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Take-Home Written Exercise 1
A researcher has been provided with a random sample of 2,658 married female employees.
The data set contains information on the following variables:
salary : monthly labour income, $1000s
kids : number of dependent children in the household (hhd)
age : age in years
educ : years of education
The researcher is interested in estimating the effect of having an additional kid in the hhd on
labour income. For this reason, the following MLR model is specified:
salaryi = β0 + β1kidsi + β2agei + β3educi + ui
, i = 1, 2, . . . , 2658 (1)
where βj
for j = 0, 1, 2, 3 are unknown coefficients to be estimated and ui
is the error term.
Estimating this model by OLS provides the following results: (2)
with standard errors in brackets.
(a) Using the results above, interpret the estimated coefficient of variable kids, βˆ1 and the
estimated coefficient of variable age, βˆ
2. Also test whether these coefficients are statistically
different from 0.
[25 marks]
(b) Do the estimated coefficients of variables kids and age have the expected sign? Justify
your answers.
[15 marks]
(c) Construct a 99% confidence interval estimate for β3 and interpret it.
[10 marks]
(d) Are the results of your hypotheses tests in part (a) and the confidence interval estimate
in part (c) valid if assumptions MLR1 to MLR5 hold, but the error term in equation one
is not normally distributed?
[10 marks]
(e) A variable that strongly explains labour income but has been omitted from the model
is ‘hours of work per month’ (hours). Suppose that this variable is now added to the
regression model of eq (1) and the new model is estimated by OLS. How will the addition
of this variable affect the estimated value of the coefficient of variable kids? In addition,
how will the addition of this variable affect the standard error of this coefficient? Justify
your answers.
[40 marks]
1
Take-Home Written Exercise 1
A researcher has been provided with a random sample of 2,658 married female employees.
The data set contains information on the following variables:
salary : monthly labour income, $1000s
kids : number of dependent children in the household (hhd)
age : age in years
educ : years of education
The researcher is interested in estimating the effect of having an additional kid in the hhd on
labour income. For this reason, the following MLR model is specified:
salaryi = β0 + β1kidsi + β2agei + β3educi + ui
, i = 1, 2, . . . , 2658 (1)
where βj
for j = 0, 1, 2, 3 are unknown coefficients to be estimated and ui
is the error term.
Estimating this model by OLS provides the following results: (2)
with standard errors in brackets.
(a) Using the results above, interpret the estimated coefficient of variable kids, βˆ1 and the
estimated coefficient of variable age, βˆ
2. Also test whether these coefficients are statistically
different from 0.
[25 marks]
(b) Do the estimated coefficients of variables kids and age have the expected sign? Justify
your answers.
[15 marks]
(c) Construct a 99% confidence interval estimate for β3 and interpret it.
[10 marks]
(d) Are the results of your hypotheses tests in part (a) and the confidence interval estimate
in part (c) valid if assumptions MLR1 to MLR5 hold, but the error term in equation one
is not normally distributed?
[10 marks]
(e) A variable that strongly explains labour income but has been omitted from the model
is ‘hours of work per month’ (hours). Suppose that this variable is now added to the
regression model of eq (1) and the new model is estimated by OLS. How will the addition
of this variable affect the estimated value of the coefficient of variable kids? In addition,
how will the addition of this variable affect the standard error of this coefficient? Justify
your answers.
[40 marks]
1