I am disregarding all the nonsensical notions of Ricardian equivalence that abound among the mainstream doomsayers who have never predicted anything of empirical note! All their predictions come to nought.

### This Post Has 14 Comments

1. Hi, Bill-

With respect to question 1,

“Now it becomes obvious that if the nominal wage (W) and the price level (P) are growing at the pace the real wage is constant. And 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.”

But the question had wages growing at the same pace as inflation. So my conclusion was that wages were stagnant in real terms, while productivity gains (equal to the inflation rate, incidentally) were going elsewhere, thus the wage share was declining in the question’s scenario. It would be impossible (I think) for wages to be growing equal to inflation, and also be growing on pace with productivity gains at the same time.

##

Also, on question 3, you reframe the solution in terms of net worth, while the question was about “expansionary effect”. These seem to be different things. Suppose a demographic cohort holds 1X GDP in bonds. Suppose then that this cohort gets old all at once and cashes this out and begins to spend that money. While the net worth has changed very little, the expansionary effect is very different, since bonds (savings/wealth) are largely inert, whereas hot money is liable to be injected to the system as spending.

With appreciation!

2. I have the same question.

The general mainstream argument seems to be that bonds are somehow magical and keep currency stocks as stocks due to their alleged magical powers. If those bonds are purchased by QE, or they aren’t issued in the first place then people with simply spend the money rather than keeping it saved.

Reserves would be ‘forced’ into riskier assets, or they would cause a wall of money buying yachts to force up prices. Either of these scenarios would therefore signal the end of the world.

What is the macro mechanism that keeps reserves as stock rather than inducing a change into flows when there aren’t any government bonds to buy? Would the general ‘desire to save’ diminish if there isn’t safe government bonds there?

Is there any evidence to back up the MMT argument that reserves and bonds are largely identical?

3. markg says:

Bill,
I am surprised you think \$1000 of US govt spending would advance human welfare. Maybe in Australia, but not in the US. I would not be surprised if only 50% of every dollar of the stimulus spending in the US advanced human welfare (unless you consider excecutive pay and corporate profits as advancing human welfare).

4. Tom Hickey says:

Neil @ 19:25

The empirical evidence is in. QE did not increase consumption or investment. The assets held as bonds (tsy’s and MBS) were simply shifted to other assets, and some of this involved external capital flows, about which the emerging nations are now complaining and saying that they don’t want to see QE2 coming their way. Capital flows toward the highest (risk-weighted) return. Present bondholders will sell current holdings if they think that the bond market has run up toward its limit with very low rates and seek better opportunities elsewhere in the US or world. Why would anyone expect anything different?

5. CharlesJ says:

Bill et. al.
Unrelated point but Ben Bernanke said the following recently:

“Overall, my assessment is that the bulk of the increase in unemployment since the recession began is attributable to the sharp contraction in economic activity that occurred in the wake of the financial crisis and the continuing shortfall of aggregate demand since then, rather than to structural factors.”

This made me think about the relationship between ‘structural’ unemployment as neoliberals assume it to be, and ‘structural’ deficits. Am I right in thinking that the structural deficit is caused by structural unemployment? If this is the case then Bernanke is also saying that he thinks the structural deficit is smaller than others think. In relation to the cuts planned for the UK by Osbourne, how will cutting child benefit reduce structural unemployment, and therefore reduce the structural deficit?

Or am I simplifying this too much? Perhaps this is an idea for a question.

Charlie

6. Fed Up says:

Burk, Bill had trouble with this type of question from another quiz. The problem is the english and interpretation.

I would say the better way to ask it is from:

“If the growth in wages (the money you get paid) keeps pace with inflation which is accelerating at the same rate as labour productivity is growing then the wage share in GDP remains constant.”

To:

“If the growth in wages (the money you get paid) keeps pace with [price] inflation, this is called the real wage, and the real wage is the same as labour productivity; then the wage share in GDP remains constant.”

In this example, I believe productivity growth would need to be zero(0).

7. Fed Up says:

Burk: I think you want a question like this:

What happens to the wage share if nominal wages grow 3%, price inflation is 3%, and productivity growth is 3%?

That would make it the real wage growth is 0% and productivity growth is 3%?

8. Richard says:

Bill,

Many thanks for this and previous quizzes. I find them helpful. However, as I have no long term background in economics, I am really struggling to understand how an economy is actually going to be controlled in a visible way that is understandable. I am trying, perhaps pointlessly, to reformulate your explanations into some form of control theory. For example: if event ‘x’ happens, the response should be ‘y’ but with the limits of ‘z’ imposed; [ but note that x, y and z are not necessarily single events; they are more likely to be events concerning multiple economic factors.

If I assume that one lone country, like Australia, followed an MMT based economic policy, what would the response of the world’s markets be? Given that they are largely inhabited by mainstream trained economists, I suspect that their response, at least in the short term would be severely damaging, but how should AUS respond? If most countries converted to MMT ideas overnight, the situation would be totally different and the economic environment for AUS, in this example, would be easier and simpler, as everyone would be on roughly the same wavelength. At least they would be trying to benefit the people and not satisfy the greedy.

Another issue – In discussing MMT with others [only a few are even prepared to listen] the almost universal view is that government money has to be borrowed from the markets. If it is not – its been printed, therefore that’s inflationary and we are back in the Weimar republic hyperinflation, seemingly instantaneously. Its a rubbish view, but its what people believe. Is there a very simple A B C primer that can be used to counter this? The other problem is that we have been taught to have the attention span of a gnat! Complex arguments and discussion just don’t cut it with most. The other explanation is that I just don’t understand, cannot explain anything and bore everyone rigid!

Many thanks for all your efforts in this blog

Richard

9. Tom,

“Why would anyone expect anything different?”

I don’t know. I think the main argument seems to be that there is a ‘flight’ from dollars. Although I’m not quite sure why anybody would be upset that somebody sold their dollars in a fit of pique because they are no longer getting free government interest on them to somebody else who now has to do something useful with them.

Of course such a flight probably alters the exchange rate in the short term (I presume down) and that seems to unnecessarily panic money people.

10. Richard,

The one I use is this:

A government has a credit card on which it can spend. However it has a magic cashback deal which means that not only does it get a percentage when it spends, but a percentage when anybody else spends the same money. Since one person’s spend is another’s income, the money will skip around the economy like a stone across a pond with a percentage deducted at every step. It’s a mathematical progression to zero.

So for any given positive tax rate, if a government spends £100 on its magic credit card it will *always* get £100 cash back in taxation.

The issue is when it will get that tax back. If everybody spends everything they earn instantly then when the government spends £100 it gets £100 back instantly from all the transactions induced. The only thing that can stop that from happening in any accounting period is if somebody somewhere along that chain saves something.

And that is the only reason we have a deficit. From all the government spending, lots of people saved something. They deferred the taxation that would have balanced the budget. And if they’re saving, they’re not spending – so how can there be any inflation?

11. Fed Up says:

Q3, “Like all government spending, the Treasury would credit the reserve accounts held by the commercial bank at the central bank. The commercial bank in question would be where the target of the spending had an account. So the commercial bank’s assets rise and its liabilities also increase because a deposit would be made.”

I think this is going to be a dumb question, but I am going to ask it anyway. How does the reserve requirement work here?

12. Fed Up says:

Q3, “Like all government spending, the Treasury would credit the reserve accounts held by the commercial bank at the central bank. The commercial bank in question would be where the target of the spending had an account. So the commercial bank’s assets rise and its liabilities also increase because a deposit would be made.”

If I get a mortgage and spend it on a house, how does that change this scenario? By that I mean there is no new gov’t spending. The new spending is from getting the mortgage.

13. Fed Up says:

Q3, “What would happen if there were bond sales? All that happens is that the banks reserves are reduced by the bond sales but this does not reduce the deposits created by the net spending. So net worth is not altered. What is changed is the composition of the asset portfolio held in the non-government sector.”

What does the scenario look like if Apple, Microsoft, and others are putting most of their earnings in the bank and not needing to spend? Is the gov’t trying to get some of the earnings setting in the bank back into circulation? I am especially interested in demand deposits and the reserve requirement here, assuming my scenario is anywhere near correct. It may not be.