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Diamond (1989) - Reputation Acquisition In Debt Markets (view source)
Revision as of 20:01, 29 April 2010
, 20:01, 29 April 2010no edit summary
==Summary==
The model is one of endogenous reputations. One possible outcome of the model is that types that can choose project choose bad projects to start with, gain a reputation through luckily not defaulting, have sufficient value from their reputation to behave (i.e. choose good projects) for some periods, and then when insufficient time remains they choose bad projects again. The solution concept is [http://en.wikipedia.org/wiki/Sequential_equilibrium Sequential Equilibrium]
==The Model==
We now (ab)use measure theory to get three results. The (ab)uses are by assuming that some population is of measure zero but that by continuity we can allow some positive measure into the population and the result will hold.
First we solve the end game with <math>f_{BG}=0 \,</math> - the end game being the part of the game from which the <math>GB \,</math> types choose bad projects forward to infinity. If the end game is bounded then the part of the game in which reputation works is unbounded. With <math>f_{BG}=0 \,</math> the interest rates are deterministic and tend towards r:
:<math>r_{t}=r\cdot \frac{\pi ^{t-1}f_{B}+1-f_{B}}{\pi ^{t}f_{B}+1-f_{B}}\,</math>
Building on this there is the case of moral hazard without adverse selection - that is there are no bad types. In this case we get the following proposition:
'''Proposition''': With no adverse selection interest rates are constant, and if reputation ever works it works immediately at <math>t=1 \,</math> and stops working at some <math>t^{\prime }<T\,</math>.
With adverse selection as well we get the alternative proposition:
'''Proposition''': If <math>r_{t} \,</math> falls over time and a type <math>GB \,</math> borrower optimally selects safe good projects at time $<math>t^{\prime \prime } \,</math> and risky bad projects at some <math>t^{\prime }<t^{\prime \prime }\,</math>, then risky bad projects are optimal for all <math>t<t^{\prime }\,</math>. This implies that if safe good projects are optimal at two dates <math>t_{1}<t_{2}\,</math>, then safe good projects are optimal for all <math>t\in \{t_{1},t_{1}+1,...,t_{2}\}\,</math>.
For further detail see either the paper or Tadelis' write-up of the paper:
*Tadelis, Steve (2007), "Topics in Contracts and Organizations: Lecture Notes", UC Berkeley, September [http://www.edegan.com/repository/Tadelis%20(2007)%20-%20Topics%20in%20Contracts%20and%20Organizations%20Lecture%20Notes.pdf pdf] [http://www.edegan.com/repository/Tadelis%20(2007)%20-%20Topics%20in%20Contracts%20and%20Organizations%20Lecture%20Notes.tex tex]
