321_09_slides13

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

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

View Full Document Right Arrow Icon
Specification and Data Problems Chapter 9
Background image of page 1

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

View Full DocumentRight Arrow Icon
Outline Using proxies for unobserved explanatory variables Missing data, Non Random Sample, Outliers Measurement error Functional form specification Testing against non-nested alternatives
Background image of page 2
Using Proxies for Unobserved Explanatory Variables
Background image of page 3

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

View Full DocumentRight Arrow Icon
Recall Recall that omitting unobserved variable may lead to biased estimates of the included parameters. One solution is the proxy variable. ~ ~ 2 1 1
Background image of page 4
Definition: Proxy Variable A variable that is related to the unobserved variable
Background image of page 5

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

View Full DocumentRight Arrow Icon
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
Background image of page 6
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
Background image of page 7

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

View Full DocumentRight Arrow Icon
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
Background image of page 8
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
Background image of page 9

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

View Full DocumentRight Arrow Icon
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
Background image of page 10
Background image of page 11

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

View Full DocumentRight Arrow Icon
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
Background image of page 12
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
Background image of page 13

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

View Full DocumentRight Arrow Icon
Background image of page 14
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.
Background image of page 15

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

View Full DocumentRight Arrow Icon
Nonrandom Samples violation of Assumption MLR.2 Two types
Background image of page 16
Image of page 17
This is the end of the preview. Sign up to access the rest of the document.

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 Right Arrow Icon
Ask a homework question - tutors are online