This document discusses endogeneity in entrepreneurship research and provides practical tips for addressing it. It begins by defining endogeneity and explaining how it violates assumptions in linear models, resulting in inconsistent estimates. Common sources of endogeneity are discussed, along with myths about how to address it. The gold standard for dealing with endogeneity is randomized experiments, but instrumental variables and selection models are better options for most research. These methods are illustrated using an example looking at the relationship between risk taking and strategic learning. The document stresses the importance of properly specifying and testing for endogeneity, especially in mediation models, to avoid type I and II errors. Strong measurement models and theoretical justification of instruments can also help minimize endogeneity.
1. Endogeneity & Entrepreneurship Research: The Case of
Entrepreneurial Orientation
University of Nebraska—Lincoln
April 2016
Brian S. Anderson, Ph.D.
Assistant Professor
University of Colorado, Boulder
brian.s.anderson@colorado.edu
4. What we want to accomplish today…
• Dispel some myths about endogeneity
• Empower you with practical tips to deal with
endogeneity in your research models/designs
• Help me make this paper better!
5. YX
ζ
y = α + βx + ζ
Some statistical assumptions of linear models…
• Variables are reliable (no measurement error)
• ζ represents the variance in y not accounted for by x
• ζ is orthogonal to x (x is exogenous)
6. YX
ζ
Endogeneity is a violation of the orthogonality
assumption between x and ζ.
ψ ≠ 0
7. So what is the practical impact of COR(ζ,x ≠ 0)?
8. YX
ζ
y = α + βx + ζ
The estimator will ‘adjust’ β to try to satisfy the
orthogonality assumption.
The result is β becomes inconsistent— β will not
converge to the population value no matter how large
the sample.
ψ ≠ 0
9. Depending on the conditions, the estimator could
attenuate β, amplify β, or β could be correct by random
chance.
Unfortunately you can’t diagnose inconsistency without
testing for its presence, but the safe a priori assumption
is that β is wrong.
10. Endogeneity also impacts zero-order correlations, so
you can’t trust those much either, which also carries
implications for meta-analyses.
11. Depending on whom you ask, the end result is that
almost all of our published empirical research is wrong.
At best, the strength of most relationships are wrong, or
at worse, assumed ‘true’ relationships are spurious.
12. What are the main sources of endogeneity for
entrepreneurship and management scholars?
• Measurement error
• Omitted variables/selection, including common
methods bias
• Simultaneity (chicken and egg problem)
• Panel structures/omitting fixed effects/autoregression
13. A few common myths—and associated (incorrect)
remedies—for endogeneity often found in the literature…
14. Endogeneity is just reverse causality. If you just flip the
model (x -> y and y -> x) and the reciprocal relationship
is insignificant, then no endogeneity (Cao et al., 2015).
15. If you just lag the potential endogenous variable (and/or
the dependent variable), you can rule out endogeneity
(D’Innocenzo et al., 2015).
16. You can rule out endogeneity with a post hoc test, such
as an Arellano-Bond model (Martinez et al., 2015).
17. So how do you really (correctly) deal with endogeneity?
18. The gold standard is the randomized experiment, but…
This assumes perfect randomization of the participants
on every observed and unobserved variable.
19. Again depending on whom you ask, because
randomization is never guaranteed, there is never an
acceptable case to rule out endogeneity on theoretical
grounds only.
Arguing for a minimal potential effect is acceptable—
such as with a natural experiment—but endogeneity is a
statistical problem that must be addressed statistically.
20. For us mere mortals, selection models (e.g., Heckman)
and instrumental variables (e.g., 2SLS) models are our
best options.
But how do we use these methods in the real-world?
23. Shameless self-promotion plug here for the Anderson,
Kreiser, Kuratko, Hornsby & Eshima (2015) EO
reconceptualization.
24. Consider this model using the same data from Anderson
et al. (2009), but corrected for measurement error and
measurement model misspecification.
Strategic
Learning
Risk Taking
ζ
There is a positive relationship between Risk Taking and
a firm’s Strategic Learning Capability (β = .35; p < .001).
25. We’re not fooled though.
Couldn’t we argue that being an effective learner imbues
confidence in my ability to take risk (simultaneity)?
Anderson et al. (2009) also suggest a number of
possible mediators of the EO-strategic learning
relationship that right now aren’t being modeled (omitted
variables).
28. We’re faced with making either a Type I or Type II error.
Which model do we retain?
29. Ultimately, our goal is to recover the ‘correct’ parameter
estimate, allowing us to draw a causal inference about
the relationship between Risk and Strategic Learning.
30. We do this by removing the portion of variance in Risk
Taking that is shared with the disturbance term (ζ).
This shared variance represents all of the unobserved
effects—including measurement error—that correlate
with Risk Taking and predict Strategic Learning.
31. In the Two Stage Least Squares (2SLS) method, the job
of partialling out this shared variance falls to our
instruments.
32. Strategic
Learning
Risk Taking
ζζ
IV1
IV2
Instruments…
• Must be individually and jointly significant
• Need at least one to identify the model; two or more
per endogenous variable to conduct over-
identification tests (this is really important)!
• Must be properly excluded (can’t correlate with ζ)
34. Strategic
Learning
Risk Taking
ζζ
IV1
IV2
Need at least one instrument to identify the model; two
or more instruments per endogenous variable are
necessary to conduct tests of the model’s assumptions.
35. A common—and partially true—myth about
instruments…
You want your instrument to correlate strongly with the
potential endogenous variable, but have no correlation
with the dependent variable.
36. Just like any predictor, however, instruments must have a
theoretical (non-spurious) connection with the
endogenous construct.
• Heavy investments in R&D are characteristic of my
industry
• Over the past three years, risk taking by executives
of my business unit in seizing and exploring chancy
initiatives has [decreased much — increased much]
37. Strategic
Learning
Risk Taking
ζζ
IV1
IV2
Instruments must be properly excluded from the second
stage of the model—the instruments should not correlate
with the disturbance term (or the actual DV).
This is the Sargan-Hansen test of over-identifying
restrictions; in SEM, the Chi-Square statistic tells us the
same thing. Also in SEM, we can actually observe these
paths using modification indices.
β/ψ = 0
39. Strategic
Learning
Risk Taking
ζζ
IV1
IV2
Endogeneity violates the assumption that COR(ζ,x ≠ 0).
In SEM, we actually observe this assumption by freeing
the ψ (psi) parameter between Risk and Learning.
If this parameter is significantly different from zero,
endogeneity is present in the model and this indicates
that we need to retain the 2SLS estimator.
ψ = .03
p = .890
40. Our instruments look good and the ψ parameter is not
significant, so it looks like no endogeneity. But there is
one more way to make sure…
41. Strategic
Learning
Risk Taking
ζζ
IV1
IV2
Fortunately, these models are ‘nested’—the model
without the ψ parameter is simply a constrained version
of the model with it, so we can just test for a significant
difference between the two.
Strategic
Learning
Risk Taking
ζζ
IV1
IV2
42. Our test is the equivalent to a Hausman endogeneity test
with 1df. If there is a significant difference between the
two models, then we retain the unconstrained—the
‘larger’—model because it fits the data better.
χ2
constrained = 21.79
χ2
unconstrained = 21.77
χ2
diff = χ2
constrained - χ2
unconstrained
χ2
diff = .02; p > .05
43. But what is harm in retaining the ‘more conservative’
model with instruments?
Isn’t a Type II error better than a Type I error?
45. 2SLS is a limited information estimator because the
instruments have removed a portion of the variance in
Risk Taking.
This means that we have less variance available to
predict changes in the variance of Strategic Learning,
and hence, lower efficiency.
46. Ultimately, if you don’t have to use instruments, that’s
great, because you have greater freedom in your
modeling approach, and—assuming consistency—
efficiency is always preferred to minimize Type II error.
But you don’t know if you have that freedom unless you
first evaluated the model with instruments.
47. Related note…consistency of parameters is different
from consistency of inference.
Can’t forget about those standard errors!
48. We rarely just publish main effect relationships, so how
does the 2SLS approach extend to mediation models?
49. Consider the following model again based on Anderson
et al. (2009)…
Structural
Organicity
Strategic
Learning
Risk Taking
ζ
ζ
50. We use the same logic as before, but now we have three
potentially endogenous relationships.
In fact, in a mediation model, endogeneity is implied.
51. In a mediation model, we theoretically expect
endogeneity to be present. Until we actually add it, the
mediator(s) is an un-modeled omitted variable that
‘connects’ the predictor with the criterion.
This means that the Baron & Kenny (1986) ‘Step 1’ is,
assuming mediation exists, [almost] always wrong.
53. Just as before, we evaluate the individual and joint
significance of the instruments, along with the exclusion
restriction of all possible endogenous paths.
55. Wait a second…what do we want significant and what
don’t we want to be significant?
Significant
• β parameter from the
instrument to the
endogenous variable
• F test of the instruments
Non-Significant
• χ2 of the overall model
• Modification indices
from the instruments to
the dependent variable
If the ψ parameter of the disturbance term covariance is
significant, you MUST retain the 2SLS model!
56. Our instruments are individually and jointly valid, the ψ
parameters are not significant, and our model does not
show evidence of misspecification.
Do we retain the model?
57. To help make this determination, we setup a series of
nested models, constraining each ψ parameter in turn
and comparing the unconstrained with the focal
constrained model.
Supporting our overall findings, none of these
comparisons were significant.
58. So we retain the more efficient estimator, which has the
(happy) result of being nomologically consistent with the
findings reported in Anderson et al. (2009).
59. What about multiple mediation models?
The same logic as a single mediator applies, but the
assumptions become increasingly difficult to satisfy.
60. A note about moderation and curvilinear relationships…
64. Stronger measurement models go a long way to
minimizing endogeneity’s impact…
• Maximize indicator reliability
• For reflective measurement models, be aggressive
about trimming less reliable indicators, but avoid
construct deficiency
• A non-significant χ2 does not guarantee against
model misspecification, but a properly specified
model will ALWAYS have a non-significant χ2
65. If the researcher is using latent constructs with
psychometric indicators, there is no reason (excuse) to
avoid accounting for measurement error.
66. The more complex the model, the more likely the model
will be misspecified in some material way, including
potentially endogenous paths.
Our bar for a strong theoretical contribution on the basis
of model complexity is therefore more likely to introduce
erroneous findings into the literature.
67. As reviewers, we need to push authors to deal
(correctly) with endogeneity in their research design, but
that also may mean educating them on the best way to
go about it given their research question.
68. Dealing with endogeneity should be an integral
component of doctoral student training from the very
beginning.