Path Dependence

Path Dependence

Lectures cover:

• What is Path Dependence?
• Construct Urn Models to understand
• different types of path dependence
• what causes path dependence
• difference between path dependent outcomes and path dependent equilibria
• Examples of Urn Models
• Polya Process, Balancing Process,
• Path dependencies is logically different from increasing returns
• Path dependencies are caused by externalities i.e. interdependencies between choices/decisions
• externalities with negative effects are more likely to be path dependent
• Compare path dependence and Markov Processes, Tipping Points and Chaos
• Key lessons - my own reflection of what this lecture means

Real-world examples:

• QWERTY typewriter keyboard
• increasing returns / virtuous cycle
• the more QWERTYs lead to more QWERTYs
• Technology
• AC vs DC
• Gasoline vs Electric Cars
• Common Law
• Influence of Precedent
• Institutional Choices
• Defined benefits
• Economic Success
• Ann Arbor vs Jackson
• Manifest Destiny of America
• Railroads 

 

Path Dependence

• Path Dependent
• Outcome probabilities depend upon the sequence of path outcomes.
• Doesn't necessarily determine, merely affects the probabilities
• What happens now depends on what happened along the path to get here
• Phat Dependent
• Outcome probabilities depend upon past outcomes outcomes but not their order
• Polya process is Phat

Urn Models

• Basic Urn Model
• Urn contains balls of various colors
• The outcome equals the color of the ball selected
• Bernoulli Model
• Fixed number of balls in the urn
• U = {B blue, R red}     ; U stands for Urn is a set of B blue and R red
• Process: Select ball and return to the urn
• P(red) = R/(B+R)
• Outcomes independent
• Polya Process
• U = {1 Blue, 1 Red}
• Process: 
• Select and return
• Add a new ball that is the same color as the ball selected
• Probabilities will change over time
• Result
• Any probability of red balls is an equilibrium and equally likely
• Any history of B blue and R red balls is equally likely
• Seeing just the set in the outcome doesn't tell you anything about the order (a Phat process) because any order is equally likely
• Example:
• Fashion: People buy leopard prints because there are more leopard prints
• Technology: People buy iPhones because they see iPhones
• Balancing Process
• U = {1 Blue, 1 Red}
• Process:
• Select and return
• Add a new ball that is the opposite color as the ball selected
• Result
• The balancing process converges to equal percentages of the two colors of balls
•  Examples
• Need to keep constituencies happy
• Selection of site for political conventions - northern or southern state
• Selection of site by Olympic committee - Asia, Europe, North America or South America
• Sway Process
•  U = {1 Blue, 1 Red}
• Process
• Select and return 
• In period t, add a ball of the same color as the selected ball and add 2^(t-s) - 2(t-s-1) of color chosen in each period s < t
• As you go back in time,the older events take on exponentially more weight over time
• Early movers have a bigger effect
• Distinguish between:
• Path Dependent Outcomes
• color of ball in a given period depends on the path
• Path Dependent Equilibrium
• percentage of red balls in long run depends on the path
• Outcomes and equilibrium
• Polya process: 
• Path-dependent outcomes
• Path-dependent equilibria
• Balancing process: 
• Path dependent outcomes
• Equilibria independent of path
• Examples of path-independent equilibria
• Manifest Destiny - America will stretch from sea to shining sea
• Railroads - Once railroads were invented, they will build themselves
• Mobile - Once invented, mobiles is the future

Path Dependence and Chaos

• Why is the difference between Path Dependence and Phat Dependence important
• Markov processes
• finite states
• fixed transition probabilities
• can get to any other state
• not simple cycle
• markov converges to a unique stochastic equilibrium
• Chaos
• Extreme Sensitivity to Initial Conditions (ESTIC)
• If initial points x and x' differ by even a tiny amount after many iterations of the outcome function, they differ by arbitraty amounts.
• Tent Map (an example of chaotic)
• x in (0,1)
• F(x) = 2x   if X <0.5,
•         = 2 - 2x if X > 0.5
• Tent Map is not path dependent
• Nothing happens along the way/path will change the end
• is deterministic
• Path dependence means what happens along the way has an impact on the outcome

Types of outcomes

• Independent
• Outcome doesn't depend on starting point or what happens along the way
• Chaotic
• Outcome depends on initial conditions
• Path dependent
• Outcome probabilities depend upon sequence of past outcomes
• Phat dependent 
• Outcome probabilities depend upon past outcomes but not their order

History is path dependent. The future is being written today.

• History/future is not independent i.e. what's happening now is happening regardless of what happened in the past. Independence means no structure.
• History/future is not chaotic i.e. initial conditions matter but it isn't the only thing that matter. Once we write the Constitution, the rest plays out deterministically
• History/future is path dependent not phat dependent because early events have a larger importance.

Path Dependence and Increasing Returns

• Increasing Returns
• More produces more
• Positive feedback / Virtuous cycles
• The more I have of something, the more I want the same thing 
• The the more other people do something, the more that other people will do it
• Example:
• The more people get QWERTY typewriters, the more people will get QWERTY typewriters
• Is increasing returns equivalent to path dependent equilibrium? No
• Increasing returns without path dependent equilibrium
• Example:
• Gas / Electric
• Always goes to equilibrium at Gas even though there is increasing returns
• Path dependent equilibrium without increasing returns
• Example
• Symbiots

• Path Dependencies comes from a different process - Externalities
• Externalities:
• interdependence between choices can create path dependence
• Decisions create externalities
• Externalities that big projects create path dependence
• Choosing Project A first results in choosing Project C next
• Choosing Project B first results in choosing Project D next
• Yi J's decision to migrate to Australia affects parents & Dai J

Path Dependence or Tipping Point

• Path Dependent Equilibrium
• percentage of red balls in the long run depends on the path
• Tipping points
• direct tips
• Comparison
• Tipping points
• a single instance in time where the long term equilibrium
• a singular event that tips the event abruptly
• diversity index - count of equilibria
• diversity index (uncertainly) is reduced abruptly
• entropy - how much information in the system
• Path Dependent Equilibrium
• accumulative effect of moving along the path
• diversity index reduces gradually
• unlike tipping point where diversity index (uncertainly) is reduced abruptly

Key Lessons

• Externalities are the reason choices we make in the past will affect choices we make in the future
• Pay more attention to choices with externalities e.g.
• Where you choose to live
• What line of work you choose to do
• What language you choose to learn
• Where possible make decisions where externalities are all positive 
• including future externalities
• this will reduce path dependencies i.e. keep your options open
• History matters when it changes transition probabilities
• Make decisions that increase transition probabilities to states you desire - to goal states
• Pay attention to externalities when making decision especially negative externalities
• Keep your options open