Endogeneity & Exogeneity

EXOGENEITY & ENDOGENEITY
Shane Thompson
Summit Consulting, LLC
© 2015

EXOGENEITY, ENDOGENEITY, & YOU
 Program evaluation, policy impacts, treatment
effects
 How does our outcome of interest (income, health,
free-throw %) change after our independent
variable of interest (education, medicine, practice)
changes?
 Often, we will have to concern ourselves with
whether our independent variable of interest is
exogenous or endogenous

EXOGENOUS VARIABLES
 An independent variable is exogenous in a dataset
if it is assigned/chosen without respect to how it
might influence the outcome of interest
 Education level assigned without regard to potential
income benefit
 Medicine assigned without respect to probability of
success
 Practice hours assigned without respect to how it might
improve performance
 Randomization of “treatment” assignment ensures
that independent variables are exogenous

ENDOGENOUS VARIABLES
 An independent variable is endogenous in a dataset if it
is assigned/chosen according to how it might determine
the outcome of interest
 Income: Bill Gates drops out of college; Shane Thompson
goes forever
 Health: Patient with family history of heart attacks takes
aspirin; patient without does not take it
 FT%: Shaq practices free throws; Steve Nash does not
 Simple comparisons of treatment-vs-control are biased
 College REDUCES income by billions of dollars!
 Aspirin INCREASES the probability of heart attacks!
 Free-throw practice REDUCES free-throw percentage!

COMMUTING TIME: SLUGGING
Weather…wait...where…who…wreck?
Exogenous or endogenous?
 The weather
 EXOGENOUS
 The time of day I get in the slug line
 ENDOGENOUS
 My destination (14th, 18th, or L’Enfant Plaza)
 ENDOGENOUS
 The gender of the driver
 EXOGENOUS
 A wreck on the HOV lanes
 EXOGENOUS

CORRELATION VS. CAUSATION
 Estimates of the effects of endogenous variables on
outcome variables are correlational
 A change in an outcome variable given a change in an
endogenous variable is potentially reflective of changes
of several other variables in the model
 Estimates of the effects of exogenous variables on
outcome variables are causal
 A change in an outcome variable given a change in an
exogenous variable is attributable to the exogenous
variable

EX: BLUE JEANS AND REVENUE
 AL and AC notice that whenever several
Summiteers wear jeans into the office, big
deliverables are generally due that day.
 In leadership meetings they alert the directors to
this amazing trend.
 Hypothesis: Wearing jeans increases revenue

# Deliverables Jeans # Deliverables Jeans
1 0 1 0
1 0 3 0
0 0 2 0
0 0 3 0
3 1 5 1
0 0 1 0
2 0 0 0
2 0 3 0
2 0 1 0
6 1 6 1
3 0 3 0
1 0 1 0
3 0 1 0
1 0 0 0
3 1 5 1
1 0 2 0
2 0 0 0
1 0 0 0
0 0 0 0
8 1 5 1
0 0 1 0
1 0 0 0
2 0 0 0
0 0 0 0
6 1 6 1

JEANS. JEANS! JEANS!
 Over the last 50 work days:
 Summit averages 5.3 deliverables when Summiteers
wear jeans
 Summit averages 1.1 deliverables when Summiteers do
NOT wear jeans
JEANS INCREASE PRODUCTIVITY!!!
JEANS INCREASE REVENUE!!!

# Deliverables Jeans Day # Deliverables Jeans Day
1 0 Monday 1 0 Monday
1 0 Tuesday 3 0 Tuesday
0 0 Wednesday 2 0 Wednesday
0 0 Thursday 3 0 Thursday
3 1 Friday 5 1 Friday

WELL, THAT’S EMBARRASSING…
 Jeans DO NOT increase deliverables and DO NOT
increase revenue.
 Still, enterprising Summiteers seek to find the
causal effect of jeans
 How might we find the CAUSAL effect of jeans?

BEST OPTION: RANDOMIZED CONTROL TRIAL
 Summit randomly assigns casual days
 Jean-wearing is exogenous to deliverables, i.e. the
assignment to wear jeans is made without regard to
how it might influence business
 Causal effect of jeans on deliverables:
Avg Deliverablesjeans – Avg Deliverablesno jeans

NON-RANDOMIZED DATA
 Jean-wearing is endogenous to deliverables, i.e.
the decision to wear jeans may be made according
to deliverable deadlines and client meetings
 Causal effect of jeans on deliverables IS NOT:
Avg Deliverablesjeans – Avg Deliverablesno jeans
 Why??

BALANCE IN TREATMENT ASSIGNMENT
Exogenous Treatment Endogenous Treatment
Treatment Control
Age
Race
Gender
Income
Age
Race
Gender
Income
Treatment Control
Younger

QUASI-EXPERIMENTAL METHODS:
MAKING ENDOGENOUS VARIABLES EXOGENOUS
 Difference-in-Difference
1. Identify a suitable control
group (Firm X)
2. Verify parallel trend in
deliverables before
treatment (controlling for
obs characteristics)
3. Verify no spillover effects
4. Jeans are exogenous,
conditional on the parallel
trend (which is
conditional on obs
characteristics)

 Regression Discontinuity
1. Summit management
allows staff above a fixed
threshold of billable hours
to wear jeans (threshold is
unknown to staff)
2. Staff just above and just
below the threshold are
equally productive
3. Jeans are exogenous
immediately above and
below threshold
Billable hours (hundreds)
Deliverablesin2014

 Propensity Score
Matching
1. Summit allows all staff to
wear jeans if they want
2. Estimate the probability
of jean-wearing given
observable staff
characteristics
3. Assume we observe ALL
relevant predictors of
jean-wearing
4. Jeans are exogenous at
each probability level

 Synthetic Control Method
1. Identify several potential control
groups (firms)
2. Construct a synthetic Summit
that is a weighted combination
of other firms
3. Constrain the synthetic Summit
to be approx equal to Summit
in observable characteristics
and deliverables before the
jeans policy
4. Jeans are exogenous,
conditional on the pre-
treatment equality between
Summit and the synthetic
control
B
A E
D
C

CONCLUSIONS
 Correlation = Causation
 Data are generally messy, poorly-tracked, and non-
experimental (rife with endogeneity!)
 Cutting edge evaluators, statisticians, and
econometricians must be able to:
1. identify endogenous and exogenous variables
2. implement statistical methods to mitigate endogeneity
 The causal effect of jeans is 10,000 additional
deliverables

Endogeneity & Exogeneity

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