The End Of Knowledge - Vault 6/74 - CVPR - 2022 - Synthetic Control Methods and Difference-In-Differences

graph LR classDef panel fill:#f9d4d4, font-weight:bold, font-size:14px classDef methods fill:#d4f9d4, font-weight:bold, font-size:14px classDef modeling fill:#d4d4f9, font-weight:bold, font-size:14px classDef evaluation fill:#f9f9d4, font-weight:bold, font-size:14px A[Synthetic Control Methods
and Difference-In-Differences] --> B[Panel
Data] A --> C[Estimation
Methods] A --> D[Modeling
Techniques] A --> E[Evaluation
Metrics] B --> B1[Multiple units
over
time. 1] B --> B2[Hypothetical treatment,
control
outcomes. 2] B --> B3[Difference between
treated, control
outcomes. 3] B --> B4[Treatment independent
of potential
outcomes. 4] B --> B5[Units adopt
treatment at
different times. 16] B --> B6[Units statistically
indistinguishable. 27] C --> C1[Weighted control
unit
combination. 5] C --> C2[Comparing changes
before, after
treatment. 6] C --> C3[Unit, time
effects control. 7] C --> C4[Probability of
treatment
assignment. 17] C --> C5[Combine outcome,
propensity score
models. 18] C --> C6[Prediction intervals
under
exchangeability. 28] D --> D1[Estimate missing
values using
approximation. 8] D --> D2[Penalty for low-rank
solutions. 9] D --> D3[Outcomes on pre-treatment
variables. 10] D --> D4[Pre-treatment on
control
outcomes. 11] D --> D5[Generalized two-way
fixed
effects. 12] D --> D6[Data into latent
factors,
loadings. 21] E --> E1[Select parameters
with held-out
data. 14] E --> E2[Measure of
prediction
accuracy. 15] E --> E3[Balance model
flexibility,
overfitting. 25] E --> E4[Variable correlation
at different
times. 26] E --> E5[Use prior distributions,
update
beliefs. 29] E --> E6[Functions balancing
covariates. 30] class A,B,B1,B2,B3,B4,B5,B6 panel class C,C1,C2,C3,C4,C5,C6 methods class D,D1,D2,D3,D4,D5,D6 modeling class E,E1,E2,E3,E4,E5,E6 evaluation

Resume:

1.- Panel data: Data with multiple units observed over time, used to estimate causal effects of treatments.

2.- Potential outcomes: Hypothetical outcomes for each unit under treatment and control conditions.

3.- Average treatment effect: The average difference between treated and control outcomes across units.

4.- Unconfoundedness: Assumption that treatment assignment is independent of potential outcomes conditional on observed covariates.

5.- Synthetic control: Method using weighted combination of control units to estimate counterfactual for treated unit.

6.- Difference-in-differences: Method comparing outcome changes between treated and control groups before and after treatment.

7.- Two-way fixed effects: Regression model with unit and time fixed effects to control for time-invariant unit characteristics and time trends.

8.- Matrix completion: Technique to estimate missing values in a matrix using low-rank approximation.

9.- Nuclear norm regularization: Penalty added to objective function to encourage low-rank solutions in matrix completion.

10.- Horizontal regression: Regressing outcomes on pre-treatment variables using control units to predict counterfactuals.

11.- Vertical regression: Regressing pre-treatment outcomes on control unit outcomes to predict counterfactuals for treated units.

12.- Interactive fixed effects: More flexible generalization of two-way fixed effects using factor models.

13.- Low-rank matrix: Matrix that can be approximated well by a product of two smaller matrices.

14.- Cross-validation: Technique to select model parameters by evaluating performance on held-out data.

15.- Root mean squared error: Measure of prediction accuracy calculated as square root of average squared prediction errors.

16.- Staggered adoption: Treatment pattern where units adopt treatment at different times but remain treated once adopted.

17.- Propensity score: Probability of treatment assignment conditional on observed covariates, used for matching or weighting.

18.- Double robust methods: Estimation techniques combining outcome regression and propensity score models for improved robustness.

19.- Matching: Method pairing treated units with similar control units based on covariates or propensity scores.

20.- Inverse probability weighting: Technique using inverse of treatment probability to weight outcomes and balance covariate distributions.

21.- Factor models: Statistical models decomposing data into latent factors and factor loadings.

22.- Synthetic difference-in-differences: Method combining synthetic control and difference-in-differences approaches.

23.- Time weights: Weights assigned to different time periods in synthetic difference-in-differences to focus on relevant periods.

24.- Unit weights: Weights assigned to control units in synthetic control methods to create counterfactual for treated unit.

25.- Bias-variance tradeoff: Balance between model flexibility and overfitting in statistical learning.

26.- Autocorrelation: Correlation between a variable's values at different time points.

27.- Exchangeability: Assumption that units are statistically indistinguishable, often used in inference for panel data.

28.- Conformal inference: Method for constructing prediction intervals with guaranteed coverage under exchangeability assumptions.

29.- Bayesian methods: Statistical approaches using prior distributions and updating beliefs based on observed data.

30.- Balancing scores: Functions of covariates that, when conditioned on, balance covariate distributions between treated and control groups.

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