Causal Estimands

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# Causal estimands

.class-info[

**Session 11**

.light[STA 379/679: Causal Inference <br>
Lucy D'Agostino McGowan
]

]

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# Average treatment effect

.box-1[
.huge[
`$$ATE = E[Y(1) - Y(0)]$$`
]
]

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<br>

.box-inv-1[
Target population: everyone
]

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.small[
# Average treatment effect among the treated
]

.box-1[
`$$ATT = E[Y(1) - Y(0) | X = 1]$$`

]

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<br>
.box-inv-1[
Target population: treated population
]

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.small[
# Average treatment effect among the controls
]

.box-1[
`$$ATC = E[Y(1) - Y(0) | X = 0]$$`
]

--
<br>
.box-inv-1[
Target population: control population
]

---
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.small[
# Average treatment effect among matchable
]

.box-1[
`$$ATM_d = E[Y(1) - Y(0) | M_d = 1]$$`
]

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<br>

.box-inv-1[
Target population: matchable population
]

---
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.small[
# Average treatment effect among matchable
]

.box-1[
A subject is evenly matchable `\((M_d = 1)\)` for a given matching process, `\(d\)`
]

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<br>

.box-1[
A subject is evenly matchable if the limit of the ratio of the number of subjects from the opposite treatment to the number from its own treatment is greater than 1 within the localized region of the covariate space around the subject defined by `\(d\)`
]

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.small[
# Average treatment effect among the overlap
]

.box-inv-1[
Target population: overlap population
]

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.box-1[Similar to the "evenly matchable"]

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.box-1[Creates a "pseudo-population" that has excellent variance properties]