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 Monday of Week 11 (i.e., 16/05/2022). 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.

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 (grams)
• smoke2: 1 if mother smokes 1-5 cigarettes per day, 0 otherwise
• smoke3: 1 if mother smokes 6-10 cigarettes per day, 0 otherwise
• smoke4: 1 if mother smokes 11 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 + β₂smoke2_i + β₃smoke3_i + β₄smoke4_i + β₅magei + β₆mmaried_i + e_i                                                                                                     (1)

(b). Interpret the estimated coefficients of smoke2, smoke3 and smoke4. (3 points)

• Conduct a hypothesis test to examine whether smoke has any impact on the infant birth- weight at all?
• What is the estimated difference in the expected birthweight of a baby whose mother is married and smokes 6-10 cigarettes a day relative to that of a baby whose mother is not married and smokes 11 or more cigarettes a day? Assume the mothers are at the same age. Keep 4 decimals for the calculation involved. (2 points)
• (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 + β₂smoke2_i + β₃smoke3_i + β₄smoke4_i + β₅magei + β₆mmaried_i + e_i  (2)

(b). Calculate and interpret the percentage differences in birthweight by comparing groups smoke2, smoke3 and smoke4 with the reference group. (3 points)

• Now, let’s simplify the model (1) and the model (2) as follows.

The model (1):     y = x^jβ₁ + mageβ₂ + e,                                        (3)

The model (2):     log(y) = x^jβ₁ + mageβ₂ + e,                                (4)

where x is a vector including other regressors, and β₁ includes the corresponding coeffi- cients.

• Derive the elasticity of birthweight with respect to mother’s age for the model (3). (3 points)
  • Derive the elasticity of birthweight with respect to mother’s age for the model (4). (3 points)

Hint: The final expressions should involve β₂, and may include y, and/or mage.

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