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
- Institutional Choices
- Economic Success
- 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
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
- 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
- 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
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