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Facts and Figures. Spring 2007. Intermediate Macro Lecture 17. 3. Debt to GDP ... Your parents care as much about you as they do about themselves: ... – PowerPoint PPT presentation

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Title: Debt

Facts and Figures
Debt to GDP
Source OECD, Marketable debt as of GDP, 2005.
Japan v. US
Source OECD, Marketable debt as of GDP,
Private Debts
The Pension Benefit Guaranty Corporation (the
PBGC) is mandated under Title IV of the Employee
Retirement Income Security Act of 1974 (ERISA) to
insure, under statutory limits, pension benefits
of participants in covered private defined
benefit pension plans in the United States. As of
September 30, 2006, between its combined
programs, the PBGC covered 44 million workers in
over 30,000 active plans and was directly
responsible for the future benefits of 1.3
million active and retired workers whose plans
had failed. The PBGC receives no taxpayer monies
and its obligations are not backed by the full
faith and credit of the United States Government.
2006 Annual Report the PBGCs combined net
position at September 30, 2006, was (18.88)
billion as compared to (23.11) billion at
September 30, 2005, representing a 4.2 billion
net improvement in the PBGCs deficit. The
Corporation has sufficient liquidity to meet its
obligations for a number of years however,
neither program at present has the resources to
fully satisfy the PBGCs long term obligations to
plan participants.
CBO estimates their current liabilities at 91
New Jersey Debt
The State of New Jersey has a debt of 29.7
billion as June 30, 2006.
There are an additional 8 billion in other
obligations, for a grand total of 37.4 billion,
or 4,452 for each of the states 8.4 million
These numbers do not include the unfunded
obligations of the state pension fund Douglas
Love, of the State Investment Council, puts the
shortfall at 56 billion.
The Debt As Insurance
Consider a model in which all income is wage
income. Suppose that Nyt3. Workers receive
wages that take on one of three values, good,
w¹15, fair, w²10, and poor, w³5. These states
occur for each worker with probability 1/3.
Ew(i)10. Suppose that the average is
achieved every period, but workers vary each
period among states,
A risk sharing scheme here could be accomplished
without a government. Workers could agree to pool
their wages giving everyone 10 ex-post. Would
workers agree to a plan to pool their wages? The
answer is yes, given diminishing marginal
Why? Philosopher John Rawls A Theory of Justice
may shed some light.
Insurance Example
Intertemporal Transfers
Suppose instead that risk is intergenerational.
Assume only one worker (or that all workers are
identical and receive the same wage.) Consider a
model of three periods,
The government sets up the following tax and
transfer scheme
The government runs a balanced budget over time,
but runs deficits in recessions, surpluses in
booms. The mindless argument that the federal
government must always balance the budget is just
that, mindless.
Is the Debt Net Wealth?
With Social Security, we determined that whether
or not this transfer constituted net wealth
depended on the present discounted value of
benefits and taxes. Robert Barro, now of Harvard
University, has argued that this may not be the
appropriate measure, since it regards agents as
myopic. If taxes are deferred to after your
death, then the old measure declared them wealth.
Barro has argued that bequest motives make agents
act as if they lived a much longer time than they
Consider our generations model with no population
growth, so assume one individual in each
generation. Suppose that the government makes the
transfer as before to the old generation.
Assume gb¹. Suppose that the government simply
keeps the bond proceeds as taxes on the young
when they are old,
In the previous model with no bequests, the old
would consume their g and the young would get
screwed. Imagine though that the generations are
linked. Your parents care as much about you as
they do about themselves
In this case, Barro shows, parents will not spend
g and simply leave it as an estate for their
Empirical Implications
  • Question, if Ricardian equivalence were true,
    what should the effect of the massive
    deficit/debt have on savings? Increase it. Yet
    the opposite has happened.
  • Closing observations
  • The decline in savings rates seems to indicate
    that agents don't care very much about their
    descendants. This is a question to bring up with
    your parents!!
  • The Ricardian equivalence does not eliminate the
    insurance results.
  • Liquidity constraints. The timing of taxes and
    benefits matters crucially.

Does the debt have to be paid back?
The answer to this is, not necessarily. Consider
our model of Social Security with growing
populations. The government here, though, levies
no taxes. It issues bonds to young consumers,
offering them interest (1r) for their money
lent. We begin the scheme of generations with a
one-time transfer to the old of
Since the government levies no taxes, the deficit
D¹ is simply G. To finance this expenditure, the
government sells bonds B¹D¹. What will be
important here are the per capita quantities
Budget Constraints
The young people of generation 2 face a period 1
budget constraint of
Since the young receive (1r) on their bonds,
their second period budget constraint is,
The government debt is rolled over each period,
General Expressions
Bond sales, since no taxes are being levied,
follow the same dynamic relation
Key Ratios
What will be critical as to whether or not the
government must pay its debt back is the growth
of aggregate income,
(We have assumed that the wage is constant, but
the population is growing. Alternatively, wage
growth (1w) could replace population growth.)
If aggregate income is growing faster than the
debt, nr, then the debt doesn't have to be paid
back. What we will show is that d, per capita
debt, is going to zero,
If nr, then the first term is progressively
going to zero.
Example Convergent Debt
Let's assume that Ny¹8, n1.0, so that Ny²16,
and so on with the population doubling every
generation. How does the government debt grow?
Let r0.25 and the initial transfer be G5, D¹5,
D²(1r)D¹(1.25)56.25. D³ (1.25)6.257.81. Is
this debt crippling the economy? Assume that
w10. Aggregate income is growing with the
population 810,1610, and so on, doubling every
generation. Let's look at what's happening to
the per capita debt. d¹ D¹/Ny¹5/8 d²6.25/16
d³7.81/32. As long as n, the rate of population
growth, exceeds the rate of interest, we need
never to pay it back. The ratio of debt to
aggregate income continues to decline 5/80,
6.25/160, 7.81/320, etc.
Debt Constraints
Let's now look at the opposite case. The
government will run into two constraints The
voluntary government budget constraint is simply
the point at which the government wants to borrow
more than people want to save,
This indicates that the government cannot
continue to roll over debt if it exceeds the
aggregate savings of the young. A second absolute
constraint is,
when the debt service exceeds aggregate income.
Divergent Debt Example
Reverse the growth rates above n0.25, r1
Ny¹4 Ny²5, etc. The population is tabulated in
the column 1. Let w10. Life cycle consumers
desire to save half of that. Voluntary savings
are given by 5Nyt and are in column 2. Aggregate
income is simply double these figures in column 3.
The debt is doubling, and in period 4, we cross
the voluntary budget constraint. The government
tries to borrow 40 dollars, but people only want
to save 39.05. By period 7, the debt service,
1160160, exceeds aggregate income of 152.5
Final Lessons
Growth is the most important thing when it comes
to evaluating the burden of the debt.
While government debt has grown enormously, see
e.g. the debt clock.
If we had a GDP clock, how fast would it be
growing. Exercise.