Unformatted text preview: )i) Why run regression with PWE if AWE not available? Proxy Variable:
In (1) we run into Omitted Variable Bias problem.
We can’t run (3) as AWE not available.
Potential solution: Use PWE as proxy to avoid OVB. Past Exam Practice Question Introduction Omitting Relevant Variable Including Irrelevant Variables Past Exam Practice Question 2005 Question 2 2)b)i) Why run regression with PWE if AWE not available? Suppose AWE = λ + µPWE → perfect proxy.
Get alternative true speciﬁcation:
LGEARN = β1 + β2 S + β3 AWE + u (15) = β1 + β2 S + β3 (λ + µPWE ) + u (16) = (β1 + β3 λ) + β2 S + β3 µPWE + u (17) Fit alternative regression:
Estimate of β2 same as if AWE used.
s.e.’s and tstatistics of S same.
tstatistic PWE same as for AWE.
R 2 same.
If know the value of µ, then retrieve estimate of β3 also with PWE. Introduction Omitting Relevant Variable Including Irrelevant Variables Past Exam Practice Question 2005 Question 2 2)b)ii) Did using proxy actually help? Logic for using proxy assumes perfect linear relation PWE to AWE.
In practice this generally holds at most approximatively.
However with imperfect proxy (chapter 8), we get into problem of
measurement error and inconsistent estimator.
Whether to use proxy or not is a judgement call sometimes.
Remember: correlation PWE to AWE here only 0.47
→ clearly imperfect proxy Introduction Omitting Relevant Variable Including Irrelevant Variables Past Exam Practice Question 2005 Question 2 2)b)ii) Did using proxy actually help? S coefﬁcient estimate: increases using PWE as proxy, but not all the
way to what is estimated in (3)
Proxy seems to eliminate SOME of the bias S coefﬁcient s.e.: increases using PWE as proxy both compared to (1)
and (3) [N.B. in (1) s.e. are wrong! Why?]
PWE coefﬁcient: clearly not a good estimate of impact of AWE on
earnings
Constant estimate: falls using PWE as proxy, but not all the way to what
is estimated in (3)
R2 : negligible improvement (remember if perfect proxy should be same in
(2) and (3)) Introduction Omitting Relevant Variable Including Irrelevant Variables Past Exam Practice Question 2005 Question 2 2)c) Why s.e. for S coefﬁcient larger in (2) than (3) Correlation S to PWE much larger than S to AWE (absolute terms)
So regression (2) has more trouble disentangling effect of S
Use of better variable should lead to sharper estimate Introduction Omitting Relevant Variable Including Irrelevant Variables Past Exam Practice Question 2005 Question 2 2)d) Link tstatistics and size of RSS change Remember: Ftest for signiﬁcance of coefﬁcient estimate βi
Restriction is to set repective coefﬁcient βi = 0
−RSS
FStatistic: F = (RSSR U /(n−U )/1
RSS
k)
(N.B. This is Fstat for 1 coefﬁcient’s signiﬁcance check!) Intuition: reject restriction if RSSR much larger than RSSU suggesting
that the restriction in fact does not hold.
Improvement in ﬁt from imposing restriction and Ftest intrinsically
related: is the improvement in ﬁt statistically signiﬁcant?
→ RSS reduc...
View
Full Document
 Spring '13
 ChristopherDougherty
 Econometrics, Regression Analysis, β2 Xi, Exam Practice Question, Past Exam Practice

Click to edit the document details