# Presentation: 407702

## Today’s Presentation begins at 2 PM Eastern TimeTitle:  	HERC Econometrics Course	Session 1 :  “Identification and Introduction”Presenter: Todd Wagner, PhD

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## Econometrics with Observational Data

- Introduction and Identification
- Todd Wagner

## Goals for Course

- To enable researchers to conduct careful analyses with existing VA (and non-VA) datasets.
- We will
- Describe econometric tools and their strengths and limitations
- Use examples to reinforce learning

## Requirements

- Familiarity with multivariate analysis
- We expect you to
- do the readings
- ask questions if you don’t understand something
- do your best

## Course faculty

- Todd Wagner, PhD (day 1 & 6)
- Wei Yu, PhD (day 2 & 3)
- Ciaran Phibbs, PhD (day 4 & 5)
- Mark Smith, PhD (day 7)
- Jim Burgess, PhD (day 8)

## Course Dates

- Introduction and identification: (Oct 11th)
- Cost as the dependent variable (I): (Oct 25th)
- Cost as the dependent variable (II): (Nov 8th)
- Non-linear dependent variables: (Dec 6th)
- Right-hand-side variables: (Dec 13th)
- Endogeneity and simultaneity: (Jan 24th)
- Efficiency: (Feb 7th)

## Course Logistics

- Please register
- Log on
_**https://hsrdtraining.webex.com**_
- Missed a class? You can catch-up:
_**http://www.hsrd.research.va.gov/for_researchers/cyber_seminars**_

## Web Ex Rules

- Mute your phone
- Don’t use the hold button
- 	If you have to make or answer another call, please hang up and then dial back in

## Features of web system 

- Main page
- Slides, white board, applications demo
- Side page
- Chat
- Questions and answers
- Informal poll
- Polls

## Randomized Clinical Trial

- RCTs are the gold-standard research design for assessing causality
- What is unique about a randomized trial?
- 	The treatment / exposure is randomly assigned
- Benefits of randomization:
- 	Causal inferences

## Randomization

- Random assignment distinguishes experimental and non-experimental design
- Random assignment should not be confused with random selection
- Selection can be important for generalizability (e.g., randomly-selected survey participants)
- Random assignment is required for understanding causation

## Limitations of RCTs

- Generalizability to real life may be low
- Hawthorne effect (both arms)
- RCTs are expensive and slow
- Can be unethical to randomize people to certain treatments or conditions
- Quasi-experimental design can fill an important role

## Elements of an Equation

- Maciejewski ML, Diehr P, Smith MA, Hebert P. Common methodological terms in health services research and their synonyms. *Med Care. *Jun 2002;40(6):477-484.

## Slide 14

## 	“i” is an index.  If we are analyzing people, then this typically refers to the person

- 	There may be other indexes

## DV

- Two covariates

- Error Term

- Intercept

## Different notation

- DV

-  j covariates

- Error Term

- Intercept

## Error term

- Error exists because
- Other important variables might be omitted
- Measurement error
- Human indeterminancy
- Understand and minimize error
- Error can be additive or multiplicative

- See Kennedy, P. _A Guide to Econometrics_

## Example: is height associated with income?

## Y=income; X=height
Hypothesis: Height is not related to income (B1=0)
If B1=0, then what is B0?
To test Hypothesis, we need to estimate B1 with a sample of data

- Hypothesis: Height is not related to income (B1=0)
- If B1=0, then what is B0?
- To test Hypothesis, we need to estimate B1 with a sample of data

## Estimators

## OLS

## Other estimators

- Least absolute deviations
- Maximum likelihood

## Choosing an Estimator

- Least squares
- Unbiasedness
- Efficiency (minimum variance)
- Asymptotic properties
- Maximum likelihood
- We’ll talk more about estimators in courses 2-4.

## What is driving the error?

## What about gender

- How could gender affect the relationship between height and income?
- Gender-specific intercept
- Interaction

## Gender Indicator Variable

- Gender Intercept

- height

## Gender-specific Indicator

- B0

- B2

## Interaction

- Interaction Term,
- Effect modification,
- Modifier

- Note: the gender “main effect”
- variable is still in the model

- height

- gender

## Gender Interaction

## Classic Linear Regression (CLR)

- Assumptions

## Classic Linear Regression

- No “superestimator”
- CLR models are often used as the starting point for analyses
- 5 assumptions for the CLR
- Variations in these assumption will guide your choice of estimator (and happiness of your reviewers)

## Assumption 1

- The dependent variable can be calculated as a linear function of a specific set of independent variables, plus an error term
- For example,

## Violations to Assumption 1

- Omitted variables
- Non-linearities
- Note: by transforming independent variables, a nonlinear function can be made from a linear function

## Testing Assumption 1

- Theory-based transformations
- Empirically-based transformations
- Common sense
- Ramsey RESET test
- Pregibon Link test
- Ramsey J. Tests for specification errors in classical linear least squares regression analysis. *Journal of the Royal Statistical Society. *1969;Series B(31):350-371.
- Pregibon D. Logistic regression diagnostics. *Annals of Statistics. *1981;9(4):705-724.

## Assumption 1 and Stepwise

- Statistical software allows for creating models in a “stepwise” fashion
- DON’T DO IT!
- Why?
- Little penalty for adding a nuisance variable
- BIG penalty for missing an important covariate

## Assumption 2 

- Expected value of the error term is 0
- 	E(ui)=0
- Violations lead to biased intercept
- A concern when analyzing cost data (Wei will talk about the smearing estimator)

## Assumption 3

- IID– Independent and identically distributed error terms
- Autocorrelation: Errors are uncorrelated with each other
- Homoskedasticity: Errors are identically distributed

## Heteroskedasticity

## Violating Assumption 3

- Effects
- OLS coefficients are unbiased
- OLS is inefficient
- Standard errors are biased
- Plotting is often very helpful
- Different statistical tests for heteroskedasticity
- GWHet--but statistical tests have limited power

## Fixes for Assumption 3

- Transforming dependent variable may eliminate it
- Robust standard errors (Huber White or sandwich estimators)
- Wei and Ciaran will address this issue in more detail in later courses

## Assumption 4

- Observations on independent variables are considered fixed in repeated samples
- E(xiui)=0
- Violations
- Errors in variables
- Autoregression
- Simultaneity

## Assumption 4: Errors in Variables

- Measurement error of dependent variable (DV) is maintained in error term.
- Error in measuring covariates can be problematic
- Is error correlated with error from DV?

## Common Violations

- Including a lagged dependent variable(s) as a covariate
- Contemporaneous correlation—often called endogeneity
- Hausman test (but very weak in small samples)
- Mark Smith will talk more about this.

## Assumption 5

- Observations > covariates
- No multicollinearity
- Solutions
- Remove perfectly collinear variables
- Increase sample size

## Any Questions?

## Statistical Software

- SAS is for data management
- R and Stata are for analyses
- _[http://www.r-project.org/](http://www.r-project.org/)_
- Stattransfer
- (Always transfer SCRSSN as double precision)

## Reading for Next Week

- Maciejewski ML et al. Common methodological terms in health services research and their synonyms. *Med Care. *Jun 2002;40(6):477-484.
- Manning WG, Mullahy J. Estimating log models: to transform or not to transform? *J Health Econ. *Jul 2001;20(4):461-494.

## Regression References

- Kennedy _A Guide to Econometrics_
- Greene.  _Econometric Analysis_.
- Wooldridge. _Econometric Analysis of Cross Section and Panel Data_.