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Good Ponzi schemes
and the price of debt
Bernardo Guimarães
CEP Annual Conference 2005
The story of Carlo Ponzi
• An unprofitable business,
• A creative borrowing strategy,
• borrowing from Peter to pay Paul,
• And a few months of glory.
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 < 1 year.
• It did manage to roll over the whole amount…
• Short run: borrowing from Peter to pay Paul.
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).
Some results
• Heterogeneity among (timing of) lenders makes a big difference,
• Role of reserves,
• Expectations about debtor’s policy,
• Effects of maturity.
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.
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.
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 > 0).
• little or no long run effects.
Benchmark model with synchronized lenders
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).
Adding heterogeneity in the model
Results:
• I can’t 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).
Good Ponzi schemes
The price of debt
Maturity
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…