Welcome!
Monday 24.05.21
Today:
• Homework review
• Recap Week 3 and 4
• Lecture + practice week 5
• Lecture (+practice) week 6
• Extra time: practice weeks 3 and 4
Week 5: Public Debt
30-40% of Exam
!It’s VERY easy!
Week 5
• Public debts and deficits
• Facts
• Debt Dynamics
• Ricardian Equivalence
• Hidden Debt (optional)
• Stabilisation Policy
Public Debt
• Measurement issues
• Only FEDERAL gvt? Also municipal/public sector?
• Business cycle corrections?
• Assets and (future) liabilities? How to value?
• Why this matters?
• Definition too narrow  encourage shifting of spending to entities outside of
defined space
• Too wide  mismeasurement risks of on-balance sheet assets & liabilities
Historical
EMU
2015
2010
2005
2000
1995
1990
1985
1980
1975
1970
1965
1960
1955
1950
1945
1940
1935
1930
1925
1920
Debt/GDP ratio, The Netherlands
180%
160%
140%
120%
100%
80%
60%
40%
20%
0%
1900
1904
1908
1912
1916
1920
1924
1928
1932
1936
1940
1944
1948
1952
1956
1960
1964
1968
1972
1976
1980
1984
1988
1992
1996
2000
2004
2008
2012
Debt/GDP ratio, USA
140
120
100
80
60
40
20
0
Hidden Debt – just so you know
• Not all debt is straightforward:
• Medicare
• Medicaid
• Social Security
• Public pension liabilities
• This “hidden” debts also contribute to the deficit, though indirectly
High Public Debt – why it’s bad
• Fuel inflationary expectations
• Solution: inflation linked bonds
• High debt  high risk premium on gvt loans  unstable debt/GDP
potentially
• High debt  low investment and economic growth rates
Summary
• Gvts borrow to pay for (part of) spending
• Definitions are tricky
• Too narrow?
• Too wide?
• Can spiral out of control  premiums and more inflation
Debt Dynamics
Public Debt Terms
• Debt Service – Interest on Debt - 𝑖𝐷
• Primary deficit – gvt spending (excl. debt service) minus taxes - 𝐺 − 𝑇
• Total deficit – primary + debt service (𝐺 − 𝑇) + 𝑖𝐷 !MEMORIZE THESE TERMS; EASY
POINTS!
• New Debt= Old debt + primary deficit + debt service:
𝐷 = 𝐷−1 + (𝐺 − 𝑇) + 𝑖𝐷−1
Formula Notation
• Variables:
• Y=income
• 𝐷𝑡 =gvt debt in period t
• G=gvt spending
• T=taxes
• i=nominal interest rate
• r=real interest rate
• New Debt:
𝐷 = 𝐷−1 + (𝐺 − 𝑇) + 𝑖𝐷−1
• Total change in gvt debt in period t:
• Where: ∆𝐷 = 𝐷 − 𝐷−1
∆𝐷 = 𝐺 − 𝑇 + 𝑖𝐷−1
Derivation: Change of Debt-to-GDP ratio
• Exercise – Assume GDP (Y) and the primary deficit grow at rate g+π.
Using the formula for “new debt”, derive the equation for the debtto-GDP ratio
• Hint: you may use this approximation:
1+𝑖
≈1+𝑖−𝑔−𝜋
1+𝑔+𝜋
Answer:
• Using the info provided we can write the formula for new
debt/GDP as:
𝐷 𝐺−𝑇
1 + 𝑖 𝐷−1
=
+
𝑌
𝑌
1 + 𝑔 + 𝜋 𝑌−1
• Then substituting in the approximation gives
𝐷
𝐺−𝑇
𝐷
∆
≈
+ 𝑖−𝑔−𝜋
𝑌
𝑌
𝑌 −1
• Where ∆
𝐷
𝐷
=
𝑌
𝑌
-
𝐷
𝑌 −1
NOTE: you MUST be able to do derive it
NOTE: having trouble? Week 5 Clip-Debt Dynamics
(first 7 minutes)
Debt Dynamics – Graphs
X-axis = time, y-axis = debt-to-GDP ratio
Debt Dynamics
𝐷
𝐺−𝑇
𝐷
∆
≈
+ 𝑖−𝑔−𝜋
𝑌
𝑌
𝑌 −1
• Similar to the Solow Dynamics, the formula above will lead to different outcomes:
• 3 scenarios, based on 𝑖 − 𝑔 − 𝜋 :
• 𝑖 <𝑔+𝜋
• Debt-to-GDP ratio is stable and approaches a steady state. Thus, debt is sustainable. Debt-to-GDP ratio
converges to:
𝐷
𝑇−𝐺
=
𝑖−𝑔−𝜋
𝑌
𝑌
• 𝑖 >𝑔+𝜋
• Debt-to-GDP ratio is unstable. Sustainability depends on primary deficit and initial situation (see next
slide)
• g – i = 0 (hypothetically)
• Debt-to-GDP grows linearly  can’t say if (un)stable
Practice – Stable ratio
1. If the debt-to-gdp ratio is stable, prove that the debt-to-gdp ratio
converges to:
𝐷
𝑇−𝐺
=
𝑖−𝑔−𝜋
𝑌
𝑌
2. Can a (real world) situation arise where D/Y is stable but also
unsustainable? Why?
Answers
1. key: change in D/Y=0
1. Substitute in and simplify
2. Yes, if politicians choose to increase gvt. Spending to ridiculous
amounts (Japan) OR if people stop paying taxes (Greece), D/Y will
be unsustainably high yet stable.
𝑖 > 𝑔 + 𝜋 – unstable
2 situations:
𝐷
𝑇−𝐺
𝑖−𝑔−𝜋
>
𝑌 0
𝑌
• Interest payments and state of the primary deficit cause debt to explode
• Country will “restructure it’s debt” (default)
𝐷
𝑇−𝐺
𝑖−𝑔−𝜋
<
𝑌 0
𝑌
• Primary deficit is sufficient to pay current interest payments  debt ratio
implodes  unstable and sustainable
• Solution is popular: tax less and/or spend more
Sustainability Gap
• If debt is unstable and unsustainable
𝑖−𝑔−𝜋
𝐷
𝑇−𝐺
>
𝑌 0
𝑌
• the sustainability gap measures required change in primary deficit needed
to make debt sustainable
𝑠 = 𝑖−𝑔−𝜋
𝐷
𝑇−𝐺
−
𝑌 0
𝑌
Summary
• D/Y can be:
• Stable or unstable
• Sustainable or unsustainable
• Your job on the exam is (usually) to figure out which combination is
true
• You may be asked to graph your findings
Debt Dynamics Standard Graph
• Assume your D/Y is unstable and at risk of becoming unsustainable.
What can be done?
𝐷
𝐺−𝑇
𝐷
∆
≈
+ 𝑖−𝑔−𝜋
𝑌
𝑌
𝑌 −1
• Change:
• Nominal interest rate? Tricky
• Inflation? Risky  investors may ask for higher interest rate
• Real economic growth? Tricky
• Primary gvt surplus? YES
• By how much? Sustainability gap
• New situation: unstable but sustainable
Debt Dynamics - Practice
Practice question 1.14
The Greek ministry of Economy and Finance has uncovered information about the true (bad) state of Greek government finances; it
estimates the government primary deficit to be 8% of GDP. Up to that moment, the estimate for the growth rate of real GDP was 4%, the
debt-to-GDP ratio is 133%, and the real interest on Greek government bonds is 2%.
Debt dynamics can be described by Δ𝑏=(𝑔−𝑡)+(𝑟−𝛾)𝑏
a. On the basis of the given data, calculate the change of the debt-to-GDP ratio during the year, and the equilibrium debt-to-GDP ratio b*.
Then determine the sustainable (or debt – stabilizing) primary government deficit for Greece. How does this relate to the actual deficit
estimated by the Greek ministry? Use a phase diagram in which you indicate the required adjustment.
b. Due to the information about the state of Greek government finances, there is a panic in financial markets. The risk premium on Greek
government bonds increases and the Greek government now faces a (real) interest of 6% on its bonds instead of the earlier 2%. Discuss
how this financial panic influences the stability of the Greek situation, keeping all other things equal. Use a phase diagram to compare
this situation to that in question a.
Debt Dynamics - Practice
Practice question 1.15
Stability of public debt. Suppose we have a country in deflation. Output growth 𝛾 is zero.
Yearly inflation 𝜋 is negative: -0.5 percent, and the nominal long-term interest i is 1.5
percent. The initial debt-to-GDP ratio b is 100 percent (so b=1). The government runs a
primary deficit ratio (g-t) equal to 1 percent of GDP during the year.
Write the equation that describes the dynamics of the debt ratio b, and calculate the
change of b during the year.
Calculate the steady-state debt ratio in this country. Compare with the existing debt ratio.
Draw the phase diagram for this case, and explain why the debt situation is or is not
sustainable
Conclusion
EASY POINTS
Practice – Full Solow Exam Question
Practice - Convergence
Practice question 2.7
Consider the case of two countries, X and Y, which have the following Cobb-Douglas production function: 𝑌(𝑡) = 𝐵𝐾 𝑡 0.5 𝐴 𝑡 𝐿 𝑡
0.5 , where 𝐵 measures aggregate productivity. The two countries differ in
the value of 𝐵. Country X has 𝐵=1, country Y has 𝐵=9/4. In both countries, capital depreciates at a rate of 𝛿=3 percent per year, population grows at rate 𝑛=2 percent per year and the growth of laboraugmenting technological progress 𝑔=1 percent per year.
a.
Derive the accumulation equation for capital per effective worker. Use it to calculate the value of capital per effective worker along the balanced-growth path, for country X and for country Y (assume
that the saving rate s is 0.4 for both countries). What do you observe?
b.
Make a graph of the two countries that shows their steady states as the intersection of the savings curve and the break-even investment lines that apply to them.
c.
Suppose capital per effective worker in country X is 48 at time 0. Suppose capital per effective worker equals 130 at the same time for country Y. Show the dynamics of capital per effective worker in
the Solow diagram you created in b).
d.
Do the two economies display convergence or divergence? Do the two countries exhibit conditional convergence or divergence?
e.
Which economy has the higher speed of convergence towards the balanced growth path equilibrium?