Christine Pal Chee 

October 30, 2013

Instrumental Variables 

Regression 
Estimating Causal Effects

 Health services research often seeks to estimate a causal 

effect

– What is the effect of [treatment] on [outcome]? 

 When can regression analysis of observational data estimate 

these effects?

 One possible method is multiple linear regression 

– Treatment must be exogenous

– If treatment is not exogenous, then estimated effects will be 

inaccurate

 When treatment is not exogenous, another method is 

necessary

– One possibility: instrumental variables (IV) regression

2 
Poll: Familiarity with IV Regression

 Advanced knowledge of IV regression 

 Somewhat familiar with IV regression 

 New to IV regression 

3 
Objectives 

 Provide an introduction to instrumental 

variables (IV) regression 

– Basic linear regression model

– Necessary conditions for a valid instrument

– Why and how instrumental variables 

regression works

– Examples

– Limitations

4 
Linear Regression Model

5 
Exogeneity 

6 
Intuition 



7 
Instrumental Variables



8 
Regression Model

9 
Instrument Relevance



10 
Instrument Exogeneity 



11
Valid Instrument

12 

X Y 

Z 
Valid Instrument

13 

X Y 

Z 
Intuition 

14 
Instrumental Variables Model

15 
Two Stage Least Squares (1)



16 
Two Stage Least Squares (2)

17 
General IV Model

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LATE

 IV regression estimates the local average

treatment effect (LATE)

– Local average treatment effect: the weighted average

of individual causal effects

 Weights are a measure of the relative degree to which

the instrument influences whether the individual

receives treatment

 “Local:” individuals who receive the most weight are

those for whom the instrument is the most influential

– Marginal effect

– In general, the local average treatment effect differs

from the average treatment effect

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Intensive Treatment for AMI

 Does more intensive treatment of acute

myocardial infarction (AMI) in the

elderly reduce mortality?

– McClellan, McNeil, Newhouse (1994)

 We want to estimate the effect on

mortality of intensive treatment of AMI

(cardiac catheterization, angioplasty,

CABG)

20 
Regression Model

21 
Endogeneity 

22 
 Evidence of selection bias

– Estimates that do not account for selection

are likely to be biased

Endogeneity (2)

23 
Instrument 

 Idea:

– Patients who live closer to hospitals that have the

capacity to perform more intensive treatments are

more likely receive those treatments (relevance)

– The distance a patient lives from a given hospital

should be independent of his health status

(exogeneity)

 Instrument (for intensive treatment): differential

distance to catheterization and revascularization

hospitals

24 
Instrument (2)

25 
Results 

 IV estimates of the effect of catheterization on mortality are

much smaller than estimates that do not take into account

selection

26 
Results (2)

 Catheterization within 90 days of AMI reduces mortality by 5 percentage

points at 1 to 4 years

 Caveats:

– Validity of results hinge on validity of the instrument

– IV estimates the LATE: this is an estimate of the marginal effect of

catheterization (for patients who would not have otherwise received treatment

if they lived relatively far from a catheterization or revascularization hospital)

– This estimate is an upper bound of the effect of catheterization

 If catheterization or revascularization hospitals offer better care other than more intensive

procedures (e.g., more beds, specialists, ICU), then mortality should be lower at those

hospitals

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Distance as an Instrument?

 What is the effect of primary care (PC) on health outcomes?

– Endogeneity: people usually see a doctor when they are sick

– Can we use distance to nearest PC clinic as an instrument for receipt of

PC?

 Patients who live closer to PC clinics are probably more likely to see a PC provider

=> relevant

 Patients who need to see a doctor often might move to live closer to health care

facilities => not exogenous

 What is the effect of emergency department (ED) services for car

accident injuries on mortality?

– Endogeneity: only seriously injured passengers are taken to the ED

– Can we use distance to the nearest ED as an instrument for treatment in an

ED?

 Only people who need medical care are taken to the ED, regardless of distance =>

not relevant

 Distance to the nearest ED is probably uncorrelated with accident severity =>

exogenous

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Other IV Examples

 Bhattacharya, et al. (2011): effect of insurance

coverage on body weight; instruments:

distribution of firm size and Medicaid coverage

for each state and year

 Doyle (2011): effect of foster care on long- and

short-term outcomes; instrument: random

assignment to investigators

 Chee (2012): effect of treatment with

antiretroviral therapy on substance use;

instrument: state Medicaid policies

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Weak Instruments

30 
Endogenous Instruments

31 
Summary 

 IV regression is powerful tool to estimate causal effects

 Conditions for a valid instrument:

– Relevance: the instrument must affect treatment

– Exogeneity: the instrument must be uncorrelated with all other 

factors that may affect outcomes

 Good instruments are difficult to find

 Using an invalid (weak or endogenous) instrument will give 

meaningless results

 Some tests available to check instrument validity, but what 

is absolutely necessary is a good “story” for why an 

instrument is relevant and exogenous

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Resources 

 Stock, James H. and Mark W. Watson, 2011. Introduction to Econometrics 

(Third Edition). Boston, MA: Addison-Wesley. (Chapter 12: 

Instrumental Variables Regression) 

 McClellan, Mark, Barbara J. McNeil, Joseph P. Newhouse, 1994. “Does 

More Intensive Treatment of Acute Myocardial Infarction in the Elderly 

Reduce Mortality?” Journal of the American Medical Association 272(11): 

859-866.

 Bhattacharya, Jay, M. Kate Bundorf, Noemi Pace, Neeraj Sood, 2011. 

“Does Health Insurance Make You Fat?” Chap. 2 in Economic Aspects of 

Obesity, University of Chicago Press. 

 Chee, Christine Pal, 2012. “Antiretroviral Therapy and the Demand for 

Substance Use.” Working Paper.

 Doyle, Joseph, 2011. “Causal Effects of Foster Care: An Instrumental- Variables Approach.” Forthcoming in Children and Youth Services Review. 

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