Tag: interest rates

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Getting real with house prices

When I worked as a professional economist at HM Treasury and later the Council of Mortgage Lenders (now part of UK Finance), I would regularly brief on the state of the affordability of housing, with a particular focus on the owner-occupied market. That was back in the late 1990s. Fast forward a quarter of a century and I recognise not only how much I have aged but also how deep-rooted and long-standing the affordability problem is.

It is perhaps not surprising that in her first speech as the new Chancellor of the Exchequer, Rachel Reeves, referenced directly the housing market and the need to address supply-side issues. She has set a target of one and a half million new homes built over the next five years.

It is therefore timely to revisit the trends in house prices across the UK. By applying the distinction between nominal and real values we get a very clear sense of the deteriorating affordability of housing.

Nominal house price patterns

The average UK actual or nominal house price in April 2024 was £281 000. As Chart 1 shows, this masks considerable differences across the UK. In England the average price was £298 000 (105 per cent of the UK average), though this is heavily skewed by London where the average price was £502 000 (178 per cent of the UK average). Meanwhile, in Scotland it was £190 000 (68 per cent of the UK average), in Wales £208 000 (74 per cent of the UK average) and in Northern Ireland it was £178 000 (74 per cent of the UK average). (Click here to download a PowerPoint copy of the chart.)

A simple comparison of the average house price in April 2024 with January 1970 reveals a 72-fold increase in the UK, an 80-fold increase in England, including a 101-fold increase in London, a 65-fold increase in Wales, a 59-fold increase in Scotland and a 45-fold increase in Northern Ireland. Whilst these figures are sensitive to the particular period over which we choose to measure, there is little doubting that upward long-term trend in house prices.

Whilst nominal prices trend upwards over time, the short-term rates of increase are highly volatile. This can be seen from an inspection of Chart 2, which shows the annual rates of increase across the four nations of the UK, as well as for London. This is evidence of frequent imbalances between the flows of property on to the market to sell (instructions to sell) and the number of people looking to buy (instructions to buy). An increase in instructions to buy (housing demand) relative to those to sell (housing supply) puts upward pressure on prices; an increase in the number of instructions to sell (housing supply) relative to those to buy (housing demand) puts downward pressure on prices. (Click here to download a PowerPoint copy of the chart.)

Chart 2 nicely captures the recent slowdown in the housing market. The inflationary shock that began to take hold in 2021 led the Bank of England to raise Bank Rate on 15 occasions – from 0.25 per cent in December 2021 to 5.25 per cent in August 2023 (which remains the rate at the time of writing, but could be cut at the next Bank of England meeting on 1 August 2024). Higher Bank Rate has pushed up mortgage rates, which has contributed to an easing of housing demand. Demand has also been dampened by weak growth in the economy, higher costs of living and fragile consumer confidence. The result has been a sharp fall in the rate of house price inflation, with many parts of the UK experiencing house price deflation. As the chart shows, the rate of deflation has been particularly pronounced and protracted in London, with house prices in January 2024 falling at an annual rate of 5.1 per cent.

Real house price patterns

Despite the volatility in house prices, such as those of recent times, the longer-term trend in house prices is nonetheless upwards. To understand just how rapidly UK house prices have grown over time, we now consider their growth relative to consumer prices. This allows us to analyse the degree to which there has been an increase in real house prices.

To calculate real or inflation-adjusted house prices, we deflate nominal house prices by the Consumer Prices Index (CPI). Chart 3 shows the resulting real house prices series across the UK as if consumer prices were fixed at 2015 levels.

The key message here is that over the longer-term we cannot fully explain the growth in actual (nominal) house prices by the growth in consumer prices. Rather, we see real increases in house prices. Inflation-adjusted UK house prices were 5.3 times higher in April 2024 compared to January 1970. For England the figure was 5.9 times, Wales 4.8 times, Scotland 4.3 times and for Northern Ireland 3.3 times. In London, inflation-adjusted house prices were 7.4 times higher. (Click here to download a PowerPoint copy of the chart.)

As we saw with nominal house prices, the estimated long-term increase in real house prices is naturally sensitive to the period over which we measure. For example, the average real UK house price in August 2022 was 5.8 times higher than in January 1970, while in London they were 8.7 times higher. But the message is clear – the long-term increase is not merely nominal, reflecting increasing prices generally, but is real, reflecting pressures that are increasing house prices relative to general price levels.

Chart 4 shows how the volatility in house prices continues to be evident when house prices are adjusted for changes in consumer prices. The UK’s annual rate of real house price inflation was as high as 40 per in January 1973; on the other hand, in June 1975 inflation-adjusted house prices were 15 per cent lower than a year earlier. (Click here to download a PowerPoint copy of the chart.)

Over the period from January 1970 to April 2024, the average annual rate of real house price inflation in the UK was 3.2 per cent. Hence house prices have, on average, grown at an annual rate of consumer price inflation plus 3.2 per cent. For the four nations, real house price inflation has averaged 3.8 per cent in England, 3.4 per cent in Wales, 3.0 per cent in Scotland and 2.9 per cent in Northern Ireland. Further, the average rate of real house price inflation in London since January 1970 has been 4.5 per cent. By contrast, that for the East and West Midlands has been 3.7 and 3.5 per cent respectively. The important point here is that the pace with which inflation-adjusted house prices have risen helps to contextualise the extent of the problem of housing affordability – a problem that only worsens over time when real incomes do not keep pace.

House building

The newly elected Labour government has made the argument that it needs to prioritise planning reform as an engine for economic growth. While this ambition extends beyond housing, the scale of the supply-side problem facing the housing market can be seen in Chart 5. The chart shows the number of housing completions in the UK since 1950 by type of tenure. (Click here to download a PowerPoint copy of the chart.)

The chart shows the extent of the growth in house building in the UK that occurred from the 1950s and into the 1970s. Over these three decades the typical number of new properties completed each year was around 320 000 or 6 per thousand of the population. The peak of house building was in the late 1960s when completions exceeded 400 000 per year or over 7.5 per thousand of the population. It is also noticeable how new local authority housing (‘council houses’) played a much larger role in the overall housing mix.

Since 1980, the average number of housing completions each year has dropped to 191 000 or 3.2 per thousand of the population. If we consider the period since 2000, the number of completions has averaged only 181 000 per year or 2.9 per thousand of the population. While it is important to understand the pressures on housing demand in any assessment of the growth in real house prices, the lack of growth in supply is also a key factor. The fact that less than half the number of properties per thousand people are now being built compared with half a century or so ago is an incredibly stark statistic. It is a major determinant of the deterioration of housing affordability.

However, there are important considerations around the protection of the natural environment that need to be considered too. It will therefore be interesting to see how the reforms to planning develop and what their impact will be on house prices and their affordability.

Articles

Statistics

Questions

  1. Explain the difference between a rise in the rate of house price inflation a rise in the level of house prices.
  2. Explain the difference between nominal and real house prices.
  3. If nominal house prices rise can real house price fall? Explain your answer.
  4. What do you understand by the terms instructions to buy and instructions to sell?
  5. What factors are likely to affect the levels of instructions to buy and instructions to sell?
  6. How does the balance between instructions to buy and instructions to sell affect house prices?
  7. How can we differentiate between different housing markets? Illustrate your answer with examples.
  8. What metrics could be used to measure the affordability of housing?
  9. Discuss the argument that the deterioration of housing affordability is the result of market failure.
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The approach to monetary and fiscal policy

The following blog is inspired by my teaching of macroeconomic issues to my final year students at Aston University. In the classes we’ve been discussing important aspects of monetary and fiscal policy design. What has become clear to me and my students is that the trade-offs which characterise the discipline of economics are certainly alive and well in the current environment in which monetary and fiscal policy choices are being made.

To demonstrate this we consider here some of the discussions we’ve had in class around central bank independence and monetary policy mandates. We’ve also looked at fiscal policy. Here we’ve examined the state of the public finances and the importance that seems to be attached to debt stabilisation and the imposition of debt rules.

Delegation and central bank mandates

My teaching this term began by introducing my students to one of the most important and influential monetary policy models. This is the model of Kydland and Prescott. Their model, published in the Journal of Political Economy in 1977 has become the theoretical bedrock for the modern-day operational independence of central banks.1

The model explores how systemically high inflation can become established in economies when policymakers have the political incentive to lower unemployment or increase output above its long-run equilibrium value. This may be the case if governments operate monetary policy rather than the central bank (of if the central bank operates monetary policy but follows government objectives). By adopting expansionary monetary policy, governments can increase their popularity.

But this is likely to be short-lived, as any increased economic activity will only be temporary (assuming that the natural-rate hypothesis holds). Soon, inflation will rise.

But, if an election is on the horizon, there may be enough time to boost output and employment before inflation rises. In other words, an expectations-augmented Phillips curve may present governments with an incentive to loosen monetary policy and worry about the inflation consequences after the election.

However, the resulting ‘inflation surprise’ through the loosening of monetary policy means a fall in real pay and therefore in purchasing power. If people suspect that governments will be tempted to loosen policy, they will keep their expectations of inflation higher than the socially optimal inflation rate. Consequently, low-inflation targets lack credibility when governments have the temptation to loosen monetary policy. Such targets are time-inconsistent because governments have an incentive to renege and deliver higher inflation through a looser monetary policy. The result is an inflation bias.

Central bank independence
To prevent this inflationary bias arising, many central banks around the world have been given some form of operational independence with a mandate centred around an inflation-rate target. By delegating monetary policy to a more conservative central bank, the problem of inflationary bias can be addressed.

Yet central bank independence is not without its own issues and this has been an important part of the discussions with my students. Today, many economies are continuing to experience the effects of the inflationary shocks that began in 2021 (see Chart 1 for the UK CPI inflation rate: click here for a PowerPoint). The question is whether the appointment of a conservative or hard-nosed hawkish central banker trades off the stabilisation of inflation for greater volatility in output or unemployment.

The inflation–output stabilisation trade-off is closely associated with the works of Kenneth Rogoff2 and John Taylor3. The latter is known for his monetary policy rule, which has become known as the ‘Taylor rule’. This advocates that a rules-based central bank ought to place weight on both inflation and output stabilisation.

This is not without its own issues, however, since, by also placing weight on output stabilisation, we are again introducing the possibility of greater inflationary bias in policy making. Hence, while the act of delegation and a rules- or target-based approach may mitigate the extent of the bias relative to that in the Kydland and Prescott model, there nonetheless still remain issues around the design of the optimal framework for the conduct of monetary policy.

Indeed, the announcement that the UK had moved into recession in the last two quarters of 2023 can be seen as evidence that an otherwise abstract theoretical trade-off between inflation and output stabilisation is actually very real.

My classroom discussions have also shown how economic theory struggles to identify an optimal inflation-rate target. Beyond accepting that a low and stable inflation rate is desirable, it is difficult to address fully the student who asks what is so special about a 2% inflation target. Would not a 3% target, for example, be preferable, they might ask?

Whilst this may sound somewhat trivial, it has real-world consequences. In a world that now seems to be characterised by greater supply-side volatility and by more frequent inflation shocks than we were used to in recent history, might a higher inflation rate target be preferable? Certainly, one could argue that, with an inflation–output stabilisation trade-off, there is the possibility that monetary policy could be unduly restrictive in our potential new macroeconomic reality. Hence, we might come to see governments and central banks in the near future revisiting the mandates that frame the operation of their monetary policy. Time will tell.

Fiscal policy and debt stabilisation

The second topic area that I have been discussing in my final-year macroeconomics classes has centred around fiscal policy and the state of the public finances. The context for this is that we have seen a significant increase in public debt-to-GDP ratios over the past couple of decades as the public sector has attempted to absorb significant economic shocks. These include the global financial crisis of 2007–8, the COVID-19 pandemic and the cost-of-living crisis. These interventions in the case of the UK have seen its public debt-to-GDP ratio more than triple since the early 2000s to close to 100% (see Chart 2: click here for a PowerPoint).

Understandably, given the stresses placed on the public finances, economists have increasingly debated issues around debt sustainability. These debates have been mirrored by politicians and policymakers. A key question is whether to have a public debt rule. The UK has in recent years adopted such a rule. The arguments for a rule centre on ensuring sound public finances and maintaining the confidence of investors to purchases public debt. A debt rule therefore places a discipline on fiscal policy, with implications for taxation and spending.

How easy it is to stick to a debt rule depends on three key factors. It will be harder to stick to the rule:

  • The higher the current debt-to-GDP ratio and hence the more it needs to be reduced to meet the rule.
  • The higher the rate of interest and hence the greater the cost of servicing the public debt.
  • The lower the rate of economic growth and hence the less quickly will tax revenues rise.

With a given debt-to-GDP ratio, a given average interest rate payable on its debt, and a given rate of economic growth, we can determine the primary fiscal balance relative to GDP a government would need to meet for the debt-to-GDP ratio to remain stable. This is known as the ‘debt-stabilising primary balance’. The primary balance is the difference between a government’s receipts and its expenditures less the interest payments on its debt.

This fiscal arithmetic is important in determining a government’s fiscal choices. It shows the implications for spending and taxation. These implications become ever more important and impactful on people, businesses, and society when the fiscal arithmetic becomes less favourable. This is a situation that appears to be increasingly the case for many countries, including the UK, as the rate of interest on public debt rises relative to a country’s rate of economic growth. As this happens, governments are increasingly required to run healthier primary balances. This of course implies a tightening of their fiscal stance.

Hence, the fiscal conversations with my students have focused on both the benefits and the costs of debt-stabilisation. In respect of the costs, a few issues have arisen.

First, as with the inflation-rate target, it is hard to identify an optimal public debt-to-GDP ratio number. While the fiscal arithmetic may offer some clue, it is not straightforward to address the question as to whether a debt-to-GDP ratio of say 100% or 120% would be excessive for the UK.

Second, it is possible that the debt stabilisation itself can make the fiscal arithmetic of debt stabilisation more difficult. This occurs if fiscal consolidation itself hinders long-term economic growth, which then makes the fiscal arithmetic more difficult. This again points to the difficulties in designing policy frameworks, whether they be for monetary or fiscal policy.

Third, a focus on debt stabilisation alone ignores the fact that there are two sides to any sector’s balance sheet. It would be very unusual when assessing the well-being of businesses or households if we were to ignore the asset side of their balance sheet. Yet, this is precisely the danger of focusing on public debt at the exclusion of what fiscal choices can mean for public-sector assets, from which we all can potentially benefit. Hence, some would suggest a more balanced approach to assessing the soundness of the public finances might involve a net worth (assets less liabilities) measure. This has parallels with the debates around whether mandates of central banks should be broader.

Applications in macroeconomics

What my teaching of a topics-based macroeconomics module this term has vividly demonstrated is that concepts, theories, and models come alive, and are capable of being understood better, when they are used to shine a light on real-world issues. The light being shone on monetary and fiscal policy in today’s turbulent macroeconomic environment is perhaps understandably very bright.

Indeed, the light being shone on fiscal policy in the UK and some other countries facing an upcoming election, is intensified further with the state of the public finances shaping much of the public discourse on fiscal choices. Hopefully, my students will continue to debate these important issues beyond their graduation, stressing their importance for people’s lives and, in doing so, going beyond the abstract.

References

  1. Rules rather than discretion: The inconsistency of optimal plans
    The Journal of Political Economy, Finn E Kydland and Edward C. Prescott (1977, 85(3), pp 473–92)

  2. The optimal degree of commitment to an intermediate monetary target
    Quarterly Journal of Economics, Kenneth Rogoff (November 1985, 100(4), pp 1169–89)

  3. Discretion versus policy rules in practice
    Carnegie-Rochester Conference Series on Public Policy, John B Taylor (December 1993, 39, pp 195–214)

Articles

Questions

  1. What is meant by time-inconsistent monetary policy announcements? How has this concept been important for the way in which many central banks now conduct monetary policy?
  2. What is meant by a ‘conservative’ central banker? Why is the appointment of this type of central banker thought to be important in affecting inflation?
  3. What is the contemporary macroeconomic relevance of the inflation–output (or inflation–unemployment) stabilisation trade-off?
  4. How is the primary balance different from the actual budget balance?
  5. What do you understand by the concept of ‘the fiscal arithmetic’. Explain how each element of the fiscal arithmetic affects the debt-stabilising primary balance?
  6. Analyse the costs of benefits of a debt-based fiscal rule.
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The Russian economy after two years of war

It’s two years since Russia invaded Ukraine. Western countries responded by imposing large-scale sanctions. These targeted a range of businesses, banks and other financial institutions, payments systems and Russian exports and imports. Some $1 trillion of Russian assets were frozen. Many Western businesses withdrew from Russia or cut off commercial ties. In addition, oil and gas imports from Russia have been banned by most developed countries and some developing countries, and a price cap of $60 per barrel has been imposed on Russian oil. What is more, sanctions have been progressively tightened over the past two years. For example, on the second anniversary of the invasion, President Biden announced more than 500 new sanctions against individuals and companies involved in military production and supply chains and in financing Russia’s war effort.

The economy in Russia has also been affected by large-scale emigration of skilled workers, the diversion of workers to the armed forces and the diversion of capital and workers to the armaments industry.

So has the economy of Russia been badly affected by sanctions and these other factors? The IMF in its World Economic Forecast of April 2022 predicted that the Russian economy would experience a steep, two-year recession. But, the Russian economy has fared much better than first predicted and the steep recession never materialised.

In this blog we look at Russia’s economic performance. First, we examine why the Russian economy seems stronger today than forecast two years ago. Then we look at its economic weaknesses directly attributable to the war.

Apparent resilience of the Russian economy

GDP forecasts have proved wrong. In April 2022, just after the start of the war, the IMF was forecasting that the Russian economy would decline by 8.5% in 2022 and by 2.3% in 2023 and grow by just 1.5% in 2024. In practice, the economy declined by only 1.2% in 2022 and grew by 3.0% in 2023. It is forecast by the IMF to grow by 2.6% in 2024. This is illustrated in the chart (click here for a PowerPoint).

Similarly, inflation forecasts have proved wrong. In April 2022, Russian consumer price inflation was forecast to be 21.3% in 2022 and 14.3% in 2023. In practice, inflation was 13.8% in 2022 and 7.4% in 2023. What is more, consumer spending in Russia has remained buoyant. In 2023, retail sales rose by 10.2% in nominal terms – a real rise of 2.8%. Wage growth has been strong and unemployment has remained low, falling from just over 4% in February 2022 to just under 3% today.

So why has the Russian economy seemingly weathered the war so successfully?

The first reason is that, unlike Ukraine, very little of its infrastructure has been destroyed. Even though it has lost a lot of its military capital, including 1120 main battle tanks and some 2000 other armoured vehicles, virtually all of its production capacity remains intact. What is more, military production is replacing much of the destroyed vehicles and equipment.

The second is that its economy started the war in a strong position economically. In 2021, it had a surplus on the current account of its balance of payments of 6.7% of GDP, reflecting large revenues from oil, gas and mineral exports. This compares with a G7 average deficit of 0.7%. It had fiscal surplus (net general government lending) of 0.8% of GDP. The G7 countries had an average deficit of 9.1% of GDP. Its gross general government debt was 16% of GDP. The G7’s was an average of 134%. This put Russia in a position to finance the war and gave it a considerable buffer against economic sanctions.

The third reason is that Russia has been effective in switching the destinations of exports and sources of imports. Trade with the West, Japan and South Korea has declined, but trade with China and various neutral countries, such as India have rapidly increased. Take the case of oil: in 2021, Russia exported 4.4 billion barrels of oil per day to the USA, the EU, the UK, Japan and South Korea. By 2023, this had fallen to just 0.6 billion barrels. By contrast, in 2021, it exported 1.9 billion barrels per day to China, India and Turkey. By 2023, this had risen to 4.9 billion. Although exports of natural gas have fallen by around 42% since 2021, Russian oil exports have remained much the same at around 7.4 million barrels per day (until a voluntary cut of 0.5 billion barrels per day in 2024 Q1 as part of an OPEC+ agreement to prop up the price of oil).

China is now a major supplier to Russia of components (some with military uses), commercial vehicles and consumer products (such as cars and electrical goods). Total trade with China (both imports and exports) was worth $147 billion in 2021. By 2023, this had risen to $240 billion.

The use of both the Chinese yuan and the Russian rouble (or ruble) has risen dramatically as a means of payment for Russian imports. Their share has risen from around 5% in 2021 (mainly roubles) to nearly 75% in 2023 (just over 37% in each currency). Switching trade and payment methods has helped Russia to circumvent many of the sanctions.

The fourth reason is that Russia has a strong and effective central bank. It has successfully used interest rates to control inflation, which is expected to fall from 7.4% in 2023 to under 5% this year and then to its target of 4% in subsequent years. The central bank policy rate was raised from 8.5% to 20% in February 2022. It then fell in steps to 7.5% in September 2022, where it remained until August 2023. It was then raised in steps to peak at 16% in December 2023, where it remains. There is a high level of confidence that the Russian central bank will succeed in bringing inflation back to target.

The fifth reason is that the war has provided a Keynesian stimulus to the economy. Military expenditure has doubled as a share of GDP – from 3.7% of GDP in 2021 to 7.5% in 2024. It now accounts for around 40% of government expenditure. The boost that this has given to production and employment has helped achieve the 3% growth rate in 2023, despite the dampening effect of a tight monetary policy.

Longer-term weaknesses

Despite the apparent resilience of the economy, there are serious weaknesses that are likely to have serious long-term effects.

There has been a huge decline in the labour supply as many skilled and professional workers have move abroad to escape the draft and as many people have been killed in battle. The shortage of workers has led to a rise in wages. This has been accompanied by a decline in labour productivity, which is estimated to have been around 3.6% in 2023.

Higher wages and lower productivity is putting a squeeze on firms’ profits. This is being exacerbated by higher taxes on firms to help fund the war. Lower profit reduces investment and is likely to have further detrimental effects on labour productivity.

Although Russia has managed to circumvent many of the sanctions, they have still had a significant effect on the supply of goods and components from the West. As sanctions are tightened further, so this is likely to have a direct effect on production and living standards. Although GDP is growing, non-military production is declining.

The public finances at the start of the war, as we saw above, were strong. But the war effort has turned a budget surplus of 0.8% of GDP in 2021 to a deficit of 3.7% in 2023 – a deficit that will be difficult to fund with limited access to foreign finance and with domestic interest rates at 16%. As public expenditure on the military has increased, civilian expenditure has decreased. Benefits and expenditure on infrastructure are being squeezed. For example, public utilities and apartment blocks are deteriorating badly. This has a direct on living standards.

In terms of exports, although by diverting oil exports to China, India and other neutral countries Russia has manage to maintain the volume of its oil exports, revenue from them is declining. Oil prices have fallen from a peak of $125 per barrel in June 2022 to around $80 today. Production from the Arabian Gulf is likely to increase over the coming months, which will further depress oil prices.

Conclusions

With the war sustaining the Russian economy, it would be a problem for Russia if the war ended. If Russia won by taking more territory in Ukraine and forcing Ukraine to accept Russia’s terms for peace, the cost to Russia of rebuilding the occupied territories would be huge. If Russia lost territory and negotiated a settlement on Ukraine’s terms, the political cost would be huge, with a disillusioned Russian people facing reduced living standards that could lead to the overthrow of Putin. As The Conversation article linked below states:

A protracted stalemate might be the only solution for Russia to avoid total economic collapse. Having transformed the little industry it had to focus on the war effort, and with a labour shortage problem worsened by hundreds of thousands of war casualties and a massive brain drain, the country would struggle to find a new direction.

Articles

Questions

  1. Argue the case for and against including military production in GDP.
  2. How successful has the freezing of Russian assets been?
  3. How could Western sanctions against Russia be made more effective?
  4. What are the dangers to Western economies of further tightening financial sanctions against Russia?
  5. Would it be a desirable policy for a Western economy to divert large amounts of resources to building public infrastructure?
  6. Has the Ukraine war hastened the rise of the Chinese yuan as a reserve currency?
  7. How would you summarise Russia’s current public finances?
  8. How would you set about estimating the cost to Russia of its war with Ukraine?
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The fiscal arithmetic of sustainable public debt: is the maths getting harder?

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.

Articles

Data

Questions

  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.