simplified notation.pdf - 1
ICS212 Fall 2022
simplified notation.pdf - 2
What is: E [ Y | D = 1] ?
Is it observable?
The expected value of the outcome Y given that treatment 1 was received. If some of the units received treatment 0 then we cannot observe this.
ICS212 Fall 2022
simplified notation.pdf - 3
What is: E [ Y1 ] ?
Is it observable?
The expected value of the outcome Y given that treatment 1 was received. If some of the units received treatment 0 then we cannot observe this.
ICS212 Fall 2022
simplified notation.pdf - 4
What is: E [ Y | D = 0]?
Is it observable?
The expected value of the outcome Y given that treatment 0 was received. If some of the units received treatment 1 then we cannot observe this.
ICS212 Fall 2022
simplified notation.pdf - 5
What is: E [ Y0 ] ?
Is it observable?
The expected value of the outcome Y given that treatment 0 was received. If some of the units received treatment 1 then we cannot observe this.
ICS212 Fall 2022
simplified notation.pdf - 6
RECAP:
E [ Y0 ] E [ Y1 ] E [ Y | D = 0] E [ Y | D = 1]
ICS212 Fall 2022
simplified notation.pdf - 7
What is: E [ Y | D = 1] - E [ Y | D = 0] ?
Is it observable?
The expected value of the Y given that treatment 1 was received minus the expected value of the outcome given that treatment 0 was received. This is the true treatment effect. It is not observable.
ICS212 Fall 2022
simplified notation.pdf - 8
What is: E [ Y0 | D = 0]?
Is it observable?
The expected value of the outcome Y after treatment 0 given that treatment 0 was received. These are the control group cases and they can be observed.
ICS212 Fall 2022
simplified notation.pdf - 9
What is: E [ Y1 | D = 1]?
Is it observable?
The expected value of the outcome Y after treatment 1 given that treatment 1 was received. These are the treatment group cases and they can be observed.
ICS212 Fall 2022
simplified notation.pdf - 10
What is: E [ Y0 | D = 1]?
Is it observable?
The expected value of the outcome Y after treatment 0 given that treatment 1 was received. These are imaginary cases and they cannot be observed.
ICS212 Fall 2022
simplified notation.pdf - 11
What is: E [ Y1 | D = 0]?
Is it observable?
The expected value of the outcome Y after treatment 1 given that treatment 0 was received. These are imaginary cases and they cannot be observed.
ICS212 Fall 2022
simplified notation.pdf - 12
What is: E [ Y0 | D = 1] - E [ Y0 | D = 0]?
Is it observable?
The difference between the expected outcome for the treatment group had they not been treated and the expected outcomes of the control group. This is not observable
ICS212 Fall 2022
SimplifiedNotationCausalInferenceLIVE
By Dan Ryan
