ECOM30002/90002 Econometrics Semester 1, 2018
Assignment 1
Instructions
• Weight: 7.5%
• Due: 4pm Monday 26 March, submit on the LMS, instructions to follow.
• Group size: minimum = 1, maximum = 4
Groups may be formed across different tutorials.
Before submission each group must register in the Group Registration item soon to be
available on the LMS.
• Each assignment must include a completed Cover Page listing every member of the group
with student ID and tutors’ names. Also indicate the ID number of the student who collected
the data.
• Equal marks will be awarded to each member of a group.
• Your assignment should be submitted as a fully typed document (pdf or Word). Question
numbers should be clearly indicated.
• Regression output must be presented in clearly labelled equation or table form. Raw R
output is not sufficient.
• Concise correct answers to questions requiring interpretation/discussion will be valued over
more lengthy unclear and/or off-topic attempts.
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ECOM30002/90002 Econometrics Semester 1, 2018
This assignment is about the relationship between individual wages and education levels. One
student in each group is responsible for obtaining data. The Excel data spreadsheet corresponding
to the ID number for that student can be obtained from here:
http://bit.ly/ECOM30002Assignment1Data2018s1.
Each spreadsheet contains a different subset of the data used in the famous paper by Angrist
and Krueger (1991). Each spreadsheet contains data on 15; 107 working men born in 1940 and
surveyed in 1980. The two variables in the spreadsheet are as follows.
LogWagei log wage in 1980 (from wages in dollars per week)
Educi years of education completed by 1980 (excluding kindergarten)
1. Descriptive statistics.
(a) Obtain summary statistics and a histogram for Wagei and briefly describe the main
features.
(b) Construct a frequency distribution for years of education and display this in a bar chart.
Briefly describe the main features.
(c) Construct a scatter plot of wages (y-axis) against education (x-axis) and briefly describe
the main features.
2. Estimate the regression
| E(WageijEduci) = β0 + β1Educi; report the estimates, and give a statistical interpretation of each coefficient. |
(PRF1) |
3. Wage regressions nearly always specify the wage variable in log form. (Hence in this case
the dataset from Angrist’s website coming with wages only in logs.)
(a) Estimate the regression
| E(log WageijEduci) = α0 + α1Educi: and report your estimates. |
(PRF2) |
(b) The usual interpretation of a regression with a logged dependent variable is that a 1
unit increase in the explanatory variable results in a α1 × 100% change in the mean of
the dependent variable:
E(WageijEduci = x + 1) – E(WageijEduci = x)
E(WageijEduci = x) × 100% ≈ α1 × 100%; (1)
i.e. the percentage change in the mean wage resulting from an extra one year of education (increasing education from x to x + 1 for any x).
Define Vi = log Wagei – E(log WageijEduci) and assume that
E(exp(Vi)jEduci) = κ0: (2)
Derive equation (1), showing your working and being clear about the nature of the
approximation (i.e. the “≈” in equation (1)).
(Refer to Tutorial 3, question 6 for how to approach this. Also if necessary see characterisation 2 here and consider small values of x in that notation for a hint for the
required approximation.)
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ECOM30002/90002 Econometrics Semester 1, 2018
(c) Instead of assumption (2), assume that
E(exp(Vi)jEduci) = κ0 + κ1Educi: (3)
Derive the resulting expression to replace (1) for the effect of an extra year of education
on mean wages.
(d) Implement your alternative expression in (c) to estimate the effect of an extra year
of education for an individual who already has 15 years of education. Compare your
estimate to the one implied by (1).
4. For each one of the observed levels of education in your sample, calculate
(a) the sample mean of wages for all individuals with that level of education,
(b) the estimated mean of wages from your estimate of (PRF1)
(c) the estimated mean of wages from your estimate of (PRF2), assuming (3) applies.
Tabulate these estimates, and come up with an appropriate graph to visualise them. Summarise the evidence you have on the statistical relationship between education and average
wages. Also briefly discuss any evidence about the appropriateness of the functional forms
of (PRF1) and (PRF2).
5. Now consider the causal implications of your estimates. To do this requires thinking about
the nature of education and how that ultimately helps to determine individual wages. Since
this a topic that has kept many many labour and education researchers busy for many many
years, it is not required (nor possible!) to be an expert in this issue. To answer the following
questions it may be helpful for to you consult the following sources.
• Chapter 4 of the QME text.
• This recent EconTalk podcast goes into all the relevant issues for this question.
• For those who want (lots!) more detail, see this survey article by David Card.
(a) Do you think your statistical results provide good estimates of the magnitude of the
causal effects of education on wages? Are the sample mean estimates in question 4(a)
more or less useful than the regression estimates to uncover the true causal effects of
education? Explain.
Your explanation should take into account the “ability bias” that has been widely discussed in wage equations, and also relate back to the lecture discussions of concepts
that can affect causal interpretations of regressions. A good explanation will require
explicitly writing out and relating the relevant causal and regression equations.
(b) Two theories for how education causally raises wages are very briefly outlined as follows.
i. Human capital. Education develops knowledge and skills (i.e. human capital)
that can be applied productively in the workplace, and this higher productivity is
rewarded with higher wages.
ii. Signalling. Completing education provides a signal to an employer about potential employee attributes such as intelligence, conscientousness and preparedness to
conform to group/social norms that could be valuable in the workplace, even if the
education itself has not been in a relevant area.
Do your statistical results suggest anything about these two possible causal mechanisms? Explain.
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