课程高级计量经济学英文课件胡ch14advanced panel data methods

Ch14

高深面板数据方法固定效应估计法随机效应模型相关随机效应方法把面板数据方法用于其他数据结构Economics

20

-

Prof.

Anderson1Fixed

Effects

EstimationWhen

there

is

an

unobserved

fixedeffect,

an

alternative

to

first

differencesis

fixed

effects

estimationConsider

the

average

over

time

of

yit

=b1xit1

+…+

bkxitk

+

ai

+

uitThe

average

of

ai

will

be

ai,

so

if

yousubtract

the

mean,

ai

will

be

differencedout

just

as

when

doing

first

differencesEconomics

20

-

Prof.

Anderson2Fixed

Effects

Estimation

(cont)If

we

were

to

do

this

estimation

by

hand,we’d

need

to

be

careful

because

we’dthink

that

df=NT–k,

but

really

is

N(T–1)–

kbecause

we

used

up

dfs

calculatingmeansLuckily,

most packages

will

do

fixedeffects

estimation

for

youThis

method

is

also

identical

to

includinga

separate

intercept

or

every

individualEconomics

20

-

Prof.

Anderson3First

Differences

vs

Fixed

EffectsFirst

Differences

and

Fixed

Effects

will

beexactly

the

same

when

T

=2For

T

>2,

the

two

methods

are

differentProbably

see

fixed

effects

estimation

moreoften

than

differences

--

probably

morebecause

it’s

easier

than

that

it’s

betterFixed

effects

easily

implemented

forunbalanced

panels,

not

just

balancedpanelsEconomics

20

-

Prof.

Anderson4Random

EffectsStart

with

the

same

basic

model

with

acomposite

error,

yit

=

b0

+

b1xit1

+

.

.

.

bkxitk+

ai

+

uitPreviously

we’ve

assumed

that

ai

wascorrelated

with

the

x’s,

but

what

if

it’snot?OLS

would

be

consistent

in

that

case,butcomposite

error

will

be

serially

correlatedEconomics

20

-

Prof.

Anderson5Random

Effects

(continued)Need

to

transform

the

model

and

do

GLSto

solve

the

problem

and

make

correctinferencesIdea

is

to

do

quasi-differencing

with

theneed

to

transform

the

model

and

do

GLSto

solve

the

problem

and

make

correctinferencesEconomics

20

-

Prof.

Anderson6Random

Effects

(continued)End

up

with

a

sort

of

weighted

average

ofOLS

and

Fixed

Effects

–

use

quasi-demeaned

data[s

(s

+Ts

)]Economics

20

-

Prof.

Anderson7l

=1-yit

-

lyi

=

b0

(1-

l)+

b1

(xit1

-

lxi1

)+...+

bk(xitk

-

xik

)+

(nit

-ni

)1

222u

a2uRandom

Effects

(continued)If

l

=

1,

then

this

is

just

the

fixedeffectsestimatorIf

l

=

0,

then

this

is

just

the

OLSestimatorSo,

the

bigger

the

variance

oftheunobserved

effect,

the

closer

it

is

to

FEThe

smaller

the

variance

of

theunobserved

effect,

the

closer

it

is

to

OLSStata

will

do

Random

Effects

for

usEconomics

20

-

Prof.

Anderson8Fixed

Effects

or

Random?More

usual

to

think

need

fixed

effects,since

think

the

problem

is

that

somethingunobserved

is

correlated

with

the

x’sThe

random

effects

estimator

isappropriate

when

the

unobserved

effectis

thought

to

be

uncorrelated

with

alltheexplanatory

variables.Economics

20

-

Prof.

Anderson9相关随机效应方法假设ai

=

a

+

gxi

+

riri与每个xit都不相关，那么也与xit的时间均值不相关，代入原模型yit

=bxit+ai+uityit

=a

+

bxit

+gxi

+

ri

+uit该模型可以用随机效应方法估计，这种方法称为相关随机效应估计法，相应的参数β的估计量称为相关随机效应估计量，伍德里奇证明了该估计量等于用固定效应方法得到的估计量。Economics

20

-

Prof.

Anderson10相关随机效应方法可以被扩展到估计如下模型：yit

=a

+

bxit

+gxi

+dzi

+

ri

+uitEconomics

20

-

Prof.

Anderson11Other

Uses

of

Panel

MethodsIt’s

possible

to

think

of

models

wherethere

is

an

unobserved

fixed

effect,

evenif

we

do

not

have

true

paneldataA

common

example

is

where

we

thinkthere

is

an

unobserved

family

effectCan

difference

siblingsCan

estimate

family

fixed

effect

modelEconomics

20

-

Prof.

Anderson12Additional

IssuesMany

of

the

things

we

already

know

aboutboth

cross

section

and

time

series

datacan

be

applied

with