Week 11: Public Debt Sustainability Flashcards
The effect on inflation
• Primary surplus for most of the period up to the late 1980s; the accumulation of primary surpluses was driving down the real debt.
• Real interest rate negative in late 1960s and throughout the 1970s; since the nominal interest rate was increasing at that time, a high and increasing inflation rate must be generating the negative real interest rate, which in turn was reducing UK’s real debt burden.
• Large surge in primary deficit during the Great Recession of 2007/8 and COVID-19.
• Real interest rate much smaller than the nominal interest rate up to early 1990s; they have been moving very close together ever since (indicating that inflation is small and more under control)
The effect of growth
An even more relevant measure is real debt relative to real GDP (GDP is a measure of the tax base; measures the capacity of a government to collect tax revenue to support debt service costs)
The relevant interest rate is the growth adjusted real interest rate 𝑖𝑡− 𝜋𝑡− 𝑔𝑦,𝑡. And the relevant measure of the primary deficit is the primary deficit relative to GDP.
• Primary surplus to GDP for most of the time up to late 1980s; accumulation
was driving down the debt ratio.
• Negative Growth adjusted real interest rate from 1955 to early 1970s; growth
was driving down the UK debt ratio during that time.
The effect of business cycles
• The primary deficit can be written as
𝐷𝑡𝑃 (𝑌t) = 𝐺𝑡− 𝑇 𝑡
• It is also useful to consider the impact of business cycles on the
deficit
- Define the cyclically adjusted deficit to be the deficit that would exist
if output was at its natural level
𝐷𝑡𝑃 (𝑌 𝑁,𝑡) = 𝑐𝑦𝑐𝑙𝑖𝑐𝑎𝑙𝑙𝑦 𝑎𝑑𝑗𝑢𝑠𝑡𝑒𝑑 𝑑𝑒𝑓𝑖𝑐𝑖𝑡
This shows the deficit implied by deliberate government fiscal
decisions.
• The cyclically adjusted deficit is smaller than the unadjusted primary
deficit in the recession of the early 1990s, the Great Recession and
the COVID-19 pandemic.
• The cyclically adjust deficit is negative (so a surplus) in the late 1990s;
the surplus is smaller than the unadjusted surplus, indicating the
economy was doing well at that time.
Stabilizing debt
- Debt does not need to be repaid if bond holders are content to hold bonds or are willing to buy new bonds as old bonds mature.
- Many investors want to hold government bonds: risk averse private
investors, pension funds, insurance companies and banks.
→ The important condition for debt sustainability is that the level of
debt is stabilised at a level where the interest payments can be
financed.
The equation for the dynamics of real debt is
∆𝐵𝑅 = 𝑖 − 𝜋 𝐵𝑅 + (𝐺 − 𝑇)
The relevant condition for stabilising real debt is for ∆𝐵𝑅 = 0 so that
(𝑇 − 𝐺) = 𝑖 − 𝜋 𝐵𝑅
- Run a real primary surplus to cover the real interest cost of debt service (in every period t).
- Note that if the real interest rate is negative, the government can run a primary deficit
Ricardian equivalence
Ricardian equivalence is the proposition that tax finance and bond finance
have equivalent effects on private expenditure.
• The standard Keynesian assumption is that household consumption
depends on current disposable income i.e. current income minus current
taxes.
• But the Ricardian equivalence proposition is based on the alternative
assumption that households base their expenditure decisions on the
present discounted value of income and taxation into the infinite future.
- According to Ricardian equivalence…
>It doesn’t matter if government spending in the current period is
financed by debt or current taxes
>There is limited effect of fiscal policy on economic activity.
Ricardian equivalence is a useful benchmark but breaks down:
• if there are imperfections in financial markets.
• if newly issued debt is assumed to last beyond the lifetime of current
taxpayers.
• if taxes are distortionary.
All three of the above conditions provide justifications for using debt finance.
• If some households do not have perfect access to financial markets, then
their current disposable income and welfare will be affected by current
taxes.
• If newly issued debt lasts beyond the lifetime of current taxpayers, then debt
finance provides a way to share costs between generations.
• If taxes are distortionary, it is optimal to smooth tax rates across time and
use debt finance to cover short-term fluctuations in government
expenditure, for example during wars and other crises such as the banking
crisis and the Covid pandemic.
Dangers of High Debt: Tax distortions
- To stabilise the debt-to-GDP ratio, a country must run a primary surplus which
is sufficiently large to finance the interest payments (in terms of the growth
adjusted real interest rate). The relevant condition for stabilising the debt-to-
GDP ratio is
(𝑇 − 𝐺) = 𝑖 − 𝜋 − 𝑔 𝐵𝑅
• If the growth adjusted real interest rate is positive, then the larger the debt
the larger the required primary surplus. For given level of expenditure, this
will imply higher tax rates and therefore more tax distortions.
Dangers of high debt: possibility of default
• If a country has a high or rapidly rising debt-to-GDP ratio, there may be
expectations of default.
• Default means the government refuses or is unable to finance payments on
outstanding debt.
Bond holders will require a default premium in order to hold new debt.
This means that the cost of debt finance will rise for a government which is in danger of default.
The higher cost of bond finance makes it more difficult to stabilise the debt-to-GDP ratio which in turn further raises expectations of default.
Dangers of high debt: Money financing and hyperinflation
• The government can also finance itself by printing money. A government which
can no-longer rely on debt finance may choose to print money or force the
central bank to create new money and buy bonds.
• An increase in money supply leads to inflation.
Suppose an economy with £10 and 10 apples. If all the money is spent on
apples, the price per apple is £1. In the next year, the government increases
money supply by 10% to £11, but still 10 apples are produced. Now the price
per apple is £1.1.
• In extreme cases, money creation can lead to hyperinflation.
Dangers of high debt: External financing and sudden stops
• Many emerging market and developing countries depend on foreign investors
to buy government debt.
• Fear of default can lead to a sudden stop where foreign investors sell bonds
and refuse to buy new bonds. This can cause large movements in exchange
rates, trade, and GDP, and require rapid changes to monetary and fiscal policy.
