The Weekend Quiz – July 8-9, 2017 – 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:

In terms of the initial impact on national income, a tax increase which aims to increase tax revenue at the current level of national income by $x is less damaging than a spending cut of $x?

The answer is True.

The question is only seeking an understanding of the initial drain on the spending stream rather than the fully exhausted multiplied contraction of national income that will result. It is clear that the tax increase increase will have two effects: (a) some initial demand drain; and (b) it reduces 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 impact on demand motivated by an decrease 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 cut

A cut in government spending (say of $1000) is what we call an exogenous withdrawal from the aggregate spending stream and this directly reduces aggregate demand by that amount. So it might be the cancellation of a long-standing order for $1000 worth of gadget X. The firm that produces gadget X thus reduces production of the good or service by the fall in orders ($1000) (if they deem the drop in sales to be permanent) and as a result incomes of the productive factors working for and/or used by the firm fall by $1000. So the initial fall in aggregate demand is $1000.

This initial fall in national output and income would then induce a further fall in consumption by 64 cents in the dollar so in Period 2, aggregate demand would decline by $640. Output and income fall further by the same amount to meet this drop in spending. In Period 3, aggregate demand falls by 0.8 x 0.8 x $640 and so on. The induced spending decrease gets smaller and smaller because some of each round of income drop is taxed away, some goes to a decline in imports and some manifests as a decline in saving.

Tax-increase induced contraction

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

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

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

Some of the decline in disposable income manifests as lost saving (20 cents in each dollar that disposable income falls in the example being used). So the lost consumption is equal to the marginal propensity to consume out of disposable income times the drop in disposable income (which if the MPC is less than 1 will be lower than the $1000).

In this case the reduction in aggregate demand is $800 rather than $1000 in the case of the cut in government spending.

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

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! I am also ignoring the empirically-questionable mainstream claims that tax increases erode work incentives which force workers to supply less labour.

You may wish to read the following blogs for more information:

Question 2:

If private households increase their saving from disposable income and firms reduce their investment expenditure, then the government has to expand its fiscal deficit to avoid employment losses.

The answer is False.

The answer also relates to the sectoral balances framework. When the private domestic sector decides to lift its saving ratio, we normally think of this in terms of households reducing consumption spending. However, if we are talking about the overall saving (spending less than total income) of the private domestic sector, it could also be evidenced by a drop in investment spending (building productive capacity).

The normal inventory-cycle view of what happens next goes like this. Output and employment are functions of aggregate spending. Firms form expectations of future aggregate demand and produce accordingly. They are uncertain about the actual demand that will be realised as the output emerges from the production process.

The first signal firms get that household consumption is falling is in the unintended build-up of inventories. That signals to firms that they were overly optimistic about the level of demand in that particular period.

Once this realisation becomes consolidated, that is, firms generally realise they have over-produced, output starts to fall. Firms layoff workers and the loss of income starts to multiply as those workers reduce their spending elsewhere.

At that point, the economy is heading for a recession. Interestingly, the attempts by households overall to increase their saving ratio may be thwarted because income losses cause loss of saving in aggregate – the is the Paradox of Thrift. While one household can easily increase its saving ratio through discipline, if all households try to do that then they will fail. This is an important statement about why macroeconomics is a separate field of study.

Typically, the only way to avoid these spiralling employment losses would be for an exogenous intervention to occur – in the form of an expanding public deficit. The fiscal position of the government would be heading towards, into or into a larger deficit depending on the starting position as a result of the automatic stabilisers anyway.

So an intuitive reasoning suggests that a demand gap opens and the only way to stop the economy from contracting with employment losses if it the government fills the spending gap by expanding net spending (its deficit).

However, this would ignore the movements in the third sector – there is also an external sector. It is possible that at the same time that the households are reducing their consumption as an attempt to lift the saving ratio, net exports boom. A net exports boom adds to aggregate demand (the spending injection via exports is greater than the spending leakage via imports).

So it is possible that the public fiscal balance could actually go towards surplus and the private domestic sector increase its overall saving (withdrawing net expenditure) if net exports were strong enough.

The important point is that the three sectors add to demand in their own ways. Total GDP and employment are dependent on aggregate demand. Variations in aggregate demand thus cause variations in output (GDP), incomes and employment. But a variation in spending in one sector can be made up via offsetting changes in the other sectors.

The following blogs may be of further interest to you:

Question 3:

During a recession, a government should use expansionary fiscal policy to restore trend real GDP growth if it wants to reduce unemployment.

The answer is False.

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

  • Trend real GDP growth rate is 3 per cent annum.
  • 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.

We can use this scenario to explore the different outcomes.

The trend rate of real GDP growth doesn’t relate to the labour market in any direct way. 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.

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 its trend growth rate of 3 per cent annum, then the output gap that emerges is 0.5 per cent per annum.

The unemployment rate will rise by this much (give or take) and reflects the fact that 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.

So the appropriate fiscal strategy does not relate to “trend output” but to the required real GDP growth rate given labour force and productivity growth. The two growth rates might be consistent but then they need not be. That lack of concordance makes the proposition false.

The following blog may be of further interest to you:

That is enough for today!

(c) Copyright 2017 William Mitchell. All Rights Reserved.

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    4 Responses to The Weekend Quiz – July 8-9, 2017 – answers and discussion

    1. anders leland says:

      I read the answers and they were much more complicated than the questions.

    2. Christer Kamb says:

      Agree anders. I would start to give the answers in a few lines. Then do the explaining. Now you read and read without really knowing if you understands the core of the reasoning. In Question 2 for example it took I while until “the external sector” was mentioned.

      By the way:
      In understanding sectoral balances I would like to have some tips on how to calculate and collect Domestic balance-data. It is very easy to get data about the Government-balance(budget). A little bit trickier to calculate the external sector and the entries measuring not the payment-balance but the Current Account. But the most difficult part is how to calculate the Domestic balance, aka S – I. I want to check the real national numbers by laborating this simple equation; S-I=(G-T)+CAD. Getting the (I)-nvestment-part from the GDP/GNP is fairly simple but how do I calculate/collect the gross/net Domestic Savings out of the national statistics? I mean not by calculate the sum backwards using (GNP – C – T). If Investments in the corporate sector is positive for a certain period then I guess you compare(add/subtract) this number against i.e the household net disposable income not used for consumtion? Working with real numbers would be great if you want to really understand things.

    3. Jim Green says:

      Regarding unemployment….two more cents from this side of the pond……

      Council of Economic Advisers/Economic Policy Institute:

      Since 1980, and as a result of automation [robots], alone–we have had excessive unemployment [hereafter UE] over 70% of the time [twice that of preceding years]–and resulting in JOBS, JOBS, JOBS, being the number one issue, and with growing intensity, in every election since 1980….

      Further, and running in parallel with our anemic Job Creation–UE has resulted in an adverse dollar loss to the market—UE eats into the bottom line…..and we know this by common sense, alone….we can’t have 10 million Americans looking for work—that can’t find any—without the loss of their income in the market having an adverse impact on the economy!

      The solution is glaringly transparent—FIX UE, i.e, fix one, and fix both!

      The enigma: WHY are we Americans having so much difficulty having our demand for JOBS addressed? And not to be rhetorical, but the culprit is our method of Job Creation since WW II—based on the archaic BELIEF that the market can provide everybody with work—it is PURE BS….in fact, this method of Job Creation has not resulted in a UE rate below 3% since 1953, leaving millions jobless in its wake, created an epidemic of gun violence in our inner-cities—and if the market fails, the jobless are out of luck!

      The bottom line is: UE is a NO ONE WINS…..the jobless lose, civility loses [Ferguson, etc.,], and the MARKET loses, to wit:

      THE LAW OF DIMINISHED INCOME TO THE MARKET FROM UNEMPLOYMENT [hereafter D/UE LAW]
      Short Definition:

      3% is the zero-sum threshold above which unemployment starts substantially undermining the Market–and the loss in income to the Market is compounded exponentially with each percentage point of increase in unemployment, above 3%.

      The proposed solution is an expanding and contracting public workforce, that expands during downturns in the market, and contracts as the market recovers [AKA The Buffer Stock Employment Model]: THE NEIGHBOR-TO-NEIGHBOR JOB CREATION ACT [Amazon, hereafter NTN]: a Pro-Market, deficit-neutral, federally mandated Social Insurance [a condition of employment], to provide a fund to hire/train our UE–triggered at 3% UE per the “legal authorization” in Public Law 15 USC § 3101 [under NTN at no time would our UE rate in America exceed 3%]. Jobs beget jobs, and for a modest 4% of salary policy cost, NTN will create more “private-sector” jobs in 6 months, than our current path [HR 2847—The HIRE Act]–in 6 years!

      Jim Green, Candidate for Congress, Dist 21, TX, 2000

      Thank you for contacting the White House

    4. Jim Green says:

      An interesting response….

      Andreas Bimba says:
      Sunday, July 9, 2017 at 12:25
      Jim, so true that mass unemployment is an inevitable shortcoming of a free market and a scourge that damages the whole economy and not just its unfortunate victims but why is 3% unemployment the upper limit before action must be taken? I think Bill would set the macroeconomic policy levers and his Job Guarantee Program to achieve close to zero unemployment and underemployment with just those transitioning between jobs or unable to work remaining unemployed, if he ever got the chance.

      Andreas….I like the opportunity for “0” UE…I just don’t think it is realistic in today’s political climate—whereas 3% is workable—is 90% effective in getting to our goal…..maybe a generation or two down the road…..today, economists are all over the map on “full employment”….for instance, Ali Velshi, economic guru for MSNBC in the U.S. believes 5% UE is “full employment”—so from his perspective we currently have full employment in the U.S.—which I see as absurd! The harbinger throughout all of the countries in the OECD is the archaic belief that “The market can provide anybody wanting a job, with a job”—it is PURE BS—but until the OECD throws out this ERRONEOUS BELIEF in their job creation policies, the Eurozone will suffer with 10% plus UE, or the extremely oppressive 25% youth UE in Greece and Spain! The stumbling blocks standing in the way of our market-driven economies evolving, are 1] the entrenched belief that Job Creation should be addressed via the “market”….and 2] being blind-sighted in looking for alternative Job Creation—they are not looking for a solution, because they [erroneously] believe they have one….

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