# Why model?

As I understood, using models is actually to apply mathematic into different problems in a unified framework.

## Intelligent Citizen of the world

Essentially, all models are wrong, but some are useful

Model is the new “lingua franca”.

• Every one should know.
• All knowledge which human has known has models in it.
• It is everywhere, at any disciplines: economics (maximize payoff), biology (brain model, gene, species), political science, linguistics, law, game theory.
• Model helps explore knowledge from data, which makes us humble.

## Clearer Thinker.

• Make you become a better thinker.
• Allow us to inductively explore.
• Understand class of outcome:
• Equilibrium.
• Cycle.
• Random.
• Complex.
• Identify logical boundaries.
• Communicate ideas, data, observations.

Constructing models includes several steps:

1. Name the parts: name all variables, factors, and constraints in the problem that are really matter, relevant to the problem. 2.

## Understand data

• Understand patterns.
• Structure information and transform into knowledge.
• Produce bounds.
• Retrodict.
• Predict other.
• Inform data collection.
• Estimate hidden parameters.
• Calibration.

## Decide, Strategize, and Design

• Decision aids: give us directions to give good decisions.
• Comparative statics.
• Counterfactual
• Identify and rank levers.
• Experimental design.
• Instituional design.
• Help choose among policies and institutions.

# Courses

## Section Structure

• The model
• Assumptions
• Results
• Applications
• Technical Details
• Measures
• Proofs
• Practice Problems
• Fertility

# Definitions

Types of model:

• Equation-based model.
• Agent based model includes:
• Individuals: the object of the model.
• Associated behaviour
• Outcomes or Aggregation at the macro level.

# Segregation and peer effects

## Sorting (homophily) and peer effects

### Peer Effect

We choose to act like other people around us. For example, if we are hanging around with people who smoke, it is likely that over time, we also become smoker.

### Sorting

We choose to live, hangout with people with the same characteristics like us. For example, If we smoke, we want to like, or stay with people who smoke like us.

The group tends to have the same characteristics among its members.

### Schelling Tipping Model

1R 2B  3W
4B Rx  5R
6B 7R  8B


The agents deciding whether stay at the current location or move out bases on theirs neighbors who have the same characteristics. The rule is used a threshold to decide. For example, if there are more than 30% neighbors like me, I will stay.

This is a model of racial (or outcome) segregation.

Observations: Even though people are tolerate, at the macro level we observe the segregation, segmentation in large-scale region. If people set their threshold especially high, that makes the whole region chaotic.

Micromotives != macrobehaviour

Exodus Tip: one agent moving causes others to move as well. Genesis Tip: some agents moving makes the agent move out.

• Index of dissimilarity

$${1 \over 2} \sum_{i=1}^{N} \left| {a_i\over A} - {b_i \over B} \right |$$

Let $A$ and $B$ are the total of agents of demographics type 1 and type 2, respectively; $a_i$ and $b_i$ is the number of agents of each demographics in an area.

### Granovetter Model

The collective behavior, e.g., social movement.

### Standing Ovation Model

We change our behavior to match out with people around us.

### Identification problem

If we observe the segregation in data, the question is did they sort the behavior, or is this the peer effect?