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A Laboratory Experiment on the Heuristic Switching Model

A Laboratory Experiment on the Heuristic Switching Model

Mikhail Anufrieva Aleksei Chernulicha Jan Tuinstrab

a University of Technology Sydney b University of Amsterdam

Symposium for Experimental Economics Dongbei University of Finance and Economics (DUFE) 29 October 2017

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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

• n predictability of past returns ...

... leading to “moderately complex” dynamics

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A Laboratory Experiment on the Heuristic Switching Model

Outline

1

Introduction

2

Experiment

3

Dynamics of the Stylized HSM and Hypotheses

4

Results of the Experiment

5

High (Large and Long) Treatment

6

Conclusion

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A Laboratory Experiment on the Heuristic Switching Model Introduction

Plan

1

Introduction

2

Experiment

3

Dynamics of the Stylized HSM and Hypotheses

4

Results of the Experiment

5

High (Large and Long) Treatment

6

Conclusion

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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)

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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 Dh(pt) = Eh,t[pt+1 + yt+1] − (1 + r)pt a Vh,t[pt+1 + yt+1] solve market clearing at time t, find equilibrium

• h Dh(pt) = 0
• pt =

1 1 + r

• h Eh,t[pt+1 + yt+1]

rational (homogeneous) expectations pt = 1 1 + r Et[pt+1+yt+1] (for i.i.d. dividends) pf = ¯ y r heterogeneous expectations pt = 1 1 + r

• h

Eh,t

• 1

1 + r

• h′

Eh′,t+1[pt+2 + yt+2] + yt+1

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A Laboratory Experiment on the Heuristic Switching Model Introduction

Example (ctd): Heterogeneous Agent Model

there are two types of investors

fundamentalists, Ef ,t[pt+1] = pf + v(pf − pt−1) chartists, Ec,t[pt+1] = pt−1 + g(pt−1 − pt−2) with g > 0

evolution of price pt = 1 1 + r

• nf ,t Ef ,t[pt+1] + nc,t Ec,t[pt+1]
• +

¯ y 1 + r evolution of fractions nf ,t+1 = exp [βπf ,t] exp [βπf ,t] + exp [βπc,t] profits πf ,t and πc,t are computed as their holdings times return pt + yt − (1 + r)pt−1 and known to everybody fundamentalists pay fixed cost C > 0

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A Laboratory Experiment on the Heuristic Switching Model Introduction

Example (ctd): Simulation

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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, Tuinstra (2016, JEBO)

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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):

1

agents use behavioral decision rules (“forecasting heuristics”)

2

agents switch between rules based on their past 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).

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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

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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

1

test assumptions and implications

2

pin down relevant heuristics (LtF)

3

estimate parameters of switching 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

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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: πh

t−1, πh t−2, . . . , πh t−ℓ, . . .

fraction of agents using heuristic h at time t, is given by discrete choice model (Manski and McFadden, 1981) nh,t = exp [αh + βπh,t−1] H

k=1 exp [αk + βπk,t−1]

, where β > 0 is the Intensity of Choice and αh ≡ 0

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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: πh

t−1, πh t−2, . . . , πh t−ℓ, . . .

fraction of agents using heuristic h at time t, is given by discrete choice model (Manski and McFadden, 1981) nh,t = exp [αh + βπh,t−1] H

k=1 exp [αk + βπk,t−1]

, where β > 0 is the Intensity of Choice and αh ≡ 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 (α1 > 0) provides beter fit

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A Laboratory Experiment on the Heuristic Switching Model Introduction

Other Studies for HSMs Estimation and Calibration

• n 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)

• n survey data: Branch (EJ, 2004), Goldbaum and

Zwinkels (JEBO, 2014)

• n experimental data: Hommes (JEDC, 2011), Anufriev

and Hommes (AEJ-Micro, 2012), Anufriev, Hommes and Philipse (JEE, 2013)

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A Laboratory Experiment on the Heuristic Switching Model Introduction

Objectives of the experiment

1

Verify if aggregate switching behavior is well described by the discrete choice model;

2

Provide estimations of the Intensity of Choice parameter for calibration purposes;

3

Study possible effects of endogeneity in profits on switching (cf., Anufriev, Bao, Tuinstra, JEBO, 2016)

4

Test a prediction of Brock-Hommes (E, 1997; JEDC, 1998) 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)

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A Laboratory Experiment on the Heuristic Switching Model Experiment

Plan

1

Introduction

2

Experiment

3

Dynamics of the Stylized HSM and Hypotheses

4

Results of the Experiment

5

High (Large and Long) Treatment

6

Conclusion

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A Laboratory Experiment on the Heuristic Switching Model Experiment

Screen

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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

• ne 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

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A Laboratory Experiment on the Heuristic Switching Model Experiment

DGP: Stylized version of the BH model

Endogenous Variables:

πA,t profit of “rational” (stabilizing but costly) heuristic πB,t profit of “naive” (cheap but destabilizing) heuristic xt “deviation of price from REE steady state” nB,t share of “naive” heuristic’s users, 1 − nB,t = nA,t

State Variable Dynamics and Profits of Heuristics xt = λnB,txt−1 + ǫt πA,t = w + γAx2

t ,

πB,t = W − γBx2

t

with λ = 2.1, γA + γB = 1, w < W, ǫt ∼ N(0, 0.1)

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A Laboratory Experiment on the Heuristic Switching Model Experiment

DGP: Stylized version of the BH model

Endogenous Variables:

πA,t profit of “rational” (stabilizing but costly) heuristic πB,t profit of “naive” (cheap but destabilizing) heuristic xt “deviation of price from REE steady state” nB,t share of “naive” heuristic’s users, 1 − nB,t = nA,t

State Variable Dynamics and Profits of Heuristics xt = λnB,txt−1 + ǫt πA,t = w + γAx2

t ,

πB,t = W − γBx2

t

with λ = 2.1, γA + γB = 1, w < W, ǫt ∼ N(0, 0.1) Exogenous Variable:

W − w = C cost difference C > 0 means that “rational” heuristic is more costly

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A Laboratory Experiment on the Heuristic Switching Model Experiment

Experiment Design and Parametrization

State variable dynamics xt = 2.1nB,txt−1 + ǫt, ǫt ∼ N(0, 0.1), x0 = 0 Two Blocks of 40 decision periods in each High: C = 8 πA,t = 1 + 0.6x2

t ,

πB,t = 9 − 0.4x2

t

Low: C = 1 πA,t = 4.95 + 0.6x2

t ,

πB,t = 5.05 − 0.4x2

t

Two treatments with 4 sessions each and rematching participants by the groups of 10

High block to Low block Low block to High block

2 extra sessions for High Treatment (N = 35, T = 60)

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A Laboratory Experiment on the Heuristic Switching Model Dynamics of the Stylized HSM and Hypotheses

Plan

1

Introduction

2

Experiment

3

Dynamics of the Stylized HSM and Hypotheses

4

Results of the Experiment

5

High (Large and Long) Treatment

6

Conclusion

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A Laboratory Experiment on the Heuristic Switching Model Dynamics of the Stylized HSM and Hypotheses

Dynamics of the Stylized HSM

Assuming discrete choice model with predisposition Probability to choose B = 1 1 + eα+β(πA,t−1−πB,t−1) and large population (nB,t = Probability to choose B) the state variable evolves as xt = λxt−1 1 + eα+β(x2

t−1−(W−w)) + ǫt =

2.1xt−1 1 + eα+β(x2

t−1−C) + ǫt

In the experiment we vary the cost difference: High Block : C = 8 Low Block : C = 0.1

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A Laboratory Experiment on the Heuristic Switching Model Dynamics of the Stylized HSM and Hypotheses

Properties of the Model Dynamics

xt = λ xt−1 1 + exp[α + β(x2

t−1 − C)]

x∗ = 0 is a steady state for all parameter values. This steady state is unique and globally stable for λ < 1. For λ > 0 the system undergoes a pitchfork bifurcation when λ = 1 + exp(α − βC). At the moment of the bifurcation two non-zero steady states, x+ > 0 and x− < 0, are created, with corresponding steady state fraction 1/λ. For λ < 0 the system undergoes a period doubling bifurcation when −λ = 1 + exp(α − βC). At the moment of the bifurcation a 2-cycle is created, with corresponding steady state fraction −1/λ.

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A Laboratory Experiment on the Heuristic Switching Model Dynamics of the Stylized HSM and Hypotheses

Bifurcation Diagrams: C = 8 vs C = 0.1

Let λ = 2.1:

0.0 0.2 0.4 0.6 0.8 1.0

• 0.4
• 0.2

0.0 0.2 0.4 β α

High Information Cost

5 10 15 20

• 0.4
• 0.2

0.0 0.2 0.4 β α

Low Information Cost

Red: the zero steady state is stable Blue: the non-zero steady states are stable

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A Laboratory Experiment on the Heuristic Switching Model Dynamics of the Stylized HSM and Hypotheses

Bifurcation Diagrams: C = 8 vs C = 0.1

Let λ = 2.1: α = 0.4 α = 0 α = −0.4

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A Laboratory Experiment on the Heuristic Switching Model Dynamics of the Stylized HSM and Hypotheses

Simulation: C = 8 vs C = 0.1

Let λ = 2.1, α = 0, β = 5:

5 10 15 20 25 30 35 40 time period

• 5
• 4
• 3
• 2
• 1

1 2 3 4 5 state variable, x

parametrization of High blocks

5 10 15 20 25 30 35 40 time period

• 0.6
• 0.4
• 0.2

0.2 0.4 0.6 state variable, x

parametrization of Low blocks

5 10 15 20 25 30 35 40 time period 0.2 0.4 0.6 0.8 1 fraction of B choice

parametrization of High blocks

5 10 15 20 25 30 35 40 time period 0.2 0.4 0.6 0.8 1 fraction of B choice

parametrization of Low blocks

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A Laboratory Experiment on the Heuristic Switching Model Dynamics of the Stylized HSM and Hypotheses

Hypotheses

• H1. There is a difference in volatility of both nB,t and

xt between the High blocks and the Low blocks.

• H2. The endogenous variable nB,t can be described by

a discrete choice model with one lag and a predisposition effect.

• H3. There is no difference between the discrete

choice models estimated for High and for Low

• blocks. In particular, the Intensity of Choice

parameter is the same.

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A Laboratory Experiment on the Heuristic Switching Model Results of the Experiment

Plan

1

Introduction

2

Experiment

3

Dynamics of the Stylized HSM and Hypotheses

4

Results of the Experiment

5

High (Large and Long) Treatment

6

Conclusion

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A Laboratory Experiment on the Heuristic Switching Model Results of the Experiment

Fraction of B-choices: High-Low Treatment I

5 10 15 20 25 30 35 40 time period 0.2 0.4 0.6 0.8 1 fraction of B choice

High: Session 1, group 1

5 10 15 20 25 30 35 40 time period 0.2 0.4 0.6 0.8 1 fraction of B choice

Low: Session 1, group 1

5 10 15 20 25 30 35 40 time period 0.2 0.4 0.6 0.8 1 fraction of B choice

High: Session 1, group 2

5 10 15 20 25 30 35 40 time period 0.2 0.4 0.6 0.8 1 fraction of B choice

Low: Session 1, group 2

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A Laboratory Experiment on the Heuristic Switching Model Results of the Experiment

Fraction of B-choices: High-Low Treatment II

5 10 15 20 25 30 35 40 time period 0.2 0.4 0.6 0.8 1 fraction of B choice

High: Session 3, group 1

5 10 15 20 25 30 35 40 time period 0.2 0.4 0.6 0.8 1 fraction of B choice

Low: Session 3, group 1

5 10 15 20 25 30 35 40 time period 0.2 0.4 0.6 0.8 1 fraction of B choice

High: Session 3, group 2

5 10 15 20 25 30 35 40 time period 0.2 0.4 0.6 0.8 1 fraction of B choice

Low: Session 3, group 2

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A Laboratory Experiment on the Heuristic Switching Model Results of the Experiment

Fraction of B-choices: Low-High Treatment I

5 10 15 20 25 30 35 40 time period 0.2 0.4 0.6 0.8 1 fraction of B choice

Low: Session 2, group 1

5 10 15 20 25 30 35 40 time period 0.2 0.4 0.6 0.8 1 fraction of B choice

High: Session 2, group 1

5 10 15 20 25 30 35 40 time period 0.2 0.4 0.6 0.8 1 fraction of B choice

Low: Session 2, group 2

5 10 15 20 25 30 35 40 time period 0.2 0.4 0.6 0.8 1 fraction of B choice

High: Session 2, group 2

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A Laboratory Experiment on the Heuristic Switching Model Results of the Experiment

Fraction of B-choices: Low-High Treatment II

5 10 15 20 25 30 35 40 time period 0.2 0.4 0.6 0.8 1 fraction of B choice

Low: Session 4, group 1

5 10 15 20 25 30 35 40 time period 0.2 0.4 0.6 0.8 1 fraction of B choice

High: Session 4, group 1

5 10 15 20 25 30 35 40 time period 0.2 0.4 0.6 0.8 1 fraction of B choice

Low: Session 4, group 2

5 10 15 20 25 30 35 40 time period 0.2 0.4 0.6 0.8 1 fraction of B choice

High: Session 4, group 2

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A Laboratory Experiment on the Heuristic Switching Model Results of the Experiment

Histograms of B-choices

High: All groups

0.2 0.4 0.6 0.8 1 fraction of B choice 10 20 30 40 50 frequency

Low: All groups

0.2 0.4 0.6 0.8 1 fraction of B choice 10 20 30 40 50 frequency

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A Laboratory Experiment on the Heuristic Switching Model Results of the Experiment

State Variable: High - Low Treatment I

5 10 15 20 25 30 35 40 time period 1 2 3 4 5 6 7 8 9 state variable, x

Session 1

High: group 1 High: group 2 Low: group 1 Low: group 2

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A Laboratory Experiment on the Heuristic Switching Model Results of the Experiment

State Variable: High - Low Treatment II

5 10 15 20 25 30 35 40 time period 1 2 3 4 5 6 7 8 9 state variable, x

Session 3

High: group 1 High: group 2 Low: group 1 Low: group 2

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A Laboratory Experiment on the Heuristic Switching Model Results of the Experiment

State Variable: Low - High Treatment I

5 10 15 20 25 30 35 40 time period 1 2 3 4 5 6 7 8 9 state variable, x

Session 2

High: group 1 High: group 2 Low: group 1 Low: group 2

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A Laboratory Experiment on the Heuristic Switching Model Results of the Experiment

State Variable: Low - High Treatment II

5 10 15 20 25 30 35 40 time period 1 2 3 4 5 6 7 8 9 state variable, x

Session 4

High: group 1 High: group 2 Low: group 1 Low: group 2

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A Laboratory Experiment on the Heuristic Switching Model Results of the Experiment

Descriptive statistics

Fraction of B-choices, nB State Variable, x Data Mean

• Std. Dev.

Mean

• Std. Dev.

Session 1. Group 1 0.58 0.27 2.43 1.52 Session 1. Group 2 0.61 0.25 2.26 1.52 High Session 2. Group 1 0.60 0.27 2.51 1.47 Session 2. Group 2 0.58 0.28 2.39 1.27 . . . . . . . . . . . . . . . All groups 0.59 0.26 2.43 1.52 Session 1. Group 1 0.56 0.23 0.26 0.22 Session 1. Group 2 0.51 0.23 0.26 0.24 Low Session 2. Group 1 0.55 0.24 0.17 0.21 Session 2. Group 2 0.56 0.24 0.13 0.28 . . . . . . . . . . . . . . . All groups 0.54 0.24 0.20 0.24

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A Laboratory Experiment on the Heuristic Switching Model Results of the Experiment

Discrete Choice Model

IoC Predisposition Zero SS Non-Zero SS Data Beta S.E. Alpha S.E. (x∗, n∗) f ′(x∗) (x+, n+) f ′(x+) Session 1. Group 1 0.08 0.01 0.31 0.11 (0,0.58) 1.22 (2.31,0.48) 0.55 Session 1. Group 2 0.12 0.02 0.38 0.11 (0,0.64) 1.35 (2.37,0.48) 0.29 High Session 2. Group 1 0.12 0.02 0.35 0.11 (0,0.65) 1.36 (2.42,0.48) 0.26 Session 2. Group 2 0.17 0.02 0.28 0.11 (0,0.75) 1.57 (2.63,0.48)

• 0.23

. . . . . . . . . . . . . . . . . . . . . . . . . . . All groups 0.12 0.01 0.25 0.04 Session 1. Group 1 3.35 0.84 0.26 0.11 (0,0.52) 1.09 (0.23,0.48) 0.82 Session 1. Group 2 5.24 0.93 0.09 0.11 (0,0.61) 1.27 (0.32,0.48) 0.45 Low Session 2. Group 1 11.35 1.66

• 0.17

0.13 (0,0.79) 1.65 (0.35,0.48)

• 0.47

Session 2. Group 2 8.67 1.47 0.10 0.11 (0,0.68) 1.43 (0.32,0.48) 0.10 . . . . . . . . . . . . . . . . . . . . . . . . . . . All groups 5.71 0.42 0.11 0.04

Table: Estimations of the DCM with one lag and predisposition.

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A Laboratory Experiment on the Heuristic Switching Model Results of the Experiment

Estimations on the Bifurcation diagram

0.0 0.2 0.4 0.6 0.8 1.0

• 0.4
• 0.2

0.0 0.2 0.4 β α

High Information Cost

5 10 15 20

• 0.4
• 0.2

0.0 0.2 0.4 β α

Low Information Cost

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A Laboratory Experiment on the Heuristic Switching Model High (Large and Long) Treatment

Plan

1

Introduction

2

Experiment

3

Dynamics of the Stylized HSM and Hypotheses

4

Results of the Experiment

5

High (Large and Long) Treatment

6

Conclusion

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A Laboratory Experiment on the Heuristic Switching Model High (Large and Long) Treatment

Fraction of B-choices: Large/Long High T

10 20 30 40 50 60 time period 0.2 0.4 0.6 0.8 1 fraction of B choice

High: Large - Long, group 1

10 20 30 40 50 60 time period 0.2 0.4 0.6 0.8 1 fraction of B choice

High: Large - Long, group 2

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A Laboratory Experiment on the Heuristic Switching Model High (Large and Long) Treatment

State Variable: Large and Long High Treatment

10 20 30 40 50 60 time period 1 2 3 4 5 6 7 8 9 state variable, x

Large - Long Sessions

Session 1 Session 2

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A Laboratory Experiment on the Heuristic Switching Model High (Large and Long) Treatment

Estimations on the Bifurcation diagram

0.0 0.2 0.4 0.6 0.8 1.0

• 0.4
• 0.2

0.0 0.2 0.4 β α

High Information Cost

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A Laboratory Experiment on the Heuristic Switching Model Conclusion

Plan

1

Introduction

2

Experiment

3

Dynamics of the Stylized HSM and Hypotheses

4

Results of the Experiment

5

High (Large and Long) Treatment

6

Conclusion

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A Laboratory Experiment on the Heuristic Switching Model Conclusion

Hypotheses and Results

• H1. There is a difference in volatility of both nB,t and

xt between the High blocks and the Low blocks. Confirmed, especially for xt.

• H2. The endogenous variable nB,t can be described by

a discrete choice model with one lag and a predisposition effect. Confirmed.

• H3. There is no difference between the discrete choice

models estimated for High and for Low blocks. There is a difference in values of parameters.

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A Laboratory Experiment on the Heuristic Switching Model Conclusion

Conclusion

1

Effect of information cost in Brock-Hommes model is confirmed.

2

At the same time, participants adapt their choice to the environment they are in. They become less sensitive to past profit differences in less stable environment. As a result aggregate dynamics become only moderately complex: e.g., asymmetric equilibrium or 2-cycle.

3

Theoretical literature of HSM may need to take it on board and endogenize the Intensity of Choice.

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A Laboratory Experiment on the Heuristic Switching Model Conclusion

THANK YOU!

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A Laboratory Experiment on the Heuristic Switching Model Experimental results

Plan

7

Experimental results

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A Laboratory Experiment on the Heuristic Switching Model Experimental results

Profits in High blocks

Figure: Profits dynamics

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A Laboratory Experiment on the Heuristic Switching Model Experimental results

Profits in Low blocks

Figure: Profits dynamics

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A Laboratory Experiment on the Heuristic Switching Model Experimental results

Table: Estimations of the discrete choice model with two lags and predisposition.

Predisposition IoC IoC Data Alpha S.E. Beta S.E. Beta2 S.E. Session 1. Group 1 0.33 0.11 0.08 0.02 0.02 0.01 Session 1. Group 2 0.40 0.11 0.12 0.02 0.02 0.02 High Session 2. Group 1 0.35 0.11 0.11 0.02

• 0.02

0.02 Session 2. Group 2 0.28 0.12 0.17 0.02 0.01 0.02 all groups and sessions 0.33 0.06 0.12 0.01 0.00 0.01 Session 1. Group 1 0.25 0.11 3.19 0.88 0.57 0.57 Session 1. Group 2 0.04 0.11 5.20 0.97

• 0.76

0.80 Low Session 2. Group 1

• 0.17

0.13 11.35 1.73 1.13 1.31 Session 2. Group 2 0.12 0.12 8.91 1.51 1.74 0.88 all groups and sessions 0.12 0.06 6.21 0.62 0.56 0.39

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A Laboratory Experiment on the Heuristic Switching Model Experimental results

Table: Estimations of the discrete choice model with three lags and predisposition.

Predisposition IoC IoC IoC Data Alpha S.E. Beta S.E. Beta2 S.E. Beta3 S.E. Session 1. Group 1 0.31 0.11 0.07 0.02 0.02 0.02

• 0.01

0.01 Session 1. Group 2 0.40 0.12 0.11 0.02 0.01 0.02 0.01 0.02 High Session 2. Group 1 0.32 0.11 0.11 0.02

• 0.03

0.02 0.00 0.01 Session 2. Group 2 0.26 0.12 0.16 0.02 0.01 0.02

• 0.02

0.02 all groups and sessions 0.31 0.06 0.11 0.01 0.00 0.01 0.00 0.01 Session 1. Group 1 0.28 0.11 3.19 0.84 0.09 0.67 0.92 0.60 Session 1. Group 2

• 0.01

0.11 5.21 0.96

• 0.85

0.83

• 0.77

0.82 Low Session 2. Group 1

• 0.12

0.13 11.45 1.73 1.64 1.36

• 1.33

1.50 Session 2. Group 2 0.17 0.12 9.14 1.53 2.11 0.89

• 0.11

0.98 all groups and sessions 0.13 0.06 6.27 0.62 0.62 0.42 0.01 0.38

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