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ECMT6007/6702: Econometric Applications Applied Project Semester 1 2022
发布时间：2022-05-03
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ECMT6007/6702: Econometric Applications
Applied Project
Semester 1 2022
Instructions:
(i) Answer the following series of questions. Each question is worth 1 mark and there are 20 questions in total.
(ii) Remember that when performing statistical tests, always state the null and alternative hy- potheses, the test statistic and its distribution under the null hypothesis, the level of signifi- cance and the conclusion of the test.
(iii) Please attach a copy of your computer output (i.e. your STATA log file) to your answers. Marks will be deducted if this is not included.
(iv) Solutions to this Applied Project must be submitted via the Course Canvas Dropbox by the due date. Late submission incurs a 5% penalty per day late.
The applied empirical project involves the application of a range of econometric methods covered
in the course so far to analysing the wages of highly skilled IT professionals in Sydney. This sample is drawn from a survey of workers in the CBD conducted by the City of Sydney in 2002. The dataset it_wages .dta has 391 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 otherwsie
• 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 average, minimum, and maximum value for each of the variables in the sample?
(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 δ 1? Is it reasonable to interpret the estimate as a measure of wage discrimination against female IT workers? Explain your reasoning.
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.
(4) What is the R2 statistic for this model, and what does it represent? This is substantially higher than the R2 statistics we have seen for log (wage) models estimated with samples drawn from the general US labour market. Provide an explanation why the R2 so high for this sample.
(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.
(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?
(7) Research on the effects of education has focussed 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 Sydney IT workers?
(8) The City of Sydney 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.
(9) Based on the model estimates for specification (2), what is predicted log (wage) when educ = 14, exper = 25, exper2 = 625 and female = 1? Construct a confidence interval for pre- dicted log (wage) in order to reflect uncertainly about the impact of the various determinants of log (wage). To obtain the standard error for the prediction, transform the model in (2) so that a parameter corresponds to the prediction, and the standard error corresponds to the (within sample) prediction error. Show the derivation of the transformed model and state which pa- rameter of the transformed model corresponds to the predicted log (wage) when educ = 14, exper = 25, exper2 = 625 and female = 1.
(10) Estimate the transformed model in Question (9) and report the 99% confidence interval for the (within sample) prediction.
(11) The confidence interval in Question (10) corresponds to the within-sample or‘conditional’pre- diction for the subsample of IT workers with those characteristics. Now consider the pre- dicted log (wage) for a specific worker. Construct the 99% confidence interval for the predicted log (wage) for an IT worker with the characteristics educ = 14, exper = 25, exper2 = 625 and female = 1 (this is the ‘unconditional’confidence interval).
(12) The dependent variable in model (2) is in log-form, and the predictions in Questions (9)–(11) relate to log (wage). Now consider the predicted wage in levels (or $’s) based on model (2). What is a consistent prediction for wage when educ = 14, exper = 25, exper2 = 625 and female = 1, based on model (2), and assuming the error term u does not have a Normal distribution? Show your working.
(13) Apply the Breusch-Pagan test for the presence of heteroskedasticity, using a 1% significance level. What do you conclude?
(14) Re-estimate model (2) using Weighted Least Squares (WLS) to correct for heteroskedasticity. Present your results in the usual form.
(15) Summarise the main differences in the estimation results for WLS compared to the OLS results. Are there important differences in the inferences obtained from the two models?
(16) 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?
(17) 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 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?
(18) Use the Quantile regression model to estimate specification (2) for the quantiles (0.10, 0.25, 0.50, 0.75, 0.90). In a table report the coefficient estimate, and standard error, for β1 at each of the quantiles. Does the estimated effect educ on log (wage) vary substantially across conditional quantiles of the log (wage) distribution? What do you conclude from these estimates?
(19) 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 an IT 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 + β4 lnstartw + 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?
(20) Another outcome which is interesting to analyse is the growth in wages over an individual’s career. Define the new variable wagegr = log (wage) − lnstartw (note the difference in logs represents a growth rate). Run the following regression:
wagegr = β0 + β1 educ + β2 exper + β3 exper2 + δ1 female + u (6)
and report the results in the usual form. What do you notice from comparing the results to those for model (5) in Question (19)? Explain the reason for this pattern of results.
