Module 4: Panel Data Methods

Question 1

Why would we want to pool cross-sections?

Answer 1

1) To increase sample size -> improved efficiency
2) Study changes over time

Question 2

For the following regression, interprect the intercept.

kids = 4.92-0.36y82-0.52y84 -0.16educ

Assume the base year is 1980 and y82 is 1982.

Answer 2

A woman without any education is predicted to have roughly 5 children in 1980.

Question 3

For the following regression, interpret y82.

kids = 4.92-0.36y82-0.52y84 -0.16educ

Assume the base year is 1980 and y82 is 1982.

Answer 3

Holding education fixed, a woman in 1982 is predicted to have roughly 0.36 less children than a woman in 1980.

Question 4

For the following regression, interpret y85.

log(wage) = 0.98+0.37y85+0.065educ -0.3female

Assume the base year is 1978 and y85 year is 1985

Answer 4

Holding everything else fixed, someone in 1985 earns roughly 37% higher hourly wages than they would have in 1978. (exact = 45%)

Question 5

For the following regression, interprect educ.

log(wage) = 0.98+0.37y85+0.065educ -0.3female

Assume the base year is 1978 and y85 year is 1985

Answer 5

Holding everything else fixed, one additional year of education results is predicted to increase hourly wages by 6.5%

Question 6

Given the regression, what was the gender pay gap in 1978?

log(wage) = B0 + B1y85 +B2educ +B3female+B4y85fem

When the base year is 1978.

Answer 6

-B3

log(wage)m78 - log(wage)w78 = (B0+B2)-(B0-B2+B) = B3

Question 7

Given the regression, what is the gender pay gap in 1985?

log(wage) = B0 + B1y85 +B2educ +B3female+B4y85fem

Given that 1978 is the base year.

Answer 7

-(B3+B4)

log(wagem85)-log(wagew85) = (B0+B1+B2)-(B0+B1+B2+B3+B4) = -(B3+B4)

Question 8

Given the following regression, what is the gender pay gap in 1985?

log(wage)=0.998+0.31y85+0.066educ-0.37female+0.14y85fem

Given that the base year is 1978.

Answer 8

Women in 1985 are predicted to earn 23% less per hour than men, all else equal. (26% with the formula)

Question 9

Given the following regression, what are the returns to education in 197

log(wage) = 1.12+0.047y85+0.056educ-0.37female+0.14y85fem+0.021y85educ

Given that 1978 is the base year.

Answer 9

Every additional year of schol is prediced to increase wages by 5.6% in 1978.

Question 10

Given the regression, what is the returns to education in 1895?

log(wage) = 1.12+0.047y85+0.056educ-0.37female+0.14y85fem+0.021y85educ

Given that the base year is 1978.

Answer 10

Every additional year of school in 1985 is predicted to increase wages by 7.6%

(educ+y85educ) = 0.056+0.021 = 0.076

Question 11

How has the returns to education changed over time. Given that returns in 1978 were 0.056 and returns in 1985 were 0.077?

Answer 11

It has increased by more than a third and the change is statistically significant at the 5% level.

change in returns = (0.021/0.056) significance = (0.021/0.01 > 2)

Question 12

What is the distinction between pooled independent cross-sections and panel data?

Answer 12

Pooled cross-sections are random samples drawn from different periods and pooled together

Panel data are observations of the smae units over time.

Question 13

What are the trade-offs of using pooled cross-secions vs panel data?

Answer 13

1) Panel data follows the same units over time, so its better at accounting for unobservables, but…
2) It’s hard to collect and plagued by atrition
3) Over time, panel data may become less representative of the whole population

Question 14

Given the regression, what happened to student performance over time?

math4 = 12.25+14.86y98 + 5.47log(rexpp)

Given the base year is 1997, math is math scores, and rexpp is…

…expenditures per student.

Answer 14

Holding expenditures fixed, there was a 14.86 percentage point increase between 1997 and 1998 in students receiving a “satisfactory” score on their math score.

Question 15

Write a theoretical model including the fixed effect.

Answer 15

yit = B0+B1Tt+B2xit+ai+uit

where i is the observation, t is the time period, and a for FE

Question 16

What does the fixed effect variable a account for?

Answer 16

Captures all omitted factors that are constant across time periods that influence yit

Question 17

What is the first-difference model?

Answer 17

It’s a model that helps deal with OVB by removing the fixed effects

Question 18

What does it mean for a first-difference model to be strictly exogenous?

Answer 18

1) Variables should not be correlated with shocks to wages in the same period (cov(x,u) = 0)
2) Past valeus should not affect current wages once we’ve accounted for them (cov(xi-1,u) = 0)
3) There is no feedback loop (cov(i+1,u) = 0)

Question 19

What are the downsides to the first-difference model?

Answer 19

1) It removes a lot of variation in the data
2) Collecting panel data is difficult/costly

Question 20

Given the regression, inerpret the variable grant.

log(scrap)= 0.597-0.189y88 + 0.057grant

where scrap = scrap rates for firms, and grant = 1 if a firm recieves it

Answer 20

A firm that received a grant is predicted to have a 5.7 percent higher scrap rate compared to a firm that didn’t recieve the grant.

Question 21

When do we decide whetehr to use first-differences or difference-in-differences?

Answer 21

Diff-n-diff is typically perferred when there are clear treatment and control groups in a natural experiement

FD may by more useful when the x you are interested in is vary over time and across multiple groups that don’t fit clearly into the diff-n-diff model