ECMT2150: Intermediate Econometrics
Intermediate Econometrics
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ECMT2150: Intermediate Econometrics
Assignment
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.
1
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 theQueens-
land Health department for the year 2005. 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 followingmodel which includesmother’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:
BirthWeigth = β0 + β1Cigarettes+ 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) EstimateModel (1) by OLS and report the results in the ‘standard form’ (i.e. coefficient estimates
and standard errors). [2 marks]
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(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 + β1Cigarettes+ 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 ofCigarettes on expectedBirthWeight? 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 child birthweight 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 + β1Cigarettes+ 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 modified White 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) EstimateModel (3) using Least AbsoluteDeviation (LAD). Does the estimated effect ofCigarettes
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]
3
(14) An alternative modelling approach is to consider whetherCigarettes affects the likelihood of a
low-birthweight birth (defined as birthweight of less than 2500 grams). Estimate the following
Linear Probability Model (LPM) using OLS with heteroskedastic-robust standard errors and
present the results in the usual form: [2 marks]
Pr (LowBirthWeight = 1) = β0 + β1Cigarettes+ β2Education
+ β3HealthCheck + β4Order + β5Girl + β6Alcohol + u (4)
(15) What are the limitations in using regression methods for analysing a binary dependent variable
such as LowBirthWeight as in Model (4)? Are these problems important in this particular
application? Explain your reasoning. [2 marks]
(16) What, if any, are the advantages of using theWLS estimator instead of theOLSwith heteroskedastic-
robust standard errors? Briefly explain your answer. [2 marks]
(17) Re-estimate Model (4) using WLS and present the results in the standard form. Do the co-
efficients estimates or standard errors differ depending on the whether the OLS (with robust
standard errors) or the WLS estimator is used? Explain your answer. [4 marks]
(18) What is the interpretation of the coefficient β1 in Model (4)? [2 marks]
(19) Based on the WLS estimator for Model (4), is β1 statistically significant against the one-sided
alternative it is positive, at the 1% level? Is the estimated effect economically large? Explain
your reasoning. [3 marks]
(20) Based on the estimation results for Models (1)–(4), what do you conclude regarding the causal
effect of a mother’s smoking during pregnancy on the health of her child at birth? Carefully
explain the reasons for your conclusion. [4 marks]