kk Flashcards
(27 cards)
What is the dependent variable in the difference-in-differences (DID) model?
πππππ’π‘πππππ‘
It represents street level pollution for area π of the city in year π‘.
What does the treatment dummy (π·π) represent in the DID model?
Equal to 1 if area π is treated with the congestion charge policy, and 0 otherwise.
What is the role of fixed effects for each area (πΌπ) in the regression?
To control for unobserved characteristics of each area that may affect pollution levels
For example, different areas may have different baseline pollution levels.
What do year fixed effects (πΏπ‘) do in the regression?
Control for time-specific factors that affect pollution across all areas
For example, a nationwide policy change in 2018 affecting all areas.
Why is the term π·πΓπ¦2017π‘ omitted in the regression specification?
It is redundant since it is the base year for the DID analysis.
What is the key assumption required for the validity of the DID method?
The parallel trends assumption
This means that in the absence of treatment, the treated and control groups would have followed the same trend over time.
Can the parallel trends assumption be tested in this case?
Yes, by examining pre-treatment trends in pollution between treated and control areas.
Which coefficient estimates the causal effect of the congestion charge on pollution in 2018?
The coefficient for π·πΓπ¦2018π‘.
Rewrite the regression model to estimate the overall difference in pollution among treated and control areas before and after treatment.
πππππ’π‘πππππ‘=πΌπ+πΏπ‘+π½π·π+πππ‘
What does including a quadratic term for sleeping hours suggest about the relationship with grades?
A suspected non-linear relationship.
What is the marginal effect of sleeping hours on the outcome?
The derivative of the outcome with respect to sleep_hours.
What is the marginal effect when sleeping hours = 8?
Specific numerical value based on the model.
What is the marginal effect when sleeping hours = 9?
Specific numerical value based on the model.
What can be concluded about the optimal amount of sleep based on marginal effects?
It must lie somewhere between 8 and 9 hours.
Are the controls for studentsβ age and sex considered βgoodβ or βbadβ?
This depends on their relevance to the causal relationship being studied.
Interpret the coefficient on the female dummy variable.
Suggests a gender gap in academic performance of 6.875 points.
Under what conditions is it appropriate to control for cognitive ability?
When it does not mediate the causal relationship between sleep hours and grades.
What does the lack of statistical significance of the interaction between ability and female suggest?
That the interaction may not be relevant in explaining academic performance.
Why is adjusted RΒ² often preferred over regular RΒ² when comparing model specifications?
It accounts for the number of predictors in the model.
Under what circumstances may missing students lead to sample selection bias?
If the missingness is related to the outcome variable.
List all variables and parameters in the OLS model.
Dependent variable, independent variables, error term, intercept, and slope coefficient.
What is the minimization problem used to derive the OLS estimator?
Minimize the sum of squared residuals.
What do the first-order conditions (FOCs) imply about the sum of OLS residuals?
The sum of residuals equals zero.
What does it mean for Μπ½1 to be an unbiased estimator of the true π½1?
On average, it equals the true parameter value across repeated samples.
