FIN 620
Emp. Methods in Finance
Lecture 5 – Instrumental Variables
Professor Todd Gormley
Announcements
n Rough draft of research proposal
due next week…
q Just 1- to 3-page (single-spaced) sketch
of your proposal is fine…
n Should clearly state your question
n Should give me idea of where you’re going
with the identification strategy
n See grading template on Canvas
q Upload it to Canvas by noon next week
q I will read and then send brief feedback
2
Background readings
n Roberts and Whited
q Section 3
n Angrist and Pischke
q Sections 4.1, 4.4, and 4.6
n Wooldridge
q Chapter 5
n Greene
q Sections 8.2-8.5
Outline for Today
n Quick review of panel regressions
n Discuss IV estimation
q How does it help?
q What assumptions are needed?
q What are the weaknesses?
n Student presentations of “Panel Data”
Quick Review [Part 1]
n What type of omitted variable does panel
data and FE help mitigate, and how?
q Answer #1 = It can help eliminate omitted
variables that don’t vary within panel groups
q Answer #2 = It does this by transforming the
data to remove this group-level heterogeneity
[or equivalently, directly controls for it using
indicator variables as in LSDV]
Quick Review [Part 2]
n Why is random effects useless
[at least in corporate finance settings]?
Quick Review [Part 3]
n What are three limitations of FE?
#1 – Can’t estimate coefficient on variables that
don’t vary within groups
#2 – Could amplify any measurement error
n For this reason, be cautious interpreting zero or small
coefficients on possibly mismeasured variables
#3 – Can’t be used in models with lagged values
of the dependent variable
Outline for Instrumental Variables
n Motivation and intuition
n Required assumptions
n Implementation and 2SLS
q Weak instruments problem
q Multiple IVs and overidentification tests
n Miscellaneous IV issues
n Limitations of IV
Motivating IV [Part 1]
n Consider the following estimation
y = b 0 + b1 x1 + ... + b k xk + u
where cov( x1 , u ) = ... = cov( xk -1 , u ) = 0
cov( xk , u ) ¹ 0
n If we estimate this model, will we get a
consistent estimate of βk?
n When would we get a consistent estimate
of the other β’s, and is this likely?
Motivation [Part 2]
q Answer #1: No. We will not get a
consistent estimate of βk
q Answer #2: Very unlikely. We will only
get consistent estimate of other β if xk is
uncorrelated with all other x
n Instrumental variables provide a
potential solution to this problem…
Instrumental variables – Intuition
q Think of xk as having ‘good’ and ‘bad’ variation
n Good variation is not correlated with u
n Bad variation is correlated with u
q An IV (let’s call it z) is a variable that explains
variation in xk, but doesn’t explain y
n I.e., it only explains the “good” variation in xk
q Can use the IV to extract the “good” variation
and replace xk with only that component!
Outline for Instrumental Variables
n Motivation and intuition
n Required assumptions
n Implementation and 2SLS
q Weak instruments problem
q Multiple IVs and overidentification tests
n Miscellaneous IV issues
n Limitations of IV
Instrumental variables – Formally
n IVs must satisfy two conditions
q Relevance condition
q Exclusion condition
n What are these two conditions?
n Which is harder to satisfy?
n Can we test whether they are true?
To illustrate these conditions, let’s start with the
simplest case, where we have one instrument, z,
for the problematic regressor, xk
Relevance condition [Part 1]
How can we test
n The following must be true… this condition?
q In the following model
xk = a 0 + a1 x1 + ... + a k -1 xk -1 + g z + v
z satisfies the relevance condition if γ≠0
q What does this mean in words?
n Answer: z is relevant to explaining the problematic
regressor, xk, after partialling out the effect of all
the other regressors in the original model
Relevance condition [Part 2]
n Easy to test the relevance condition!
q Just run the regression of xk on all the other
x’s and the instrument z to see if z explains xk
q As we see later, this is what people call the
‘first stage’ of the IV estimation
Exclusion condition [Part 1]
How can we test
n The following must be true… this condition?
q In the original model, where
y = b 0 + b1 x1 + ... + b k xk + u
z satisfies the exclusion condition if cov(z, u)=0
q What does this mean in words?
n Answer: z is uncorrelated with the disturbance, u…
i.e., z has no explanatory power with respect to y
after conditioning on the other x’s;
Exclusion condition [Part 2]
n Trick question! You cannot test the
exclusion restriction [Why?]
q Answer: You can’t test it because u is unobservable
q You must find a convincing economic argument as
to why the exclusion restriction is not violated
Side note – What’s wrong with this?
n I’ve seen some try to use the below
argument as support for the exclusion
restriction… what’s wrong with it?
q Estimate the below regression…
y = b 0 + b1 x1 + ... + b k xk + g z + u
q If γ=0, then exclusion restriction likely holds...
i.e., they argue that z doesn’t explain y after
conditioning on the other x’s
Side note – Answer
n If the original regression doesn’t give
consistent estimates, then neither will this one!
q cov(xk, u)≠0, so the estimates are still biased
q Moreover, if we believe the relevance condition,
then the coefficient on z is certainly biased because
z is correlated with xk
What makes a good instrument?
n Bottom line, an instrument must be justified
largely on economic arguments
q Relevance condition can be shown formally, but
you should have an economic argument for why
q Exclusion restriction cannot be tested… you need
to provide a convincing economic argument as to
why it explains y, but only through its effect on xk
Outline for Instrumental Variables
n Motivation and intuition
n Required assumptions
n Implementation and 2SLS
q Weak instruments problem
q Multiple IVs and overidentification tests
n Miscellaneous IV issues
n Limitations of IV
Implementing IV estimation
n You’ve found a good IV, now what?
n One can think of the IV estimation as
being done in two steps
q First stage: regress xk on other x’s & z
q Second stage: take predicted xk from first
stage and use it in original model instead of xk
This is why we also call IV estimations
two stage least squares (2SLS)
First stage of 2SLS
n Estimate the following
xk = a 0 + a1 x1 + ... + a k -1 xk -1 + g z + v
Problematic regressor Instrumental
All other non-problematic
[i.e., cov(xk, u)≠0] variable
variables that explain y
q Get estimates for the α’s and γ
q Calculate predicted values, xˆk , where
xˆk = aˆ 0 + aˆ1 x1 + ... + aˆ k -1 xk -1 + gˆ z
Second stage of 2SLS
n Use predicted values to estimate
y = b 0 + b1 x1 + ... + b k xˆk + u
Predicted values replace the problematic regressor
q Can be shown (see textbook for math) that
this 2SLS estimation yields consistent
estimates of all the β when both the relevance
and exclusion conditions are satisfied
Intuition behind 2SLS
n Predicted values represent variation in xk
that is ‘good’ in that it is driven only by
factors that are uncorrelated with u
q Specifically, predicted value is linear function of
variables that are uncorrelated with u
n Why not just use other x’s? Why need z?
q Answer: Can’t just use other x’s to generate
predicted value because then predicted value
would be collinear in the second stage
Reduced Form Estimates [Part 1]
n The “reduced form” estimation is when
you regress y directly onto the instrument,
z, and other non-problematic x’s
y = b 0 + b1 x1 + ... + b k -1 xk -1 + d z + u
q It is an unbiased and consistent estimate of the
effect of z on y (presumably through the
channel of z’s effect on xk)
Reduced Form Estimates [Part 2]
n It can be shown that the IV estimate for
xk , bˆkIV, is simply given by…
Reduced form coefficient
dˆ estimate for z
bˆ IV
=
k
gˆ First stage coefficient
estimate for z
q I.e., if you don’t find effect of z on y in
reduced form, then IV is unlikely to work
n IV estimate is just scaled version of reduced form
Practical advice [Part 1]
n Don’t state in your paper’s intro that
you use an IV to resolve an identification
problem, unless…
q You also state what the IV you use is
q And provide a strong economic argument as
to why it satisfies the necessary conditions
Don’t bury the explanation of your IV! Researchers
that do this almost always have a bad IV. If you really
have a good IV, you’ll be willing to defend it in the intro!
Practical advice [Part 2]
n Don’t forget to justify why we should
believe the exclusion restriction holds
q Too many researchers only talk
about the relevance condition
q Exclusion restriction is equally important
Practical Advice [Part 3]
n Do not do two stages on your own!
q Let the software do it; e.g., in Stata, use the
IVREG or XTIVREG (for panel data) commands
n Three ways people will mess up when
trying to do 2SLS on their …
#1 – Standard errors will be wrong
#2 – They try using nonlinear models in first stage
#3 – They will use the fitted values incorrectly
Practical Advice [Part 3-1]
n Why will standard errors be wrong if you
try to do 2SLS on your own?
q Answer: Because the second stage uses
‘estimated’ values that have their own
estimation error. This error needs to be
considered when calculating standard errors!
Practical Advice [Part 3-2]
n People will try using predicted values
from non-linear model, e.g., Probit or
Logit, in a ‘second stage’ IV regression
q But only linear OLS in first stage guarantees
covariates and fitted values in second stage
will be uncorrelated with the error
n I.e., this approach is NOT consistent
n This is what we call the “forbidden regression”
Practical Advice [Part 3-3]
n In models with quadratic terms, e.g.
y = b 0 + b1 x + b 2 x + u
2
people often try to calculate one fitted
value x̂ using one instrument, z, and then
plug in x̂ and x̂ 2 into second stage…
q Seems intuitive, but it is NOT consistent!
q Instead, you should just use z and z2 as IVs!
Practical Advice [Part 3]
n Bottom line… if you find yourself plugging
in fitted values when doing an IV, you are
probably doing something wrong!
q Let the software do it for you; it will prevent
you from doing incorrect things
Practical Advice [Part 4]
n All x’s that are not problematic, need to be
included in the first stage!!!
q You’re not doing 2SLS, and you’re not getting
consistent estimates if this isn’t done
q This includes things like firm and year FE!
n Yet another reason to let statistical
software do the 2SLS estimation for you!
Practical Advice [Part 5]
n Always report your first stage results & R2
n There are two good reasons for this…
[What are they?]
q Answer #1: It is direct test of relevance
condition… i.e., we need to see γ≠0!
q Answer #2: It helps us determine whether
there might be a weak IV problem…
Outline for Instrumental Variables
n Motivation and intuition
n Required assumptions
n Implementation and 2SLS
q Weak instruments problem
q Multiple IVs and overidentification tests
n Miscellaneous IV issues
n Limitations of IV
Consistent, but biased
n IV is a consistent, but biased, estimator
q For any finite number of observations, N,
the IV estimates are biased toward the
biased OLS estimate
q But, as N approaches infinity, the IV
estimates converge to the true coefficients
n This feature of IV leads to what we call
the weak instrument problem…
Weak instruments problem
n A weak instrument is an IV that doesn’t
explain very much of the variation in the
problematic regressor
n Why is this an issue?
q Small sample bias of estimator is greater when
the instrument is weak; i.e., our estimates, which
use a finite sample, might be misleading…
q t-stats in finite sample can also be wrong
Weak IV bias can be severe [Part 1]
n Hahn and Hausman (2005) show that
finite sample bias of 2SLS is ≈
j r (1 - r 2 )
Nr 2
q j = number of IVs [we’ll talk about
multiple IVs in a second]
q ρ = correlation between xk and u
q r2 = R2 from first-stage regression
q N = sample size
Weak IV bias can be severe [Part 2]
j r (1 - r 2 )
Nr 2
A low explanatory power in
More instruments, which we’ll talk first stage can result in
about later, need not help; they help large bias even if N is large
increase r2, but if they are weak (i.e.,
don’t increase r2 much), they can
still increase finite sample bias
Detecting weak instruments
n Number of warning flags to watch for…
q Large standard errors in IV estimates
n You’ll get large SEs when covariance between
instrument and problematic regressor is low
q Low F statistic from first stage
n The higher F statistic for excluded IVs, the better
n Stock, Wright, and Yogo (2002) find that an F
statistic above 10 likely means you’re okay…
Excluded IVs – Tangent
n Just some terminology…
q In some ways, can think of all non-
problematic x’s as IVs; they all appear in first
stage and are used to get predicted values
q But, when people refer to excluded IVs, they
refer to the IVs (i.e., z’s) that are excluded
from the second stage
Outline for Instrumental Variables
n Motivation and intuition
n Required assumptions
n Implementation and 2SLS
q Weak instruments problem
q Multiple IVs and overidentification tests
n Miscellaneous IV issues
n Limitations of IV
More than one problematic regressor
n Now, consider the following…
y = b 0 + b1 x1 + ... + b k xk + u
where cov( x1 , u ) = ... = cov( xk - 2 , u ) = 0
cov( xk -1 , u ) ¹ 0
cov( xk , u ) ¹ 0
n There are two problematic regressors, xk-1 and xk
n Easy to show that IVs can solve this as well
Multiple IVs [Part 1]
n Just need one IV for each
problematic regressor, e.g., z1 and z2
n Then, estimate 2SLS in similar way…
q Regress xk on all other x’s (except xk-1)
and both instruments, z1 and z2
q Regress xk-1 on all other x’s (except xk)
and both instruments, z1 and z2
q Get predicted values, do second stage
Multiple IVs [Part 2]
n Need at least as many IVs as problematic
regressors to ensure predicted values are not
collinear with the non-problematic x’s
q If # of IVs match # of problematic x’s,
model is said to be “Just Identified”
“Overidentified” Models
n Can also have models with more IVs
than # of problematic regressors
q E.g., m instruments for h problematic
regressors, where m > h
q This is what we call an overidentified model
n Can implement 2SLS just as before…
Overidentified model conditions
n Necessary conditions very similar
q Exclusion restriction = none of the
instruments are correlated with u
q Relevance condition
E.g., you can’t
just have one IV n Each first stage (there will be h of them) must
that is correlated have at least one IV with non-zero coefficient
with all the
n Of the m instruments, there must be at least h of
problematic
regressors, and them that are partially correlated with problematic
all the other IVs regressors [otherwise, model isn’t identified]
are not
Benefit of Overidentified Model
n Assuming you satisfy the relevance and
exclusion conditions, you will get more
asymptotic efficiency with more IVs
q Intuition: you can extract more ‘good’
variation from the first stage of the estimation
However, Overidentification Dilemma
n Suppose you are a very clever
researcher…
q You find not just h instruments for h
problematic regressors, you find m > h
n First, you should consider yourself very clever
[a good instrument is hard to come by]!
n But why might you not want to use the m-h
extra instruments?
Answer – Weak instruments
n Again, as we saw earlier, a weak
instrument will increase likelihood of finite
sample bias and misleading inferences!
q If have one good IV, not clear you want to
add some extra (less good) IVs...
Practical Advice – Overidentified IV
n Helpful to always show results using “just
identified” model with your best IVs
q It is least likely to suffer small sample bias
q In fact, the just identified model is median-
unbiased making weak instruments critique
less of a concern
Overidentification “Tests” [Part 1]
n When model is overidentified, you can
supposedly “test” the quality of your IVs
n The logic of the tests is as follows…
q If all IVs are valid, then we can get consistent
estimates using any subset of the IVs
q So, compare IV estimates from different subsets; if
find they are similar, this suggests the IVs okay
Overidentification “Tests” [Part 2]
n But I see the following all the time…
q Researcher has overidentified IV model
q All the IVs are highly questionable in that
they lack convincing economic arguments
q But authors argue that because their model
passes some “overidentification test” that
the IVs must be okay
n What is wrong with this logic?
Overidentification “Tests” [Part 3]
n Answer = All the IVs could be junk!
q The “test” implicitly assumes that some
subset of instruments is valid
q This may not be the case!
n To reiterate my earlier point…
q There is no test to prove an IV is valid! Can
only motivate that the IV satisfies exclusion
restriction using economic theory
“Informal” checks – Tangent
n It is useful, however, to try some
“informal” checks on validity of IV
q E.g., One could show the IV is uncorrelated
with other non-problematic regressors or with
y that pre-dates the instrument
n Could help bolster economic argument that IV
isn’t related to outcome y for other reasons
n But don’t do this for your actual outcome, y, why?
Answer = It would suggest a weak IV (at best)
Outline for Instrumental Variables
n Motivation and intuition
n Required assumptions
n Implementation and 2SLS
q Weak instruments problem
q Multiple IVs and overidentification tests
n Miscellaneous IV issues
n Limitations of IV
Miscelleneous IV issues
n IVs with interactions
n Constructing additional IVs
n Using lagged y or lagged x as IVs
n Using group average of x as IV for x
n Using IV with FE
n Using IV with measurement error
IVs with interactions
n Suppose you want to estimate
y = b 0 + b1 x1 + b 2 x2 + b3 x1 x2 + u
cov( x1 , u ) = 0
where
cov( x2 , u ) ¹ 0
q Now, both x2 and x1x2 are problematic
q Suppose you can only find one IV, z.
Is there a way to get consistent estimates?
IVs with interactions [Part 2]
n Answer = Yes! In this case, one can
construct other instruments from the one IV
q Use z as IV for x2
q Use x1z as IV for x1x2
n Same economic argument used to
support z as IV for x2 will carry
through to using x1z as IV for x1x2
Constructing additional IV
n Now, suppose you want to estimate
y = b 0 + b1 x1 + b 2 x2 + b3 x3 + u
cov( x1 , u ) = 0
Now, both x2 and x3
where cov( x , u ) ¹ 0
2 are problematic
cov( x3 , u ) ¹ 0
q Suppose you can only find one IV, z, and you
think z is correlated with both x2 and x3…
Can you use z and z2 as IVs?
Constructing additional IV [Part 2]
n Answer = Technically, yes. But
probably not advisable…
q Absent an economic reason for why z2 is
correlated with either x2 or x3 after
partialling out z, it’s probably not a good IV
n Even if it satisfies the relevance condition, it
might be a ‘weak’ instrument, which can be
problematic [as seen earlier]
Lagged instruments
n It has become common in CF to use
lagged variables as instruments
n This usually takes two forms
q Instrumenting for a lagged y in dynamic
panel model with FE using a lagged lagged y
q Instrumenting for problematic x or lagged y
using lagged version of the same x
Example where lagged IVs are used
n As noted last week, we cannot estimate
models with both a lagged dep. var. and
unobserved FE
yi ,t = a + r yi ,t -1 + b xi ,t + fi + ui ,t , r <1
q The lagged y independent variable will be
correlated with the error, u
q One proposed solution is to use lagged values
of y as IV for problematic yi,t-1
Using lagged y as IV in panel models
n Specifically, papers propose using first
differences combined with lagged values,
like yi,t-2 , as instrument for yi,t-1
q Could work in theory, …
n Lagged y will likely satisfy relevance criteria
n But exclusion restriction requires lagged values of y to
be uncorrelated with differenced residual, ui,t – ui,t-1
Is this plausible in corporate finance?
Lagged y values as instruments?
n Probably not…
q Lagged values of y will be correlated with
changes in errors if errors are serially correlated
q This is common in corporate finance,
suggesting this approach is not helpful
[See Holtz-Eakin, Newey, and Rosen (1988), Arellano
and Bond (1991), Blundell and Bond (1998) for more
details on these type of IV strategies]
Lagged x values as instruments? [Part 1]
n Another approach is to make assumptions
about how xi,t is correlated with ui,t
q Idea behind relevance condition is x is
persistent and predictive of future x or future y
[depends on what you’re trying to instrument]
q And exclusion restriction is satisfied if we assume
xi,t is uncorrelated with future shocks, u
Lagged x values as instruments? [Part 2]
n Just not clear how plausible this is…
q Again, serial correlation in u (which is very common
in CF) all but guarantees the IV is invalid
q An economic argument is generally lacking,
[and for this reason, I’m very skeptical of these strategies]
[See Arellano and Bond (1991), Arellano and Bover (1995)
for more details on these type of IV strategies]
Using group averages as IVs [Part 1]
n Will often see the following…
yi , j = a + b xi , j + ui , j
q yi,j is outcome for observation i (e.g., firm)
in group j (e.g., industry)
q Researcher worries that cov(x,u)≠0
q So, they use group average, x-i , j , as IV
1
x- i , j = å
J - 1 iÎ j
xk , j J is # of observations
in the group
k ¹i
Using group averages as IVs [Part 2]
n They say…
q “group average of x is likely correlated with
own x” – i.e., relevance condition holds
q “but group average doesn’t directly affect y”
– i.e., exclusion restriction holds
n Anyone see a problem?
Using group averages as IVs [Part 3]
n Answer =
q Relevance condition implicitly assumes
some common group-level heterogeneity,
fj , that is correlated with xij
q But if model has fj (i.e., group fixed effect),
then x-i , j must violate exclusion restriction!
n This is a bad IV [see Gormley and Matsa
(2014) for more details]
?
Other Miscellaneous IVs
n As noted last class, IVs can also be
useful in panel estimations
#1 – Can help identify effect of variables that
don’t vary within groups [which we can’t
estimate directly in FE model]
#2 – Can help with measurement error
#1 – IV and FE models [Part 1]
n Use the following three steps to identify
variables that don’t vary within groups…
#1 – Estimate the FE model
#2 – Take group-averaged residuals, regress them
onto variable(s), x’, that don’t vary in groups
(i.e., the variables you couldn’t estimate in FE model)
n Why is this second step (on its own) problematic?
n Answer: because unobserved heterogeneity (which
is still collinear with x’) will still be in error (because
it partly explains group-average residuals)
#1 – IV and FE models [Part 2]
n Solution in second step is to use IV!
#3 – Use covariates that do vary in group (from
first step) as instruments in second step
n Which x’s from first step are valid IVs?
n Answer = those that don’t co-vary with unobserved
heterogeneity but do co-vary with variables that don’t
vary within groups [again, economic argument needed here]
q See Hausman and Taylor (1981) for details
q Done in Stata using XTHTAYLOR
#2 – IV and measurement error [Part 1]
n As discussed last week, measurement
error can be a problem in FE models
n IVs provide a potential solutions
q Pretty simple idea…
q Find z correlated to mismeasured variable,
but not correlated with u; use IV
#2 – IV and measurement error [Part 2]
n But easier said then done!
q Identifying a valid instrument requires researcher
to understand exact source of measurement error
n This is because the disturbance, u, will include the
measurement error; hence, how can you make an
economic argument that z is uncorrelated with it if you
don’t understand the measurement error?
[See Biorn (2000) and Almeida, Campello, and Galvao
(RFS 2010) for examples of this strategy]
Outline for Instrumental Variables
n Motivation and intuition
n Required assumptions
n Implementation and 2SLS
q Weak instruments problem
q Multiple IVs and overidentification tests
n Miscellaneous IV issues
n Limitations of IV
Limitations of IV
n There are two main limitations to discuss
q Finding a good instrument is hard; even the
seemingly best IVs can have problems
q External validity can be a concern
Subtle violations of exclusion restriction
n Even the seemingly best IVs can violate
the exclusion restriction
q Roberts and Whited (pg. 31, 2011) provide a
good example of this in description of
Bennedsen et al. (2007) paper
q Whatever group is discussing this paper
next week should look… J
Bennedsen et al. (2007) example [Part 1]
n Paper studies effect of family CEO
succession on firm performance
q IVs for family CEO succession using
gender of first-born child
n Families where the first child was a boy are
more likely to have a family CEO succession
n Obviously, gender of first-born is totally
random; seems like a great IV…
Any guesses as to what might be wrong?
Bennedsen et al. (2007) example [Part 2]
n Problem is that first-born gender may
be correlated with disturbance u
q Girl-first families may only turnover firm
to a daughter when she is very talented
q Therefore, effect of family CEO turnover
might depend on gender of first born
q I.e., gender of first born is correlated with
u because it includes interaction between
problematic x and the instrument, z!
External vs. Internal validity
n External validity is another concern of IV
[and other identification strategies]
q Internal validity is when the estimation
strategy successfully uncovers a causal effect
q External validity is when those estimates are
predictive of outcomes in other scenarios
n IV (done correctly) gives us internal validity
n But it doesn’t necessarily give us external validity
External validity [Part 1]
n Issue is that IV estimates only tell us about
subsample where the instrument is predictive
q Remember, you’re only making use
of variation in x driven by z
q So, we aren’t learning effect of x for
observations where z doesn’t explain x!
n It’s a version of LATE (local average
treatment effect) and affects interpretation
External validity [Part 2]
n Again, consider Bennedsen et al (2007)
q Gender of first born may only predict likelihood
of family turnover in certain firms…
n I.e., family firms where CEO thinks females (including
daughters) are less suitable for leadership positions
q Thus, we only learn about effect of family
succession for these firms
q Why might this matter?
External validity [Part 3]
n Answer: These firms might be different in
other dimensions, which limits the external
validity of our findings
q E.g., Could be that these are poorly run firms…
n If so, then we only identify effect for such
poorly run firms using the IV
n And effect of family succession in well-run
firms might be quite different…
External validity [Part 4]
n Possible test for external validity problems
q Size of residual from first stage tells us something
about importance of IV for certain observations
n Large residual means IV didn’t explain much
n Small residual means it did
q Compare characteristics (i.e., other x’s) of
observations of groups with small and large
residuals to make sure they don’t differ much
Summary of Today [Part 1]
n IV estimation is one possible way to
overcome identification challenges
n A good IV needs to satisfy two conditions
q Relevance condition
q Exclusion condition
n Exclusion condition cannot be tested; must
use economic argument to support it
Summary of Today [Part 2]
n IV estimations have their limits
q Really hard to find good IV
q Weak instruments can be a problem,
particularly when you have more IVs
than problematic regressors
q External validity can be a concern
In First Half of Next Class
n Natural experiments [Part 1]
q How do they help with identification?
q What assumptions are necessary to
make causal inferences?
q What are their limitations?
n Related readings… see syllabus
Assign papers for next week…
n Gormley (JFI 2010)
q Foreign bank entry and credit access
n Bennedsen, et al. (QJE 2007)
q CEO family succession and performance
n Giroud, et al (RFS 2012)
q Debt overhang and performance
Break Time
n Let’s take our 10-minute break
n We’ll do presentations when we get back
