Chapter 14 Fixed Effects Regressions Least Square Dummy Variable Approach (EC220)

7/24/2019 Chapter 14 Fixed Effects Regressions Least Square Dummy Variable Approach (EC220)

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Christopher Dougherty

EC220 - Introduction to econometrics

(chapter 14)

Slideshow !i"ed e!!ects regressions #SD$ method

%riginal citation

Dougherty, C. (2012) EC220 - Introduction to econometrics (chapter 14). [eaching !esource"

# 2012 he $uthor

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the user to remi, t/ea*, and 'ui&d upon the /or* e%en or commercia& purposes, as &ong as the user

credits the author and &icenses their ne/ creations under the identica& terms.

httpcreati%ecommons.org&icenses'y-sa.0

http&&learningresources'lse'ac'u&


2/26

In the third ersion o! the !i"ed e!!ects approach* nown as the least s+uares dummy

aria,le (#SD$) method* the uno,sered e!!ect is ,rought e"plicitly into the model'

i"ed e!!ects estimation (least s+uares dummy aria,le method)

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I.ED EEC/S EESSI%S #SD$ 3E/%D

1


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I! we de!ine a set o! dummy aria,lesAi* whereA

iis e+ual to 1 in the case o! an o,seration

relating to indiidual iand 0 otherwise* the model can ,e rewritten as shown'


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ormally* the uno,sered e!!ectis now ,eing treated as the coe!!icient o! the indiidual-

speci!ic dummy aria,le* theiA

iterm representing a !i"ed e!!ect on the dependent aria,le

Yi!or indiidual i (this accounts !or the name gien to the !i"ed e!!ects approach)'


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aing re-speci!ied the model in this way* it can ,e !itted using %#S'


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ote that i! we include a dummy aria,le !or eery indiidual in the sample as well as an

intercept* we will !all into the dummy aria,le trap'


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/o aoid this* we can de!ine one indiidual to ,e the re!erence category* so that 1is its

intercept* and then treat theias the shi!ts in the intercept !or the other indiiduals'


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oweer* the choice o! re!erence category is o!ten ar,itrary and accordingly the

interpretation o! theinot particularly illuminating'


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5lternatiely* we can drop the 1intercept and de!ine dummy aria,les !or all o! the

indiiduals* as has ,een done here' /heinow ,ecome the intercepts !or each o! the

indiiduals'6



10/26


iti

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ote that* in common with the !irst two ersions o! the !i"ed e!!ects approach* the #SD$

method re+uires panel data'

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6ith cross-sectional data* one would ,e de!ining a dummy aria,le !or eery o,seration*

e"hausting the degrees o! !reedom' /he dummy aria,les on their own would gie a per!ect

,ut meaningless !it'10



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I! there are a large num,er o! indiiduals* using the #SD$ method directly is not a practical

proposition* gien the need !or a large num,er o! dummy aria,les'


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13/26

oweer* it can ,e shown mathematically that the approach is e+uialent to the within-

groups method and there!ore yields precisely the same estimates'


E+uialent to within-groups method

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/hus in practice we always use the within-groups method rather than the #SD$ method'

7ut it may ,e use!ul to now that the within-groups method is e+uialent to modelling the

!i"ed e!!ects with dummy aria,les'



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/he only apparent di!!erence ,etween the #SD$ and within-groups methods is in the

num,er o! degrees o! !reedom' It is easy to see !rom the #SD$ speci!ication that there are

nT8 k8 ndegrees o! !reedom i! the panel is ,alanced'



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In the within-groups approach* it seemed at !irst that there were nT8 k' oweer ndegrees

o! !reedom are consumed in the manipulation that eliminate thei* so the num,er o!

degrees o! !reedom is really nT8 k8 n'



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/o illustrate the use o! a !i"ed e!!ects model* we return to the e"ample in Section 1 and use

all the aaila,le data !rom 19:0 to 199;* 20*) (0'012)

Soon-to-,e- 0'09; 0'04? 80'0;1

married (0'009) (0'010) (0'00:)

Single 8 8 80'10;

(0'012)

R2 0'


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/he ta,le shows the e"tra hourly earnings o! married men and o! men who are single ,ut

married within the ne"t !our years' /he omitted category in the !irst two columns is single

men who are still single !our years later'15


#S= 19:08199;

Dependent aria,le logarithm o! hourly earnings

%#S i"ed e!!ects

3arried 0'1:4 0'10; 8

(0'00>) (0'012)

Soon-to-,e- 0'09; 0'04? 80'0;1

married (0'009) (0'010) (0'00:)

Single 8 8 80'10;

(0'012)

R2 0'


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/he controls (not shown) are the same as in the e"ample in the !irst slideshow on panel

data'

16


#S= 19:08199;


%#S i"ed e!!ects

3arried 0'1:4 0'10; 8

(0'00>) (0'012)

Soon-to-,e- 0'09; 0'04? 80'0;1

married (0'009) (0'010) (0'00:)

Single 8 8 80'10;

(0'012)

R2 0'


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/he !irst column gies the estimates o,tained ,y simply pooling the o,serations and using

%#S with ro,ust standard errors' /he estimates are ery similar to those in the wage

e+uation !or 19:: in the e"ample in the !irst slideshow onpanel data'17


#S= 19:08199;


%#S i"ed e!!ects

3arried 0'1:4 0'10; 8

(0'00>) (0'012)

Soon-to-,e- 0'09; 0'04? 80'0;1

married (0'009) (0'010) (0'00:)

Single 8 8 80'10;

(0'012)

R2 0'


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/he second column gies the !i"ed e!!ects estimates* using the within-groups method* with

single men as the re!erence category' /he third gies the !i"ed e!!ects estimates with

married men as the re!erence category'20


#S= 19:08199;


%#S i"ed e!!ects

3arried 0'1:4 0'10; 8

(0'00>) (0'012)

Soon-to-,e- 0'09; 0'04? 80'0;1

married (0'009) (0'010) (0'00:)

Single 8 8 80'10;

(0'012)

R2 0'


22/26

/he !i"ed e!!ects estimates are considera,ly lower than the %#S estimates* suggesting that

the %#S estimates were in!lated ,y uno,sered heterogeneity' eertheless the pattern is the

same'21


#S= 19:08199;


%#S i"ed e!!ects

3arried 0'1:4 0'10; 8

(0'00>) (0'012)

Soon-to-,e- 0'09; 0'04? 80'0;1

married (0'009) (0'010) (0'00:)

Single 8 8 80'10;

(0'012)

R2 0'


23/26

%ur !indings con!irm that married men earn more than single men' @art o! the di!!erential

appears to ,e attri,uta,le to the characteristics o! married men* since men who are soon-

to-marry ,ut still single also enAoy a signi!icant earnings premium'22


#S= 19:08199;


%#S i"ed e!!ects

3arried 0'1:4 0'10; 8

(0'00>) (0'012)

Soon-to-,e- 0'09; 0'04? 80'0;1

married (0'009) (0'010) (0'00:)

Single 8 8 80'10;

(0'012)

R2 0'


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oweer i! we mae married men the omitted category* as in the third column* we !ind that

soon-to-,e-married men earn signi!icantly less than married men' /hus part o! the

marriage premium appears to ,e attri,uta,le to the e!!ect o! marriage itsel!'2


#S= 19:08199;


%#S i"ed e!!ects

3arried 0'1:4 0'10; 8

(0'00>) (0'012)

Soon-to-,e- 0'09; 0'04? 80'0;1

married (0'009) (0'010) (0'00:)

Single 8 8 80'10;

(0'012)

R2 0'


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ence ,oth hypotheses relating to the marriage premium appear to ,e partly true'

24


#S= 19:08199;


%#S i"ed e!!ects

3arried 0'1:4 0'10; 8

(0'00>) (0'012)

Soon-to-,e- 0'09; 0'04? 80'0;1

married (0'009) (0'010) (0'00:)

Single 8 8 80'10;

(0'012)

R2 0'


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Copyright Christopher Dougherty 2011'

/hese slideshows may ,e downloaded ,y anyone* anywhere !or personal use'

Su,Aect to respect !or copyright and* where appropriate* attri,ution* they may ,e

used as a resource !or teaching an econometrics course' /here is no need to

re!er to the author'

/he content o! this slideshow comes !rom Section 14'2 o! C' Dougherty*

Introduction to Econometrics* !ourth edition 2011* %"!ord Bniersity @ress'

5dditional (!ree) resources !or ,oth students and instructors may ,e

downloaded !rom the %B@ %nline esource Centre

http&&www'oup'com&u&orc&,in&9>:0199?;>0:9&'

Indiiduals studying econometrics on their own and who !eel that they might

,ene!it !rom participation in a !ormal course should consider the #ondon School

o! Economics summer school course

EC212 Introduction to Econometrics

http&&www2'lse'ac'u&study&summerSchools&summerSchool&ome'asp"or the Bniersity o! #ondon International @rogrammes distance learning course

20 Elements o! Econometrics

www'londoninternational'ac'u&lse'

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Chapter 14 Fixed Effects Regressions Least Square Dummy Variable Approach (EC220)

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