Econometrics-I-13

# Econometrics-I-13 - Applied Econometrics William Greene...

This preview shows pages 1–10. Sign up to view the full content.

Applied Econometrics William Greene Department of Economics Stern School of Business

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

View Full Document
Applied Econometrics 13. Instrumental Variables
The Problem 1 2 Cov( , ) , K variables Cov( , ) , K variables is OLS regression of y on ( , ) cannot estimate ( , ) consistently. Some other estimator is needed. Additional structure: = + wh = + + = endogenous y X Y X 0 Y 0 Y X Y Y Z V β δ ε ε ε β δ Π ere Cov( , )= . An estimator based on ( , ) may be able to estimate ( , ) consistently. instrumental variable ( Z 0 X IV) Z ε β δ

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

View Full Document
Instrumental Variables Framework:  y    =    X β   +   ε , K variables in  X . There exists a set of K variables,  such that             plim( Z’X/n   0   but  plim( Z’ ε /n) =  0 The variables in  Z  are called instrumental variables. An alternative (to least squares) estimator of  β  is              b IV   =  ( Z’X ) -1 Z’y We consider the following: Why use this estimator? What are its properties compared to least squares? We will also examine an important application
The First IV Study (Snow, J., On the Mode of Communication of Cholera, 1855) London Cholera epidemic, ca 1853-4 Cholera = f(Water Purity,u)+ ε . Effect of water purity on cholera? Purity=f(cholera prone environment (poor, garbage  in streets, rodents, etc.). Regression does not work.     Two London water companies      Lambeth                      Southwark ======|||||======            Main sewage discharge Paul Grootendorst: A Review of Instrumental Variables Estimation of Treatment Effects… http://individual.utoronto.ca/grootendorst/pdf/IV_Paper_Sept6_2007.pdf

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

View Full Document
IV Estimation Cholera=f(Purity,u)+ ε Z = water company Cov(Cholera,Z)= δ Cov(Purity,Z) Z is randomly mixed in the population (two full  sets of pipes) and uncorrelated with behavioral  unobservables, u) Cholera= α + δ Purity+u+ ε Purity = Mean+random variation+ λ u Cov(Cholera,Z)=  δ Cov(Purity,Z)
IV Estimators Consistent b IV  = ( Z’X ) -1 Z’y            = ( Z’X /n) -1  ( Z’X /n) β + ( Z’X /n) -1 Z’ ε /n          =  β + ( Z’X /n) -1 Z’ ε /n    β Asymptotically normal (same approach to proof as  for OLS) Inefficient – to be shown.

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

View Full Document
LS as an IV Estimator The least squares estimator is         ( X X ) -1 X y   =  ( X X ) -1 Σ i x i y i                            =   β    + ( X X ) -1 Σ i x i ε i   If plim( X’X /n) =  Q  nonzero    plim( X’ ε /n)  =  0   Under the usual assumptions LS is an IV estimator    X  is its own instrument.
IV Estimation Why use an IV estimator ?  Suppose that  X  and  ε   are  not  uncorrelated.  Then least squares is  neither unbiased nor consistent. Recall the proof of consistency of least squares:

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 06/20/2011 for the course ECON 803 taught by Professor Pp during the Spring '11 term at Thammasat University.

### Page1 / 38

Econometrics-I-13 - Applied Econometrics William Greene...

This preview shows document pages 1 - 10. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online