Tag: fiscal arithmetic

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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.

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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.
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The wellbeing of the public finances

In a little over a decade economies around the world have experienced two ‘once-in-a-lifetime’ shocks. First, there was the global financial crisis of the late 2000s, which saw an unsustainable expansion of banks’ balance sheets that resulted in a global economic slowdown. Now in 2020, a global health emergency has meant unprecedented falls in economic activity. In both cases, the public sector has been the economy’s shock absorber but this has had dramatic effects on its financial wellbeing. We consider here the effect on the UK public finances and reflect on their sustainability in light of the recent Fiscal Sustainability Report published by the Office of Budget Responsibility (OBR).

The COVID-19 pandemic saw the government initiate a range of fiscal interventions to support people and businesses. Interventions directly affecting public-sector spending included a series of employment support measures. These included the Coronavirus Job Retention Scheme, commonly referred to as the furlough scheme, the Self-employed Income Support scheme, a ‘Kickstart Scheme’ of work placements for universal credit recipients aged between 16 and 24 and a ‘Job Retention Bonus’ whereby employers can receive a one-off payment of £1,000 for every furloughed employee continuously employed from the cessation of the Job Retention Scheme on 31 October through to 31 January 2021.

Further spending interventions have included small business grant schemes, such as the Coronavirus Small Business Grant Fund, the coronavirus Retail, Hospitality and Leisure Grant Fund and the Coronavirus Local Authority Discretionary Grants Fund.

Meanwhile, taxation relief measures have included a business rates holiday for retail, hospitality and leisure businesses and a reduced rate of VAT of 5 per cent for hospitality, accommodation and attractions until 12 January 2021.

OBR’s central scenario

The OBR in its Fiscal Stability Report in July 2020 attempts to assess the wellbeing of the public finances not just in the short term but in the medium and longer term too. This longer-term perspective allows it to assess the sustainability of the public finances.

Its analysis is based on some key assumptions, including population growth and future demands on public services, but, understandably, the timing of this report has necessitated some key assumptions around path of the economy, including the extent to which the economy will experience scarring effects, also known as hysteresis effects. While the analysis does not incorporate the Chancellor’s measures announced in its summer statement on the 8 July, including the kickstart scheme, job retention bonus and the reduced rate of VAT, which would have a material effect on this year’s numbers, the OBR concludes that there would be less significant impact on its medium-term analysis.

In what it describes as its ‘central scenario’ the OBR forecasts that national output (real GDP) will fall by 12 per cent in 2020 before growing by 9 per cent in 2021 and 4 per cent in 2022. National output therefore reaches its pre-virus peak at the end of 2022. However, 20 quarters on from the pandemic shock in Q1 2020 output is estimated to be 3.2 per cent less than it would otherwise have been, while the cumulative loss of output is expected to be 6.4 per cent over the period. The cumulative loss of output in the 20 quarters following the financial crisis (Q2 2008) is estimated to have been 9.3 per cent of actual cumulative output.

While national output is expected to be permanently lower because of the pandemic, consistent with hysteresis, the forecast assumes that the longer-term growth rate is unaffected. In other words, there is not expected to be what some now refer to as ‘super hysteresis’, whereby the scarring effects have persistent effects on rates of capital accumulation, innovation and productivity, which therefore depress structural economic growth rates.

Meanwhile, the unemployment rate is expected to peak at 11.9 per cent in the final quarter of this year, before falling to 8.8 per cent in Q4 2021 and 6.3 per cent in Q4 2022. By Q4 2025 the unemployment rate is forecast to be 5.1 per cent, one percentage point higher than the OBR was forecasting at the time of the Budget in March.

Spending and receipts

Chart 1 shows shows the predicted paths of (nominal) public-sector receipts and expenditures as a percentage of (nominal) GDP. Receipts are expected come in at £740 billion this financial year (excluding the impact of the summer statement measures), some £133 billion lower than was forecast at the time of the March budget. This will amount to a 10 per cent fall in receipts in the financial year, driven by a much-shrunken economy. However, the fact that nominal GDP falls somewhat more means that the receipts-to-GDP ratio ticks up slightly. (Click here for a PowerPoint of the chart.)

Public-sector spending is expected to be higher in 2020/21 than was forecast in the March by £135 million (excluding the summer statement measures) reflecting the COVID-19 interventions. This would result in spending rising to £1.06 trillion, a 20 per cent rise in the financial year. It would also mean that public-sector spending as a share of GDP rises to 54 per cent – its highest since 1945/46.

Going forward, in cash terms receipts are permanently lower than forecast because GDP is lower, though as a share of GDP cash receipts increase very slightly, but remain below what was expected at the time of the March budget. Spending in cash terms is expected to fall back by close to 8 per cent next financial year before increasing by 3 per cent per year up to 2024/25. This means that the spending-to-GDP ratio falls back to around 43 per cent by 2024/25, a couple of percentage points higher than was forecast back in March.

Deficits and debt

The difference between spending and receipts is known as public-sector net borrowing. While the extent of borrowing can be inferred by inspection of Chart 1, it can be seen more readily in Chart 2 which plots the path of public-sector net borrowing as a share of GDP.

The OBR is now forecasting a budget deficit of £322 billion (excluding the summer statement measures) in 2020/21 compared to £55 billion at the time of the March Budget. This would be equivalent to over 16 per cent of GDP, the highest since the Second World War. In a follow-up presentation on the Fiscal Stability Report on the 14 July the OBR suggested that the inclusion of summer statement measures could mean the deficit being as high as £375 billion, implying a deficit-to-GDP ratio of just shy of 19 per cent. (Click here for a PowerPoint of the chart.)

Deficits represent borrowing and are therefore a flow concept. The accumulated deficits over the years (minus any surpluses) gives total debt, which is a stock concept. The public-sector’s net debt is its gross debt less its liquid assets, principally deposits held with financial institutions and holdings of international reserves. This is also affected by Bank of England interventions, such as the Term Funding Scheme which enables banks and building societies to borrow funds at close to Bank Rate for up to four years. Nonetheless, the key driver of net debt-to-GDP ratio going forward is the persistence of deficits.

Chart 3 shows the expected path of the net debt-to-GDP ratio. The OBR expects this to exceed 100 per cent in 2020/21 for the first time since 1960/61. This reflects an increase in cash terms of the stock of net debt to £2.2 trillion, up from £1.8 trillion at the end of 2019/20, as well as a fall in GDP. By 2024/25 the net debt stock is expected to have risen to £2.6 trillion, £600 billion more than expected at the time of the March budget, with the net debt-to-GDP ratio still above 100 per cent at 102.1 per cent. (Click herefor a PowerPoint of the chart.)

Sustainability

The higher debt-to-GDP ratio raises longer-term questions about the sustainability of the public finances. The government is currently reviewing its fiscal rules and is expected to report back in time for the autumn budget. A key question is what debt-stabilising level might be considered appropriate. Is it the 102 per cent that the OBR is predicting at the end of 2024/25 (the medium-term horizon)? Or is it the 75 per cent that was being forecast for this point back in the March budget? This has profound implications for the fiscal arithmetic and, specifically, for the primary balance (the difference between non-interest spending and receipts) that the public sector needs to run.

If the government accepts a higher debt-to-GDP ratio as a ‘new norm’ that eases the fiscal arithmetic somewhat. However, some economists would be concerned about the economic consequences of larger public-sector debts, most notably so-called potential crowding-out effects on private-sector investment if upward pressure on interest rates was to materialise (see the news item MMT – a Magic Money Tree or Modern Monetary Theory?).

Even if the higher stabilising debt level was deemed appropriate, the OBR’s report analysis suggests problems in the government meeting this because it could still be running a primary deficit of 3.7 per cent of GDP by 2024/25. Therefore, even with interest rates expected to be lower than economic growth rates in 2024/25 (a negative growth-corrected interest rate) that enable governments to run primary deficits and yet maintain debt-to-GDP ratios, the debt-stabilising primary deficit for 2024/25 is estimated at only 3.2 per cent. All in all, this points to difficult fiscal choices ahead.

Articles

Questions

  1. What do you understand by the term financial wellbeing? What might this mean in respect of the government?
  2. What is meant by the fiscal arithmetic of government debt? Explain the factors that determine the fiscal arithmetic and the path of government debt?
  3. What is the difference between an increase in the size of a government deficit and an increase in the stock of government debt?
  4. Discuss the economic argument that, following the COVID-19 pandemic, government should avoid a return to an agenda of fiscal austerity ?
  5. What is the difference between the budget deficit, the primary deficit and the structural deficit?
  6. What are hysteresis effects? Discuss their relevancy in the design of the UK’s COVID-19 interventions.