Good Ponzi schemes and the price of debt

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Good Ponzi schemes and the price of debt
Bernardo Guimarães CEP Annual Conference 2005
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• The story of Carlo Ponzi
• An unprofitable business,
• A creative borrowing strategy,
• borrowing from Peter to pay Paul,
• And a few months of glory.

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• National debts
• Average maturity of OECD countries debts 4.5-6
  years.
• Size of debt 60, 80, 100 of their GDP.
• Debt maturing in 1 year or less 10-20 of
  countries GDPs.
• How can a country pay that?
• Emerging markets shorter maturities.
• Brazil in 2000 maturity of 50 of internal debt
  lt 1 year.
• It did manage to roll over the whole amount
• Short run borrowing from Peter to pay Paul.

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• Purpose of this paper
• Framework for studying debt roll-over.
• Focus on the price of debt.
• Related Literature
• Coordination and the price of debt (Morris and
  Shin, 2004).
• static model, expectations, coordination.
• The deficit gamble (Bohn, 1995 and Ball et al,
  1998).
• sustainability of deficits (long run question).

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• Some results
• Heterogeneity among (timing of) lenders makes a
  big difference,
• Role of reserves,
• Expectations about debtors policy,
• Effects of maturity.

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• Benchmark model
• The debtor
• Stochastic cash flow ( Dq N(mq,sq) ).
• Stock of cash q --- also affected by interest
  payments.
• May issue debt (D)
• Goes bankrupt and defaults when there is not
  enough money.
• Lenders are paid pro-rata if there is some
  money.
• Objective
• Survive as long as it can.

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• Benchmark model with synchronized lenders
• The lenders
• Continuum of lenders (measure 1, they have
  limited money).
• They all come at the same time and stay for
  exactly DT. Then, they leave the economy and
  another set of lenders come in.
• Assumption lenders perfectly coordinate.

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• Benchmark model with synchronized lenders
• Equilibrium
• Lenders get 0 expected return.
• Debtor may choose to borrow
• from a small fraction of lenders.
• only when q is not too bad.
• Ponzi scheme may provide a little help to
  survive (if mq gt 0).
• little or no long run effects.

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Benchmark model with synchronized lenders
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• Adding heterogeneity in the model
• Lenders
• At every period (Dt, small), l.Dt lenders
  arrive.
• Lenders time in the economy geometric
  distribution
• (l.Dt).(l.Dt) stay for 1 period,
• (l.Dt).(l.Dt).(1 l.Dt) stay for 2 periods,
• (l.Dt).(l.Dt).(1 l.Dt)2 stay for 3 periods,
• and so on.
• One state variable (D) tells me all about
  maturity of debt (no memory, no need to keep
  track of history).

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• Adding heterogeneity in the model
• Results
• I cant calculate the optimal borrowing scheme
  for the debtor
• but numerical examples show a much larger
  impact in the odds of surviving.
• Key reason externality provided by former
  lenders (they are stuck in their position).

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Good Ponzi schemes
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The price of debt
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Maturity
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• Forward looking behavior of the interest rate.
• Results
• interest rate paid today may be lower if debtor
  is expected to borrow even with worse values of q
  in the future.
• however, the optimal scheme may be not borrow in
  the case of so bad values of q.
• short-run biased debtor may be willing to tie
  its hands, but that may not be optimal