微观计量经济学模型ModelofMicroeconometrics.docx

微观计量经济学模型ModelofMicroeconometrics.docx

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微观计量经济学模型ModelofMicroeconometrics

微观计量经济学模型（ModelofMicroeconometrics）

1.1GeneralizedLinearModels

Threeaspectsofthelinearregressionmodelforaconditionallynormallydistributedresponseyare:

（1）Thelinearpredictor

throughwhich

.

（2）

is

（3）

GLMs:

extends

（2）and（3）tomoregeneralfamiliesofdistributionsfory.Specifically,

mayfollowadensity:

:

canonicalparameter,dependsonthelinearpredictor.

:

dispersionparameter,isoftenknown.

Also

and

arerelatedbyamonotonictransformation,

CalledthelinkfunctionoftheGLM.

SelectedGLMfamiliesandtheircanonicallink

Family

Canonicallink

Name

binomial

logit

gaussian

identity

poisson

log

1.2BinaryDependentVariables

Model:

Intheprobitcase:

equalsthestandardnormalCDF

Inthelogitcase:

equalsthelogisticCDF

Example:

（1）Data

Consideringfemalelaborparticipationforasampleof872womenfromSwitzerland.

Thedependentvariable:

participation

Theexplainvariables:

income,age,education,youngkids,oldkids,foreignyesandage^2.

R:

library（"AER"）

data（"SwissLabor"）

summary（SwissLabor）

participationincomeageeducation

no:

471Min.:

7.187Min.:

2.000Min.:

1.000

yes:

4011stQu.:

10.4721stQu.:

3.2001stQu.:

8.000

Median:

10.643Median:

3.900Median:

9.000

Mean:

10.686Mean:

3.996Mean:

9.307

3rdQu.:

10.8873rdQu.:

4.8003rdQu.:

12.000

Max.:

12.376Max.:

6.200Max.:

21.000

youngkidsoldkidsforeign

Min.:

0.0000Min.:

0.0000no:

656

1stQu.:

0.00001stQu.:

0.0000yes:

216

Median:

0.0000Median:

1.0000

Mean:

0.3119Mean:

0.9828

3rdQu.:

0.00003rdQu.:

2.0000

Max.:

3.0000Max.:

6.0000

（2）Estimation

R:

swiss_prob=glm（participation~.+I（age^2）,data=SwissLabor,family=binomial（link="probit"））

summary（swiss_prob）

Call:

glm（formula=participation~.+I（age^2）,family=binomial（link="probit"）,

data=SwissLabor）

DevianceResiduals:

Min1QMedian3QMax

-1.9191-0.9695-0.47921.02092.4803

Coefficients:

EstimateStd.ErrorzvaluePr（>|z|）

（Intercept）3.749091.406952.6650.00771**

income-0.666940.13196-5.0544.33e-07***

age2.075300.405445.1193.08e-07***

education0.019200.017931.0710.28428

youngkids-0.714490.10039-7.1171.10e-12***

oldkids-0.146980.05089-2.8880.00387**

foreignyes0.714370.121335.8883.92e-09***

I（age^2）-0.294340.04995-5.8933.79e-09***

---

Signif.codes:

0‘***’0.001‘**’0.01‘*’0.05‘.’0.1‘’1

（Dispersionparameterforbinomialfamilytakentobe1）

Nulldeviance:

1203.2on871degreesoffreedom

Residualdeviance:

1017.2on864degreesoffreedom

AIC:

1033.2

NumberofFisherScoringiterations:

4

（3）Visualization

Plottingparticipationversusage

R:

plot（participation~age,data=SwissLabor,ylevels=2:

1）

（4）Effects

Averagemarginaleffects:

Theaverageofthesamplemarginaleffects:

R:

fav=mean（dnorm（predict（swiss_prob,type="link"）））

fav*coef（swiss_prob）

（Intercept）incomeageeducationyoungkids

oldkidsforeignyesI（age^2）

Theaveragemarginaleffectsattheaverageregressor:

R:

av=colMeans（SwissLabor[,-c（1,7）]）

av=data.frame（rbind（swiss=av,foreign=av）,foreign=factor（c（"no","yes"）））

av=predict（swiss_prob,newdata=av,type="link"）

av=dnorm（av）

av["swiss"]*coef（swiss_prob）[-7]

av["foreign"]*coef（swiss_prob）[-7]

swiss:

（Intercept）incomeageeducationyoungkids

oldkidsI（age^2）

Foreign:

（Intercept）incomeageeducationyoungkids

oldkidsI（age^2）

（5）Goodnessoffitandprediction

Pseudo-R2:

asthelog-likelihoodforthefittedmodel,

asthelog-likelihoodforthemodelcontainingonlyaconstantterm.

R:

swiss_prob0=update（swiss_prob,formula=.~1）

1-as.vector（logLik（swiss_prob）/logLik（swiss_prob0））

[1]0.1546416

Percentcorrectlypredicted:

R:

table（true=SwissLabor$participation,pred=round（fitted（swiss_prob）））

pred

true01

no337134

yes146255

67.89%

ROCcurve:

TPR（c）:

thenumberofwomenparticipatinginthelaborforcethatareclassifiedasparticipatingcomparedwiththetotalnumberofwomenparticipating.

FPR（c）:

thenumberofwomennotparticipatinginthelaborforcethatareclassifiedasparticipatingcomparedwiththetotalnumberofwomennotparticipating.

R:

library（"ROCR"）

pred=prediction（fitted（swiss_prob）,SwissLabor$participation）

plot（performance（pred,"acc"））

plot（performance（pred,"tpr","fpr"））

abline（0,1,lty=2）

●Extensions:

Multinomialresponses

Forillustratingthemostbasicversionofthemultinomiallogitmodel,amodelwithonlyindividual-specificcovariates,.

data（"BankWages"）

Itcontains,foremployeesofaUSbank,anorderedfactorjobwithlevels"custodial","admin"（foradministration）,and"manage"（formanagement）,tobemodeledasafunctionofeducation（inyears）andafactorminorityindicatingminoritystatus.Therealsoexistsafactorgender,butsincetherearenowomeninthecategory"custo