Econ3120, Fall, 2016

Causality And CorrelationEconomic Department, Saint Louis University

Instructor: Xi Wang

A Typical Routine of Scientific Research

• Find a pattern

• Develop models of the world, namely a simplified description of the world; Or Give a explaination for the pattern, namely Establish Causality.

• Use Data or Experiments to test this Model

Find a pattern

• Example 1: You found we can stand steadliy on ground

• Example 2: Bill Gates and Zuckerberg, who are dropout of Harverd, are pretty Rich, it seems that Dropout are rich!

Is this pattern Robust? Or is it a pattern?

• Example 1: You found we can stand steadliy on ground; Yes! Everyone found this pattern. Then the earth is flat! And people once believed in this.

• Example: Bill Gates and Zuckerberg, who are dropout of Harverd, are pretty Rich, Find a pattern

No! When we look at our data, we found “College Premium”: College graduate earn more. Reject Hypothesis!

• Hypothesis is “Dropout are (relatively) rich”

• More on College Premium: http://www.nber.org/digest/jan08/w12984.html

Test 1

• Example: You found we can stand steadliy on ground; Yes! Everyone found this pattern.

• Model: Earth is Flat!

• Is it true? If it is, then Straight line will give you the shortest distance from A to B. Right? Hence straight routine on the map should be the best routine to travel.

Test 1

Magellan: is he able to come back, if earth is flat?

Summary 1

• Pattern

• Give a describing theory or Model; (Describe our world?-----Positive Economics)

• Test it!

Another Example on Model: Economic Model

• Model: Investing in one extra year of education increased your future wage by 10 percent

• One extra year of high school should be different with one extra year of medical school, right?

• Exactly 10 percent? Not 9.9%? Not 8%? not 13%?

• Hence!

• Model is an approximation.

• But this approximation can be tested with data or experiments

Another type of Model

• Pattern

• Propose a causal relationship

• Test

How do ants find their way Home

• Pattern:

• Ants search food outside their home, right? After find food, they grab them and go back.

• Ants can find their way home, emm...... Why?

• Propose: They can see their home!

• Test: Put them in a black room and check whether they can find their way home

How do ants find their way Home

• Results: Yes, they can!

• It implies they have some other orientation tool.

• Propose: Smell.

• Test: We use detergent to draw a cycle around their home.

• This will elimate the smell

• Check whether they can find their way home

• No! They cannot or at least most of the ants cannot find way home!

African Ants

• This kind of Ants do not need smell to track back

• They can find their way back even if we elimate the smell

• How do they find their way home then?

• Ok----- Scientist proposed a very interesting theory to explain this• They state that: this kind of ant can count steps.• WOW, How to test it then?

Causality and correlation

Causality and correlation

Causality and Correlation

• There can be several kinds of relationship between A and B. Example: What is the relationship bewteen this chicken and egg.

Causality and correlation

Causality and correlation: An Example

• In data(Pattern), out students who take music courses in high school score better on their SATs than students who do not take music courses in high school. Some educators have argued that this relationship is causal: more music courses cause higher SAT score (Hypothesis).

• First, in Data, we can only observe there is a correlation, which gives us a hint that there may be a causality.

• Correlation is not causality.

Causality and correlation: An Example

• People who get higher score do not need to take the exam again, hence have more time to spend on something else, i.e dancing, playing music.

• Reverse causality

• People who gets higher score tends to have a better education when he was young. And music is a part of that child training plan. Hence he got this interest when he/she was a child.

• Ommitted variable