Instructions:

(i)  The Assignment is worth 60 marks in total. Marks allocated for each question are indicated.

(ii)  Submit your typed solutions to this Assignment as a single PDF to the Course Canvas Assign- ment Dropbox by the due date.  This Assignment is not covered by ‘Simple Extension’ since the due date is less than ten (10) days. Late submission incurs a 5% penalty per day late.

(iii)  When performing statistical tests, always state the null and alternative hypotheses, the test statistic and its distribution under the null hypothesis, the level of significance and the con- clusion of the test.

(iv)  An additional 10 marks will be awarded for the quality of the presentation of your report. Neat

tables and formulae will earn more marks. Screenshots of output will earn no marks.

(v)  You must attach a copy of your computer output (i.e. your STATA log file) as an appendix to your answers. This is easy to do. At the top of your ‘do file’ write:

log  using  file_name.log,  replace

where ‘file_name.log’ is the name of your file. Don’t forget to close your log file at the end of your ‘do file’. Marks will be deducted if this information is not included.

Questions

The assignment involves the application of a range of econometric methods covered in ECMT2150 to analyse the effect of smoking during pregnancy on infant birthweight. This is an important topic as it has life-long health implications, including increased risk of chronic diseases in later life, poor cognitive development and delayed social development.

The dataset for the assignment, BirthWeight.dta, comes from a sample drawn from the Victo- rian Health department for the year 2003. There are 781 observations and 8 variables including:

•  LowBirthWeight =1 if a low birthweight (i.e. < 2500 grams), =0 otherwise

•  Education = Mother’s level of education measured in years

•  HealthCheck = Total number of antenatal visits to a health care professional

•  Order = Birth order (i.e.  1=1st born, 2=2nd born, etc.)

•  Alcohol = Average number of standard alcoholic drinks per day during pregnancy

•  BirthWeight = Baby’s birthweight measured in grams

•  Cigarettes = Average number of cigarettes smoked

•  Girl =1 if the baby is a girl, =0 otherwise

(1)  What is the mean, standard deviation, minimum, and maximum value for each of the variables in the dataset? Present your results in table form.  [2 marks]

(2)  What fraction of mothers in the sample reported smoking during pregnancy? Among women who smoked, what is the average number of cigarettes smoked per day?  Given these values, is the overall sample average a good, meaningful measure of the ‘typical’ woman in this case? Explain your reasoning. [2 marks]

(3)  Consider the following model which includes mother’s education (Education), the use of health care services (HealthCheck), the birth-order of the child (Order) and an indicator of whether the baby is a Girl as determinants of BirthWeight:

BirthW eigth = β0 + β1 Cigarettes + β2Education

+ β3HealthCheck + β4Order + β5Girl + u   (1)

Do you expect β2  to be positive or negative? Briefly explain your reasoning.  [2 marks]

(4)  Do you expect β3  in Model (1) to be positive or negative? Provide one reason why β3  may be positive, and one reason why β3  may be negative.  [2 marks]

(5)  Estimate Model (1) by OLS and report the results in the ‘standard form’ (i.e. coefficient estimates and standard errors).  [2 marks]

(6)  Test the hypothesis that Order and Girl are jointly insignificant in determining child birth- weight, holding the other variables constant. Use a 1% significance level in your test. [2 marks]

(7)  Consider an expanded version of Model (1) which includes an interaction between Order and Girl:

BirthWeight = β0 + β1 Cigarettes + β2Education

+ β3HealthCheck + β4Order + β5Girl + β6Order × Girl + u   (2)

In terms of the parameters of Model (2), what is the partial effect of birth order on expected BirthWeight? [2 marks]

(8)  Construction the interaction effect variable Order  × Girl and estimate Model (2).  Test the statistical significance of β6  against the one-sided alternative that the coefficient is positive, with a 5% significance level. What do you conclude?  [3 marks]

(9)  How does inclusion of the interaction term Order × Girl in Model (2) affect the estimated effect of Cigarettes on expected BirthWeight? That is, does the estimate of β1 differ between Models (1) and (2)? From this exercise, is it important to allow for the interaction between child’s birth order and sex in estimating the causal effect of tobacco consumption by the mother during pregnancy on expected child birthweight?  [3 marks]

(10)  Another health risk factor that may influence childbirthweight is consumption of alcohol dur- ing pregnancy.  If Alcohol has a negative impact on child birthweight, what is the effect of

omitting this explanatory variable from Model (1)? Explain your reasoning.  [3 marks]

(11)  Estimate the following expanded version of Model (1):

BirthWeight = β0 + β1 Cigarettes + β2Education

+ β3HealthCheck + β4Order + β5Girl + β6Alcohol + u   (3)

Test the null hypothesis that Alcohol has no effect on BirthWeight (against the one-sided alternative that it has a negative effect), other things equal, using a 10% significant level.  [2 marks]

(12)  Apply the Breusch-Pagan test for the presence of heteroskedasticity to Model (3) using a 1% significance level. Present the formal hypothesis test. Is there evidence against the assumption of homoskedastic variance? [3 marks]

(13)  Estimate Model (3) using Least Absolute Deviation (LAD). Does the estimated effect of Cigarettes on BirthWeight for the conditional median differ from the OLS estimate (i.e.   conditional    mean)? What do you conclude from these estimates? (Hint: look up the command bsqreg) [3    marks]