Econometrics with 

Observational Dat

Introduction and IdentificatioIntroduction and Identificatio

Todd Wagner
Goals for Course

 To enable researchers to conduct ca

analyses with existing VA (and non analyses with existing VA (and non 

datasets. 

 We will 

– Describe econometric tools and their 

strengths and limitations

– Use examples to reinforce learning 
Goals of Today’s Clas

 Understanding causation with 

ob ti l d t bservational 

d

a

ta 

 Describe elements of an equation Describe elements of an equation  Example of an equation  Assumptions of the classic linear m
Terminology

 Confusing terminology is a major barr

interdisciplinary research interdisciplinary research 

– Multivariable or multivariate – Endogeneity or confounding – Interaction or Moderation 

– Right or Wrong 

 Maciejewski ML Weaver ML and He

Maciejewski ML, Weaver ML and He

(2011) Med Care Res Rev 68 (2): 156-
Polls
Understanding Causatio

Understanding Causatio

Randomized Clinical Trial

 RCTs are the gold RCTs are the gold 

-standard research d

standard research d

assessing causality



Wh i i b d i d i

hat 

is un

ique a

bout a ran

dom

ize

d tr

i

The treatment / ex

posure is randoml

y ass

 Benefits of randomization: 

C l i Causal 

i

n

ferences 
–

Randomization

 Random assignment distinguishes 

experimental and non experimental and non-experimental 

experimental 

 Random assignment should not be c

with random selection 

– Selection can be important for genera

Selection can be important for genera

(e.g., randomly-selected survey partic

Random assignment is required for Random assignment is required for 

understanding causation 
Limitations of RCTs 

 Generalizability to real life may be low 

– E l i it i lt i l t 

Exc

lus

ion criter

ia may result 

in a se

lec

t s

 Hawthorne effect (both arms)  RCTs are expensive and slow  C b an 

be unethi calt o ran

dom

ize peop

le 

certain treatments or conditions 

 Quasi-experimental design can fill an 

important role important role 
Can Secondar

y 

Data Hel

understand Causation

Coffee may make high achievers slack o
Observational Data 

 Widely available (especially in VA Permit quick data analysis at a low  May be realistic/ generalizable May be realistic/ generalizable  Key independent variable may no

exogenous – 

it may 

be en

dogenou
Endogeneity

 A variable is said to be endogeno

when it is correlated w ith the error (assumption 4 in the classic linear 

 If there exists a loop of causality b

th i d t d t the independent and d ependent va

of a model leads, then there is 

endogeneity 
u o ess o w u oco e ed 

Endogeneity 

 Endogeneity can come from: 

– 

Measurement error 

– 

A

u

t

o

reg

ress

i

on 

with a

u

tocorr

elated 

– Simultaneity – Omitted variables – Sample selection Sample selection 
Elements of an Equati

Maciejewski ML, Diehr P, Smith MA, Hebert P. Common methodolo

health services research and their synonyms. Med Care. Jun 2002
Terms

 Univariate– the statistical expressi

one variable one variable 

 Bivariate– the expression of two 

variables 

 Multivariate– the expression of m

one variable (can be dependent or one variable (can be dependent or

independent variables)
Covariate, RHS variable, 

Predictor, independent variable 

Intercept 

Dependent variable Dependent variable Outcome measure 

Note the similarity to the equation of a line (y=mx+B)
“i” is an index.

If we are analyzing people,then th

g p p 

typically refers to the person There may be other indexes There may be other indexes 
te

Two covariates 

In rcept

DV 
Different notation

j covariates j covariates 

Intercept 

DV 
Error term

 Error exists because 

1. Other important variables might be om

Other important variables might be om

2. Measurement error 3. Human indeterminacy 

 Understand error structure and mini

Understand error structure and mini

error 

 Error can be addi i li t ve or mul i t plicati

See Kennedy, P. A Guide to Econometrics
Example: is height associated 

income?
es s: e s o e ed 

 Y=income; X=height Y=income; X=height 

Hypothes

is: H

e

i

ght i

s n

ot r

elated t

income (B

1=0)

 If B

1=0, then what is B

0? 
t t t

Height and Income

0000 200000 15000 me 0 10000 

Incom 

5000 0 

60 65 70 

height 

H d d ib h d t ? How do we want to describe the data?
Estimator 

 A statistic that provides informatio

the parameter of interest (e g heithe parameter of interest (e.g., hei

 Generated by applying a function 

data 

 Many common esti mators 

– Mean and median (univariate estim– Ordinary least squares (OLS) (multi

estimator) 
Ordinary Least Squares (O

00 000 20000 0000 1500 0000 100 0 50 

60 65 70 

height 

Fitted values Income 
Other estimators

 Least 

ab lt so

l

u

te 

deviations 

 Maximum 

lik lih lik

elihoo

d 

00 50000 2000 100000 1 50000 0 

60 65 70 

height 

Fitted values Incom
Choosing an Estimato

 Least squares  Unbiasedness  Efficiency (minimum variance) 

Asymp

t

otic properties 

 Maximum likelihood  Goodness of fit  We’ll talk more about identifying the “

estimator throughout this course estimator throughout this course. 
000

How is the OLS fit?

000 20000000 15000000 100 0 50 

60 65 70 

height 

Fitted values Income 
What about gender? 

 How could gender affect the relati

b t h i ht d i ? b

e

tween 

h

e

i

ght and 

income? 

– Gende

r-s

pecific interce

pt 

– Interaction 
Gender Indicator Variab

height

GenGen
Gender-specific Indicat

200000 150000 100000 50000

B1 is the slope of the line 

0 

60 65 70 

height 

B2 

B0 
Interaction

height gender

Interaction TEffect modifModifier Modifier 

Note: the gender “mavariable is still in the 
Gender Interaction

200000 0 150000 100000 50000 Interaction allows two 

groups to have different 

l 0 

60 65 70 7

height 

slopes 
Classic Linear Classic Linear

Regression (CLR) Regression (CLR)

Assumptions
Classic Linear Regressi

 No “superestimator”  CLR models are often used as the 

point for analyses point for analyses 

 5 assumptions for the CLR  Variations in these assumption wi

your choice of estimator (and happyour choice of estimator (and happof your reviewers) 
Assumption 1

 The dependent variable can be cal

as a linear functi on of a specific se

independent variables, plus an erro

 For example, 
Violations to Assumptio

 Omitted variables  Non-linearities 

– Note: by transforming independent Note: by transforming independent 

variables, a nonlinear function can b

from a linear f nction from a linear 

function 
Testing Assumption 1 

 Theory-based transformations  Empirically Empirically

-based transformations based transformations 

 Common sense  Ramsey RESET test  Pregibon Link test Pregibon Link test Ramsey J Tests for specification errors in classical linear least squares Ramsey 

J. Tests for specification errors in classical linear least squares 

analysis. Journal of the Royal Statistical Society. 1969;Series B(31)

Pregibon D. Logistic regression diagnostics. Annals of Statistics. 1981;9
“ ”

Assumption 1 and Stepw

 Statistical software allows for crea

mod l e s in a “stepwi hi se” f ashion 

 Be careful when using it. Be careful when using it. 

– Little penalty for adding a nuisance – BIG penalty for missing an importa

covariate
Assumption 2 

 Expected value of the error term i

E

(

u

i

)=0 



Vi l i l d bi d i i

o

lat

ions 

lea

d to biased 

intercep

t

 A concern when analyzing cost da

A concern when analyzing cost da
Assumption 3 

 IID– Independent and identically 

di t ib t t di

s

t

rib

u

t

e

d error 

terms 

– Autocorrelation: Errors are uncorrel

with each other 

– Homoskedasticity: Errors are identi

Homoskedasticity: Errors are identidistributed 
Heteroskedasticity
Violating Assumption 

 Effects 

– OLS coefficients are unbiased OLS coefficients are unbiased – OLS is inefficient – Standard errors are biased 

 Plotting is often very helpful Plotting is often very helpful  Different statistical tests for heteroske

– GWHet--

but statistical tests have limited 
Fixes for Assumption 3 

 Transforming dependent variable 

eli

m

ina

te it 

 Robust standard errors (Huber Wh

sandwich estimators) 
Assumption 4 

 Observations on independent varia

are consid d fi d i t d 

idered fixed 

in repea

t

e

d sa

 E(x

i

u

i

 E(x

i

u

i

)0 =

0

 Violations 

– Errors in variables 

Endogeneity 

– A toregression A

utoregression 

– Simultaneity 
easu e e t e o o d de t v

Assumption 4: Assumption 4:

Errors in Variables



Measu

r

e

m

e

nt 

err

or 

of depe 

nde

nt v

(DV) is maintained in error term. 

 OLS assumes that covariates are 

measured without error. measured without error. 

 Error in measuring covariates can 

problematic 
Common Violations

 Including a lagged dependent variable

covariate covariate 

 Contemporaneous correlation 

– Hausman test 

(but ver

y weak in small sam

 Instrumental variables offer a potentia

Instrumental variables offer a potentia

solution 
Assumption 5 

 Observations > covariates  No multicollinearity  Solutions 

– Remove perfectly collinear variable– Increase sample si e Increase sample si

ze 
Any Questions?
Statistical Software 

 I frequently use SAS for data 

managemen

t 

 I use Stata for my analyses  Stattransfer Stattransfer 
Regression References 

 Kennedy A Guide to Econometric Greene. Econometric Analysis.  Wooldridge Wooldridge. Econometric Analys

Econometric Analys

Cross Section and Panel Data. 

 Winship and Morgan (1999) The Esti

of Causal Effects from Observational of Causal Effects from Observational 

Annual Review of Sociology, pp. 659-