Etf2100: Introductory Econometrics - Assessment Answer

ETF2100 Econometrics Assessment Task

(a) Estimate the following regression model by least squares. Provide Eviews output. No need to report the result in full in equation form. bweighti = β1 + β2smoke2i + β3smoke3i + β4smoke4i + β5magei + β6mmariedi + ei (1)
(b) Interpret the estimated coefficients of smoke2, smoke3 and smoke4
(c) Does smoking 1-5 cigarettes per day have a statistically significant negative effect on baby birthweight (keeping all other factors the same)? Write out the test in full using the t-statistic approach and 5% significant level. Hint: this is a one-tailed test.
(d) 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?
(e) Now consider a similar model but with log of birthweight as dependent variable. Estimate this model and provide Eviews output. No need to report the
result in full in equation form. ln(bweight)i = β1+β2smoke2i+β3smoke3i+β4smoke4i+β5magei+β6mmariedi+ei (2)
(f) Using the results from part (e), interpret the coefficient of smoke3 using both the “rough” calculation and the “exact” calculation. Report your answers to 2 decimal place.

(g) Based on the model in part (e), test at 5% significance level the null hypothesis that smoking 11 or more cigarettes per day reduces birthweight by no more than smoking 6-10 cigarettes per day, against the hypothesis that smoking 11 or more cigarettes per day reduces birthweight by more than smoking 6-10 cigarettes per day. Use a t-statistic approach and write down all the steps used to conduct your test. You can use Eviews to calculate the test statistics.

Question 2
This question concerns a model investigating whether having more children drives parents to consume more alcohol.

ln(ALC)i = β1 + β2INCOMEi + β3NKi + ei (3)
ALC is percent of income spent on alcohol, INCOME is household income (in 10,000 dollars), and NK is number of children. The model is estimated using a data from a survey of 1,278 households.
(a) Describe in mathematics and/or in words what is meant by BLUE (best linear unbiased estimator)? Make sure to explain what is meant by each of the relevant
properties.
(b) What assumptions are needed to prove the least square estimators is BLUE?
(c) We suspect that the error variance might be larger for households with more children. We save the least squares residuals from estimating model (3), calling them EHAT. We then run the auxiliary regression and get the results EHAT \ 2 = 0.015 + 0.023INCOME−0.043NK+0.354INCOME2+0.053NK2+0.023(INCOME×NK) with an R2 = 0.0301. Is there evidence of heteroskedasticity? Set up the hypothesis test and carry out the test at 1% significance level. Write out all steps of the test. (d) Based on your conclusion in part(c), can we claim that the least squares estimators for model (3) is BLUE? Does your conclusion in part (c) have a consequence on the unbiasedness property of least squares estimators? If so, explain.
(e) Suppose the error term is heteroskedastic since the variance of the error ei depends on the independent variable NK in the following way:

Var(ei) = σ 2 × 1 NKi

(4) How would you obtain estimators for β1, β2, β3, and β4 that are BLUE?

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