A Laboratory Experiment on the Heuristic Switching Model A Laboratory Experiment on the Heuristic Switching Model Mikhail Anufriev a Aleksei Chernulich a Jan Tuinstra b a University of Technology Sydney b University of Amsterdam Symposium for Experimental Economics Dongbei University of Finance and Economics (DUFE) 29 October 2017 1 / 53
A Laboratory Experiment on the Heuristic Switching Model Summary Experiment focusing on one (of the two) key mechanisms of Heuristic Switching Models and ... ... testing implications of Brock-Hommes (ECMA 1997, JEDC 1998) model Consistently with the model : high information cost of rational rule cause instability Evidence of endogenous change in switching ... consistent with Intensity of Choice parameter reacting on predictability of past returns ... ... leading to “moderately complex” dynamics 2 / 53
A Laboratory Experiment on the Heuristic Switching Model Outline Introduction 1 Experiment 2 Dynamics of the Stylized HSM and Hypotheses 3 Results of the Experiment 4 High (Large and Long) Treatment 5 Conclusion 6 3 / 53
A Laboratory Experiment on the Heuristic Switching Model Introduction Plan Introduction 1 Experiment 2 Dynamics of the Stylized HSM and Hypotheses 3 Results of the Experiment 4 High (Large and Long) Treatment 5 Conclusion 6 4 / 53
A Laboratory Experiment on the Heuristic Switching Model Introduction 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) bayesian and belief-based learning reinforcement learning 2000s- heterogeneous expectations (Heterogeneous Agent Models) 5 / 53
A Laboratory Experiment on the Heuristic Switching Model Introduction Example: Model of Financial Market demand for the long-lived asset of a myopic MV trader 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 ] solve market clearing at time t , find equilibrium 1 � � h D h ( p t ) = 0 p t = h E h , t [ p t + 1 + y t + 1 ] � 1 + r rational (homogeneous) expectations � (for i.i.d. dividends) p f = ¯ 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 6 / 53 h h ′
A Laboratory Experiment on the Heuristic Switching Model Introduction 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 ) 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 7 / 53
A Laboratory Experiment on the Heuristic Switching Model Introduction Example (ctd): Simulation 8 / 53
A Laboratory Experiment on the Heuristic Switching Model Introduction HAMs and their Empirical Validation HAMs assume several expectational rules (affecting trading behavior); these rules get reinforced from their past profit. Do the data support this theory? Empirical Studies Branch (2004), 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) Experimental Studies Hommes et al (2005, 2008), Heemeijer et al (2009), Anufriev and Hommes (2012), Bao et al (2012), Pfajfar and Žakelj (2014), Assenza et al (2015), Anufriev, Bao, 9 / 53 Tuinstra (2016, JEBO)
A Laboratory Experiment on the Heuristic Switching Model Introduction Heuristic Switching Models Rational Expectation Hypothesis: Restrictive theoretical assumptions and Limited empirical validity. Heterogeneous Agent Models (HAMs): agents use behavioral decision rules (“forecasting 1 heuristics”) agents switch between rules based on their past 2 performances (Brock and Hommes, 1997). Applications: Financial markets (endogenous bubbles and crashes and a lot of “stylized facts”), Macroeconomics (persistence of inflation, different policy implications). 10 / 53
A Laboratory Experiment on the Heuristic Switching Model Introduction Brock-Hommes model (ECMA, 1997; JEDC, 1998) Setup Supply/Demand-driven market where participants must form expectations about future price The equilibrium is stable under costly Rational expectations and unstable under free Naive expectations Discrete choice is based on past profits Prediction If cost of RE is high, prices exhibit bubble/crash paterns Mechanism Near equilibrium two heuristics give similar forecasts and, due to fix cost of RE, majority uses naive rule Dynamics diverge and naive expectations get less precise Eventually majority switches to Rational expectations and price returns towards equilibrium 11 / 53
A Laboratory Experiment on the Heuristic Switching Model Introduction Role of Lab Experiments HAMs are empirically successful, tractable, intuitive... ...but the dynamics depends on the chosen heuristics and their cost and also parameters of switching. Experiments with paid human subjects allow to test assumptions and implications 1 pin down relevant heuristics (LtF) 2 estimate parameters of switching 3 in a controlled environment. Switching Experiments Anufriev, Bao, and Tuinstra (JEBO, 2016) tested switching between 2 , 3 or 4 heuristics on exogenous data This paper: binary choice on endogenous data 12 / 53
A Laboratory Experiment on the Heuristic Switching Model Introduction General setup of switching models agents’ choices are distributed over H different heuristics. past payoffs of heuristics are known: π h t − 1 , π h t − 2 , . . . , π h t − ℓ , . . . fraction of agents using heuristic h at time t , is given by discrete choice model (Manski and McFadden, 1981) exp [ α h + βπ h , t − 1 ] n h , t = , � H k = 1 exp [ α k + βπ k , t − 1 ] where β > 0 is the Intensity of Choice and α h ≡ 0 13 / 53
A Laboratory Experiment on the Heuristic Switching Model Introduction General setup of switching models agents’ choices are distributed over H different heuristics. past payoffs of heuristics are known: π h t − 1 , π h t − 2 , . . . , π h t − ℓ , . . . fraction of agents using heuristic h at time t , is given by discrete choice model (Manski and McFadden, 1981) exp [ α h + βπ h , t − 1 ] n h , t = , � H k = 1 exp [ α k + βπ k , t − 1 ] where β > 0 is the Intensity of Choice and α h ≡ 0 Anufriev, Bao, and Tuinstra (JEBO, 2016) found that: (i) intensity of choice is not the same across treatments, but depends on past predictability of profits; (ii) model with predisposition ( α 1 > 0 ) provides beter fit 13 / 53
A Laboratory Experiment on the Heuristic Switching Model Introduction Other Studies for HSMs Estimation and Calibration on financial data: Boswijk, Hommes and Manzan (JEDC, 2007), Goldbaum and Mizrach (JEDC, 2008), Chiarella, He and Zwinkels (JEBO, 2014), Cornea-Madeira, Hommes, and Massaro (JBES, 2017) on survey data: Branch (EJ, 2004), Goldbaum and Zwinkels (JEBO, 2014) on experimental data: Hommes (JEDC, 2011), Anufriev and Hommes (AEJ-Micro, 2012), Anufriev, Hommes and Philipse (JEE, 2013) 14 / 53
A Laboratory Experiment on the Heuristic Switching Model Introduction Objectives of the experiment Verify if aggregate switching behavior is well described 1 by the discrete choice model; Provide estimations of the Intensity of Choice parameter 2 for calibration purposes; Study possible effects of endogeneity in profits on 3 switching (cf., Anufriev, Bao, Tuinstra, JEBO, 2016) Test a prediction of Brock-Hommes (E, 1997; JEDC, 1998) 4 model about the effects of information cost difference between heuristics (e.g., rational expectations vs. naive) Low: stable dynamics High: locally unstable but bounded (bubbles and crashes) 15 / 53
A Laboratory Experiment on the Heuristic Switching Model Experiment Plan Introduction 1 Experiment 2 Dynamics of the Stylized HSM and Hypotheses 3 Results of the Experiment 4 High (Large and Long) Treatment 5 Conclusion 6 16 / 53
A Laboratory Experiment on the Heuristic Switching Model Experiment Screen 17 / 53
A Laboratory Experiment on the Heuristic Switching Model Experiment Experiment Individual discrete choice experiment with group effect 10 Participants: choose between alternatives A and B during 40 periods in one Block and then during 40 periods in another Block are informed that the profits of alternatives depend on their and other participants’ choices are not informed about the functional forms of profit generating processes are shown the history of past profits (graph and table) Additional Sessions: 35 participants, 60 periods 18 / 53
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