Linear regression model estimate

QUESTION 1.
(a) Estimate the following linear regression model
𝑑𝑖𝑠𝑎𝑏𝑖𝑙𝑖𝑡𝑦1 = 𝛽! + 𝛽" ∗ 𝑒𝑐𝑎𝑔𝑒26 + 𝛽# ∗ 𝑚𝑎𝑙𝑒1 + 𝑒
To do so click on Statistics >> Linear Models and related >>Linear regression:
Dependent Variable: disability1
Independent Variables:
(1) Constant (this is included automatically – you do not need to do anything)
(2) Person's age in reference year (ecage26)
(3) male1
***Provide a copy of the STATA regression output.
(b) What are the values of the estimated coefficients 𝛽4!, 𝛽4", and 𝛽4#? Interpret the values 𝛽4" and 𝛽4#?
(c) Use the fitted regression model
𝑑𝚤𝑠𝑎𝑏𝚤𝑙𝚤𝑡𝑦1
7
= 𝛽4! + 𝛽4" ∗ 𝑒𝑐𝑎𝑔𝑒26 + 𝛽4# ∗ 𝑚𝑎𝑙𝑒1
to calculate the predicted probability of a disability for a sixty year old male. Show your calculations.
(d) Still using the fitted regression model, find the age at which the predicted probability of a disability for a
male is equal to 0. Also, find the age at which the predicted probability of a disability for a male is equal to
unity. Show your calculations.
(e) Considering your answers in part (d) and the range of variation of ecage26 (which can be found using the
command summarize ecage26) explain briefly whether the linear probability model estimated in this
question yields nonsensical probabilities (i.e. probabilities that are not between 0 and 1)?
QUESTION 2.
(a) Estimate the following linear regression:
𝑎𝑡𝑖𝑛𝑐42 = 𝛽! + 𝛽" ∗ 𝑒𝑐𝑎𝑔𝑒26 + 𝛽# ∗ 𝑚𝑎𝑙𝑒1 + 𝛽$ ∗ 𝑚𝑎𝑙𝑒𝑎𝑔𝑒 + 𝑒
To do so click on Statistics >> Linear Models and related >>Linear regression:
Dependent Variable: After Tax Income (atinc42)
Independent Variables:
(1) Constant (this is included automatically – you do not need to do anything)
(2) Person's age in reference year (ecage26)
(3) male1
(4) maleage
***Provide a copy of the regression output
(b) What is the estimated effect of age on after tax income for a female?
What is the estimated effect of age on after tax income for a male?
(c) Consider the following hypothesis: the effect of age on after tax income is identical for males and females.
Conduct a statistical test to verify if the data support that hypothesis. Use a level of significance of 5% and
explain how you proceed. Hint: all the information you need to conduct this test appears on the regression
output from part (a).
State at least one economic reason that could explain why this hypothesis is rejected.

Sample Solution