1 / 42

Default and Fragility in the Payment System

Default and Fragility in the Payment System. March, 2004. Scott Freeman Department of Economics, University of Texas at Austin. Paula Hernandez-Verme Department of Economics, Texas A&M University. Outline. Motivation. The environment. The Planner’s Problem. Trade and travel patterns.

ince
Download Presentation

Default and Fragility in the Payment System

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Default and Fragility in the Payment System March, 2004 Scott Freeman Department of Economics, University of Texas at Austin Paula Hernandez-Verme Department of Economics, Texas A&M University

  2. Outline • Motivation. • The environment. • The Planner’s Problem. • Trade and travel patterns. • Optimality and Fragility under Alternative Settlement Rules. • Conclusions and extensions.

  3. 1. Motivation Payment System Arrangements to settle debt (obligations). • CHIPS clears and settles over $1.2 trillion daily • with only $2.4 billion in pre-funding. • Most consumption and investment purchases, and all financial transactions are conducted with debt settled by third parties (checks, electronic fund transfers), not with cash. If the payments system is fragile, the entire market economy is fragile, i.e.: vulnerable to Pareto dominated equilibria with low financial activity. 

  4. Net Debt = IOUs payable – IOUs receivable Gross Debt = IOUs payable

  5. Rules of Settlement of Debt Net settlement Gross settlement • In a given period, must bring cash to clearnetdebt. • Credit risk (default) and potential spillover. • Fedwire, CHIPS. • In a given period, must bring cash to clear gross debt. • Reserves. Unwinding (Strict) Amount owed is independent of default by others. Debt Forgiveness Amount owed depends on default by others.

  6. Requirements of Theoretical Modeling of the Payment System, Zhou (2000) • Consumption/Investment debt: the system design affects the allocation of real resources. • Treat consumption/investment debt as distinct from payment debt, which is created only for payment needs. • Incorporate settlement liquidity shortage. Done Begun • Incorporate credit risk. Perfect enforcement Previous analysis (1)-(3) or Exogenous default probabilities

  7. (1)-(3) are insufficient guides for settlement policy. Without endogenous default choices, we cannot discuss the effect of settlement rules on: • Default incentives. • The stability of the payments system.

  8. Camera and Li (2003): • Strategic complementarity and multiplicity of equilibria. • Descentralized payments system. • Lack of study of local stability analysis of equilibria. Kahn, McAndrews and Roberds (2000): Closer to our attempt. But absence of: • Fiat money as the payments instrument. • Proposal of net settlement with debt forgiveness. • Local stability analysis of equilibria.

  9. Our Question: When debtors have the option to default, which rule for the settlement of debt has equilibria that are: • Optimal (right long-run incentives)? • Unique and Stable (free from systemic risk)?

  10. We present a model with the following features: • Exchange involving debt. • Debt cleared by third parties. • Debt settlement requires final payment using fiat money. • Debtors have a nontrivial default option. • Interdependence of default decisions.

  11. 2. The Environment • Closed, endowment economy. • 2 period-lived overlapping generations: young and old. • Population is constant and time is discrete. Outer Islands • There are I outer islands. • A continuum of households with unit mass in each of the outer islands. • There are I different goods: each good is island-specific. • Contracts cannot be enforced in the outer islands.

  12. Central Island • A place where all contracts are enforced. • Think about the civil and monetary authority being here. • There may be a location-specific utility/disutility of going to the Central Island. Utility of living under the law in a place where contracts can be enforced.

  13. Endowments: • Each young household born in island i (i=1,2,…I) is endowed with w units of the island-i-specific good. • Old households have no endowment of goods. • There is a generation of initial old endowed with the constant money supply M.

  14. Preferences: Ex-ante identical households  same utility function: Consumption when old Consumption when young Location-specific utility, random Utility from going to the Central Island Utility from going to outer islands  = Net utility = c - o

  15. The good you have is not the good you want: Young households born in island i wish to consume only the good specific to island (i+1). Oldhouseholds born in island i want to consume only the good specific to island (i+I/2) (Modulo I).

  16. 3. The Planner’s Problem • No rules of settlement. • The only constraint is feasibility. Household’s Expected Utility Feasible Set s.t. Social Optimum 

  17. Utility if travel to C.I. Utility if stay away from C.I. Or: Feasible set

  18. The Social Optimum is characterized by: 1. From 2. • Golden Rule. • c1 = consumption acquired with debt, c2 = consumption acquired with fiat money. Optimality involves some default 3. Optimality involves no default

  19. 4. Trade and Travel Patterns Intra-generational trade: - Young with young (outer islands). - Old with old (Central Island). First part Each period has two parts Inter-generational trade: Young with old. Second part

  20. First Part of the Period Second Part of the Period Buyer i travels to island i+1 to purchase good i+1. Issues IOUs. Young Household i sells remainder of good i to incoming old households in exchange for fiat money. Seller i stays in island i: waits for buyers Household chooses whether to travel to Central Island or not. Household i travels to another island to purchase a consumption good. Old Intra-generational trade Inter-generational trade.

  21. About the IOUs : • They constitute “consumption debt”: goods acquired for the promise of future payment (debt for goods). • Promise must be repaid next period on the Central Island: only time when people will get together. • The repayment of debt can only be enforced in the Central Island. • Only fiat money is useful to old agents for their purchases in the outer islands. Therefore, old agents will require fiat money for the repayment of debt. • r= gross real interest rate promised on the debt issued.

  22. Utility of Central Island Travel: • At the beginning of the period, the old household j observes the realization of the random variable ,j. • ,j = utility that old household j derives only if it chooses to travel to the Central Island during the first part of the period. • ,j is i.i.d. across households and islands and it is stationary. • f(,j ) is the pdf, with support on Ex-ante preferences are identical, but they are different ex-post. If j < *j, do not travel to Central Island  choose to default *j  cut-off value for household j If j*j, do travel to the central island  chooses not to default

  23. If old household goes to the Central Island: • Carries fiat money from the previous period. • Must repay its debt. • Gets paid only by households who show up in the Central Island. • Consumes goods. • R = effective real interest rate paid on loans. • Gets the utility j .  = utility of going to the C.I. – utility of not going to C.I. If old household doesn’t go to the Central Island: • Carries fiat money from the previous period. • Does not repay its debt. • Does not get paid for the debt it accepted the previous period. • Consumes goods.

  24. 5. Alternative Rules for the Settlement of Debt We examine 3 alternative rules: • A Flexible Net Settlement Rule (Debt Forgiveness). • A Net Settlement Rule with Unwinding (Strict). • A Gross Settlement Rule.

  25. Net Settlement Gross Settlement • IOUs receivable can be used to pay IOUs payable. • Bring cash for anything extra: net debt. • IOUs receivable cannot be used to pay IOUs payable. • Bring enough cash to pay gross debt. Net debt = IOUs payable – IOUs receivable

  26. Suppose: • Your gross debt is $100 payable, and you have $100 receivable. • Only 80% of the people who owe you money show up at the Central Island. Net Settlement with Debt Forgiveness Strict Net Settlement • You pay $100. • You get paid $80. • You pay $80. • You get paid $80.

  27. A) A Flexible Net Settlement Rule • Only net debt matters. • π = fraction of old households traveling to the Central Island. • Debt forgiveness: Old households who travel to the Central Island pay only a fraction π of their debt.  Gross debt =  (IOUs payable) Net debt = IOUs receivable - (IOUs payable) If <1  debt forgiveness kicks in: debt and IOUs receivable reduced by the same percentage.

  28. Equilibrium: 1. 2. Some default 3. No default  The resulting equilibrium is: • Unique. • Optimal.

  29. Cut-off value chosen by household j as a function of *-j Nash equilibrium 0 Cut-off value chosen by the other households

  30. B) A Strict Net Settlement Rule • Only net debt matters. • Old households who travel to the Central Island pay the total value of their debt but receive only a fraction of what they are owed. • π = fraction of old households traveling to the Central Island. Gross debt = IOUs payable  Net debt = IOUs receivable - (IOUs payable) The amount you owe is independent of the fraction of households who default.

  31. Equilibria: System of 3 equations in 3 unknowns Intra-temporal choice Inter-temporal choice Cut-off value

  32. Equilibria are complicated. No-uniqueness seems typical. • Strategic Complementarities may be present: If you think that no one else will show up at the Central Island, you may not want to show up either. The more others default, the more you want to default. Because others’ default does reduce what you receive but it does not reduce what you owe. Why?

  33. Due to strategic complementarities, the reaction function has a positive slope. If multiple equilibria: • Equilibria that are Pareto-ranked. • Could implement a policy rule to get to a Pareto superior allocation. • Multiplier effects: interior solution.

  34. optimal

  35. optimal

  36. C) A Gross Settlement Rule • IOUs receivable cannot be used to pay IOUs payable. • Bring enough cash to pay gross debt  additional constraint on real money balances. Intra-temporal choice Inter-temporal choice Cut-off value

  37. A Gross Settlement Rule is weakly Pareto inferior to a Strict Net Settlement rule. • Equilibrium allocations resulting from an unconstrained gross settlement rule (=0) are identical to those resulting from a strict net settlement rule. • For each equilibrium resulting from a constrained gross settlement rule (>0)there is a Pareto superior equilibrium resulting from a strict net settlement rule.

  38. 6. Conclusions When debtors have the option to default, which rule for the settlement of debt has equilibria that are: • Optimal (right long-run incentives)? • Unique and Stable (free from systemic risk)? A Flexible Net Settlement Rule With Debt forgiveness A Flexible Net Settlement Rule With Debt forgiveness

  39. Pareto Ranking of Settlement Rules If If Order Net settlement with debt forgiveness Net settlement with debt forgiveness 1 Strict net settlement with universal repayment Strict net settlement Strict net settlement, other equilibria 2 Gross settlement (unconstrained) Gross settlement (unconstrained) Gross settlement (constrained) Gross settlement (constrained) 3

More Related