topic 3 notes Econometrics
Preface
Notes designed to complement ECON20110/30370 lectures.
Focus on mathematical aspects of econometrics.
Lecture slides emphasize application and intuition.
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Table of Contents
7 Endogeneity and Causal Inference
7.1 Causal Models and Endogeneity
Distinction between descriptive and causal analysis.
Causal analysis essential for evaluating interventions.
Counterfactual approach to identify causal relationships.
Descriptive Analysis vs Causal Analysis
Regression can aim for prediction or causal relationships.
Prediction Focus:
OLS used as a descriptive tool.
Orthogonality condition holds, enabling consistent estimators.
Issues like omitted variable bias do not affect predictions.
Causal Analysis Focus:
Identify and measure causal influences.
Essential to control for confounding factors (ceteris paribus).
7.2 Exogeneity and Consistent Estimation of Causal Effects
Key model where outcome variable Y is influenced by multiple variables.
Identify if E(ε) = 0 and cov(X_l, ε) = 0.
Exogeneity condition crucial for consistent estimation of causal effects.
7.3 Endogeneity
Endogeneity arises when explanatory variables are correlated with the error term.
Challenges conventional regression assumptions.
Biased OLS estimates when orthogonality fails.
7.4 Sources of Endogeneity
Common Sources:
Omitted variable bias.
Wrong functional form.
Measurement error.
Simultaneous causality bias.
Sample selection bias.
7.5 Omitted Variable Bias (OVB)
OVB occurs when a key determinant is omitted, affecting observed relationships.
OVB Formula:
Derived under conditions of OVB; critical to understand the direction of bias.
7.5.1 The OVB Formula — Simple Setting
Example: Representing wages as a function of years of education and ability.
Impact of omitting ability on estimated effect of education.
7.6 Functional Form Misspecification
Arises when the model fails to summarize the true causal relationship.
Need for careful evaluation of model specifications.
7.7 Measurement Error
Distortion from inaccuracies in data collection (e.g., survey errors).
Impacts reliability of regression analyses.
7.7.1 Measurement Error in X
Measurement error in X affects estimates through bias.
7.7.2 The Classical Measurement Error in X Problem — Attenuation Bias
Underestimates true effects due to measurement error, particularly concerned in regression models.
7.7.3 Measurement Error in Y
Measurement error in Y increases error variance without introducing bias if uncorrelated with X.
7.8 Simultaneity Bias
Occurs when independent variables influence each other.
Example: Demand and supply equations; challenges the traditional causal model assumptions.
7.9 Missing Data and Sample Selection Bias
Different effects of missing data:
Missing Data Completely at Random: No bias induced.
Missing Data Conditional on X: Unbiased but less precise.
Sample Selection Bias: Correlation with Y leads to biased estimates.
7.10 Possible Solutions to Endogeneity
Strategies include excluding omitted variables, using instrumental variables (IV), and performing RCTs.
Addressing Endogeneity with Instrumental Variables (IV)
8.1 Endogeneity and the Problem of Inconsistent OLS
OLS implications when variables exhibit endogeneity.
8.2 Instrumental Variables: Validity Requirements
Necessary conditions for IV to be effective include relevance, exogeneity, and exclusion.
8.3 Two-Stage Least Squares (2SLS)
Method for obtaining consistent estimates in the presence of endogeneity.
Used for estimating causal models using the IV technique.
8.4 Important Considerations and Results for 2SLS
The quality of IV selection and the model structure affects results.
Appendix 8.A The Over-Identifying Restrictions Test
Tests to validate the instruments used in IV analysis, emphasizing the need for theoretical grounding alongside empirical results.