Module 3: MRA and Logrithmic Form

Question 1

When do you consider to take the natural log of the dependent variable?

Answer 1

1) has no zeros and is most often greater than 1
2) has a wide range
3) is measured in dollars

Question 2

What is the general format to interpreting log-log forms?

Answer 2

A one percent increase in x leads to a B percent increase in y

Note: coefficients are elasicities

Question 3

What is the general format to interpreting level-log forms?

Answer 3

A one unit increase in x leads to an approximate 100*B percent increase in y

Note: also called semi-elasticities

Question 4

Interpret the variable tenure for the following regression

ln(wage)=0.56+0.09educ -0.253female -0.007female*educ+0.17ln(tenure) -0.025 nonwhite

Answer 4

Each one percent increase in tenure is associtated with a 0.17% increase in wage

At mean of duration and wage, its an $.11 raise every 6 months

Question 5

What is the exact formula? When do we use it?

Answer 5

exact=100*(e^(B-1))
When the coefficient of B is greater than 0.1

Question 6

Given the regression, interprect the impact of tenure on wage

ln(wage)=0.56+0.083educ -0.189female -0.008female*educ+0.047tenure -0.001tenure^2 -0.027nonwhite

Mean of tenure = 5.1

Answer 6

An additonal year on the job is expected to add 3.7% to hourly wage

wage=100(e^(0.047-0.0025.1)-1)

Question 7

T/F: You can compare adjusted R^2s from similar log-log and level-log regressions.

Answer 7

F: they are different functional forms and cannot be compared from R^2s

Question 8

What are the null and alternative hypothesis for the Ramsey RESET test?

Answer 8

H0: B = 0, there is no misspecification
Ha: B != 0, model is misspecified

Want high p-values for this test

Question 9

What can you do when you find evidence of misspecification with the RESET test?

Answer 9

1) Look for an appropriate squared term
2) Take the natural log of y or an x, as appropriate
3) include appropriate interactions
4) consider the linear model if a nonlinear is chosen

Question 10

Interpret female in the following regression

ln(wage)=0.56+0.083educ -0.189female -0.008female*educ+0.047tenure -0.001tenure^2 -0.027nonwhite

When mean educ is 12.6 years

Answer 10

At the mean level of educ, females earn 25% less per hour than their male counterparts.

100[exp(-0.189-0.00812.6)-1]=-25.2

Question 11

Interpret educ given the following regression

ln(wage)=0.56+0.083educ -0.189female -0.008female*educ+0.047tenure -0.001tenure^2 -0.027nonwhite

Answer 11

An additional year of education is expected to add 7.8% to hourly wage for woman and 8.7% for men.

100*[exp(0.083-0.008female)-1]