Government Debt Dynamics

Question 1

dynamics of the debt to GDP ratio relationship

Answer 1

T-G/Y = (r-g)B/Y

T-G is the primary budget balance
(+ve surplus)

Y- GDP

r real interest rates

g real growth rate of GDP

B existing debt stock

T-G/Y primary balance as a proportion of GDP

B/Y national debt as a proportion of GDP

Question 2

government expenditure two categories (in year)

Answer 2

Government spending G

Interest payments on existing public debt, B, accumulated in the past equals rB

Question 3

source governemnt rev

Answer 3

Taxes T

Question 4

government budget equation

Answer 4

∆B= -(T-G) + rB

change in public debt primary budget + interest payments

Question 5

technical point

Answer 5

use real interest rate to capture the impact of inflation on the sustainability of debt

inflation good for borrowers as it reduces real value of nominal debt

govt reduces nominal debt by allowing inflation

as UK borrow around 5% and inflation running at well above 2% allows for low or even negative borrowing costs

counter, higher inflation means higher nominal interest rates and less QE or Quantitative tightening

Question 6

public finances as income shares

Answer 6

interested in sustainability of national debt levels- national debt ration B/Y

for B/Y to remain constant numerator and denominator must grow at same rate

T-G/Y = (r-g)B/Y

Question 7

stable and unstable equilibria

Answer 7

scenario 1

T-G/Y = (r-g)B/Y

g-r >0 then G-T>0 is a stable equilibrium for some debt ratio

implies that some debt ratio towards which an economy will always gravitate

nominal interest rate i being less than the nominal growth rate of GDP

scenario 1 normal for most developed countries allows for high debt ratios to be sustainable

Scenario 2

if g-r <0 then T-G > 0 unstable equilibrium

if the debt ratio is too high it will keep increasing

if the debt ratio is too low it will keep falling

any point above/below equilibrium interest payments exceed/subseed grow in Y plus the Primary surplus

Question 8

Greece in scenario 2

Answer 8

Greece can run a persistent budget surpluses

debt ratio b/y starts below unstable equilibrium

initially have to pay down the debt below the unstable equilibrium from where it will continue to decrease

initial paydown not politically viable in eurozone, as would require rich countries to transfer money to poor countries

Question 9

scenario 1 analysis

Answer 9

any debt ratio is stable as long as g>r

high debt ratios not the end of the world if we can grow

central bank can help with r if necessary

sub optimal policy of tightening belts

hysteresis- being stuck in a period of slow growth (recession) can itself do long run damage to an economy

hysterisis modeled, being stuck below the natural rate could lower the natural rate ( leftwards shift in LAS)

Question 10

hysteresis

Answer 10

idea that recessions can affect the natural rate output,unemployment adversely in the long run

e.g individuals may lose skill

long term unemployed may give up looking

Question 11

hysteresis in another way

Answer 11

real economic growth g is key to sustainable national debts

cutting G does damage to public services and infrastructure it would be ashame if also didn’t help bring down national debt

at times be a need for more active role for fiscal policy even if counter intuitive