计量济学第8方差什么.pdf

计量经济学

Chapter8

Heteroskedasticity

WhatisHeteroskedasticity

1.TestingforHeteroskedasticity

◼Breusch-Pagan(BP)TestforHeteroskedasticity

◼WhiteTestforHeteroskedasticity

2.WeightedLeastSquare(WLS)

◼EstimationofWLS

HomoskedasticityAssumption

◼Wehavebeenassumingthevarianceof

theresidualtobeaconstant,i.e.

22

◼V(u|x,…,x)=s,notsh(X).

i1k

◼Whenthevarianceoftheresidualvaries

byobservations,theordinaryregressionis

nolongerBLUE

◼Inparticular,itdoesnothavetheminimum

variance,andit’svarianceestimateisno

longerunbiased

InferenceMightBeInvalid

◼Asaconsequenceofheteroskedasticity,

ourusualtorFtestsarenolongervalid

◼Forexample:

PlotofPurchaseversusHouseholde

$7,000

$6,000

e$5,000

s

a$4,000

h

c$3,000

r

u

P$2,000

$1,000

$0

$0$50,000$100,000$150,000$200,000

e

^

RecallhowwederivedVar(β|X)?

i

◼Again,withoutlostofgenerality,letj=1

◼Agoodstartingpointistousetheformula

2

ˆ

ˆ

b=b+(ru/ˆ

r

11i1ii1

^

◼Notingthat,conditioningonallthex’s,ri1

arenotrandom,theu