Week 6

Question 1

Define panel data

Answer 1

Panel data comprises quantities gathered from multiple entities, such as individuals, countries, and companies, collected at regular intervals and arranged chronologically.

Question 2

Write out a simple regression equation for panel data

Answer 2

Equation: 𝑦(𝑖𝑡) = 𝛽0 + 𝛽1 𝑥(𝑖𝑡,1) + 𝛽2 𝑥(𝑖𝑡,2) + 𝛽3 𝑥(𝑖𝑡,3) + ⋯ + 𝛽(𝑘) 𝑥(𝑖𝑡,𝑘) + 𝜀(𝑖𝑡)
● 𝑖: cross-sectional entity (e.g., person, household, firm, country)
● 𝑡: time (e.g., day, month, year)

Question 3

Why do researchers use panel data? (4)

Answer 3

• Rich in information, captures changes in time.
• Potentially, like an increase in sample size.
• Possibility to control for time-invariant effect–> Any individual-specific attributes that do not vary across time.
  Helps mitigate omitted variable bias.

Question 4

How would researchers be able to account for time-invariant effects? (2)

Answer 4

• Including dummy variables for each “cross-sectional entity”
  
  • This means including specific indicators for each group, like a separate one for each country in a study, so any unique characteristics of each country are accounted for.
• Using a regression with “fixed effects”

Question 5

How does a regression with “fixed effects” look? What does it do?

Answer 5

• Fixed effects regression allows intercept of the regression to vary freely across individuals or groups —> You are giving each equation a “baseline” or starting point which accounts for the differences of each cross-sectional entity.
  
  • Generally 𝛼(i) is added just before the error term at the end of the regression.
    ○ Where “i” would be the cross-sectional entity
  • This assumes that each cross-sectional entity has a number of unique characteristics that may affect the dependent variable.
    Firm fixed effects–> For each firm, a separate dummy variable

Question 6

What is the “pooled OLS” assumption?

Answer 6

• This is the assumption that there are no unique characteristics or fixed differences between groups. It quite simply “pools” all of the observations into one large group.
  
  • This is a very strong assumption which is often not realistic.

Question 7

When should you use a fixed effects model?

Answer 7

• If you are concerned about omitted factors that may be correlated with key predictors at the entity level.
• Interpretation of results is similar to OLS.

Question 8

What are some limitations to the FE model? (3) And (1) possibility.

Answer 8

Limitations:
- FE can only estimate the effects of variables that change overtime.
- Although they account for time-invariant effects, they cannot measure the impact it has on the regression.
- All stable characteristics are captured by the entity dummies, meaning there is this limits the researcher from separating the impact of the stable traits from the overall group effect (it gets “absorbed).
- It can only estimate the effects of variables that change over time.
Possibility:
- You can study how time-changing variables interact with stable group traits in an FE model.

Question 9

Give the 5 assumptions of a Robustness Check

Answer 9

1. What does your analysis assume? (A)
2. If ‘A’ is not true, then the results may be wrong in way (B) [estimate too high/low, standard errors too small, etc…)
3. Assumption ‘A’ may not be true in the analysis because of (C)
4. Either: (D) is a test to see whether ‘A’ is true or not.
   Or: ‘D’ is an alternate analysis that does not assume ‘A’, which shows how big of a problem ‘B’ is.
5. If: ‘A’ is not true
   Or: ‘B’ is a big problem
   Then I will do (E) instead of the original analysis.