4. Panel Data Methods Flashcards
(12 cards)
What is cross-section
Taking data from one unit at one point in time, essentially a snapshot
Why pooled cross-section
Increasing sample size to improve efficiency
studies change over time
How dos PCS compare to prior material
- Same OLS and IV/2SLS
- Same interpretations of coefficients
- Same hypothesis testing
- Same heteroskedastic-robust SE methods
- Typically putting dummies for each time period
kidshat = 4.92 - 0.36y86 - 0.52y84 - 0.16
Interpret each coefficient keeping in mind years in this data set are 80, 82, and 84
Intercept: All else held constant, a woman in 1980 without any education is associated with almost 5 children
By82: All else constant, a woman in 82 is predicted to have ~0.36 fewer children than a woman in 80
log(wage) = 0.98 + 0.37y85 + 0.065educ − 0.3female
Interpret each coefficient keeping in mind years in this data set are 78 and 85
By85: All else held constant, an individual in 85 is predicted to earn 37% higher hourly wages than someone in 78 (would have to exponentiate giving us 45%)
Beduc: AEC, each additional year of education increases hourly wage by approximately 6.5%.
Bfemale: AEC, a woman is predicted to earn 30% less than her male counterpart (35% after exponentiation)
How to study changes over time in PCS?
By creating an interaction term by multiplying two other variables.
For example: Studying the gender pay gap by multiplying y85 and female for the CPS data
log(wage) = β0 + β1y85 + β2educ + β3female + β4y85fem
How would you find the gender pay gap in 78 and 85?
log(wage)m78 − log(wage)w78
(β0 + β2educ) − (β0 + β2educ + β3) = − β3
log(wage)m85 − log(wage)w85
( β0 + β1 + β2 educ ) − ( β0 + β1 + β2 educ + β3 + β4 ) = − ( β3 + β4 )
log(wage) = 0.998 + 0.31y85 + 0.066educ − 0.37female + 0.14y85fem
What is the pay gap in 78 and 85?
βfemale = −0.37. Women in 1978 are predicted to earn 37% less per hour than men, all else equal. Closer to 45% using the exact formula.
βfemale + βy85fem = −0.37 + 0.14 = −0.23 Women in 1985 are predicted to earn 23% (or 26% with formula) less than men, all else equal.
The pay gap decreased over this time period by a statistically significant amount (5% level): 0.14/0.056 > 2.
How to approach pooled cross-section data with interaction terms?
Look at returns to the dependent variable across time frames
Compare the change over time by comparing the change in the two time periods
Check for statistical significance by finding the t stat
What is the difference between pooled independent cross-sections and panel data?
PICS: Random samples drawn from different periods are pooled together, these samples are independent from each other
Panel: Observations of the same units over time
Trade-off of using PCS vs Panel
Panel => same units, preferred for policy analysis, harder to collect and often affected by attrition
Remind yourself of the research question!
yit =β0 +β1Tt +β2xit1 +… +βkxitk +uit
what does i, t, Tt stand for?
i: unit
t: 1,2
Tt: dummy for time periods
