321_09_slides13

# 321_09_slides13 - Specification and Data Problems Chapter 9...

This preview shows pages 1–17. Sign up to view the full content.

Specification and Data Problems Chapter 9

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Outline Using proxies for unobserved explanatory variables Missing data, Non Random Sample, Outliers Measurement error Functional form specification Testing against non-nested alternatives
Using Proxies for Unobserved Explanatory Variables

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Recall Recall that omitting unobserved variable may lead to biased estimates of the included parameters. One solution is the proxy variable. ~ ~ 2 1 1
Definition: Proxy Variable A variable that is related to the unobserved variable

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Suppose Where is unobservable, but we have a proxy variable, x 3 , such that u x x x y 3 3 2 2 1 1 0 3 x 3 3 3 0 3 v x x
Necessary Assumptions for Consistent Estimates of β 1 and β 2 Using Proxy 1. u is uncorrelated with x 1 , x 2 , , and x 3 . 2. v 3 is uncorrelated with x 1 , x 2 , and x 3 i.e. 3 3 0 3 3 3 2 1 3 , , x x x x x x x

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
If these are true we have Our composite error has mean zero and is uncorrelated with x 1 , x 2 , and x 3 . Thus, estimating using the proxy one can find unbiased estimates of 0 , 1 , 2 , and 3 . 3 3 v u e
If however, where v 3 is uncorrelated with x 1 , x 2 , and x 3 we have It can be shown that 3 3 3 2 2 1 1 0 3 v x x x x 3 3 3 3 3 2 2 3 2 1 1 3 1 0 3 0 v u x x x y 1 3 1 1 ˆ plim 2 3 2 2 ˆ plim

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Example: WAGE2.dta Using IQ as a proxy for ability. In the model The concern is that education is positively correlated with ability which is in the error term and positively correlated with wages thus, get biased estimates. u black urban south married tenure er educ lwage 7 6 5 4 3 2 1 0 exp

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
When it is difficult to obtain a proxy, it is possible to include a lagged dependent variable the value of the dependent variable from a previous time period. Since we expect the same unobservables to have influenced the lagged observations this is a way of controlling for the unobservables. u y x x y k k k 1 1 1 1 0
Example: CRIME2.dat The concern is that one of the explanatory variables may be correlated with something in the error term (e.g. increased expenditures improve reporting conventions) thus get biased estimates. u lawexpc unem crmrte 87 2 87 1 0 87 log log

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Missing Data If the data are missing at random , then the size of the sample is simply reduced and there are no consequences as far as the unbiasedness and consistency of the OLS estimates. The t and F test are also still valid.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Nonrandom Samples violation of Assumption MLR.2 Two types
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 07/11/2011 for the course ECON 321 taught by Professor Louis during the Fall '09 term at Waterloo.

### Page1 / 54

321_09_slides13 - Specification and Data Problems Chapter 9...

This preview shows document pages 1 - 17. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online