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Heterogeneous Agent Models Experiments Heuristic Switching Model HS-Hidden Markov-M Conclusion (Towards a) Bayesian Estimation of the Heuristic Switching Model using Experimental Data Mikhail Anufriev a Cars Hommes b Valentyn Panchenko c a University of Technology, Sydney b University of Amsterdam c University of New South Wales Sant’Anna School of Advanced Studies, Pisa 25 May, 2015 Anufriev, Hommes, Panchenko UTS, UvA, UNSW (Towards a) Bayesian Estimation of the Heuristic Switching Model using Experimental Data

Heterogeneous Agent Models Experiments Heuristic Switching Model HS-Hidden Markov-M Conclusion Outline Motivation: Heterogeneous Agent Models Learning to Forecast Experiments Heuristic Switching Model Heuristic Switching Hidden Markov Model Conclusion Anufriev, Hommes, Panchenko UTS, UvA, UNSW (Towards a) Bayesian Estimation of the Heuristic Switching Model using Experimental Data

Heterogeneous Agent Models Experiments Heuristic Switching Model HS-Hidden Markov-M Conclusion Expectations in Economic Theory ◮ economy is an expectation feedback system ◮ expectations affect our decisions and realizations ◮ expectations may be affected by past experience ◮ expectations play the key role in most economic models 30s-60s naive and adaptive expectations 70s-90s rational expectations 90s- models of learning and bounded rationality ◮ adaptive learning (OLS-learning) ◮ belief-based learning ◮ reinforcement learning ◮ heterogeneous expectations and switching (Heterogeneous Agent Models) Anufriev, Hommes, Panchenko UTS, UvA, UNSW (Towards a) Bayesian Estimation of the Heuristic Switching Model using Experimental Data

Heterogeneous Agent Models Experiments Heuristic Switching Model HS-Hidden Markov-M Conclusion Example: Model of Financial Market ◮ demand for the risky asset D h ( p t ) = E h , t [ p t + 1 + y t + 1 ] − ( 1 + r ) p t a V h , t [ p t + 1 + y t + 1 ] ◮ solving market clearing eq. at time t find the equilibrium price 1 � � h D h ( p t ) = 0 p t = h E h , t [ p t + 1 + y t + 1 ] � 1 + r ◮ rational expectations � (for i.i.d. dividends) p t = ¯ 1 y p t = 1 + r E t [ p t + 1 + y t + 1 ] r ◮ heterogeneous expectations � � 1 1 � � p t = E h ′ , t + 1 [ p t + 2 + y t + 2 ] + y t + 1 E h , t 1 + r 1 + r h h ′ Anufriev, Hommes, Panchenko UTS, UvA, UNSW (Towards a) Bayesian Estimation of the Heuristic Switching Model using Experimental Data

Heterogeneous Agent Models Experiments Heuristic Switching Model HS-Hidden Markov-M Conclusion Example (ctd): Heterogeneous Agent Model ◮ there are two types of investors ◮ fundamentalists, E f , t [ p t + 1 ] = p f + v ( p f − p t − 1 ) with 0 ≤ v < 1 ◮ chartists, E c , t [ p t + 1 ] = p t − 1 + g ( p t − 1 − p t − 2 ) with g > 0 ◮ evolution of price 1 ¯ y � � p t = n f , t E f , t [ p t + 1 ] + n c , t E c , t [ p t + 1 ] + 1 + r 1 + r ◮ evolution of fractions exp [ βπ f , t ] n f , t + 1 = exp [ βπ f , t ] + exp [ βπ c , t ] ◮ profits π f , t and π c , t are computed as their holdings times return p t + y t − ( 1 + r ) p t − 1 and known to everybody ◮ fundamentalists pay fixed cost C > 0 Anufriev, Hommes, Panchenko UTS, UvA, UNSW (Towards a) Bayesian Estimation of the Heuristic Switching Model using Experimental Data

Heterogeneous Agent Models Experiments Heuristic Switching Model HS-Hidden Markov-M Conclusion Example (ctd): Simulation Anufriev, Hommes, Panchenko UTS, UvA, UNSW (Towards a) Bayesian Estimation of the Heuristic Switching Model using Experimental Data

Heterogeneous Agent Models Experiments Heuristic Switching Model HS-Hidden Markov-M Conclusion Empirical Validation of HAMs ◮ on financial data: Boswijk, Hommes and Manzan (2007), Goldbaum and Mizrach (2008), De Jong, Verschoor, and Zwinkels (2009), Kouwenberg and Zwinkels (2010), Franke and Westerhoff (2011), Chiarella, He and Zwinkels (2014); ◮ on survey data: Branch (2004); Experiments with paid human subjects allow to investigate heuristics and switching in a controlled environment, estimate parameters, test hypotheses. ◮ Learning to Forecast Experiments ◮ Switching Experiments Anufriev, Hommes, Panchenko UTS, UvA, UNSW (Towards a) Bayesian Estimation of the Heuristic Switching Model using Experimental Data

Heterogeneous Agent Models Experiments Heuristic Switching Model HS-Hidden Markov-M Conclusion Experiments about expectations Learning-to-forecast experiments: Hommes et al (2005, RFS; 2008, JEBO), Adam (2009, EJ), Heemeijer, Hommes, Sonnemans and Tuinstra (2009, JEDC) Experiment with few (six) students who know only qualitative features. Story: ◮ each of you is a forecaster of price working for a financial firm ◮ several firms are in the market ◮ price is affected by demand and supply ◮ higher forecasts lead to a higher demand [or to a higher supply] ◮ your payoff (salary) depends on the forecast precision Information: ◮ observe past prices, own forecasts and payoffs Anufriev, Hommes, Panchenko UTS, UvA, UNSW (Towards a) Bayesian Estimation of the Heuristic Switching Model using Experimental Data

Heterogeneous Agent Models Experiments Heuristic Switching Model HS-Hidden Markov-M Conclusion Computer Screen � � 1 − 1 × 1 49 ( p t − p e t , h ) 2 , 0 e t , h = max earnings per period: 2 euro Anufriev, Hommes, Panchenko UTS, UvA, UNSW (Towards a) Bayesian Estimation of the Heuristic Switching Model using Experimental Data

Heterogeneous Agent Models Experiments Heuristic Switching Model HS-Hidden Markov-M Conclusion Learning to Forecast Experiments Two treatments Negative feedback Positive feedback Price Price 120 120 100 100 80 80 60 60 40 40 20 20 80 100 120Prediction 80 100 120Prediction 20 40 60 20 40 60 p t = 60 − 20 � p e � p t = 60 + 20 � p e � t − 60 + ε t t − 60 + ε t 21 21 Anufriev, Hommes, Panchenko UTS, UvA, UNSW (Towards a) Bayesian Estimation of the Heuristic Switching Model using Experimental Data

Heterogeneous Agent Models Experiments Heuristic Switching Model HS-Hidden Markov-M Conclusion Rational Benchmark If everybody predicts fundamental price p f = 60, then p t = p f + ε t 70 fundamental price price under rational expectations 65 60 Price 55 1 0.5 50 0 -0.5 45 -1 0 10 20 30 40 50 40 0 10 20 30 40 50 Time Anufriev, Hommes, Panchenko UTS, UvA, UNSW (Towards a) Bayesian Estimation of the Heuristic Switching Model using Experimental Data

Heterogeneous Agent Models Experiments Heuristic Switching Model HS-Hidden Markov-M Conclusion Negative Feedback Experiment Anufriev, Hommes, Panchenko UTS, UvA, UNSW (Towards a) Bayesian Estimation of the Heuristic Switching Model using Experimental Data

Heterogeneous Agent Models Experiments Heuristic Switching Model HS-Hidden Markov-M Conclusion Positive Feedback Experiment Anufriev, Hommes, Panchenko UTS, UvA, UNSW (Towards a) Bayesian Estimation of the Heuristic Switching Model using Experimental Data

Heterogeneous Agent Models Experiments Heuristic Switching Model HS-Hidden Markov-M Conclusion Negative Feedback Experiment: all sessions 80 60 Price 40 20 0 10 20 30 40 50 Time Anufriev, Hommes, Panchenko UTS, UvA, UNSW (Towards a) Bayesian Estimation of the Heuristic Switching Model using Experimental Data

Heterogeneous Agent Models Experiments Heuristic Switching Model HS-Hidden Markov-M Conclusion Positive Feedback Experiment: all sessions 80 60 Price 40 20 0 10 20 30 40 50 Time Anufriev, Hommes, Panchenko UTS, UvA, UNSW (Towards a) Bayesian Estimation of the Heuristic Switching Model using Experimental Data

Heterogeneous Agent Models Experiments Heuristic Switching Model HS-Hidden Markov-M Conclusion Estimation of Individual Predictions OLS regressions of individual predictions on the lagged variables Identified intuitive behavioural rules: p e i , t = α 1 p t − 1 + α 2 p e i , t − 1 + ( 1 − α 1 − α 2 ) 60 + γ ( p t − 1 − p t − 2 ) ◮ adaptive heuristic p e t + 1 = wp t + ( 1 − w ) p e t ◮ trend heuristic p e t + 1 = p t + γ ( p t − p t − 1 ) Anufriev, Hommes, Panchenko UTS, UvA, UNSW (Towards a) Bayesian Estimation of the Heuristic Switching Model using Experimental Data

Heterogeneous Agent Models Experiments Heuristic Switching Model HS-Hidden Markov-M Conclusion Background Heuristic Switching Model with heterogeneous expectations ◮ introduced in Anufriev and Hommes (2012, AEJ-Micro) and Anufriev, Hommes and Philipse (2013, JEE) ◮ applied to several “learning to forecast experiments” ◮ Hommes et al (2005, RFS; 2008, JEBO), Heemeijer et al (2009, JEDC) ◮ applied in experimental papers Bao et al (2011, JEDC), Assenza et al (2009, CeNDEF WP) Key features in forecasting agents use simple rules of thumb, heuristics (Tversky and Kahneman, 1974) in learning agents switch between different forecasting rules on the basis of their performances (Brock and Hommes, 1997) Anufriev, Hommes, Panchenko UTS, UvA, UNSW (Towards a) Bayesian Estimation of the Heuristic Switching Model using Experimental Data

Heterogeneous Agent Models Experiments Heuristic Switching Model HS-Hidden Markov-M Conclusion Evolution of Individual Predictions Predictions in Negative Feedback Experiment 80 prediction price 70 Price, Predictions 60 50 40 0 10 20 30 40 50 Anufriev, Hommes, Panchenko UTS, UvA, UNSW (Towards a) Bayesian Estimation of the Heuristic Switching Model using Experimental Data