Questions on homework assignment 2:
Q1: In the table of question 1, the unit of the variable pershh, which is described in the text
as the number of persons in the households, is stated as "years". Why that?
A1: You are right, the unit is supposed to be "persons". Fortunately, this has no impact on
the solution of the related questions.
Q2: The last sentence of question 1, part g) reads " Manipulate this equation to show that the
proportional change in price attributable to a pool is …". Now there is no pool
mentioned anywhere in the question and it does not relate to the subsequent formula.
A2: Right again. The correct text is supposed to be " Manipulate this equation to show that
the proportional change in household expenses attributable to employees is …". Sorry
about this confusion.
Q3: In question 3, a variable with the name "finc" occurs in the text of the sub-questions, but
there is no variable with that name in the datafile hhexpBF.dta.
A3: Yes, right and sorry again. The variable name in hhexpBF.dta is "hhexp" instead of
"finc". I will mention Q1-Q3 in the class during the course hours on Wednesday and
Thursday. A respectively corrected version of the assignment is already available from
the course homepage.
Q4: In question 1, part i) you ask something about the household expenses of an "averagesized household". Therefore we would need the size of an average household.
A4: Correct. So please read the whole text of the whole question fully and carefully.
Questions on course contents:
Q5: The Goldfeld-Quandt Test for heteroskedasticity proposes (1) to split the sample into
two approximately equal subsamples, (2) to compute the estimated error variances (σ²1
and σ²2) for each one of them and (3) to calculate the test-statistic (GD-statistic) by
dividing the both error variances. Question: how do I determine which σ²goes to the
numerator and which to the denominator?
A5: The larger σ² goes to the numerator (you split the sample in two groups based on your
suspicion that there is an area, where the error variance is significantly larger).
Q6: I understand that we calculate the GLSs in the case of proportional heteroskedasticity by
transforming the dependent and independent variables via their division by the
squareroot of the variable related to the error. But how do we calculate the GLSs in a
sample with heteroskedastic partition?
A6: In the case of heteroskedastic partition we have to divide the observed values of y and
the x-es by the σ² that we calculate for theirher partition. So all values of y and x that we
observed from units, which fall in the partition with σ²= σ²1 will have to be divided by
σ²1, the values in the partition that yield σ²2 will have to be divided by σ²2. The result is
a constant variance of the error term over the whole sample (and this is what we are
looking for).
Q7: I still didn't get the idea on how to reject or accept a hypothesis based on the p-value.
A7: The p-value designates the percentage of the area under the reference distribution (tdistribution, F-distribution etc., always corresponding to the test that you apply) in
which your test statistics (= the respectively calculated test-value of your observed value
or empirical distribution) would be located, if it would be part of your reference statistic.
So if you accept a probability of error of, say, 5%, then any p-value <0,05 leads to the
rejection of your H0. If your accepted probability of error is only 1%, then any p-value
<0,01 leads to the rejection of your H0 .
Questions on exam:
Q8: I read the exam questions of the last years and there where questions on mathematical
proofs? Do we have to calculate with such types of questions also this year?
A8: Everything which was discussed during the course might be subject to questions in the
exam. Now we postponed the discussion of the mathematical proofs for unbiasedness,
precision and formulae on variances up to now and will probably discuss them only in
the 4 hours on the afternoon after the exam. In this case they cannot be the subject of the
exam questions. But who knows, probably we will find the time before ….