Tag: potential output

The past decade or so has seen large-scale economic turbulence. As we saw in the blog Fiscal impulses, governments have responded with large fiscal interventions. The COVID-19 pandemic, for example, led to a positive fiscal impulse in the UK in 2020, as measured by the change in the structural primary balance, of over 12 per cent of national income.

The scale of these interventions has led to a significant increase in the public-sector debt-to-GDP ratio in many countries. The recent interest rates hikes arising from central banks responding to inflationary pressures have put additional pressure on the financial well-being of governments, not least on the financing of their debt. Here we discuss these pressures in the context of the ‘r g’ rule of sustainable public debt.

Public-sector debt and borrowing

Chart 1 shows the path of UK public-sector net debt and net borrowing, as percentages of GDP, since 1990. Debt is a stock concept and is the result of accumulated flows of past borrowing. Net debt is simply gross debt less liquid financial assets, which mainly consist of foreign exchange reserves and cash deposits. Net borrowing is the headline measure of the sector’s deficit and is based on when expenditures and receipts (largely taxation) are recorded rather than when cash is actually paid or received. (Click here for a PowerPoint of Chart 1)

Chart 1 shows the impact of the fiscal interventions associated with the global financial crisis and the COVID-19 pandemic, when net borrowing rose to 10 per cent and 15 per cent of GDP respectively. The former contributed to the debt-to-GDP ratio rising from 35.6 per cent in 2007/8 to 81.6 per cent in 2014/15, while the pandemic and subsequent cost-of-living interventions contributed to the ratio rising from 85.2 per cent in 2019/20 to around 98 per cent in 2023/24.

Sustainability of the public finances

The ratcheting up of debt levels affects debt servicing costs and hence the budgetary position of government. Yet the recent increases in interest rates also raise the costs faced by governments in financing future deficits or refinancing existing debts that are due to mature. In addition, a continuation of the low economic growth that has beset the UK economy since the global financial crisis also has implications for the burden imposed on the public sector by its debts, and hence the sustainability of the public finances. After all, low growth has implications for spending commitments, and, of course, the flow of receipts.

The analysis therefore implies that the sustainability of public-sector debt is dependent on at least three factors: existing debt levels, the implied average interest rate facing the public sector on its debts, and the rate of economic growth. These three factors turn out to underpin a well-known rule relating to the fiscal arithmetic of public-sector debt. The rule is sometimes known as the ‘r g’ rule (i.e. the interest rate minus the growth rate).

Underpinning the fiscal arithmetic that determines the path of public-sector debt is the concept of the ‘primary balance’. This is the difference between the sector’s receipts and its expenditures less its debt interest payments. A primary surplus (a positive primary balance) means that receipts exceed expenditures less debt interest payments, whereas a primary deficit (a negative primary balance) means that receipts fall short. The fiscal arithmetic necessary to prevent the debt-to-GDP ratio rising produces the following stable debt equation or ‘r g’ rule:

On the left-hand side of the stable debt equation is the required primary surplus (PS) to GDP (Y) ratio. Moving to the right-hand side, the first term is the existing debt-to-GDP ratio (D/Y). The second term ‘r g’, is the differential between the average implied interest rate the government pays on its debt and the growth rate of the economy. These terms can be expressed in either nominal or real terms as this does not affect the differential.

To illustrate the rule consider a country whose existing debt-to-GDP ratio is 1 (i.e. 100 per cent) and the ‘r g’ differential is 0.02 (2 percentage points). In this scenario they would need to run a primary surplus to GDP ratio of 0.02 (i.e. 2 percent of GDP).

The ‘r g‘ differential

The ‘r g’ differential reflects macroeconomic and financial conditions. The fiscal arithmetic shows that these are important for the dynamics of public-sector debt. The fiscal arithmetic is straightforward when r = g as any primary deficit will cause the debt-to-GDP ratio to rise, while a primary surplus will cause the ratio to fall. The larger is g relative to r the more favourable are the conditions for the path of debt. Importantly, if the differential is negative (r < g), it is possible for the public sector to run a primary deficit, up to the amount that the stable debt equation permits.

Consider Charts 2 and 3 to understand how the ‘r g’ differential has affected debt sustainability in the UK since 1990. Chart 2 plots the implied yield on 10-year government bonds, alongside the annual rate of nominal growth (click here for a PowerPoint). As John explains in his blog The bond roller coaster, the yield is calculated as the coupon rate that would have to be paid for the market price of a bond to equal its face value. Over the period, the average annual nominal growth rate was 4.5 per cent, while the implied interest rate was almost identical at 4.6 per cent. The average annual rate of CPI inflation over this period was 2.8 per cent.

Chart 3 plots the ‘r g’ differential which is simply the difference between the two series in Chart 2, along with a 12-month rolling average of the differential to help show better the direction of the differential by smoothing out some of the short-term volatility (click here for a PowerPoint). The differential across the period is a mere 0.1 percentage points implying that macroeconomic and financial conditions have typically been neutral in supporting debt sustainability. However, this does mask some significant changes across the period.

We observe a general downward trend in the ‘r g’ differential from 1990 up to the time of the global financial crisis. Indeed between 2003 and 2007 we observe a favourable negative differential which helps to support the sustainability of public debt and therefore the well-being of the public finances. This downward trend of the ‘r g’ differential was interrupted by the financial crisis, driven by a significant contraction in economic activity. This led to a positive spike in the differential of over 7 percentage points.

Yet the negative differential resumed in 2010 and continued up to the pandemic. Again, this is indicative of the macroeconomic and financial environments being supportive of the public finances. It was, however, largely driven by low interest rates rather than by economic growth.

Consequently, the negative ‘r g’ differential meant that the public sector could continue to run primary deficits during the 2010s, despite the now much higher debt-to-GDP ratio. Yet, weak growth was placing limits on this. Chart 4 indeed shows that primary deficits fell across the decade (click here for a PowerPoint).

The pandemic and beyond

The pandemic saw the ‘r g’ differential again turn markedly positive, averaging 7 percentage points in the four quarters from Q2 of 2020. While the differential again turned negative, the debt-to-GDP ratio had also increased substantially because of large-scale fiscal interventions. This made the negative differential even more important for the sustainability of the public finances. The question is how long the negative differential can last.

Looking forward, the fiscal arithmetic is indeed uncertain and worryingly is likely to be less favourable. Interest rates have risen and, although inflationary pressures may be easing somewhat, interest rates are likely to remain much higher than during the past decade. Geopolitical tensions and global fragmentation pose future inflationary concerns and a further drag on growth.

As well as the short-term concerns over growth, there remain long-standing issues of low productivity which must be tackled if the growth of the UK economy’s potential output is to be raised. These concerns all point to the important ‘r g’ differential become increasingly less negative, if not positive. If so the fiscal arithmetic could mean increasingly hard maths for policymakers.




  1. What is meant by each of the following terms: (a) net borrowing; (b) primary deficit; (c) net debt?
  2. Explain how the following affect the path of the public-sector debt-to-GDP ratio: (a) interest rates; (b) economic growth; (c) the existing debt-to-GDP ratio.
  3. Which factors during the 2010s were affecting the fiscal arithmetic of public debt positively, and which negatively?
  4. Discuss the prospects for the fiscal arithmetic of public debt in the coming years.
  5. Assume that a country has an existing public-sector debt-to-GDP ratio of 60 percent.
    (a) Using the ‘rule of thumb’ for public debt dynamics, calculate the approximate primary balance it would need to run in the coming year if the expected average real interest rate on the debt were 3 per cent and real economic growth were 2 per cent?
    (b) Repeat (a) but now assume that real economic growth is expected to be 4 per cent.
    (c) Repeat (a) but now assume that the existing public-sector debt-to-GDP ratio is 120 per cent.
    (d) Using your results from (a) to (c) discuss the factors that affect the fiscal arithmetic of the growth of public-sector debt.

On 10 March, the House of Representatives gave final approval to President Biden’s $1.9tr fiscal stimulus plan (the American Rescue Plan). Worth over 9% of GDP, this represents the third stage of an unparalleled boost to the US economy. In March 2020, President Trump secured congressional agreement for a $2.2tr package (the CARES Act). Then in December 2020, a bipartisan COVID relief bill, worth $902bn, was passed by Congress.

By comparison, the Obama package in 2009 in response to the impending recession following the financial crisis was $831bn (5.7% of GDP).

The American Rescue Plan

The Biden stimulus programme consists of a range of measures, the majority of which provide monetary support to individuals. These include a payment of $1400 per person for single people earning less than $75 000 and couples less than $150 000. These come on top of payments of $1200 in March 2020 and $600 in late December. In addition, the top-up to unemployment benefits of $300 per week agreed in December will now continue until September. Also, annual child tax credit will rise from $2000 annually to as much as $3600 and this benefit will be available in advance.

Other measures include $350bn in grants for local governments depending on their levels of unemployment and other needs; $50bn to improve COVID testing centres and $20bn to develop a national vaccination campaign; $170bn to schools and universities to help them reopen after lockdown; and grants to small businesses and specific grants to hard-hit sectors, such as hospitality, airlines, airports and rail companies.

Despite supporting the two earlier packages, no Republican representative or senator backed this latest package, arguing that it was not sufficiently focused. As a result, reaction to the package has been very much along partisan lines. Nevertheless, it is supported by some 90% of Democrat voters and 50% of Republican voters.

Is the stimulus the right amount?

Although the latest package is worth $1.9tr, aggregate demand will not expand by this amount, which will limit the size of the multiplier effect. The reason is that the benefits multiplier is less than the government expenditure multiplier as some of the extra money people receive will be saved or used to reduce debts.

With $3tr representing some 9% of GDP, this should easily fill the estimated negative output gap of between 2% and 3%, especially when multiplier effects are included. Also, with savings having increased during the recession to put them some 7% above normal, the additional amount saved may be quite small, and wealthier Americans may begin to reduce their savings and spend a larger proportion of their income.

So the problem might be one of excessive stimulus, which in normal times could result in crowding out by driving up interest rates and dampening investment. However, the Fed is still engaged in a programme of quantitative easing. Between mid-March 2020 and the end of March 2021, the Fed’s portfolio of securities held outright grew from $3.9tr to $7.2tr. What is more, many economists predict that inflation is unlikely to rise other than very slightly. If this is so, it should allow the package to be financed easily. Debt should not rise to unsustainable levels.

Other economists argue, however, that inflationary expectations are rising, reflected in bond yields, and this could drive actual inflation and force the Fed into the awkward dilemma of either raising interest rates, which could have a significant dampening effect, or further increasing money supply, potentially leading to greater inflationary problems in the future.

A lot will depend what happens to potential GDP. Will it rise over the medium term so that additional spending can be accommodated? If the rise in spending encourages an increase in investment, this should increase potential GDP. This will depend on business confidence, which may be boosted by the package or may be dampened by worries about inflation.

Additional packages to come

Potential GDP should also be boosted by two further packages that Biden plans to put to Congress.

The first is a $2.2tr infrastructure investment plan, known as the American Jobs Plan. This is a 10-year plan to invest public money in transport infrastructure (such as rebuilding 20 000 miles of road and repairing bridges), public transport, electric vehicles, green housing, schools, water supply, green power generation, modernising the power grid, broadband, R&D in fields such as AI, social care, job training and manufacturing. This will be largely funded through tax increases, such as gradually raising corporation tax from 21% to 28% (it had been cut from 35% to 21% by President Trump) and taxing global profits of US multinationals. However, the spending will generally precede the increased revenues and thus will raise aggregate demand in the initial years. Only after 15 years are revenues expected to exceed costs.

The second is a yet-to-be announced plan to increase spending on childcare, healthcare and education. This should be worth at least $1tr. This will probably be funded by tax increases on income, capital gains and property, aimed largely at wealthy individuals. Again, it is hoped that this will boost potential GDP, in this case by increasing labour productivity.

With earlier packages, the total increase in public spending will be over $8tr. This is discretionary fiscal policy writ large.




  1. Draw a Keynesian cross diagram to show the effect of an increase in benefits when the economy is operating below potential GDP.
  2. What determines the size of the benefits multiplier?
  3. Explain what is meant by the output gap. How might the pandemic and accompanying emergency health measures have affected the size of the output gap?
  4. How are expectations relevant to the effectiveness of the stimulus measures?
  5. What is likely to determine the proportion of the $1400 stimulus cheques that people spend?
  6. Distinguish between resource crowding out and financial crowding out. Is the fiscal stimulus package likely to result in either form of crowding out and, if so, what will determine by how much?
  7. What is the current monetary policy of the Fed? How is it likely to impact on the effectiveness of the fiscal stimulus?

Is there a ‘magic money tree’? Is it desirable for central banks to create money to finance government deficits?

The standard thinking of conservative governments around the world is that creating money to finance deficits will be inflationary. Rather, governments should attempt to reduce deficits. This will reduce the problem of government expenditure crowding out private expenditure and reduce the burden placed on future generations of having to finance higher government debt.

If deficits rise because of government response to an emergency, such as supporting people and businesses during the Covid-19 pandemic, then, as soon as the problem begins to wane, governments should attempt to reduce the higher deficits by raising taxes or cutting government expenditure. This was the approach of many governments, including the Coalition and Conservative governments in the UK from 2010, as econommies began to recover from the 2007/8 financial crisis.

Modern Monetary Theory‘ challenges these arguments. Advocates of the theory support the use of higher deficits financed by monetary expansion if the money is spent on things that increase potential output as well as actual output. Examples include spending on R&D, education, infrastructure, health and housing.

Modern monetary theorists still accept that excess demand will lead to inflation. Governments should therefore avoid excessive deficits and central banks should avoid creating excessive amounts of money. But, they argue that inflation caused by excess demand has not been a problem for many years in most countries. Instead, we have a problem of too little investment and too little spending generally. There is plenty of scope, they maintain, for expanding demand. This, if carefully directed, can lead to productivity growth and an expansion of aggregate supply to match the rise in aggregate demand.

Government deficits, they argue, are not intrinsically bad. Government debt is someone else’s assets, whether in the form of government bonds, savings certificates, Treasury bills or other instruments. Provided the debt can be serviced at low interest rates, there is no problem for the government and the spending it generates can be managed to allow economies to function at near full capacity.

The following videos and articles look at modern monetary theory and assess its relevance. Not surprisingly, they differ in their support of the theory!




  1. Compare traditional Keynesian economics and modern monetary theory.
  2. Using the equation of exchange, MV = PY, what would a modern monetary theorist say about the effect of an expansion of M on the other variables?
  3. What is the role of fiscal policy in modern monetary theory?
  4. What evidence might suggest that money supply has been unduly restricted?
  5. When, according to modern monetary theory, is a rising government deficit (a) not a problem; (b) a problem?
  6. Is there any truth in the saying, ‘There’s no such thing as a magic money tree’?
  7. Provide a critique of modern monetary theory.

On 2 November, the Bank of England raised Bank rate from 0.25% to 0.5% – the first rise since July 2007. But was now the right time to raise interest rates? Seven of the nine-person Monetary Policy Committee voted to do so; two voted to keep Bank Rate at 0.25%.

Raising the rate, on first sight, may seem a surprising decision as growth remains sluggish. Indeed, the two MPC members who voted against the rise argued that wage growth was too weak to justify the rise. Also, inflation is likely to fall as the effects of the Brexit-vote-induced depreciation of sterling on prices feeds through the economy. In other words, prices are likely to settle at the new higher levels but will not carry on rising – at least not at the same rate.

So why did the other seven members vote to raise Bank Rate. There are three main arguments:

Inflation, at 3%, is above the target of 2% and is likely to stay above the target if interest rates are not raised.
There is little spare capacity in the economy, with low unemployment. There is no shortage of aggregate demand relative to output.
With productivity growth being negligible and persistently below that before the financial crisis, aggregate demand, although growing slower than in the past, is growing excessively relative to the growth in aggregate supply.

As the Governor stated at the press conference:

In many respects, the decision today is straightforward: with inflation high, slack disappearing, and the economy growing at rates above its speed limit, inflation is unlikely to return to the 2% target without some increase in interest rates.

But, of course, the MPC’s forecasts may turn out to be incorrect. Many things are hard to predict. These include: the outcomes of the Brexit negotiations; consumer and business confidence and their effects on consumption and investment; levels of growth in other countries and their effects on UK exports; and the effects of the higher interest rates on saving and borrowing and hence on aggregate demand.

The Bank of England is well aware of these uncertainties. Although it plans two more rises in the coming months and then Bank Rate remaining at 1% for some time, this is based on its current assessment of the outlook for the economy. If circumstances change, the Bank will adjust the timing and total amount of future interest rate changes.

There are, however, dangers in the rise in interest rates. Household debt is at very high levels and, although the cost of servicing these debts is relatively low, even a rise in interest rates of just 0.25 percentage points can represent a large percentage increase. For example, a rise in a typical variable mortgage interest rate from 4.25% to 4.5% represents a 5.9% increase. Any resulting decline in consumer spending could dent business confidence and reduce investment.

Nevertheless, the Bank estimates that the effect of higher mortgage rates is likely to be small, given that some 60% of mortgages are at fixed rates. However, people need to refinance such rates every two or three years and may also worry about the rises to come promised by the Bank.


Bank of England deputy says interest rate rise means pain for households and more hikes could be in store Independent, Ben Chapman (3/11/17)
UK interest rates: Bank of England shrugs off Brexit nerves to launch first hike in over a decade Independent, Ben Chu (2/11/17)
Bank of England takes slow lane after first rate hike since Reuters, David Milliken, William Schomberg and Julian Satterthwaite (2/11/17)
First UK rate rise in a decade will be a slow burn Financial Times, Gemma Tetlow (2/11/17)
The Bank of England’s Rate Rise Could Spook Britain’s Economy Bloomberg, Fergal O’Brien and Brian Swint (3/11/17)
Bank of England hikes rates for the first time in a decade CNBC, Sam Meredith (2/11/17)
Interest rates rise in Britain for the first time in a decade The Economist (2/11/17)

Bank of England publications

Bank of England Inflation Report Press Conference, Opening Remarks Financial Times on YouTube, Mark Carney (2/11/17)
Bank of England Inflation Report Press Conference, Opening Remarks Bank of England, Mark Carney (2/11/17)
Inflation Report Press Conference (full) Bank of England on YouTube (2/11/17)
Inflation Report Bank of England (November 2017)
Monetary Policy Summary and minutes of the Monetary Policy Committee meeting ending on 1 November 2017 Bank of England (2/11/17)


  1. Why did the majority of MPC members feel that now was the right time to raise interest rates whereas a month ago was the wrong time?
  2. Why did the exchange rate fall when the announcement was made?
  3. How does a monetary policy of targeting the rate of inflation affect the balance between aggregate demand and aggregate supply?
  4. Can monetary policy affect potential output, or only actual output?
  5. If recent forecasts have downgraded productivity growth and hence long-term economic growth, does this support the argument for raising interest rates or does it suggest that monetary policy should be more expansionary?
  6. Why does the MPC effectively target inflation in the future (typically in 24 months’ time) rather than inflation today? Note that Mark Carney at the press conference said, “… it isn’t so much where inflation is now, but where it’s going that concerns us.”
  7. To what extent can the Bank of England’s monetary policy be described as ‘discretionary’?

The article below looks at the economy of Brazil. The statistics do not look good. Real output fell last year by 3.8% and this year it is expected to fall by another 3.3%. Inflation this year is expected to be 9.0% and unemployment 11.2%, with the government deficit expected to be 10.4% of GDP.

The article considers Keynesian economics in the light of the case of Brazil, which is suffering from declining potential supply, but excess demand. It compares Brazil with the case of most developed countries in the aftermath of the financial crisis. Here countries have suffered from a lack of demand, made worse by austerity policies, and only helped by expansionary monetary policy. But the effect of the monetary policy has generally been weak, as much of the extra money has been used to purchase assets rather than funding a growth in aggregate demand.

Different policy prescriptions are proposed in the article. For developed countries struggling to grow, the solution would seem to be expansionary fiscal policy, made easy to fund by lower interest rates. For Brazil, by contrast, the solution proposed is one of austerity. Fiscal policy should be tightened. As the article states:

Spending restraint might well prove painful for some members of Brazilian society. But hyperinflation and default are hardly a walk in the park for those struggling to get by. Generally speaking, austerity has been a misguided policy approach in recent years. But Brazil is a special case. For now, anyway.

The tight fiscal policies could be accompanied by supply-side policies aimed at reducing bureaucracy and inefficiency.


Brazil and the new old normal: There is more than one kind of economic mess to be in The Economist, Free Exchange Economics (12/10/16)


  1. Explain what is meant by ‘crowding out’.
  2. What is meant by the ‘liquidity trap’? Why are many countries in the developed world currently in a liquidity trap?
  3. Why have central banks in the developed world found it difficult to stimulate growth with policies of quantitative easing?
  4. Under what circumstances would austerity policies be valuable in the developed world?
  5. Why is crowding out of fiscal policy unlikely to occur to any great extent in Europe, but is highly likely to occur in Brazil?
  6. What has happened to potential GDP in Brazil in the past couple of years?
  7. What is meant by the ‘terms of trade’? Why have Brazil’s terms of trade deteriorated?
  8. What sort of policies could the Brazilian government pursue to raise growth rates? Are these demand-side or supply-side policies?
  9. Should Brazil pursue austerity policies and, if so, what form should they take?