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微观计量经济学模型ModelofMicroeconometricsdoc
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
1.241929965-0.2209318580.6874661850.006358743-0.236682273
oldkidsforeignyesI（age^2）
-0.0486901700.236644422-0.097504844
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
1.495137092-0.2659758800.8276281450.007655177-0.284937521
oldkidsI（age^2）
-0.058617218-0.117384323
Foreign:
（Intercept）incomeageeducationyoungkids
1.136517140-0.2021795510.6291152680.005819024-0.216593099
oldkidsI（age^2）
-0.044557434-0.089228804
（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,anordere
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