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“Pooling, Separating, and Semiseparating Equilibria in Financial Markets: Some Experimental Evidence”. Charles B. Cadsby, Murray Frank, Vojislav Maksimovic, Review of Financial Studies 3(3), 315-342 (1990). Myers and Majluf (1984).

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pooling separating and semiseparating equilibria in financial markets some experimental evidence

“Pooling, Separating, and SemiseparatingEquilibria in Financial Markets: Some Experimental Evidence”

Charles B. Cadsby, Murray Frank, Vojislav Maksimovic, Review of Financial Studies 3(3), 315-342 (1990)

myers and majluf 1984
Myers and Majluf (1984)

Question: How do investors and firms deal with asymmetric information?

Firms have information that investors do not about their quality. How do firms and investors interact to fund projects?

myers and majluf 19841
Myers and Majluf (1984)
  • Two types of firms, i = H, L
  • Each firm gets
    • Ai if they do not undertake a project
    • (1-s)(Bi) if they undertake the project
    • Therefore, firms should undertake a project iff

E(1-s)(Bi) > Ai

  • Each investor gets
    • 0 if no project is undertaken
    • sBi – C if they finance the project
    • Therefore, investors should bid as long as

sE(Bi) > C  s = C/sE(Bi)

myers and majluf 19842
Myers and Majluf (1984)
  • With asymmetric information, H firms will have to give more equity than they would with symmetric information.
  • Pooling equilibria – all projects are undertaken
    • Amount H firms lose due to uncertainty less than their gain from the project
  • Separating equilibria – only L firms undertake projects
    • Amount H firms lose due to uncertainty greater than their gain from the project
cadsby et al 1990
Cadsby et. al. (1990)
  • Let’s test this experimentally!
  • When theory predicts a unique equilibrium, will it happen?
  • When theory predicts multiple equilibria, which will occur?
  • NB: In the interest of time, I will not discuss semiseparatingequilibria or signaling models, though these are important parts of the Cadsby et. al. paper.
symmetric information theoretical results
Symmetric Information: Theoretical Results
  • If I tell you whether the firm was H or L.
  • Investors should demand s* such that
    • s* (1250) = 300  s* = 24% for H firms
    • s* (625) = 300  s* = 48% for L firms
  • Payoffs to firms would be
    • 76% of 1250 = 950 for H firms
    • 52% of 625 = 325 for L firms
  • Both firms will undertake projects.
game 1 theoretical results
Game 1 – Theoretical Results

I did not tell you whether the firm was H or L.

Now beliefs matter – as an investor, it matters what I believe is, given you offer me a project, the probability that you are H or L.

game 1 theoretical results1
Game 1 – Theoretical Results
  • Potential belief #1: Both firms undertake all projects.
  • Investors demand:
    • s* (0.5 x 1250 + 0.5 x 750) = 300  s* = 30%
  • Firms get:
    • 70% of 1250 = 875, if H  undertake
    • 70% of 750 = 525, if L  undertake
  • Beliefs work!
game 1 theoretical results2
Game 1 – Theoretical Results
  • Potential belief #2: Only L firms undertake projects.
  • Investors demand:
    • s* (750) = 300  s* = 40%
  • Firms get:
    • 60% of 1250 = 750, if H  undertake
    • 60% of 750 = 450, if L  undertake
  • Beliefs do not work.
game 1 theoretical results3
Game 1 – Theoretical Results

Therefore, we should have a pooling equilibrium where every project is undertaken and s* = 30%.

game 2 theoretical results
Game 2 – Theoretical Results

I did not tell you whether the firm was H or L.

Beliefs matter – as an investor, it matters what I believe is, given you offer me a project, the probability that you are H or L.

game 2 theoretical results1
Game 2 – Theoretical Results
  • Potential belief #1: Both firms undertake all projects.
  • Investors demand:
    • s* (0.5 x 625 + 0.5 x 375) = 300  s* = 60%
  • Firms get:
    • 40% of 625 = 250, if H  undertake
    • 40% of 375 = 150, if L  undertake
  • Beliefs work!
game 2 theoretical results2
Game 2 – Theoretical Results
  • Potential belief #2: Only L firms undertake projects.
  • Investors demand:
    • s* (375) = 300  s* = 80%
  • Firms get:
    • 20% of 625 = 125, if H  do not undertake
    • 20% of 375 = 75, if L  undertake
  • Beliefs work!
game 2 theoretical results3
Game 2 – Theoretical Results
  • Will we see:
        • Pooling equilibrium, s* = 60%?

Both H and L undertake projects

        • Separating equilibrium, s* = 80%

Only L undertakes projects

cadsby et al results
Cadsby et. al. Results

(related to the experiments replicated here)

If a unique equilibrium is predicted, it is observed.

If multiple equilibria are predicted, a pooling equilibrium is observed.

Note that it is a bit unclear whether we were acting in accordance with the pooling equilibrium in our Game 1. In our Game 2, the separating equilibrium share value was found in the second experiment (inconsistent with Cadsby et. al.results), but both firms entered the market. This is inconsistent with both the theory and the Cadsby et. al. results.