## Amplification: Conceptual and Empirical Frameworks

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### Different Sources of Amplification
- Direct Contagion
  - Financial institutions are interconnected; failure of one adversely affects other connected institutions.
- Indirect Contagion
  - Financial institutions interact via the market; the failure of one adversely affects market conditions which hurt other institutions.
- Strategic Complementarities
  - Financial institutions want to take the same action at the same time amplifying an underlying shock.

*Presented by Itay Goldstein, Wharton School, University of Pennsylvania, at the IMF-LSE Symposium.*

### Understanding Strategic Complementarities: Basic Model (Bebchuk and Goldstein (2011) example)
- Setup
  - Continuum [0,K] of banks, each one holds $1.
  - Need to decide whether to invest in a risk free asset, generating 1, or lend.
  - Lending generates 1+R if projects succeed. Specifically, return is:
    - payoff = { 1+R if aggregate lending sufficient (condition expressed with θ and A) ; 0 otherwise } (as in the source representation).
  - θ is fundamental; A is aggregate lending. A = n, where n is proportion of banks deciding to lend.

### Multiple Equilibria and Threshold Regions
- Three ranges of fundamentals (θ):
  - Below lower dominance region (symbolized in source): Unique equilibrium: (efficient) credit freeze.
  - Between lower dominance threshold and upper threshold (intermediate region): Multiple equilibria: either lending or (inefficient) credit freeze.
  - Above upper dominance region: Unique equilibrium: lending.

### Global-Games Approach: Signals and Uniqueness Conditions
- Assumptions on information
  - Fundamental θ is normally distributed with mean y (public news) and standard deviation σ_y (precision, τ_y = 1/σ_y).
  - Banks obtain signals: x_i = θ + ε_i, where ε_i is normally distributed with mean 0 and standard deviation σ_ε (precision, τ_ε = 1/σ_ε).
- Uniqueness condition
  - As long as private information is sufficiently precise relative to public information (formally, condition written in source involving τ_y and τ_ε), there is a unique equilibrium where:
    - Banks lend if and only if their signals are above x*.
    - Lending succeeds if and only if the fundamentals are above θ*.

### Equilibrium Characterization (limit case)
- When banks observe very precise signals (σ_ε approaches infinity in the source representation):
  - x* and θ* converge to the same value: θ* = R/(1+R) (as expressed in the source).
- Three ranges of fundamentals (limit case):
  - Below θ* − R/(1+R): Efficient credit freeze.
  - Between θ* − R/(1+R) and θ* + R/(1+R): Inefficient credit freeze.
  - Above θ* + R/(1+R): No credit freeze.

### Amplification Mechanisms and Triggers for Credit Freeze
- What may trigger a credit freeze?
  - A downward shift in fundamentals:
    - Fundamentals drop to a level below θ*.
  - A decrease in banks’ capital:
    - Suppose that banks lost a fraction l of their capital, the threshold for a credit freeze would increase.
- Implication
  - Small changes in underlying fundamentals or bank conditions can lead to big effects on outcome due to endogenous banks’ response.

### Capturing Sources of Amplification in Stress Tests
- Direct Contagion
  - Understand network of institutions’ interconnections and exposures.
- Indirect Contagion
  - Model institutions’ effects on the markets and vice versa:
    - Price pressures induced by asset fire sales.
    - Effect of price decrease on other institutions.
  - These effects might be different over time:
    - E.g., greater price impact in downturns.

### How to Account for Strategic Complementarities (challenges and steps)
- First, understand theoretical reasons for complementarities:
  - Within institutions:
    - Liquidity transformation.
    - Rollover and default dynamics.
  - Across institutions:
    - Network externalities.
    - Relative performance.
- Second, find empirical evidence for the presence of complementarities:
  - Similar behavior across institutions in certain times.
  - Stronger aggregate reaction in cases of stronger complementarities (Chen, Goldstein, and Jiang, 2010).
- Third, consider mitigating factors:
  - Identify institutions that will take a contrarian action and stabilize the market.
  - It is important to consider all market players and their different motives and behaviors.

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_Source: https://www.imf.org/-/media/files/news/seminars/mcm-lse-goldstein_session3.pdf_