微观计量经济学模型ModelofMicroeconometrics.doc

微观计量经济学模型（Model of Microeconometrics ）

1.1 Generalized Linear Mod els

Three aspects of the linear regression model for a conditionally normally distributed response y are:

(1) The linear predictor βηT i i x = through which )|(i i i x y E =μ. (2) i i x y | is ),(2σμi N (3) i i ημ=

GLMs: extends (2)and(3) to more general families of distributions for y. Specifically, i i x y | may follow a density:

⎭

⎬⎫+⎩⎨⎧-=);()

(exp ),;(φφθθφθy c b y y f

θ:canonical parameter, depends on the linear predictor.

φ:dispersion parameter, is often known.

Also i η and i μ are related by a monotonic transformation,

i i g ημ=)(

Called the link function of the GLM.

Selected GLM families and their canonical link

1.2 Binary Depend ent Variables

Model:

n i x F p x y E T i i i i ,......2,1),()|(===β

In the probit case: F equals the standard normal CDF In the logit case: F equals the logistic CDF

Example:

(1)Data

Considering female labor participation for a sample of 872 women from Switzerland.

The dependent variable: participation The explain variables:

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

library("AER")

data("SwissLabor")

summary(SwissLabor)

participation income age education

no :471 Min. : 7.187 Min. :2.000 Min. : 1.000

yes:401 1st Qu.:10.472 1st Qu.:3.200 1st Qu.: 8.000

Median :10.643 Median :3.900 Median : 9.000

Mean :10.686 Mean :3.996 Mean : 9.307

3rd Qu.:10.887 3rd Qu.:4.800 3rd Qu.:12.000

Max. :12.376 Max. :6.200 Max. :21.000 youngkids oldkids foreign

Min. :0.0000 Min. :0.0000 no :656

1st Qu.:0.0000 1st Qu.:0.0000 yes:216

Median :0.0000 Median :1.0000

Mean :0.3119 Mean :0.9828

3rd Qu.:0.0000 3rd Qu.:2.0000

Max. :3.0000 Max. :6.0000

(2) Estimation

R:

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

summary(swiss_prob)

Call:

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

data = SwissLabor)

Deviance Residuals:

Min 1Q Median 3Q Max

-1.9191 -0.9695 -0.4792 1.0209 2.4803

Coefficients:

Estimate Std. Error z value Pr(>|z|)

(Intercept) 3.74909 1.40695 2.665 0.00771 **

income -0.66694 0.13196 -5.054 4.33e-07 ***

age 2.07530 0.40544 5.119 3.08e-07 ***

education 0.01920 0.01793 1.071 0.28428

youngkids -0.71449 0.10039 -7.117 1.10e-12 ***

oldkids -0.14698 0.05089 -2.888 0.00387 **

foreignyes 0.71437 0.12133 5.888 3.92e-09 ***

I(age^2) -0.29434 0.04995 -5.893 3.79e-09 ***

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