ECMT2150: Intermediate Econometrics
Applied Project
Semester 2 2022
Instructions:
(i) The Applied Project is worth 30 marks in total. Marks allocated for each question are indi-
cated.
(ii) 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.
(iii) Solutions to this Applied Project must be submitted via the Course Canvas Assignment Drop-
box by the due date. Late submission incurs a 5% penalty per day late.
(iv) Please attached a copy of your computer output (i.e. your STATA log file) as an appendix to
your answers. Marks will be deducted if this is not included.
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Questions
The applied empirical project involves the application of a range of econometric methods covered
in the course to analysing the wages of highly skilled public sector (PS) employees in Canberra.
This sample is drawn from a survey of workers in the CBD conducted by the ACT government in
2002.
The dataset can_gov_wages.dta has 386 observations and 11 variables:
• educ = years of completed education
• exper = years of labour market experience
• highsch = 1 if high school graduate, 0 otherwise
• university = 1 if university graduate, 0 otherwise
• postgrad = 1 if undertaken post-graduate studies, 0 otherwise
• tafe = 1 if attended TAFE, 0 otherwise
• basiced = 1 if did not complete high school, 0 otherwise
• educn = a noisy measure of educ
• wage = weekly wage ($)
• female = 1 if female, 0 otherwise
• startwage = starting weekly wage ($)
(1) What is the mean, standard deviation, minimum, and maximum value for each of the variables
in the dataset? [2 marks]
(2) Estimate the simple regression model:
log (wage) = β0 + δ1 female+ u (1)
and report the results in the usual form. What is the interpretation of the coefficient δ1? Is
it reasonable to interpret the estimate as a measure of wage discrimination against female PS
workers? Explain your reasoning. [2 marks]
(3) Estimate the following model, which includes additional controls for human capital:
log (wage) = β0 + β1 educ+ β2 exper + β3 exper2 + δ1 female+ u (2)
and report the results in the usual form. What is the interpretation of the coefficient β1 in the
model? Is the estimated effect practically significant? Explain your reasoning. [2 marks]
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(4) What is the R2 statistic for this model, and what does it represent? This is substantially higher
than theR2 statistics we have seen previously in lectures for log (wage)models estimated with
samples drawn from the general labour market. Provide a possible explanation why the R2 is
relatively high for this sample. [2 marks]
(5) How has the magnitude of the estimate of δ1 changed due to the inclusion of the extra explana-
tory variables in the model? Explain the reason for this change. [2 marks]
(6) What is the estimated effect of an additional year of experience on the expected log (wage)?
At what value of exper is the expected log (wage)maximised (other things equal)? How many
observations in the sample have exper exceeding this level? [3 marks]
(7) Research on the effects of education has focused on possible ‘sheep-skin’ effects – which are
higher wages associated with the completion of a qualification over and above the return for
numbers of years required to gain the qualification. These effects are essentially a nonlinear
return for the actual completion of a credential or qualification (‘sheep-skin’ being the origi-
nal parchment on which qualifications were recorded). To test for such effects, estimate the
following model:
log (wage) = β0 + β1 educ+ β2 exper + β3 exper2 + δ1 female
+ δ2 highsch+ δ3 university + δ4 postgrad+ δ5 tafe+ u (3)
and test the hypothesis that highsch, university, postgrad and tafe are jointly insignificant,
using a 1% significance level. (Set out the full hypothesis test). Is there evidence of significant
sheep-skin effects for Canberra PS workers? [3 marks]
(8) TheACT government survey included an additional measure of educational attainment – educn
– which is similar to educ except it is based on a less precise survey question and contains noise
(random measure error) in the responses. Estimate the model:
log (wage) = β0 + β1 educn+ β2 exper + β3 exper2 + δ1 female+ u (4)
using this imprecise measure of educational attainment. What is the estimate for β1 and explain
why this differs from that in model (2) based on the more accurate measure of education. [2
marks]
(9) Apply the modified White test for the presence of heteroskedasticity to model (2) using a 1%
significance level. What do you conclude?
(10) Apply the RESET Test to model (2) using a 1% significance level. Present the formal hypothesis
test. Is there evidence of neglected nonlinearities in the model specification? [2 marks]
(11) The specification in model (2) allows for a simple intercept difference for men and women. It is
possible that the intercept and slope coefficients differ for men and women. Perform the CHOW
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Test for the null hypothesis that all the coefficients are the same for men and women using a
1% significance level. What do you conclude? [4 marks]
(12) The model specifications we have been estimating could be subject to omitted variable bias due
to unobserved ability. One way to address this problem is to add a proxy for ability to the
model. The sample contains information on the individual’s starting wage startwage, which is
the wage in their very first job as a PS worker. Explain why lnstartw = log (startwage) may
be a useful proxy for ability, and estimate the model:
log (wage) = β0 + β1 educ+ β2 exper + β3 exper2 + δ1 female+ β4lnstartw + u (5)
What is the estimate β1 in this model? Assuming lnstartw is a valid proxy for ability, what does
this new estimate for β1 imply about the relationship between unobserved ability and educ? [4
marks]
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