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Instructions:
Basic Econometrics (ECOM30001/ECOM90001)
The University of Melbourne’s Department of Economics
Semester 1, 2021: ECOM30001/ECOM90001: Basic Econometrics
Introduction to Assignment 2
The (statistical) link between a worker’s level of education and the (hourly) wage they get is of interest to researchers and policymakers. Consider the econometric model below:
ln wagei = 0 + 1 educi + Xi + I (1), where X represents a comprehensive set of control variables that are important drivers of wages and I is a random error with N (0, 2 ).
While it is predicted that 1 > 0 means that more educated workers get higher salaries (subject to other wage determinants), you are more interested in the size of 1.
1
The assignment2.csv data file contains 2,086 observations on people who were between the ages of 24 and 34 at the time of the interview and can be used to estimate the econometric model (1). The variables in this data file are as follows:
lnwage=Hourly wage’s natural logarithm
educ=Years of schooling completed
Years on the job=Exper=Years on the job=Years on the job=Years on the
Years on the job expersq=Years on the job expersq=Years on the job expersq=Y If you dwell in a disadvantaged area, squared disadv=1; otherwise, it’s 0.
If you live in a major city, set city=1; otherwise, set city=0.
For these individuals 10 years prior to the interview, the data set includes the following variables:
If you resided in a big city 10 years ago, city10=1; else, city10=0.
region
If you resided in area j 10 years ago, you got a 1; otherwise, you got a 0, and j = 1, 2,… 9
The data file also includes the following information on the parents’ education:
Mother’s years of education are over. motheduc=years Mother’s of education are over.
both nohs=1 fatheduc=Completed years of schooling of father 0 if neither parent graduated from high school; otherwise,
To accomplish this assignment, you will need to use the following packages:
stargazer: a tool for quickly obtaining regression results.
AER : for estimating linear models using the Instrumental Variable (IV) estimator in R car : for conveniently running hypothesis tests in R sandwich : for calculating robust standard errors in R AER : for estimating linear models using the Instrumental Variable (IV) estimator in R
These can be installed straight from the packages tab in RStudio or by using the command install.packages() with the package name in brackets.
Note: You must use the R statistical software to complete this assignment.
Please provide a copy of your R script file along with your assignment for an extra five (5) points.
Please send your whole R script file as an Appendix to the conclusion of your assignment. You simply need to submit a single file that contains both your assignment answers and your R script file for your assignment. In Canvas, do not submit your R script as a separate file.
2 a) 10 points] Consider the econometric model below:
ln wagei = 0 + 1 educi + 2 experi + 3 expersq100i + 4 disadvi + 5 cityi + 6 city10i + X 9 j=2 7j region10 j I + I (2)
It’s worth noting that: expersq100i = expersqi 100 = exper2 I 100 I [2 points] In model (2), what is the meaning of population parameter 1? ii) [2 marks] In model (2), what is the meaning of the population parameter 4?
iii) [6 points] Estimate the econometric model (2) with resilient (Huber-White) standard errors using the Ordinary Least Squares (OLS) method. Test the hypothesis that all variables related to the individual’s geographic location 10 years ago are key drivers of salaries using the automobile package and a 5% threshold of significance. The null and alternative hypotheses, the distribution of the test statistic, and your conclusion should all be stated clearly in your response.
b) [6 points] Consider an expanded version of model (2) that adds the two (2) parental education variables (motheduc and fatheduc).
ln wagei = 0 + 1 educi + 2 experi + 3 expersq100i + 4 disadvi + 5 cityi + 6 city10i + X 9 j=2 7j region10 j I + 8 motheduci + 9 fatheduci + I (3)
Estimate the econometric model (3) with resilient (Huber-White) standard errors using the Ordinary Least Squares (OLS) method. Test the hypothesis that the parental education factors are mutually important drivers of earnings using the vehicle package and a 5% threshold of significance. The null and alternative hypotheses, the distribution of the test statistic, and your conclusion should all be stated clearly in your response. It’s worth noting that model (2) is a restricted model.
3 c) [4 points] Take a look at the econometric model (3). Do you believe that the condition COV(educi, I |Xi) = 0 is likely to be met? Describe at least one probable explanation why this criterion may not be met. Explain the ramifications for the OLS estimator if this criterion is not met.
d) [6 points] The sample is drawn from a huge country with a significant number of universities spread out across the country. Take the following indicator variable into consideration:
1 if nearuniv = 1 if nearuniv = 1 if nearuniv = 1 if nearuniv 0 if the individual lives in a neighborhood with a university nearby at the age of 14, otherwise
It has been proposed that proximity to a university influences educational choices. Individuals who grew up in a community without a university suffer a greater educational expense. In the face of these increased expenditures, these persons should, all else being equal, obtain less education. Explain the two conditions that must be met for nearuniv to be considered a legitimate instrumental variable. Do you believe these two requirements are likely to be met? Explain why you think that is or why you don’t think that is.
e) [9 points] Explain what the Weak Instruments problem is all about. Explain the implications of employing the Instrumental Variable estimator (IV) with weak instruments for statistical inference.
Using the robust (Huber-White) variance estimator, calculate the following reduced form for educ:
educi = 0 + 1 nearunivi + 2 experi + 3 expersq100i + 4 disadvi + 5 cityi + 6 city10i + X 9 j=2 7j region10 j I + 8 motheduci + 9 fatheduci + I (4)
Is there any evidence that nearuniv is a weak instrument based on your estimation results for this reduced form? Explain why you think that is or why you don’t think that is.
f) [6 points] The reason for adopting nearuniv as an educational tool is that being close to a university reduces the expense of acquiring a university education.
This means that being close to a university should have a stronger impact on educational achievements for those who can afford a university-level 4 education. Individuals from lower-income households could be one such category in the face of liquidity limitations. Consider the following variable as a proxy for a household with a low income:
1 if both nohs are equal. If neither parent graduated from high school, motheduc 12 & fatheduc 12 0; else
Using the robust (Huber-White) variance estimator, calculate the following reduced form for educ:
educi = 0 + 1 nearunivi + 2 both nohsi + 3 nearunivi both nohsi + 4 experi + 5 expersq100i + 6 disadvi + 7 cityi + 8 city10i + X 9 j=2 9j region10 j I + 10 motheduci + 11 fatheduci + I (5)
At the 5% level of significance, test the hypothesis that being close to a university when you’re 14 enhances educational attainment more for those who grew up in low-income families than for people who didn’t. The null and alternative hypotheses, the distribution of the test statistic, and your decision should all be stated clearly in your response.
5 g) [26 points] Consider the following example of a structural econometric model:
ln wagei = 0 + 1 educi + 2 experi + 3 expersq100i + 4 disadvi + 5 cityi + 6 city10i + X 9 j=2 j=2 j=2 j=2 j=2 j=2 j=2 j=2 j=2 j=2 j=2 j=2 j=2 j=2 j=2 j=2 j=2
region1 (Region 1) is the deleted category in 7j region10 j I + 8 motheduci + 9 fatheduci + I (6).
I [1 point] Estimate this structural model using the IV estimator with robust (Huber-White) standard errors, using educ as the only endogenous variable and nearuniv as an instrumental variable, using the IV estimator with robust (Huber-White) standard errors. Make a report on your findings.
ii) [6 points] Test the hypothesis that schooling has a favorable influence on labor market earnings at the 5% level of significance. The null and alternative hypotheses, the distribution of the test statistic, and your decision should all be stated clearly in your response.
iii) [6 points] Test the hypothesis that all of the parental education variables are mutually major drivers of earnings using the vehicle package and a 5% threshold of significance. The null and alternative hypotheses, the distribution of the test statistic, and your conclusion should all be stated clearly in your response.
iv) [2 points] Compare and contrast your estimate for 1 and its standard error in model (6) to that derived in part (b) using the OLS estimator for model (3).
v) [4 points] The OLS estimator in model (3) will not be consistent if COV(educi, I |Xi) 6= 0. Furthermore, assuming nearuniv is a valid instrument, the IV estimator for 1 in model (6) will yield a consistent estimate of the causal influence of schooling on labor market earnings. Taking a look at your estimations for 1 Provide and explain a possible source of COV(educi, I |Xi) 6= 0 in model using the IV estimator and those derived using the OLS estimator (part b) (3).
vi) [7 points] Calculate the marginal (partial) effect of years of labor market experience using your model (6) estimates, based on the sample median of years of labor market experience. Test the null hypothesis that, at the sample median level of labor market experience, an extra year of labor market experience improves average salaries by at least 4%, all else being equal, at a 5% level of significance.
Assume you want to find the sample median for the variable exper in the assign2.csv data file.
6 assign2$exper median exper = median(assign2$exper)
RUBRIC |
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Excellent Quality 95-100%
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Introduction
45-41 points The background and significance of the problem and a clear statement of the research purpose is provided. The search history is mentioned. |
Literature Support 91-84 points The background and significance of the problem and a clear statement of the research purpose is provided. The search history is mentioned. |
Methodology 58-53 points Content is well-organized with headings for each slide and bulleted lists to group related material as needed. Use of font, color, graphics, effects, etc. to enhance readability and presentation content is excellent. Length requirements of 10 slides/pages or less is met. |
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Average Score 50-85% |
40-38 points More depth/detail for the background and significance is needed, or the research detail is not clear. No search history information is provided. |
83-76 points Review of relevant theoretical literature is evident, but there is little integration of studies into concepts related to problem. Review is partially focused and organized. Supporting and opposing research are included. Summary of information presented is included. Conclusion may not contain a biblical integration. |
52-49 points Content is somewhat organized, but no structure is apparent. The use of font, color, graphics, effects, etc. is occasionally detracting to the presentation content. Length requirements may not be met. |
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Poor Quality 0-45% |
37-1 points The background and/or significance are missing. No search history information is provided. |
75-1 points Review of relevant theoretical literature is evident, but there is no integration of studies into concepts related to problem. Review is partially focused and organized. Supporting and opposing research are not included in the summary of information presented. Conclusion does not contain a biblical integration. |
48-1 points There is no clear or logical organizational structure. No logical sequence is apparent. The use of font, color, graphics, effects etc. is often detracting to the presentation content. Length requirements may not be met |
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Basic Econometrics assignment for ECOM30001