Please enable JavaScript.
Coggle requires JavaScript to display documents.
EMIA - Coggle Diagram
EMIA
4 - Potential Outcomes Model
Key definitions and causal parameters
1 - Conditional Expectation Function and Ordinary Least Squares
Conditional Expectation Function
Decomposition property
Prediction property (MMSE criterion)
Law of Iterated Expectations
Ordinary Least Squares (OLS)
OLS estimator - minimization problem
OLS residuals - residual maker matrix
Unbiasedness of the OLS estimator
Conditional Variance of the OLS estimator (under spherical disturbances
Estimated variance of the OLS estimator
OLS in a univariate model with constant (from Frisch-Waugh-Lovell theorem)
Goodness of Fit
OLS Bias Derivations
Omitted Variable Bias
Measurement error in the regressor
2 - Instrumental Variables
Instrumental Variables (IV) estimator
IV estimator as a ratio of covariances (single endogenous regressor)
Unbiasedness of the IV estimator
IV Estimator Derivation (Just-Identified Case)
Estimated variance of the IV estimator
Two-Stage Least Squares (2SLS) Estimator
Equivalence of IV and 2SLS (Just-Identified Case)
Estimated Variance of 2SLS (Homoskedastic Case)
2SLS Estimator Formula
Weak Instrument Bias
2SLS Bias Approximation
3 - panel
Panel Data Models
Pooled OLS
Random Effects (RE)
Model Notation
FIxed Effects / Within Estimator
Two-Way Fixed Effects