Heterogeneous Agents and NonNormal Fundamentals

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Heterogeneous Agents and Non-Normal Fundamentals

• Marianna Grimaldi
• Remco Zwinkels
• WEHIA 2005 Colchester
• June 13, 2005

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What do we know? (1)
Dutch Guilder / US Dollar Exchange Rate, daily
returns
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What do we know? (2)
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What do we know? (3)

• Macro-economic variables
• Volatility Clustering
• Engle (1982, 1983), Hodrick (1989), Bekaert
  (1996), Cumperayot et al. (2003), Zwinkels (2005)
• Heavy Tails
• Cumperayot and De Vries (2003), Zwinkels (2005)

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Position in Literature

• Classical
• All movements in the exchange rate find their
  source in the underlying macroeconomic
  fundamentals (Friedman, 1953)
• New Lines
• Heterogeneous Agents (Brock Hommes, 97)
• Micro Founded Macro Models (Obstfeld Rogoff,
  95,96)
• Market Microstructure (Evans Lyons, 02)

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This paper

• Introduce ARCH-process as fundamental value in
  heterogeneous agents model
• We find that
• Heterogeneous Agents model Mimics Empirical
  Results
• Disconnection in level and variance IF there is a
  bubble
• Dynamics Caused by Trader Interaction OR
  Fundamental Dynamics, dependent on fraction of
  chartists

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Heterogeneous Agents Model De Grauwe Grimaldi
(EER 2005)

• Exchange Rate is Weighted Average of Expectations
• Two types of agents Fundamentalists Chartists
• Weights determined by fraction of traders
• Agents update their strategy subject to profits

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Heterogeneous Agents Model (1)

• Mean-Variance Utility
• Invest at home or abroad

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Heterogeneous Agents Model (2)

• Equilibrium Exchange Rate -gt Function of Future
  Expectations

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Heterogeneous Agents Model (3)

• Fundamentalist Expectation -gt Mean Reversion
• Chartist Expectation -gt Adaptive

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Heterogeneous Agents Model (4)

• Variance of Forecasts -gt Function of Forecasting
  Error

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Heterogeneous Agents Model (5)

• Weight (fraction) of Fundamentalists
• Weight (fraction) of Chartists

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Heterogeneous Agents Model (6)

• Profits -gt Equal to Exchange Rate Return

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Alternative Fundamental

• First Random Walk
• Now first-order ARCH-process

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Simulation Level
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Simulation Returns
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Simulation Histogram
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Simulation Alternative
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GARCH Estimation

• Estimate relation (augmented ARMA-GARCH)
• Effect level fundamental rate on level exchange
  rate
• Effect variance fundamental on variance exchange
  rate
• Differentiate between sub-samples
• Normal
• Bubble

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Results GARCH Estimation

• Estimation Results, percentage of significant
  coefficients
• Normal if distance between exchange rate and
  fundamental smaller than 2.5

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Sensitivity to Threshold (1)
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Extremes

• Does an extreme value in the fundamental coincide
  
• with an extreme value in the exchange rate?
• Dummy
• Value 1 if absolute return is larger than
  2St.Dev
• Value 0 otherwise
• Put Exchange Rate dummy versus Fundamental dummy
  in
• a cross-plot -gt Test on independence

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Results Extremes

• Percentage of cases in which there is significant
  transmission of extreme shocks
• Connected if the distance between exchange rate
  and fundamental is smaller than 2.5

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Sensitivity to Threshold (2)
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Logit Estimation

• Estimate the sensitivity of the probability of
  extreme return to
• Occurrence of fundamental extreme (dummy)
• Fundamental volatility
• Exchange rate volatility
• Chartist weight
• Cross term independent misalignment

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Results Logit estimation
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Explanation from the Model
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Conclusion

• Exchange Rate Dynamics caused by
• Fundamentals if Misalignment is Small
• Extrapolative Behavior if Misalignment is Large
• Following these results
• Exchange Rate is Constantly Disconnected from
  Fundamental (Meese Rogoff 83)
• Large fraction of traders is chartist (Allen
  Taylor 92)