ETF2100/5900 Introductory Econometrics-526互联

ETF2100/5900 Introductory Econometrics
Assignment 2 — A Case Study on the Birth-weight of Baby
Important notes:
1. This is an individual assignment. This assignment is worth 20% of this unit’s total mark.
Marks will be deducted for late submission on the following basis: 10% for each day late,
up to a maximum of 3 days. Assignments more than 3 days late will not be marked.
2. Submission deadline for coursework is 11:55 pm Friday of Week 11 (i.e., 19/05/2023).
Please submit a soft copy through Moodle. Name the soft copy as follows: student
ID Name.doc (or .pdf). Pdf file is preferred, but word file is also fine. Also, on the
title page, please make sure you provide the student ID and name correctly.
3. Notation used in the assignment needs to be typed correctly and properly. Incorrect (or
inconsistent) notations are treated as wrong answers.
We are interested in studying whether a mother’s smoking affects the birthweight of her baby.
The dataset for this question is birthweight2019.csv available on Moodle. The variables you
need are as follows:
• bweight: infant birthweight (kilogram)
• smoke2: 1 if mother smokes 1-5 cigarettes per day, 0 otherwise
• smoke3: 1 if mother smokes 6 or more cigarettes per day, 0 otherwise
• mmarried: 1 if mother married, 0 otherwise
• mage: mother’s age
Questions:
1. (a). Estimate the following regression model, and report the estimated coefficients and the
associated standard errors. (1 points)
bweighti = β1 + β2smoke2i + β3smoke3i + β4magei + β5mmariedi + ei (1)
(b). Interpret the estimated coefficients of smoke2 and smoke3. (3 points)
1
2. Conduct a hypothesis test to examine whether smoke has any impact on the infant birthweight at all?
3. What is the estimated difference in the expected birthweight of a baby whose mother is
married and smokes 6 or more cigarettes a day relative to that of a baby whose mother is
not married and smokes 1-5 cigarettes per day? Assume the mothers are at the same age.
Keep 4 decimals for the calculation involved. (2 points)
4. (a). Now consider a similar model but with log of birthweight as dependent variable.
Estimate this model, and report the estimated coefficients and the associated standard
errors. (1 points)
log (bweight)i = β1 + β2smoke2i + β3smoke3i + β4magei + β5mmariedi + ei (2)
(b). Calculate and interpret the percentage differences in birthweight by comparing groups
smoke2 and smoke3 with the reference group. (3 points)
5. Now, let’s simplify the model (1) and the model (2) as follows.
The model (1): y = x
′β
∗ + mage · β4 + e, (3)
The model (2): log(y) = x
′β
∗ + mage · β4 + e, (4)
where x is a vector including other regressors, and β
∗
includes the corresponding coefficients.
(a). Derive the elasticity of birthweight with respect to mother’s age for the model (3). (3
points)
(b). Derive the elasticity of birthweight with respect to mother’s age for the model (4). (3
points)
Hint: The final expressions should involve β4, and may include y, and/or mage.