Correlation vs. Causation Quiz

Correlation vs. Causation

• Correlation implies a relationship between two variables, but doesn't prove causation. Correlation shows when one variable changes, the other tends to change, but doesn't show if one causes the change in the other.

• Causation means a change in one variable directly causes a change in the other. There's a direct cause-and-effect relationship.

• Correlation does not imply causation.

Topics Covered

• Differences between correlation and causation
• The evaluation problem
• OLS estimator and selection bias

Learning Objectives

• Understand the difference between correlation and causation
• Recognize the importance of causality
• Argue for or against causation claims seen in the real world
• Describe difficulties in estimating causal effects and why OLS estimation might not yield causal estimates
• Mathematically derive selection bias
• Explain selection bias and how it arises

Material for this Lecture

• Basic material: slides/lectures (including discussions or diversions)
• Recommended readings:
  • Leamer (1983), "Let's take the con out of econometrics," American Economic Review
  • DiNardo and Pischke (1997), "The returns to computer use revisited: have pencils changed the wage structure too?," Quarterly Journal of Economics
  • Angrist (1998), "Estimating the labor market impact of voluntary military service using social security data on military applicants," Econometrica
  • Angrist (2010), "The credibility revolution in empirical economics: how better research designs is taking the con out of econometrics," Journal of Economic Perspectives

Why Study Econometrics?

• Applied economists seek to understand labor markets and inform public policy

• This requires identifying causal effects, not just correlations

• Changing a factor of interest should cause a change in the outcome, rather than simply being accompanied by a change

Differences Between Correlation and Causation

• Causation suggests a change in one variable is the reason for a change in the other variable.
• Correlation claims: When X goes up, Y goes up.
• Causation claims: If X goes up, then Y goes up.
• Correlation has no direction, causation does.

Other Examples

• Radio report claimed TV viewing increases mortality; could TV watching cause death?
• Private tutoring was associated with worse student performance. Did tutoring worsen performance?
• Laid-off workers often suffered from mental distress. Does losing a job cause mental distress or vice-versa?

Main Concerns When Estimating Causal Effects

• Omitted Variable Bias: An unobserved third factor can influence observed trends, creating false correlations. Example: more TV-watching by ill people and higher mortality rates.
• Reverse Causality: The relationship is reversed from what is assumed. Example: tutoring students with weaker performance to improve, instead of students with weaker performance opting for tutoring. This is often a bidirectional problem.

The Evaluation Problem

• Estimating causal effects is about comparing potential outcomes for a given individual under different conditions (treated or not)
• In practice, we cannot observe the counterfactual where everything remains the same except for the treatment
• Missing data and filling in using other information to evaluate the treatment

Ordinary Least Squares (OLS) Estimator

• The observed outcome (y) relates to the treatment (D = 0 or 1) and a potential outcome
• OLS can be used to examine this relationship
• Understanding how OLS works with the treatment variables is important to understanding treatment effects.

Selection Bias

• When there's selection bias, the treatment impacts outcomes in ways that are unrelated to the effect we are measuring (the average outcome in the population for each treatment group)
• Treatment effects are dependent on unobserved factors that are not part of the model.

Selection Bias (cont'd)

• For there to be no selection bias, the unobserved error term needs to be independent of whether the individual is treated (e.g., have a tutor or not)
• We need to control for observables (measurable/observable factors) as well as unobservables (non-measurable factors) to account for selection bias and get closer to the treatment effect.

Selection Bias (cont'd)

• The assumption about no selection bias would need to hold when controlling for the observable factors in the equation that estimates potential outcomes.

An Example: The Returns to Education

• A model showing an expected outcome based on factors like schooling and ability, where ability is not observable
• The unobserved factor leads to biased estimates, where selection bias would come into play.

Selection Bias in the Example

• Selection bias in the ability example comes from inability to directly control for the unobserved ability
• The bias will arise when ability is related to factors that influence the treatment or the outcome being examined

Estimating Causal Effects

• OLS is better at estimating causal effects when we can control for observable factors
• Selection on unobservables means we cannot know what would have happened without the treatment. This bias arises due to unobservable aspects of the individual that influence both treatment and outcome.

Understanding the Direction of the Bias

• Scenario 1: Voluntary programs may attract more motivated employees upward bias
• Scenario 2: Forced interventions for low-performing students may be associated with lower ability, leading to a downward bias.

To conclude

• OLS provides unbiased estimates only if selection is just on observable factors.
• It is important to understand how to evaluate causal effects in cases of selection on unobservables or unobserved heterogeneity.