Saturday Quiz – January 22, 2011 – 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 economy-wide average nominal wages fail to keep pace with the inflation rate then it means the profit share in GDP is rising.

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 nominal 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.

However, if the real wage is falling we cannot conclude that the wage share is also falling. Given the nature of ratios, if the numerator (in this case, the real wage) is falling but not by as much as the denominator (in this case, labour productivity) then the overall ratio can actually be rising.

I provided this graphic in the blog – When will the workers wake up? 0 and it shows index numbers (1970=100) for Real Earnings and Labour Productivity to give you some idea of how each has grown over the last 40 years. I chose Australia, Japan, Norway, the UK and the USA for comparison being a broad selection of different types of economies.

While the relationship between real earnings growth and labour productivity growth over this period is interesting in itself for each individual country, I also set equivalent vertical axis scale so you can also compare between countries.

You can see that in the nations shown real wages growth has lagged behind labour productivity growth (to varying degrees). You also see that workers in Norway have enjoyed much better outcomes than workers elsewhere. The US stands out clearly as the worst performed nation.

In most cases the real wage is actually rising but the wage share is falling (profit share rising) because productivity growth is rising faster.

The following blogs may be of further interest to you:

• The origins of the economic crisis
• The fiscal stimulus worked but was captured by profits
• When will the workers wake up?

Question 2:

The net worth of the non-government sector would not alter if the government issued bonds to exactly match ($-for-$) the increase in net public spending or not.

The answer is True.

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 textbooks fail to convey an understanding 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.

So in terms of the specific question, you need to consider the reserve operations that accompany deficit spending. 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 above. 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.

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

• Why history matters
• Building bank reserves will not expand credit
• Building bank reserves is not inflationary
• The complacent students sit and listen to some of that
• Saturday Quiz – February 27, 2010 – answers and discussion

Question 3:

The wider the spread between the price the central bank sets on the reserves it provides the commercial banks on demand (so-called penalty rates) and the target policy rate the more difficult it becomes for the central bank to ensure the quantity of reserves is appropriate for maintaining its target policy rate.

The answer is True.

The facts are as follows. First, central banks will always provided enough reserve balances to the commercial banks at a price it sets using a combination of overdraft/discounting facilities and open market operations.

Second, if the central bank didn’t provide the reserves necessary to match the growth in deposits in the commercial banking system then the payments system would grind to a halt and there would be significant hikes in the interbank rate of interest and a wedge between it and the policy (target) rate – meaning the central bank’s policy stance becomes compromised.

Third, any reserve requirements within this context while legally enforceable (via fines etc) do not constrain the commercial bank credit creation capacity. Central bank reserves (the accounts the commercial banks keep with the central bank) are not used to make loans. They only function to facilitate the payments system (apart from satisfying any reserve requirements).

Fourth, banks make loans to credit-worthy borrowers and these loans create deposits. If the commercial bank in question is unable to get the reserves necessary to meet the requirements from other sources (other banks) then the central bank has to provide them. But the process of gaining the necessary reserves is a separate and subsequent bank operation to the deposit creation (via the loan).

Fifth, if there were too many reserves in the system (relative to the banks’ desired levels to facilitate the payments system and the required reserves then competition in the interbank (overnight) market would drive the interest rate down. This competition would be driven by banks holding surplus reserves (to their requirements) trying to lend them overnight. The opposite would happen if there were too few reserves supplied by the central bank. Then the chase for overnight funds would drive rates up.

In both cases the central bank would lose control of its current policy rate as the divergence between it and the interbank rate widened. This divergence can snake between the rate that the central bank pays on excess reserves (this rate varies between countries and overtime but before the crisis was zero in Japan and the US) and the penalty rate that the central bank seeks for providing the commercial banks access to the overdraft/discount facility.

So the aim of the central bank is to issue just as many reserves that are required for the law and the banks’ own desires.

Now the question seeks to link the penalty rate that the central bank charges for providing reserves to the banks and the central bank’s target rate. The wider the spread between these rates the more difficult does it become for the central bank to ensure the quantity of reserves is appropriate for maintaining its target (policy) rate.

Where this spread is narrow, central banks “hit” their target rate each day more precisely than when the spread is wider.

So if the central bank really wanted to put the screws on commercial bank lending via increasing the penalty rate, it would have to be prepared to lift its target rate in close correspondence. In other words, its monetary policy stance becomes beholden to the discount window settings.

The answer is True because the central bank cannot operate with wide divergences between the penalty rate and the target rate and it is likely that the former would have to rise significantly to choke private bank credit creation.

You might like to read this blog for further information:

• US federal reserve governor is part of the problem
• Building bank reserves will not expand credit
• Building bank reserves is not inflationary

Question 4:

Assume that a national is continuously running an external deficit of 2 per cent of GDP. In this economy, if the private domestic sector successfully saves overall, we would always find:

(a) A public budget deficit.

(b) A public budget surplus.

(c) Cannot tell because we don’t know the scale of the private domestic sector saving as a % of GDP.

The answer is Option (a) – A public budget deficit.

This question requires an understanding of the sectoral balances that can be derived from the National Accounts. But it also requires some understanding of the behavioural relationships within and between these sectors which generate the outcomes that are captured in the National Accounts and summarised by the sectoral balances.

Refreshing the balances (again) – we know that from an accounting sense, if the external sector overall is in deficit, then it is impossible for both the private domestic sector and government sector to run surpluses. One of those two has to also be in deficit to satisfy the accounting rules.

The important point is to understand what behaviour and economic adjustments drive these outcomes.

So here is the accounting (again). 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. The sectoral balances derived are:

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

A simplification is to add (I – S) + (X – M) and call it the non-government sector. Then you get the basic result that the government balance equals exactly $-for-$ (absolutely or as a per cent of GDP) the non-government balance (the sum of the private domestic and external balances).

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

So what economic behaviour might lead to the outcome specified in the question?

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 reference to the specific 2 per cent of GDP figure was to place doubt in your mind. In fact, it doesn’t matter how large or small the external deficit is for this question.

Assume, now that the private domestic sector (households and firms) seeks to increase its saving ratio and is successful in doing so. Consistent with this aspiration, households may cut back on consumption spending and save more out of disposable income. The immediate impact is that aggregate demand will fall and inventories will start to increase beyond the desired level of the firms.

The firms will soon react to the increased inventory holding costs and will start to cut back production. How quickly this happens depends on a number of factors including the pace and magnitude of the initial demand contraction. But if the households persist in trying to save more and consumption continues to lag, then soon enough the economy starts to contract – output, employment and income all fall.

The initial contraction in consumption multiplies through the expenditure system as workers who are laid off also lose income and their spending declines. This leads to further contractions.

The declining income leads to a number of consequences. Net exports improve as imports fall (less income) but the question clearly assumes that the external sector remains in deficit. Total saving actually starts to decline as income falls as does induced consumption.

So the initial discretionary decline in consumption is supplemented by the induced consumption falls driven by the multiplier process.

The decline in income then stifles firms’ investment plans – they become pessimistic of the chances of realising the output derived from augmented capacity and so aggregate demand plunges further. Both these effects push the private domestic balance further towards and eventually into surplus

With the economy in decline, tax revenue falls and welfare payments rise which push the public budget balance towards and eventually into deficit via the automatic stabilisers.

If the private sector persists in trying to increase its saving ratio then the contracting income will clearly push the budget into deficit.

So if there is an external deficit and the private domestic sector saves (a surplus) then there will always be a budget deficit. The higher the private saving, the larger the deficit.

The following Graph and related Table shows you the sectoral balances written as (G-T) = (S-I) – (X-M) and how the budget deficit rises as the private domestic saving rises.

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!

Premium Question 5:

At present inflation and nominal interest rates are low and constant) so assume they are both zero and constant. Consider a country with a public debt to GDP ratio of 100 per cent which the mainstream economists consider to be dangerously high. The mainstream prescription is to run primary budget surpluses to stabilise and then reduce the debt ratio. Under the circumstances given, this strategy will only work if there is real GDP growth.

The answer is False.

First, some background theory and conceptual development.

While Modern Monetary Theory (MMT) places no particular importance in the public debt to GDP ratio for a sovereign government, given that insolvency is not an issue, the mainstream debate is dominated by the concept. The unnecessary practice of fiat currency-issuing governments of issuing public debt $-for-$ to match public net spending (deficits) ensures that the debt levels will always rise when there are deficits.

But the rising debt levels do not necessarily have to rise at the same rate as GDP grows. The question is about the debt ratio not the level of debt per se.

Rising deficits often are associated with declining economic activity (especially if there is no evidence of accelerating inflation) which suggests that the debt/GDP ratio may be rising because the denominator is also likely to be falling or rising below trend.

Further, historical experience tells us that when economic growth resumes after a major recession, during which the public debt ratio can rise sharply, the latter always declines again.

It is this endogenous nature of the ratio that suggests it is far more important to focus on the underlying economic problems which the public debt ratio just mirrors.

Mainstream economics starts with the flawed analogy between the household and the sovereign government such that any excess in government spending over taxation receipts has to be “financed” in two ways: (a) by borrowing from the public; and/or (b) by “printing money”.

Neither characterisation is remotely representative of what happens in the real world in terms of the operations that define transactions between the government and non-government sector.

Further, the basic analogy is flawed at its most elemental level. The household must work out the financing before it can spend. The household cannot spend first. The government can spend first and ultimately does not have to worry about financing such expenditure.

However, in mainstream (dream) land, the framework for analysing these so-called “financing” choices is called the government budget constraint (GBC). The GBC says that the budget deficit in year t is equal to the change in government debt over year t plus the change in high powered money over year t. So in mathematical terms it is written as:

which you can read in English as saying that Budget deficit = Government spending + Government interest payments – Tax receipts must equal (be “financed” by) a change in Bonds (B) and/or a change in high powered money (H). The triangle sign (delta) is just shorthand for the change in a variable.

However, this is merely an accounting statement. In a stock-flow consistent macroeconomics, this statement will always hold. That is, it has to be true if all the transactions between the government and non-government sector have been correctly added and subtracted.

So in terms of MMT, the previous equation is just an ex post accounting identity that has to be true by definition and has no real economic importance.

But for the mainstream economist, the equation represents an ex ante (before the fact) financial constraint that the government is bound by. The difference between these two conceptions is very significant and the second (mainstream) interpretation cannot be correct if governments issue fiat currency (unless they place voluntary constraints on themselves and act as if it is a financial constraint).

Further, in mainstream economics, money creation is erroneously depicted as the government asking the central bank to buy treasury bonds which the central bank in return then prints money. The government then spends this money.

This is called debt monetisation and you can find out why this is typically not a viable option for a central bank by reading the Deficits 101 suite – Deficit spending 101 – Part 1 – Deficit spending 101 – Part 2 – Deficit spending 101 – Part 3.

Anyway, the mainstream claims that if governments increase the money growth rate (they erroneously call this “printing money”) the extra spending will cause accelerating inflation because there will be “too much money chasing too few goods”! Of-course, we know that proposition to be generally preposterous because economies that are constrained by deficient demand (defined as demand below the full employment level) respond to nominal demand increases by expanding real output rather than prices. There is an extensive literature pointing to this result.

So when governments are expanding deficits to offset a collapse in private spending, there is plenty of spare capacity available to ensure output rather than inflation increases.

But not to be daunted by the “facts”, the mainstream claim that because inflation is inevitable if “printing money” occurs, it is unwise to use this option to “finance” net public spending.

Hence they say as a better (but still poor) solution, governments should use debt issuance to “finance” their deficits. Thy also claim this is a poor option because in the short-term it is alleged to increase interest rates and in the longer-term is results in higher future tax rates because the debt has to be “paid back”.

Neither proposition bears scrutiny – you can read these blogs – Will we really pay higher taxes? and Will we really pay higher interest rates? – for further discussion on these points.

The mainstream textbooks are full of elaborate models of debt pay-back, debt stabilisation etc which all claim (falsely) to “prove” that the legacy of past deficits is higher debt and to stabilise the debt, the government must eliminate the deficit which means it must then run a primary surplus equal to interest payments on the existing debt.

A primary budget balance is the difference between government spending (excluding interest rate servicing) and taxation revenue.

The standard mainstream framework, which even the so-called progressives (deficit-doves) use, focuses on the ratio of debt to GDP rather than the level of debt per se. The following equation captures the approach:

So the change in the debt ratio is the sum of two terms on the right-hand side: (a) the difference between the real interest rate (r) and the GDP growth rate (g) times the initial debt ratio; and (b) the ratio of the primary deficit (G-T) to GDP.

The real interest rate is the difference between the nominal interest rate and the inflation rate.

This standard mainstream framework is used to highlight the dangers of running deficits. But even progressives (not me) use it in a perverse way to justify deficits in a downturn balanced by surpluses in the upturn.

Many mainstream economists and a fair number of so-called progressive economists say that governments should as some point in the business cycle run primary surpluses (taxation revenue in excess of non-interest government spending) to start reducing the debt ratio back to “safe” territory.

Almost all the media commentators that you read on this topic take it for granted that the only way to reduce the public debt ratio is to run primary surpluses. That is what the whole “credible exit strategy” rhetoric is about and what is driving the austerity push around the world at present.

The standard formula above can easily demonstrate that a nation running a primary deficit can reduce its public debt ratio over time. So it is clear that the public debt ratio can fall even if there is an on-going budget deficit if the real GDP growth rate is strong enough. This is win-win way to reduce the public debt ratio.

But the question is analysing the situation where the government is desiring to run primary budget surpluses.

Consider the following Table which captures the variations possible in the question. In Year 1, the B/Y(-1) = 1 (that is, the public debt ratio at the start of the period is 100 per cent). The (-1) just signals the value inherited in the current period. We have already assumed that the inflation rate and the nominal interest rate are constant and zero, which means that the real interest rate is also zero and constant. So the r term in the model is 0 throughout our stylised simulation.

This is not to dissimilar to the situation at present in many countries.

In Year 1, there is zero real GDP growth and the Primary Budget Balance is also zero. Under these circumstances, the debt ratio is stable.

Now in Year 2, the fiscal austerity program begins and assume for the sake of discussion that it doesn’t dent real GDP growth. In reality, a major fiscal contraction is likely to push real GDP growth into the negative (that is, promote a recession). But for the sake of the logic we assume that nominal GDP growth is 1 per cent in Year 2, which means that real GDP growth is also 1 per cent given that all the nominal growth is real (zero inflation).

We assume that the government succeeds in pushing the Primary Budget Surplus to 1 per cent of GDP. This is the mainstream nirvana – the public debt ratio falls by 2 per cent as a consequence.

In Year 3, we see that the Primary Budget Surplus remains positive (0.5 per cent of GDP) but is now below the positive real GDP growth rate. In this case the public debt ratio still falls.

In Year 4, real GDP growth contracts (0.5 per cent) and the Primary Budget Surplus remains positive (1 per cent of GDP). In this case the public debt ratio still false which makes the proposition in the question false.

So if you have zero real interest rates, then even in a recession, the public debt ratio can still fall and the government run a budget surplus as long as Primary Surplus is greater in absolute value to the negative real GDP growth rate. Of-course, this logic is just arithmetic based on the relationship between the flows and stocks involved. In reality, it would be hard for the government to run a primary surplus under these conditions given the automatic stabilisers would be undermining that aim.

In Year 5, the real GDP growth rate is negative 1.5 per cent and the Primary Budget Surplus remains positive at 1 per cent of GDP. In this case the public debt ratio rises.

Of-course, the public debt ratio will be reduced if the
But the best way to reduce the public debt ratio is to stop issuing debt. A sovereign government doesn’t have to issue debt if the central bank is happy to keep its target interest rate at zero or pay interest on excess reserves.

The discussion also demonstrates why tightening monetary policy makes it harder for the government to reduce the public debt ratio – which, of-course, is one of the more subtle mainstream ways to force the government to run surpluses.

The following blog may be of further interest to you:

• Saturday Quiz – November 27, 2010 – answers and discussion