Quantitative Research Methods – Introduction to Applied Statistics

Third meeting

• Causality
  • Causal effects
  • Counterfactuals | Potential outcomes model
  • Randomized Controlled Experiments (RCTs)

• Set working directory;
• Open a new notebook document;

Are Emily and Greg more employable than Lakisha and Jamal? A field experiment on labor market discrimination. American Economic Review, vol. 94, no. 4, pp. 991–1013.

• Is there any racial discrimination in the US job market?

resume <- read.csv("resume.csv")

head(resume)

names(resume)

race_table <- table(race = resume$race, call = resume$call)
addmargins(race_table)
race_table

prop.table(table(resume$race), 1)
prop.table(table(resume$race), 2)

mean(resume$call[resume$race == "black"])

incremental = TRUE

• For every \( i \), The \( T{i} \) treatment effect could be defined, as \( Y_{i}(1) - Y_{i}(0) \), where \( Y_{i}(1) \) is the outcome in the treatment group, while \( Y_{i}(0) \) represents the outcome in the control group
• Fundamental problem of causal inference

• Counterfactuals
  • What if…
• David Hume

The key goal of causal inference is to predict counterfactuals

• Randomization creates homogeneous groups, therefore the difference between the two groups could be attributed to the treatment
• It eliminates selection bias
• Rule of Large Numbers
• Hawthorne effect

\( Y_{i}(1) - Y_{i}(0) \)

Sample Average Treatment Effect (SATE): a sample average of individual-level causal effects

\( SATE = \frac{1}{n}\sum_{n}^{i=1}\left \{ Y_{i}(1) - Y_{i}(0) \right \} \)

incremental = TRUE

• Can we really observe SATE?
• Not really, that's why we use _difference-in-means estimator \( \hat{\tau} = \frac{1}{n_{1}}\sum_{i=1}^{n}T_{i}Y_{i} - \frac{1}{n_{0}}\sum_{i=1}^{n}(1-T_{i})Y_{i} \)

• RCTs could be hard to analyze
• Violation of the protocol
  • Contamination;
  • Non-compliance;
  • Missing values;
  • Measurement error;

• Experimental effect
  • Heterogeneity
  • Failure of correctly understanding the causal effect
• Generalization of the results
  • Internal vs. external validity