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Questions and Answers
What is the primary distinction between correlation and causation?
What is the primary distinction between correlation and causation?
Which of the following best describes causality in research?
Which of the following best describes causality in research?
What role does the OLS estimator play in estimating causal effects?
What role does the OLS estimator play in estimating causal effects?
What is the evaluation problem in the context of causality?
What is the evaluation problem in the context of causality?
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Which of the following statements reflects the difficulties associated with selection bias?
Which of the following statements reflects the difficulties associated with selection bias?
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How can one recognize the importance of causality in real-world claims?
How can one recognize the importance of causality in real-world claims?
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What is the objective of studying econometrics as suggested in the lecture material?
What is the objective of studying econometrics as suggested in the lecture material?
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Which reading material was suggested for advanced understanding of econometrics?
Which reading material was suggested for advanced understanding of econometrics?
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What does δ represent in the OLS regression equation?
What does δ represent in the OLS regression equation?
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For there to be no selection bias, which condition must be satisfied?
For there to be no selection bias, which condition must be satisfied?
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What is a necessary assumption for OLS to yield causal estimates?
What is a necessary assumption for OLS to yield causal estimates?
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What does the equation E [yi |Di = 1] − E [yi |Di = 0] represent?
What does the equation E [yi |Di = 1] − E [yi |Di = 0] represent?
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In the covariance formula, what does cov (Di , ϵi ) = 0 indicate?
In the covariance formula, what does cov (Di , ϵi ) = 0 indicate?
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What does the term ϵ represent in the OLS regression model?
What does the term ϵ represent in the OLS regression model?
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Why is selection bias a concern in estimating treatment effects?
Why is selection bias a concern in estimating treatment effects?
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If $E[ϵi] = 0$, what is implied about the error term?
If $E[ϵi] = 0$, what is implied about the error term?
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What does reverse causality imply in a causal relationship?
What does reverse causality imply in a causal relationship?
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What is the evaluation problem associated with estimating causal effects?
What is the evaluation problem associated with estimating causal effects?
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In the context of the evaluation problem, what is a counterfactual?
In the context of the evaluation problem, what is a counterfactual?
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What does the ordinary least squares (OLS) estimator primarily help to analyze?
What does the ordinary least squares (OLS) estimator primarily help to analyze?
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What kind of data problem arises in estimating the effect of a treatment on individuals?
What kind of data problem arises in estimating the effect of a treatment on individuals?
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What do we typically seek to compare in the evaluation problem?
What do we typically seek to compare in the evaluation problem?
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What does the treatment variable in the context of OLS estimation represent?
What does the treatment variable in the context of OLS estimation represent?
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Why is it difficult to estimate causal effects purely from observational data?
Why is it difficult to estimate causal effects purely from observational data?
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What is the primary goal for applied labor economists?
What is the primary goal for applied labor economists?
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What distinguishes a causal claim from a correlation claim?
What distinguishes a causal claim from a correlation claim?
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What problem may arise from omitted variables bias?
What problem may arise from omitted variables bias?
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What does the example of television viewing and mortality illustrate?
What does the example of television viewing and mortality illustrate?
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In the example regarding private tutoring, what important issue is raised?
In the example regarding private tutoring, what important issue is raised?
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What conclusion can be drawn from the claim that laid-off workers suffer from mental distress?
What conclusion can be drawn from the claim that laid-off workers suffer from mental distress?
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Which statement correctly summarizes the difference between correlation and causation?
Which statement correctly summarizes the difference between correlation and causation?
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What is a key challenge when estimating causal effects?
What is a key challenge when estimating causal effects?
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What is the selection on observables or conditional independence assumption?
What is the selection on observables or conditional independence assumption?
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What happens if the ability variable A is omitted from the estimation of the model?
What happens if the ability variable A is omitted from the estimation of the model?
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What does a positive covariance between ability A and schooling S imply for the estimator β?
What does a positive covariance between ability A and schooling S imply for the estimator β?
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Under what condition is OLS more likely to produce causal estimates?
Under what condition is OLS more likely to produce causal estimates?
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What is a potential reason for selection bias in treatment assignments?
What is a potential reason for selection bias in treatment assignments?
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In the estimated model y = α + βS + u, what does the term u represent?
In the estimated model y = α + βS + u, what does the term u represent?
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Which of the following statements about selection bias is true?
Which of the following statements about selection bias is true?
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What is the significance of the covariance term in determining selection bias?
What is the significance of the covariance term in determining selection bias?
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Study Notes
Correlation vs. Causation
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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.
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Causation means a change in one variable directly causes a change in the other. There's a direct cause-and-effect relationship.
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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?
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Applied economists seek to understand labor markets and inform public policy
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This requires identifying causal effects, not just correlations
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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.
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Description
Test your understanding of the critical differences between correlation and causation. This quiz covers key concepts such as the evaluation problem, selection bias, and the OLS estimator. Assess your ability to distinguish between correlation and causality and recognize real-world implications.
