Patrick Power
Economics PhD @ Boston University
Diagrams
Causal Inference
\hat{\phi} := \hat{E}[D \vert Z=1] - \hat{E}[D \vert Z=0]
\hat{\beta} := \hat{E}[Y \vert Z=1] - \hat{E}[Y \vert Z=0]
\frac{\hat{\beta} \times 4}{900} = \frac{\frac{\beta}{\hat{\phi}} \times 4}{900 + C}
\text{ROI} := \frac{\text{500} \times 4}{900}
Average Annual Effect for Lower Income Individuals
Per individual cost of the program
X
X
X^{-1}
X_i^{-1}
X_i
\Omega
\Omega_n
Population Probability Space
Sample
Probability Space
A
\mathcal{X}
Learnable
\Big(\Omega, \mathcal{F}, \mathbb{P}\Big)
Part 1
Part 2
Part 3
\{1, 2, 3, 4, 5, 6\}
Denotes Set
Sample Space
Population
Samples
\tau
\mathcal{A}
President
Impose Tariffs
?
Regulate Imports
President
Impose Tariffs
?
Regulate Imports
An Unusual & Extraordinary Threat to the U.S.
Treated
Control
\tilde{Y}_i(1)
\tilde{Y}_i(0)
Filled in Subsets Denote "Attrition"
Tom Thibodeau Fired
2025
Team Not Ready
Poor Strategy
Unpopular
Rick Carlisle
Fired
2003
Team Not Ready
Poor Strategy
Unpopular
Diagrams: Causal Inference
By Patrick Power
