Econ20003 - quantitative methods - find the average

Question

Question 1:

The following model has been used to estimate the relationship between the wage per hour and the levels of education and experience.

ln (Wage) = β₀ + β₁Edu + β₂Edu² + β₃Exper + β₄Exper² + β₅Edu x Exper + β₆Gen + e

Here are some EViews outputs:

Dependent Variable: ln(Wage)
Method: Least Squares
Sample: 1 1000
Included observations: 1000

Variable	Coefficient	Std. Error	t-Statistic	Prob.
C	1.132346	0.339795	3.332438	0.0009
EDU	0.047058	0.013693	3.403065	Not Given
EDU2	0.002598	0.001113	2.333455	0.0198
EXPER	0.05641	0.00984	5.732665	0
EXPER2	-0.000676	8.98E-05	-7.529335	0
EDUEXP	0.001019	0.000509	2.002315	0.0455
GEN	-0.136837	0.091748	Not Given	Not Given
R-squared	Not Given	Mean dependent var		2.856988
Adjusted R-squared	Not Given	S.D. dependent var		Not Given
S.E. of regression	0.504434	Akaike info criterion		1.476217
Sum squared resid	252.6727	Schwarz criterion		1.510571
Log likelihood	-731.1084	Hannan-Quinn criter.		1.489274
F-statistic	55.09055	Durbin-Watson stat		2.026595
Prob(F-statistic)	0

Wage = wage per hour Edu = level of Education in years
Exper = Years of experience in the job
Gen = a dummy variableequal to 1 if the individual is a female and 0 otherwise
Answer the following questions:
a) Report the results of the regression.

b) Comment on the effect of Education on ln(Wage).

c) Derive an expression for the Elasticity of Wage with respect to Experience. Calculate the Elasticity for a female person with (i) 16 years of education & 10 years of experience and (ii) 10 years of education & 10 years of experience. Interpret your results.

d) For two individuals with equal levels of Education and Experience, calculate the difference between the wages of a female and a male person. Comment on the difference.

e) Test the overall significance of the model at the 1% level (assuming all OLS assumptions are valid).

f) Given that the correlation coefficient between Exp and Exp2 is 0.9, comment on whether the model suffers from multicollinearity.

Question 2:

Background: Health insurance companies and governments are interested in knowing which factors determine people's decisions to visit doctors. A researcher has collected data on 300 individuals on the following variables:

Doctor =A dummy variable=1(if theindividual visited a doctor in a given year) and= 0 (otherwise) ln Income =log ( Income of the indivdual 1000)
Sex =1(if the person is a Male) = 0 (otherwise)
Age =Age of the person

The data is available in the EXCEL file Q2A3.xlsx. The researcher considers the following discrete outcome model where the decision to take private insurance is related to other variables

P(Doctor =1) = P{β₀ + β₁lnIncome + β₂Sex + β₃ Age}

Undertake the following:

a) Estimate a Logit model for this data set. Report the EViews output [you don't have to write any equations, R_p² etc, just report the EViews table from your estimation].

b) Comment on the effect of Income, Sex and Age on the probability of visiting a doctor (you are not required to compute marginal effects).

c) Find the average marginal effect of lnIncome and interpret this estimate.

d) Test whether being male increases the probability of visiting a doctor.

e) Estimate a Probit model and report the EViews output [just EViews output].

f) Find the average marginal effects for ln Income from the Probit model and interpret this estimate.

g) Test the overall significance of the Logit model (write down the six steps).

h) Calculate an appropriate goodness of fit measure for the estimated Logit and Probit models and use it to choose your preferred model.

Attachment:- Q2A3.xlsx