Report of Progress on
Simulating Lifetime Saving Decisions
&
My Proposal
System Dynamics Colloquium
May 19, 2017
MIT
System Dynamics Group
Stephen Weinberg
[email protected]
Babak Bahaddin
[email protected]
Luis Luna-Reyes
[email protected]
David Andersen
[email protected]
System Dynamics Group
2
General Problem
• Many economic challenges are dynamic:
decisions today affect our options tomorrow
• It is very difficult to model rational actors in
a dynamic framework with more than, say, 3
decision variables
• Now model the decision maker’s psychology
at the same time????
• Quickly becomes intractable
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Countervailing Biases
• Occur when one class of cognitive bias “offsets”
or “compensates” for another
• Exploring Such Joint Biases is the ultimate aim
of our work
• Here’s one example
• Overconfidence about investment returns makes
someone “Too Willing” to invest in Risky Funds
• Fear of Loss makes someone “Too Unwilling” to
invest in Risky Funds
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Sample Problem
• Why consume today?
• Get utility now!
• Future utility is discounted
• Why save?
•
•
•
•
Income may go down in the future
Even out consumption over time
Investment returns
Expenses may go up in the future
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5
Optimal Solution
You backwards induct a decision rule about how much to
consume each period as a result of inherited wealth.
• Consumption (c)
• Income Growth (G)
• Discount Factor (δ): how much less people care about
the future compared to the present. (0< δ<1).
• Interest Rate (r)
• Coefficient of Relative Risk Aversion (ρ): how much
someone dislikes fluctuations in consumption.
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“This Vensim Simulation Exactly Reproduces results using simplified Euler methods”
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Step 2 - Misperceptions
• Introduce errors in perception of different
parameters
• Map interaction of these errors
How does overconfidence in interest rate offset
misperception of your personal level of risk
comfort?
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Misperceiving one Parameter
An individual thinks that the Interest Rate (r) is
20% higher than what it really is.
r' = 1.2 r
(Overconfidence Bias)
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This is what the individual expects to happen.
This is what actually
This ishappens
the Optimal Solution with the real value of r.
(based on the wrong decisions for Consumption behavior
and
its initial
value).
(the Exact
graph
we saw
before)
System Dynamics Group
• We know that sometimes these biases cancel each other out
• If we only consider r and 𝜌:
• For each value of r’ there is a 𝜌′ that can redeems the impact of r’.
𝛿 𝐺 1+𝑟
𝜌′ = log 𝛿 𝐺
1
𝜌
= 𝛿 𝐺 1 + 𝑟′
𝛿 𝐺 1 + 𝑟′
1+𝑟
𝛿 𝐺 1+𝑟
𝑟 =
𝛿 𝐺
′
𝜌′
when
𝜌
𝑟′
When
𝑟
System Dynamics Group
1
𝜌′
𝜌
𝜌′
𝜌
−1
𝑟′
= 1.038
𝑟
𝑟′
see = 2.057
𝑟
= 1.2, we expect to see
= 1.2, we expect to
𝜌′ = 1.2 𝜌
Absolute Distinction from
the Optimal Solution (Annual Consuption Growth
rate)
r' = 1.2 r
0.3
0.009
0.008
0.25
0.007
0.2
0.006
0.005
0.15
0.004
0.1
0.003
0.002
0.05
0.001
0
0
0
2
4
6
Misperceived to Real CRRA (𝜌′/𝜌)
8
10
0.9
0.95
1
1.05
Misperceived to Real Interest Rate (r'/r)
Figure 4. The absolute discrepancy between the "Optimal Annual Growth in Consumption" and
the "Real Annual Growth in Consumption" in different scenarios where the interest rate and the
Coefficient of Relative Risk Aversion are perceived to be 20% higher respectively.
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1.1
1.15
Annual Consuption
Growth rate (𝜌′ = 1.2 𝜌)
Optimal consumption growth = 0.01185
Optimal Initial consumption = 830.7
Absolute Distinction from
the Optimal Solution
0.009
0.008
0.007
0.006
0.005
Graph 1:
consumption growth = 0.01185
Initial consumption = 837
0.004
0.003
0.002
0.001
0
0.9
0.95
1
1.05
1.1
1.15
Absolute Distinction from
the Optimal Solution
Utility (𝜌′ = 1.2 𝜌)
4
3.5
Graph 2:
consumption growth = 0.0098
Initial consumption = 871.2
3
2.5
2
1.5
1
0.5
0
0.9
0.95
1
1.05
1.1
Misperceived to Real Interest Rate (r'/r)
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1.15
Findings
• We can offset the effect of a misperceived parameter, if and only if we
have at least two absolute maxima in our unbiased model.
• Simulation > Euler equation
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Our Current Project:
1. Analyzing the “Individual Utility Function” model in behavioral economics.
2. Developing a simulation platform (Exact Econ Model 1) to replicate the simplest version of LUF model.
(The Euler equation)
 Building confidence in the simulation: matching the optimized behavior in the simulation with the
optimized behavior reflected in the Euler equation.
3. Introducing the effect of misperceived parameters
4. Creating a feedback-rich model based on heuristics for consumption (Heuristic Dynamic Model 1)
 Examining different heuristics
 Finding one best heuristic based on the variance of the resulted lifetime utility from the optimized
behavior
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Under Construction!
Thoughts?
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My Proposal
I need your advice!
I am about to write my proposal.
I want to study Social Effects in Engineering Models.
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My Interest:
Water Resource Management
Less than 3% of all the water resources are Fresh.
Together, the Antarctic and Greenland ice sheets
contain more than 99 percent of the freshwater
ice on Earth.
IRAN is in the Economic Water Scarcity phase. It
will approach the Physical Water Scarcity by 2025
(World Resources Institute).
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Final Results
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Our model represents
One individual,
One agent,
One company, or
One generation...
With Specific Settings
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Applications
• Concepts such as consumption, savings, and utility are mostly used for resource management and planning
• By resources we do not only mean MONEY
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Inter-Generational Optimized Use
Externalities
DELAY
Our Generation
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Our future selves
Our Children
Future of Our Current Project:
1. Introducing the first psychological bias to the model one by one: (Four times)
 different versions of EEM for each bias
‐ Transferring new EEMs to an open-source program
‐ Finding (or developing) an optimization package
‐ super computers?
‐ matching the optimized behavior in the simulation with the optimized behavior reflected in the
literature.
6. Improving the heuristics in HDM1 and creating new HDMs based on the new structure of the system
7. Using the platform to explore main interactions among the four biases
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My Proposal - #1:
1. PROBLEM: Interaction of two subjects in a competitive environment
2. RESEARCH QUESTION: What is the role of countervailing biases in reaching out the target lifetime
utility for each subject?
3. MAIN LITERATURE: Competitive Space in Behavioral economics, Cognitive biases, Optimization
4. SOURCES OF DATA: Theoretical model based on literature, no data needed.
5. MAIN TASKS:
1. Creating a simulation based on the interaction of at least two EEMs based on the literature
2. Creating a corresponding HDM between the two subjects
3. Implementing the interactions within different scenarios and heuristics.
6. POTENTIAL DISSERTATION COMMITTEE: David Andersen, Stephen Weinberg, and …
System Dynamics Group
My Proposal - #2:
1. PROBLEM: Intergenerational natural resource management
2. RESEARCH QUESTION: How do biases affect intergenerational discounting rate and negative
externalities?
3. MAIN LITERATURE: Behavioral economics, Cognitive biases, Natural resource management,
intergenerational discounting
4. SOURCES OF DATA: Theoretical model based on literature, no data needed.
5. MAIN TASKS:
1. Creating a simulation based on the interaction of at least two EEMs based on the literature
3. Creating a corresponding HDM including a delay between the two subjects
4. Implementing the interactions within different scenarios and heuristics.
6. POTENTIAL DISSERTATION COMMITTEE: David Andersen and Stephen Weinberg and …
System Dynamics Group
My Proposal - #3:
1. PROBLEM: Optimization in numerical-intensive analyses
2. RESEARCH QUESTION: How can the current optimization methods in the open-source packages be
improved? (case: lifetime utility)
3. MAIN LITERATURE: Optimization methods, optimization in System Dynamics, Lifetime Utility
Function, optimization packages in programing
4. SOURCES OF DATA: Theoretical model based on literature, online optimization packages.
5. MAIN TASKS:
1. Comparing different optimization methods for a simple conceptual model
2. Different optimization results for the case of Lifetime Utility Function
3. Expanding current optimization methods in an open source platform
6. POTENTIAL DISSERTATION COMMITTEE: David Andersen and Stephen Weinberg and …
System Dynamics Group
My Proposal - #4:
1. PROBLEM: System Archetypes in Water Resource Management
2. RESEARCH QUESTION: What are the common soci-economical behavioral patterns in WRM?
3. MAIN LITERATURE: System Archetypes, Water Resource (Mis-)Management cases, Models for WRM
4. SOURCES OF DATA: Theoretical model based on literature, USGS, New Mexico State University’s
Department of Animal & Range Sciences, Mahab in Iran, interview
5. MAIN TASKS:
1. Finding examples of System Archetypes in Water Resource Management (Done)
2. Simulating System Archetypes based on the work done by Rod MacDonald and George Richardson
3. System Archetype Simulations in Water Resource Management
6. POTENTIAL DISSERTATION COMMITTEE: David Andersen, Eliot Rich, Ali Mirchi, (Kaveh
Madani?), …
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