Download Instrumental Variables

Instrumental Variables
Saralyn J Miller
EDU 7314
Overview of Presentation
• Understanding IV
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History
Defined
Assumptions
Endogeneity
Exogenous Variable - Instrument
Angrist example paralleled with an education example
• Statistical Understanding of IV
– Present 2 equations
• Card Example
– Overview of article
– Replicate his study in R
• In-class Example
• Other Examples of IV in Education
History of IV
• Historically IV has mostly been used by economists and
statisticians (Angrist & Kreuger, 2001).
• Philip G. Wright (econometrician) vs. Sewell Wright
(biologist) (Wright, 1928).
– Philip had written about the problem of endogenous variation in
previous papers.
– Sewell had discovered the use of an instrument, but the
variables were already exogenous, so the analysis was
unnecessary.
– Stylometric analysis of their writing (Stock & Trebbi, 2003
• Authors found Philip to be the writer and founder of IV
• 1940’s IV was rediscovered
• 1953 Theil introduced the two stage least squares method
for computing IV
Instrumental Variables Defined
• Causality is difficult to prove, even in
experimental research.
• In education, randomization is what is used to
determine causality.
• However, we can’t always randomize or
create a true experiment.
• The IV method is a quasi-experimental
research method used to estimate causal
relationships.
Regression Assumption
• One of the assumptions of the error term in a regression analysis is that
the error must be independent and identically distributed.
– Error variance is the same for all values.
– Error is not related to other error values.
– Error is normally distributed.
• Use IV when the independent variable is correlated with unobservable
error.
• 3 reasons why this assumption might be violated:
– Omitted variable bias: When an unobservable variable is capturing some of
the dependent variable and this unobservable variable is not in your model.
Instead, the variables you have included are picking up some of the
unobserved and the unobserved needs to be accounted for on it’s own. In
other words, there are other variables that can explain the outcome measure
and your variable is picking up some of this explanation (omitted variable
bias).
– Measurement error – causation is not determined due to error in the
collection of the data
– Reverse Causality – direction of causality is not determined.
http://www.unescap.org/tid/artnet/mtg/gravity_d4s1_shepherd.pdf
Endogeneity
• When an independent variable correlates with
unobservable error we call this endogeneity.
– Endogenous variables: variables that are correlated
with error term. You can’t say that the independent
variables cause the dependent variable.
– Often the factors that affect an outcome depend on
that outcome (reverse causality).
– Example
• The more shots Kobe Bryant takes, the lower the percentage
of wins for the Lakers. Does an increase in shots that Kobe
takes cause the Lakers to lose? Or does the loss of the game
and the fact that teammates are not making shots cause
Kobe to take more shots? (http://drbseconomicblog.blogspot.com/2009/01/kobe-andreverse-causality.html )
Endogeneity
• Sometimes in a linear model some of the variables are
endogenous, meaning the regressors or variables are
correlated with the error term.
– Ex: Effect of military service on future earnings (Angrist,
1990).
• Military service is endogenous.
– Does the military cause a soldier’s future earnings to be a certain amount
when he or she leaves the service? Or are there certain characteristics of
those that join the military that influence future earnings?
» An individual’s choice to enter the service might be indicative of the
individual’s expected future earnings. There are some individuals
that choose to go into the military because their expected future
earnings are low. Therefore, their enrollment is related to the fact
that those that join the service might on average have lower future
earnings.
» Also, veterans have certain observed and unobserved characteristics
that affect their decision to enroll and these could be related to
earnings.
http://financialaccess.org/node/2042
What do we do when you have an
endogenous variable?
• An exogenous variable or instrument can “fix”
endogeneity.
– These variables are correlated with the regressors, but
are uncorrelated with the error term.
– We call these exogenous variables instruments.
– Ex: Since determining earnings is dependent on other
things such as expected earnings, Angrist (1990) used
the Vietnam draft as an instrument. It is correlated
with entering the service, but is not correlated with
earnings. The draft system is exogenous.
Qualities of an Instrument –
Exogenous Variable
• It must be correlated with the independent
variable.
• It must be uncorrelated with the error of the
dependent variable.
• Assumption of IV: Instrument must be
exogenous.
Example
• Joshua Angrist’s 1990 work.
• He analyzed the difference in earnings between
veterans and non-veterans.
• But analyzing this difference does not tell us the
causal impact of military service on future earnings.
• In education – we “fix” this problem by randomly
placing students into treatment and control
conditions.
• We can’t always randomize. What if we gave students a
choice on whether they wanted to attend tutoring sessions
(Reardon, 2010) because we could not randomly assign
students to a condition?
Example Continued
• A young person’s decision to enter the military could be
affected by his/her expectations of future earnings. This is an
endogeneity problem: does military service affect future
earnings or does the prospect of future earnings affect the
decision to enter the military?
• Veterans have observed and unobserved characteristics that
affect their reason for entering the military. We cannot control
for the unobserved characteristics.
• Tutoring session example (Reardon, 2010): A student’s
decision to attend tutoring could be affected by his/her
expectations of how it will affect academic achievement. Does
tutoring affect achievement or does the prospect of future
grades affect the decision to go to tutoring?
What did Angrist do?
• He used the Vietnam draft lottery as an
instrument (exogenous variable).
– The draft lottery is correlated with serving in the
military.
– The draft lottery is only correlated with future
earnings of military personnel through enrollment in
the military.
• Tutoring session could use a lottery system too.
– The lottery would be correlated with those that go to
tutoring.
– The lottery would be correlated with future grades
only through attendance to the tutoring program.
Problem
• What about those who were drafted and
avoided the draft?
• Or those who were not drafted, but felt
compelled to fight anyway?
• What about the students who were picked for
the lottery, but chose not to go because they
didn’t think it would help?
• Or those that were not picked, but really felt
like they needed the help?
Answer
• The IV method recognizes that those described previously
cannot be included in the sample. It is not an average
treatment effect for the whole sample, but is a local
average treatment effect (LATE)
• Military earnings example only tells you the treatment
effect on those who pulled a “bad” number and served and
those who pulled a “good” number and did not serve.
• Tutoring example: only tells you the treatment effect on
those who were picked for tutoring and attended and those
who were not picked for tutoring and did not attend.
• Therefore we are only measuring a treatment effect for
compliers, which makes this method less generalizable.
IV Limitations & Advantages
• Limitations
– LATE
– Estimates can be biased when not a binary choice, but
an ordered choice (use LIV to correct).
– There is not usually a theoretical model that the
relationships are based on except when a natural
experiment is created.
– Only generalizable to those that benefit from the
instrument.
• Advantages
– Can be used to estimate a causal relationship when
randomization is not applicable.
Statistical Understanding of IV
• Think of IV models as 2 separate equations.
K  x1' B3  IVB 4  e2
yi  x1' B1  K ' B 2  e1
– Y is the outcome variable
– K is the variable related to the instrument
– IV is the instrument related to K
– e is the error
Typical Regression
Endogenous
Exogenous
X1
e1
DV
X2
Instrumental Variable Regression
Exogenous
Instrumental
Variable
Endogenous
Exogenous
X1
e1
X2
How do we find a good instrument and
test the instrument’s validity?
• You can use theory and past research to
provide evidence for an instrument.
• Hausman test
• Check correlation between independent
variable and instrument.
Example in R – Card data
• Explanation of Card (1993) study
• Replicate study using Card data (Card, 1993;
Hamersma, 2009).
Using Geographic Variation in College Proximity
to Estimate the Return to Schooling (Card, 1993)
• Does level of education or number of years of schooling
effect wages or earnings?
– You would think yes!
– BUT, the studies that show earnings gains are controversial
because educational levels are NOT randomly assigned.
Individuals choose their level of education. Education is
endogenous.
– The effect of schooling is difficult to determine and you cannot
randomly assign some children to school.
– The author needs an exogenous variable. Card uses geographic
differences in the proximity to a college.
• Overall finding: When college proximity is used as an
instrument in place of education, the author finds that the
return to education is approximately 50% higher than the
OLS estimate.
Why is Education Endogenous to
Earnings?
• Ability bias – if some individuals have an
ability that explains earnings despite
education, then those that earn higher
schooling will have an upward-biased level of
earnings (IQ).
• Measurement error- All of the data was
student reported. We could argue that there is
a negative correlation between earnings error
and observed schooling.
Is College Proximity Exogenous?
• Card proposes college proximity as an exogenous variable.
College proximity needs to be related to wages, but only
through education.
• If you are poor, the likelihood of attending college increases
if you live near one, so proximity is related to education.
• He checked this by looking at the effect of college proximity
on predicted education given other demographic variables.
Biggest effect was men with low chance of continuing
education. (if you live near a college, then there is a lower
cost of higher education so there is a bigger effect on
education outcomes of poorer children)
Recap
• We’re trying to predict the effect of schooling
on wages.
• Education is our key independent variable that
is endogenous.
• Wage (log of wages) is our dependent
variable.
• College proximity is our exogenous
instrument.
Variables Used in Card analysis
•
•
•
•
•
•
•
•
•
•
lwage = log(wages)
educ = years of schooling, 1976
exper = age – educ – 6
expersq
black = 1 if black
south = 1 if in south, 1976
smsa = 1 if in metropolitan area, 1976
reg661-reg668 = 1 for region lived in, 1966
smsa66 = 1 if in metropolitan area, 1966
nearc4 = 1 if near 4 year college, 1966
3 Step Process for Replicating Card’s Findings
(Card, 1992; Hamersma, 2009)
###Load Stata file###
library(foreign)
card.data<-read.dta("card.dta")
attach(card.data)
head(card.data)
id nearc2 nearc4 educ age fatheduc motheduc weight momdad14 sinmom14 step14
1 2
0
0
7 29
NA
NA 158413
1
0
0
2 3
0
0
12 27
8
8 380166
1
0
0
3 4
0
0
12 34
14
12 367470
1
0
0
4 5
1
1
11 27
11
12 380166
1
0
0
5 6
1
1
12 34
8
7 367470
1
0
0
6 7
1
1
12 26
9
12 380166
1
0
0
reg661 reg662 reg663 reg664 reg665 reg666 reg667 reg668 reg669 south66 black
1
1
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
5
0
1
0
0
0
0
0
0
0
0
0
6
0
1
0
0
0
0
0
0
0
0
0
smsa south smsa66 wage enroll kww iq married libcrd14 exper
lwage expersq
1
1
0
1 548
0 15 NA
1
0
16 6.306275
256
2
1
0
1 481
0 35 93
1
1
9 6.175867
81
3
1
0
1 721
0 42 103
1
1
16 6.580639
256
4
1
0
1 250
0 25 88
1
1
10 5.521461
100
5
1
0
1 729
0 34 108
1
0
16 6.591674
256
6
1
0
1 500
0 38 85
1
1
8 6.214608
64
Step 1: OLS Estimate without Instrument
We find education is SSD, but we can make the case that it is endogenous.
m1<-
lm(lwage~educ+exper+expersq+black+south+smsa+reg661+reg662+reg663+reg664+reg665+reg666+reg667+reg668+
smsa66)
summary(m1)
Call:
lm(formula = lwage ~ educ + exper + expersq + black + south + smsa + reg661 + reg662 + reg663 + reg664 +
reg665 + reg666 + reg667 + reg668 + smsa66)
Residuals:
Min
1Q
-1.62326 -0.22141
Median
0.02001
3Q
0.23932
Max
1.33340
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 4.7393766 0.0715282 66.259 < 2e-16 ***
educ
0.0746933 0.0034983 21.351 < 2e-16 ***
exper
0.0848320 0.0066242 12.806 < 2e-16 ***
expersq
-0.0022870 0.0003166 -7.223 6.41e-13 ***
black
-0.1990123 0.0182483 -10.906 < 2e-16 ***
south
-0.1479550 0.0259799 -5.695 1.35e-08 ***
smsa
0.1363845 0.0201005
6.785 1.39e-11 ***
reg661
-0.1185698 0.0388301 -3.054 0.002281 **
reg662
-0.0222026 0.0282575 -0.786 0.432092
reg663
0.0259703 0.0273644
0.949 0.342670
reg664
-0.0634942 0.0356803 -1.780 0.075254 .
reg665
0.0094551 0.0361174
0.262 0.793503
reg666
0.0219476 0.0400984
0.547 0.584182
reg667
-0.0005887 0.0393793 -0.015 0.988073
reg668
-0.1750058 0.0463394 -3.777 0.000162 ***
smsa66
0.0262417 0.0194477
1.349 0.177327
--Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 0.3723 on 2994 degrees of freedom
Multiple R-squared: 0.2998,
Adjusted R-squared: 0.2963
F-statistic: 85.48 on 15 and 2994 DF, p-value: < 2.2e-16
What do we know so far?
• Education is the key variable and is SSD, but
education is endogenous and is not
accounting for individual ability.
• Card uses college proximity as an instrument
to correct endogenous scenario. College
proximity is correlated with wages, but only
through education
• We want to check to see if college proximity is
correlated with education.
Step 2: Is college proximity an exogenous determinant of wages?
m2<-lm(educ~exper+expersq+black+south+smsa+reg661+reg662+reg663+reg664+reg665+reg666+reg667+reg668+smsa66+nearc4)
summary(m2)
Call:
lm(formula = educ ~ exper + expersq + black + south + smsa + reg661 + reg662 + reg663 + reg664 + reg665 + reg666 +
reg667 + reg668 + smsa66 + nearc4)
Residuals:
Min
1Q
Median
3Q
Max
-7.54513 -1.36996 -0.09103 1.27836 6.23847
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 16.8485239 0.2111222 79.805 < 2e-16 ***
exper
-0.4125334 0.0336996 -12.241 < 2e-16 ***
expersq
0.0008686 0.0016504
0.526 0.598728
black
-0.9355287 0.0937348 -9.981 < 2e-16 ***
south
-0.0516126 0.1354284 -0.381 0.703152
smsa
0.4021825 0.1048112
3.837 0.000127 ***
reg661
-0.2102710 0.2024568 -1.039 0.299076
reg662
-0.2889073 0.1473395 -1.961 0.049992 *
reg663
-0.2382099 0.1426357 -1.670 0.095012 .
reg664
-0.0930890 0.1859827 -0.501 0.616742
reg665
-0.4828875 0.1881872 -2.566 0.010336 *
reg666
-0.5130857 0.2096352 -2.448 0.014442 *
reg667
-0.4270887 0.2056208 -2.077 0.037880 *
reg668
0.3136204 0.2416739
1.298 0.194490
smsa66
0.0254805 0.1057692
0.241 0.809644
nearc4
0.3198989 0.0878638
3.641 0.000276 ***
--Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 1.941 on 2994 degrees of freedom
Multiple R-squared: 0.4771,
Adjusted R-squared: 0.4745
F-statistic: 182.1 on 15 and 2994 DF, p-value: < 2.2e-16
Step 2: Is college proximity an exogenous determinant of wages?
m3<-lm(lwage~exper+expersq+black+south+smsa+reg661+reg662+reg663+reg664+reg665+reg666+reg667+reg668+smsa66+nearc4)
summary(m3)
Call:
lm(formula = lwage ~ exper + expersq + black + south + smsa + reg661 + reg662 + reg663 + reg664 + reg665 + reg666 +
reg667 + reg668 + smsa66 + nearc4)
Residuals:
Min
1Q
Median
3Q
Max
-1.57387 -0.25161 0.01483 0.27229 1.38522
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 5.9896107 0.0434375 137.890 < 2e-16 ***
exper
0.0540214 0.0069336
7.791 9.07e-15 ***
expersq
-0.0022207 0.0003396 -6.540 7.21e-11 ***
black
-0.2698014 0.0192855 -13.990 < 2e-16 ***
south
-0.1514588 0.0278638 -5.436 5.90e-08 ***
smsa
0.1646968 0.0215645
7.637 2.96e-14 ***
reg661
-0.1354657 0.0416546 -3.252 0.00116 **
reg662
-0.0450389 0.0303145 -1.486 0.13746
reg663
0.0091190 0.0293467
0.311 0.75602
reg664
-0.0701587 0.0382651 -1.833 0.06683 .
reg665
-0.0250439 0.0387187 -0.647 0.51780
reg666
-0.0123840 0.0431315 -0.287 0.77404
reg667
-0.0294058 0.0423056 -0.695 0.48706
reg668
-0.1496489 0.0497234 -3.010 0.00264 **
smsa66
0.0218819 0.0217616
1.006 0.31472
nearc4
0.0420679 0.0180776
2.327 0.02003 *
--Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 0.3993 on 2994 degrees of freedom
Multiple R-squared: 0.1947,
Adjusted R-squared: 0.1907
F-statistic: 48.25 on 15 and 2994 DF, p-value: < 2.2e-16
Step 3: Does education effect wages when college proximity is used as the instrument?
library(AER)
m4<ivreg(lwage~educ+exper+expersq+black+south+smsa+reg661+reg662+reg663+reg664+reg665+reg666+reg667+reg668+smsa66|
nearc4+exper+expersq+black+south+smsa+reg661+reg662+reg663+reg664+reg665+reg666+reg667+reg668+smsa66)
summary(m4)
Call:
ivreg(formula = lwage ~ educ + exper + expersq + black + south + smsa + reg661 + reg662 + reg663 + reg664 + reg665
+ reg666 + reg667 + reg668 + smsa66 | nearc4 + exper + expersq + black + south + smsa + reg661 + reg662 +
reg663 + reg664 + reg665 + reg666 + reg667 + reg668 + smsa66)
Residuals:
Min
1Q
Median
3Q
Max
-1.83164 -0.24075 0.02428 0.25208 1.42760
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 3.7739651 0.9349470
4.037 5.56e-05 ***
educ
0.1315038 0.0549637
2.393 0.016793 *
exper
0.1082711 0.0236586
4.576 4.92e-06 ***
expersq
-0.0023349 0.0003335 -7.001 3.12e-12 ***
black
-0.1467757 0.0538999 -2.723 0.006504 **
south
-0.1446715 0.0272846 -5.302 1.23e-07 ***
smsa
0.1118083 0.0316620
3.531 0.000420 ***
reg661
-0.1078142 0.0418137 -2.578 0.009972 **
reg662
-0.0070465 0.0329073 -0.214 0.830460
reg663
0.0404445 0.0317806
1.273 0.203252
reg664
-0.0579172 0.0376059 -1.540 0.123640
reg665
0.0384577 0.0469387
0.819 0.412671
reg666
0.0550887 0.0526597
1.046 0.295587
reg667
0.0267580 0.0488287
0.548 0.583735
reg668
-0.1908912 0.0507113 -3.764 0.000170 ***
smsa66
0.0185311 0.0216086
0.858 0.391193
--Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 0.3883 on 2994 degrees of freedom
Multiple R-Squared: 0.2382,
Adjusted R-squared: 0.2343
Wald test: 51.01 on 15 and 2994 DF, p-value: < 2.2e-16
Compare OLS to IV Estimator
lm(formula = lwage ~ educ + exper + expersq + black +
south + smsa + reg661 + reg662 + reg663 + reg664 +
reg665 + reg666 + reg667 + reg668 + smsa66)
Residuals:
Min
1Q
-1.62326 -0.22141
Median
0.02001
3Q
0.23932
Max
1.33340
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 4.7393766 0.0715282 66.259 < 2e-16 ***
educ
0.0746933 0.0034983 21.351 < 2e-16 ***
exper
0.0848320 0.0066242 12.806 < 2e-16 ***
expersq
-0.0022870 0.0003166 -7.223 6.41e-13 ***
black
-0.1990123 0.0182483 -10.906 < 2e-16 ***
south
-0.1479550 0.0259799 -5.695 1.35e-08 ***
smsa
0.1363845 0.0201005
6.785 1.39e-11 ***
reg661
-0.1185698 0.0388301 -3.054 0.002281 **
reg662
-0.0222026 0.0282575 -0.786 0.432092
reg663
0.0259703 0.0273644
0.949 0.342670
reg664
-0.0634942 0.0356803 -1.780 0.075254 .
reg665
0.0094551 0.0361174
0.262 0.793503
reg666
0.0219476 0.0400984
0.547 0.584182
reg667
-0.0005887 0.0393793 -0.015 0.988073
reg668
-0.1750058 0.0463394 -3.777 0.000162 ***
smsa66
0.0262417 0.0194477
1.349 0.177327
--Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1
‘ ’ 1
Residual standard error: 0.3723 on 2994 degrees of
freedom
Multiple R-squared: 0.2998,
Adjusted R-squared:
0.2963
F-statistic: 85.48 on 15 and 2994 DF, p-value: < 2.2e16
ivreg(formula = lwage ~ educ + exper + expersq + black +
south + smsa + reg661 + reg662 + reg663 + reg664 +
reg665 + reg666 + reg667 + reg668 + smsa66 | nearc4
+ exper + expersq + black + south + smsa + reg661 +
reg662 + reg663 + reg664 + reg665 + reg666 + reg667
+ reg668 + smsa66)
Residuals:
Min
1Q
Median
3Q
Max
-1.83164 -0.24075 0.02428 0.25208 1.42760
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 3.7739651 0.9349470
4.037 5.56e-05 ***
educ
0.1315038 0.0549637
2.393 0.016793 *
exper
0.1082711 0.0236586
4.576 4.92e-06 ***
expersq
-0.0023349 0.0003335 -7.001 3.12e-12 ***
black
-0.1467757 0.0538999 -2.723 0.006504 **
south
-0.1446715 0.0272846 -5.302 1.23e-07 ***
smsa
0.1118083 0.0316620
3.531 0.000420 ***
reg661
-0.1078142 0.0418137 -2.578 0.009972 **
reg662
-0.0070465 0.0329073 -0.214 0.830460
reg663
0.0404445 0.0317806
1.273 0.203252
reg664
-0.0579172 0.0376059 -1.540 0.123640
reg665
0.0384577 0.0469387
0.819 0.412671
reg666
0.0550887 0.0526597
1.046 0.295587
reg667
0.0267580 0.0488287
0.548 0.583735
reg668
-0.1908912 0.0507113 -3.764 0.000170 ***
smsa66
0.0185311 0.0216086
0.858 0.391193
--Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1
‘ ’ 1
Residual standard error: 0.3883 on 2994 degrees of
freedom
Multiple R-Squared: 0.2382,
Adjusted R-squared:
0.2343
Wald test: 51.01 on 15 and 2994 DF, p-value: < 2.2e-16
Effect of education increased from 0.075 to 0.131. Card (1993): “The implied instrumental variables
estimates of the earnings gain per year of additional schooling at 10-14% are substantially above the
earnings gains estimated by a conventional ordinary least squares procedure (7.3%)”
Example 2
• Does cigarette smoking have an effect on child
birth weight (Wooldridge, 2002)?
– What is the dependent variable?
– What is the independent variable?
– Do we have an endogeneity problem?
– This examples uses cigarette prices as the exogenous
variable or as the instrument in the analysis
Insert Data into R
bwght<-read.dta("bwght.dta")
head(bwght)
faminc cigtax cigprice bwght fatheduc motheduc parity male white cigs
1
13.5
16.5
122.3
109
12
12
1
1
1
0
2
7.5
16.5
122.3
133
6
12
2
1
0
0
3
0.5
16.5
122.3
129
NA
12
2
0
0
0
4
15.5
16.5
122.3
126
12
12
2
1
0
0
5
27.5
16.5
122.3
134
14
12
2
1
1
0
6
7.5
16.5
122.3
118
12
14
6
1
0
0
lbwght bwghtlbs packs
lfaminc
1 4.691348
6.8125
0 2.6026897
2 4.890349
8.3125
0 2.0149031
3 4.859812
8.0625
0 -0.6931472
4 4.836282
7.8750
0 2.7408400
5 4.897840
8.3750
0 3.3141861
6 4.770685
7.3750
0 2.0149031
attach(bwght)
Step 1: What is the first regression
analysis we should calculate?
Step 2: Check the instrument
Are cigarette prices correlated with number of cigarettes smoked
per day while pregnant?
What did we find?
Other Examples of IV (Angrist & Kreuger, 2001)
IV in Educational Research
•
•
•
•
•
•
•
Tutoring voucher system
Remediation programs
Schooling effects
Effects of absences on achievement
Effects of attendance on earnings
Effects of class size on achievement
Effects of hours spent in algebra on math
achievement
References
Angrist, J. (1990). Lifetime earnings and the vietname era draft lottery: Evidence from social security
administrative records. American Economic Review, 80(3), 313-336.
Angrist, J. D. & Kreuger, J. D. (2001). Instrumental variables and the search for identification: From
supply and demand to natural experiments. Journal of Economic Perspectives, 15(4), 69-85.
Card, D. (1993). Using geographic variation in college proximity to estimate the return to schooling.
NBER Working Paper Series, 4483, 1-37 Retrieved from ??.
Bauchet, J. (2009). Of instrumental variables and sample definition. Financial Access Initiative.
Retrieved November 1, 2010, from http://financialaccess.org/node/2042.
Hamersma, S. (2009). Homework # 2: ECO 7427 answer key. Retrieved from
http://bear.warrington.ufl.edu/hamersma/Teaching/ECO7427/Homework/Homework2-AK.pdf
Reardon, S. (2010, March). Using instrumental variables in educational research. Presentation at
Society for Research on Educational Effectiveness. Retrieved from
http://www.sree.org/conferences/2010/program/
Shepherd, B. (2008). Session 1: Dealing with endogeneity. Retrieved from
http://www.unescap.org/tid/artnet/mtg/gravity09_tues3.pdf
Stock, J. H. & Trebbi, F. (2003). Retrospective: Who invented instrumental variable regression? Journal of
Economic Perspectives, 17(3), 177-194.
Wilson, B. (2009). Kobe and reverse causality. Brooks Wilson’s Economics Blog. Retrieved November 1,
2010, from http://drbseconomicblog.blogspot.com/2009/01/kobe-and-reverse-causality.html.
Wooldridge, J. (2002). Introductory econometrics: A modern approach. (2nd Ed?) South-Western College
Pub, City?.
Wright, P. G. (1928). The tariff on animal and vegetable oils. New York: Macmillan.