Lecture Notes: Randomized Controlled Trials and Regression Analysis
Introduction to Randomized Controlled Trials (RCTs)
Definition: RCTs create two comparable groups - a treatment group and a control group.
Purpose: The control group provides a counterfactual, helping to determine causal relationships by understanding what would have happened if the treatment was not applied.
Importance of Counterfactuals
Causal Analysis: A correct counterfactual allows us to conclude causation.
Alternative Approach:
When RCTs are not feasible, identify a correct counterfactual for those receiving treatment.
Example: To assess the impact of college on wages, compare individuals who attended college with those who went straight to the workforce.
Concept of Ceteris Paribus
Definition: Latin phrase meaning "all else equal."
Application: In causal analysis, to determine the impact of college, imagine splitting a person's life into two paths—one attending college, the other not.
Challenges in Causal Analysis
Non-Comparable Groups: Differences in IQ, family income, and work experience can skew results.
Experience Factor: Skipping college provides work experience, influencing income.
Regression Analysis
Purpose: Correct biases by estimating relationships between dependent and independent variables.
How It Works: Controls for specified variables, estimating independent effects.
Example: Regression compares individuals with similar IQ, family income, and work experience to isolate the effect of college on income.
Outcome: A more accurate estimation shows college increases income by 28%, not 37%.
Issues with Regression: Omitted Variable Bias
Definition: Leaving out variables that affect both the treatment and outcome leads to biased results.
Examples of Omitted Variables:
Student aptitude, motivation, and inclination.
Different college opportunities, such as legacy admissions.
Case Study on Omitted Variable Bias
1999 Study on Nightlights and Myopia:
Initial Claim: Nightlights cause myopia in infants.
Overlooked Factor: Genetics - parents with myopia were more likely to use nightlights for their convenience.
Conclusion: The correlation was due to a third factor (genetics), not the nightlight itself.
Conclusion
Regression is a powerful tool for causal analysis, but must account for all relevant variables.
Continuous effort is required to identify and control for omitted variables to avoid biased conclusions.