Microsoft Word - EC655 Midterm.docx
EC655 – Econometrics
Department of Economics
Wilfrid Laurier University
Fall 2020
Midterm
Date and Time: Wednesday November 11, 9:00am – Friday, November 13, 9:00am
Structure:
• This is a take-home test over 48 hours
• You will answer 6 of the following 8 questions
• If you answer more than 6 questions, I will grade only the first 6.
• Each question has equal weight. The weight of subquestions are noted in the question
• It is open book and open internet
• You are prohibited from collaborating in any way with other people on the midterm.
This means no discussing the questions in person, by phone, using chat services,
question boards, email, etc.
• If you draw your answer from another source (e.g. the textbook, the internet), you must
eference it. The normal rules of plagiarism apply to this exam.
• Instructor help on the test will be limited to clarification questions only
Submission Instructions:
• Submit your midterm to Gradescope when complete. Note that you can submit as
many times as you wish before the due date.
• You are required to hand-write your responses to each question on paper (i.e. do not
use a word processor unless you have accommodations through ALC)
o I would suggest answering each sub-question on a separate piece of paper
• Sign your name below the response to each question
• Upload your hand-written responses to Gradescope in one of two ways:
a) Take a photo of your response to each question separately, and then upload
each image
) Scan your questions into a single PDF, then upload it and tag each question
Questions
1. (12 points) Suppose you obtain the following results from regressing y on an intercept, x,
and w: ?" = 2 + 3? + 4?, R2 = 0.8. What coefficient estimates and R2 would you get from
egressing y on an intercept and ?"?
2. (12 points) In the linear regression model, multicollinearity leads to bias, not in the
egression coefficients themselves, but in the estimation of their variances. True, False, or
Uncertain. Explain.
3. (12 points) A friend is regressing y on x and w. He notices that the graph of y against the
OLS residuals has a definite pattern – it looks like an upward sloping line. He comes to you
for advice about what this means and what he should do about it. What would you
suggest?
4. (12 points) In your last assignment you used TSLS to estimate a regression of ln(wage) on
educ, age, ma
ied, smsa. In this regression, you treated age, ma
ied, and smsa as included
exogenous variables, and you used excluded instruments nearc2 and nearc4 as excluded
instruments for educ. The results of this were as follows:
ivreg2 lwage age ma
ied smsa (educ = nearc2 nearc4), robust
IV (2SLS) estimation
--------------------
Estimates efficient for homoskedasticity only
Statistics robust to heteroskedasticity
XXXXXXXXXXNumber of obs = XXXXXXXXXX
XXXXXXXXXXF( 4, 2704) = XXXXXXXXXX
XXXXXXXXXXProb > F = XXXXXXXXXX
Total (centered) SS = XXXXXXXXXX XXXXXXXXXXCentered R2 = XXXXXXXXXX
Total (uncentered) SS = XXXXXXXXXX XXXXXXXXXXUncentered R2 = XXXXXXXXXX
Residual SS = XXXXXXXXXX XXXXXXXXXXRoot MSE = XXXXXXXXXX
------------------------------------------------------------------------------
| XXXXXXXXXXRobust
lwage | Coef. Std. E
. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
XXXXXXXXXXeduc | XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX
XXXXXXXXXXage | XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX
ma
ied | XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX
XXXXXXXXXXsmsa | XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX
_cons | XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX
------------------------------------------------------------------------------
Underidentification test (Kleibergen-Paap rk LM statistic): XXXXXXXXXX
XXXXXXXXXXChi-sq(2) P-val = XXXXXXXXXX
------------------------------------------------------------------------------
Weak identification test (Cragg-Donald Wald F statistic): XXXXXXXXXX981
XXXXXXXXXXKleibergen-Paap rk Wald F statistic): XXXXXXXXXX
Stock-Yogo weak ID test critical values: 10% maximal IV size XXXXXXXXXX
XXXXXXXXXX15% maximal IV size XXXXXXXXXX
XXXXXXXXXX20% maximal IV size XXXXXXXXXX
XXXXXXXXXX25% maximal IV size XXXXXXXXXX
Source: Stock-Yogo XXXXXXXXXXReproduced by permission.
NB: Critical values are for Cragg-Donald F statistic and i.i.d. e
ors.
------------------------------------------------------------------------------
Hansen J statistic (overidentification test of all instruments): XXXXXXXXXX
XXXXXXXXXXChi-sq(1) P-val = XXXXXXXXXX
------------------------------------------------------------------------------
Instrumented: XXXXXXXXXXeduc
Included instruments: age ma
ied smsa
Excluded instruments: nearc2 nearc4
------------------------------------------------------------------------------
Now consider the following alternative strategy: you run the same first stage regression, and
save the residuals (call them res). Then, regress lwage on educ, age, ma
ied, smsa, and res.
The results of this regression are below.
egress educ age ma
ied smsa nearc2 nearc4
predict res, resid
egress lwage educ age ma
ied smsa res
Source | SS XXXXXXXXXXdf MS Number of obs = 2,709
-------------+----------------- XXXXXXXXXXF(5, 2703) = XXXXXXXXXX
Model | XXXXXXXXXX XXXXXXXXXX5678 Prob > F = XXXXXXXXXX
Residual | XXXXXXXXXX, XXXXXXXXXXR-squared = XXXXXXXXXX
-------------+----------------- XXXXXXXXXXAdj R-squared = XXXXXXXXXX
Total | XXXXXXXXXX, XXXXXXXXXXRoot MSE = XXXXXXXXXX
------------------------------------------------------------------------------