13.1 Regressions and discrimination Flashcards
What is regression (in statistics/econometrics)?
Regression is a statistical method used to understand the relationship between one outcome (often called the “dependent variable” or Y) and one or more explanatory factors (the “independent variables” or X’s).
* It typically fits a line (or curve) to data points so we can predict the average value of Y based on given X values.
* In its simplest form (simple linear regression), we have one X variable and we find the “best fit” line that minimizes the overall distance from each data point to the line.
How does a simple linear regression usually work in practice?
Collect Data: We gather observations of our outcome of interest (Y) and one explanatory variable (X).
What is multiple regression, and why is it useful?
How could we use regression to measure discrimination in a sports setting?
We can compare outcomes (like salaries, playing time, or contract offers) across different groups (e.g., based on race, gender, or other characteristics) while controlling for performance-related variables (e.g., points per game, batting average).
* If a certain group systematically gets lower outcomes even after controlling for performance, that suggests potential discrimination.
What does controlling for performance mean in a discrimination study?
“Controlling for performance” means including performance metrics (like batting average, goals, assists, etc.) in the regression model so that any difference in salary (for example) is not just because one group might perform differently.
* This way, any remaining difference (the group coefficient) is more likely due to unexplained factors—possibly discrimination—rather than performance differences.
How do we incorporate ‘group’ differences (e.g., race, gender) into a regression?
We create a dummy variable (also known as an indicator variable), coded as:
* 1 if the player belongs to a specific group (e.g., female athletes), and
* 0 otherwise (e.g., male athletes).
Then we add it to the regression equation. Its coefficient estimates the average difference between the groups, holding other factors constant.
What does the coefficient on the ‘Group’ dummy (β2) represent in an equation like:
What does it mean if
β3 is significantly negative in that interaction model?
It would imply that for the same increase in performance, the group indicated by the dummy sees a smaller increase in salary than the other group—indicative of a different (likely discriminatory) reward structure for performance.
In the provided graph, what are the red lines and the difference
β2 or β3?
How do you interpret the final results when looking for discrimination?
- Look at the sign & size of the group coefficient(s): is there a negative (or positive) difference that is large in magnitude?
- Check statistical significance (p-values, confidence intervals): is the difference (coefficient) statistically unlikely to be zero?
- Control for relevant factors: ensure you’ve included all major performance variables, position, experience, etc. to avoid leaving out crucial explanations.
What do we conclude if we find a significant negative coefficient for a specific group, even after controlling for performance?
- It strongly suggests that members of that group are being under-rewarded (e.g., paid less) for the same performance compared to others.
- While not absolute proof of discrimination (other unobserved factors might exist), it is commonly interpreted as evidence of discriminatory practices if no other plausible explanations are apparent.
