Heterogeneous Expectations Model Learning to Forecast Experiments Animal Spirits, Heterogeneous Expectations and the Amplification and Duration of Crises Tiziana Assenza (Universita Catolica Milano) William Brock (University of Wisconsin) Cars Hommes (University of Amsterdam) UvA, CeNDEF 14th Annual DNB Research Conference Complex Systems: Towards a Better Understanding of Financial Stability and Crises, Amsterdam, November 3-4, 2011 Cars Hommes UvA, CeNDEF Animal Spirits and Heterogeneous Expectations
Heterogeneous Expectations Model Learning to Forecast Experiments Animal Spirits (Keynes) much of (macro)economic activity is governed by animal spirits ◮ people have non-economic motives ◮ they are not always rational in pursuit of economic interests Keynes : animal spirits are the main source of economic fluctuations ... but animal spirits disappeared from the neoclassical, rational model Cars Hommes UvA, CeNDEF Animal Spirits and Heterogeneous Expectations
Heterogeneous Expectations Model Learning to Forecast Experiments Animal Spirits (Akerlof and Shiller, 2009) How human psychology drives the economy, and why it matters for global capitalism 5 animal spirits: confidence, fairness, corruption, money illusion and stories ◮ cornerstone animal spirit: confidence ◮ behavioral economics : how the economy really works, when people are human ◮ animal spirits difficult to conceptualize, model and measure Goal of this paper : dynamic equilibrium model of agents’ confidence Main Result : sudden collapse of confidence accelerates and amplifies downturn or crisis and slows down recovery Cars Hommes UvA, CeNDEF Animal Spirits and Heterogeneous Expectations
Heterogeneous Expectations Model Learning to Forecast Experiments Main hypothesis: heterogeneous expectations Brock and Hommes, 1997 main tool for modeling confidence in market for loans ◮ lenders’ heterogeneous expectations about the (exogenous) probability of succes /failure of borrowers Main finding : ◮ In the presence of a (small) fraction of pessimistic beliefs , an unexpected negative shock to credit markets triggers these pessimistic beliefs to become self-fulfilling , amplifying a “crisis" and slowing down recovery Cars Hommes UvA, CeNDEF Animal Spirits and Heterogeneous Expectations
Heterogeneous Expectations Model Learning to Forecast Experiments Plan of the Talk ◮ Heterogeneous Expectations Model Heuristics Switching Model ◮ Learning to Forecast Experiments ◮ a simple heterogeneous expectations model of the crisis Cars Hommes UvA, CeNDEF Animal Spirits and Heterogeneous Expectations
Heterogeneous Expectations Model Learning to Forecast Experiments Some Literature Related to this Talk ◮ Hommes, C.H. (2011) The Heterogeneous Expectations Hypothesis: Some Evidence from the Lab, Journal of Economic Dynamics & Control , 35, 1-24. ◮ Assenza, T., Brock, W.A. and Hommes, C.H. (2011), Animal Spirits, Heterogeneous Expectations and the Amplification and Duration of Crises Cars Hommes UvA, CeNDEF Animal Spirits and Heterogeneous Expectations
Heterogeneous Expectations Model Learning to Forecast Experiments Heterogeneous Expectations Heuristics Switching Model ◮ agents choose from a number of simple forecasting heuristics ◮ adaptive learning : some parameters of the heuristics are updated over time, e.g. anchor ≡ average ◮ performance based reinforcement learning: (extension of Brock and Hommes, Econometrica 1997) agents evaluate the performances of all heuristics, and tend to switch to more successful rules; impacts are evolving over time Cars Hommes UvA, CeNDEF Animal Spirits and Heterogeneous Expectations
Heterogeneous Expectations Model Learning to Forecast Experiments Four forecasting heuristics ◮ adaptive rule p e 1 , t + 1 = 0 . 65 p t − 1 + 0 . 35 p e ADA 1 , t ◮ weak trend-following rule p e 2 , t + 1 = p t − 1 + 0 . 4 ( p t − 1 − p t − 2 ) WTR ◮ strong trend-following rule p e 3 , t + 1 = p t − 1 + 1 . 3 ( p t − 1 − p t − 2 ) STR ◮ anchoring and adjustment heuristics with learnable anchor p e 4 , t + 1 = 0 . 5 p av LAA t − 1 + 0 . 5 p t − 1 + ( p t − 1 − p t − 2 ) Cars Hommes UvA, CeNDEF Animal Spirits and Heterogeneous Expectations
Heterogeneous Expectations Model Learning to Forecast Experiments Evolutionary Switching Brock and Hommes, ( Econometrica 1997) ◮ performance measure of heuristic i is � 2 + η U i , t − 2 p t − 1 − p e � U i , t − 1 = − i , t − 1 parameter η ∈ [ 0 , 1 ] – the strength of the agents’ memory ◮ discrete choice model with asynchronous updating exp ( β U i , t − 1 ) n i , t = δ n i , t − 1 + ( 1 − δ ) � 4 i = 1 exp ( β U i , t − 1 ) parameter δ ∈ [ 0 , 1 ] – the inertia of the traders parameter β ≥ 0 – the intensity of choice Cars Hommes UvA, CeNDEF Animal Spirits and Heterogeneous Expectations
Heterogeneous Expectations Model Learning to Forecast Experiments Computer Screen Learning to Forecast Experiment Cars Hommes UvA, CeNDEF Animal Spirits and Heterogeneous Expectations
Heterogeneous Expectations Model Learning to Forecast Experiments Asset Pricing Experiment Simulation Benchmarks Rational Expectation Naive Expectation 70 70 simulated price simulated price fundamental fundamental 65 65 60 60 55 55 50 50 45 45 40 40 0 10 20 30 40 50 0 10 20 30 40 50 Period Period Sample Average Expectation AR 2 Expectation 70 70 simulated price simulated price fundamental fundamental 65 65 60 60 55 55 50 50 45 45 40 40 0 10 20 30 40 50 0 10 20 30 40 50 Period Period Cars Hommes UvA, CeNDEF Animal Spirits and Heterogeneous Expectations
Heterogeneous Expectations Model Learning to Forecast Experiments Asset Pricing Experiment (with Robot Trader) Group 2 Group 5 70 70 fundamental price experimental price fundamental price experimental price 65 65 60 60 Price 55 55 50 50 45 45 40 40 Group 1 Group 6 70 70 fundamental price experimental price fundamental price experimental price 65 65 60 60 Price 55 55 50 50 45 45 40 40 Group 4 Group 7 90 70 fundamental price experimental price fundamental price experimental price 80 65 70 60 60 Price 50 55 40 50 30 45 20 10 40 0 10 20 30 40 50 0 10 20 30 40 50 Cars Hommes UvA, CeNDEF Animal Spirits and Heterogeneous Expectations
Heterogeneous Expectations Model Learning to Forecast Experiments Stochastic Simulations (one step ahead forecast) Anufriev and Hommes (2009) ◮ uses past experimental data ◮ same information as participants in experiments Parameters fixed at: β = 0 . 4 , η = 0 . 7 , δ = 0 . 9 ◮ initial fractions equal , i.e. n ht = 0 . 25 ◮ initial prices as in experiments Cars Hommes UvA, CeNDEF Animal Spirits and Heterogeneous Expectations
Heterogeneous Expectations Model Learning to Forecast Experiments Group 5 (Convergence) experimental prices simulated prices, predictions and errors Parameters: β = 0 . 4 , η = 0 . 7 , δ = 0 . 9 Group 5 65 Fractions of 4 rules in the simulation for Group 5 Price 55 ADA WTR STR LAA 1 0.8 simulation experiment 45 ADA WTR STR LAA 65 0.6 55 0.4 Predictions 0.2 45 2 0 0 35 -2 0 10 20 30 40 50 0 10 20 30 40 50 Cars Hommes UvA, CeNDEF Animal Spirits and Heterogeneous Expectations
Heterogeneous Expectations Model Learning to Forecast Experiments Group 6 (Constant Oscillations) experimental prices simulated prices, predictions and errors Parameters: β = 0 . 4 , η = 0 . 7 , δ = 0 . 9 Group 6 65 Fractions of 4 rules in the simulation for Group 2 Price 55 ADA WTR STR LAA 1 0.8 simulation experiment 45 ADA WTR STR LAA 65 0.6 55 0.4 Predictions 0.2 45 5 0 0 35 -5 0 10 20 30 40 50 0 10 20 30 40 50 Cars Hommes UvA, CeNDEF Animal Spirits and Heterogeneous Expectations
Heterogeneous Expectations Model Learning to Forecast Experiments Group 7 (Damping Oscillations) experimental prices simulated prices, predictions and errors Parameters: β = 0 . 4 , η = 0 . 7 , δ = 0 . 9 Group 7 75 Fractions of 4 rules in the simulation for Group 7 65 Price ADA WTR STR LAA 1 55 0.8 45 simulation experiment 75 ADA WTR STR LAA 0.6 65 0.4 55 Predictions 45 0.2 10 0 0 -10 0 10 20 30 40 50 0 10 20 30 40 50 Cars Hommes UvA, CeNDEF Animal Spirits and Heterogeneous Expectations
Heterogeneous Expectations Model Learning to Forecast Experiments Conclusion based on Experiments ◮ simple heterogeneous expectations heuristics switching model fits experimental data quite nicely ◮ performance based reinforcement learning: (extension of Brock and Hommes, Econometrica 1997) agents evaluate the performances of all heuristics, and tend to switch to more successful rules; impacts are evolving over time ◮ agents use simple heuristics such as ◮ adaptive expectations ◮ trend following rules ◮ anchor and adjustment rules Cars Hommes UvA, CeNDEF Animal Spirits and Heterogeneous Expectations
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