Week 02 - Introduction to Causality

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# Week 02 - Introduction to Causality
## How do we know if X causes Y?
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### Danilo Freire
### 30th January 2019

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# Today's Agenda

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* Questions about RMarkdown?

* What is causal inference?

* Correlation vs causation

* Treatment effects and potential outcomes

* Randomised Controlled Trials
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# Brief Recap

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* Last week you learned how to:

- Load `.csv` files 
  
  - Download datasets from the internet
  
  - Create and run `.R` scripts 
  
  - Create `.Rmd` documents (different extension!)
  
  - Print a pdf with your results
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# RMarkdown

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* Questions?
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.center[![:scale 60%](doc.png)]
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# Causal Inference

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# Causal Inference

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* What is causal inference?
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* Causal: relationship where one factor causes the other
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* Inference: our ability to derive conclusion from facts and observations
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* _Causal inference is an attempt to estimate a causal connection between two variables based on an observed effect_
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# Causal Inference

.center[![:scale 110%](candidate.png)]

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# Causal Inference

.center[![:scale 110%](germany.png)]

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# Causal Inference

.center[![:scale 80%](democracy.png)]
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.font150[Which question is harder to answer?]
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# Causal Inference

.center[![:scale 80%](cpi.png)]
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# Does X cause Y?

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* Does _X_ occur at the same time as _Y_?

* If _X_ goes up or down, does _Y_ also go up or down?

* If _X_ is happens, does _Y_ also happen?
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.font150[* _Are X and Y causally related because of that?_]
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.font150[**NO**]
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# Does X cause Y?

.center[![:scale 100%](eng.png)]
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# Does X cause Y?

.center[![:scale 100%](kentucky.png)]
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# Causal Inference - Notation

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* Treatment variable = _T_

* Two potential outcomes = _Y_ when _T = 0_ and _Y_ when _T = 1_
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* Example

- Treatment: getting a university degree
  
  - Potential outcome: salary with a university degree _(Y when T = 1)_ versus salary without a university degree _(Y when T = 0)_
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# Causal Inference - Notation

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* The causal effect of the treatment _T_ is the difference in _Y_ with and without _T_
  
* `\(Y(T = 1) - Y(T = 0)\)` or `\(Y_{1} - Y_{0}\)`
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.center[![:scale 100%](causal01.png)]
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* Why is that a problem?
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# Fundamental Problem

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* _We can never observe Y where T = 1 and T = 0 at the same time_

* We only observe _one_ outcome at a time, that's why it is called the _potential_ outcomes framework
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# Fundamental Problem

.center[![:scale 60%](causal02.png)]

.center[[Holland, Paul (1986), p. 947](https://www.jstor.org/stable/2289064)]
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# Sample Average Treatment Effect

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* Solution: we estimate the _average causal effect_ in the groups that received and did not receive the treatment

* We call it the _Sample Average Treatment Effect_, or SATE
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.center[![:scale 100%](sate.png)]

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* But is that enough?
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* _Not quite_
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# Randomisation

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* The best solution to the problem of selection bias is _randomisation_

* If the researcher randomised the treatment, she can be sure that it is unrelated to any observable characteristic

* We also assume randomised treatment is uncorrelated with any _unobservable_ characteristic too

* Randomised Controlled Trials (RCTs): the researcher creates treatment and control groups

* If all other characteristics are equivalent on average between the two groups, _the difference between them is caused by the treatment effect_
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# Randomisation

.center[![:scale 85%](rct.png)]
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# Internal versus External Validity

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* RCTs have very strong internal validity, that is, there is very little chance the result is derived from causes other than the treatment

* However, they may not generalise well. Why? 
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* Samples may not reflect the whole population of interest
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# Homework

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* Watch these three videos (they're all short): 
  - <https://youtu.be/vtSCZcKXw1w>
  - <https://youtu.be/9j_HWkrSxzI> 
  - <https://youtu.be/crpuBZv6XtA>

* Start `swirl()` CAUSALITY1
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# See you on Wednesday!