These data are taken from the 1980 Census. These data were provided by Professor William Evans of the University of Maryland and were used in his paper with Joshua Angrist Children and Thier Parents’ Labor Supply: Evidence from Exogenous Variation in Family Size, American Economic Review, June 1998, Vol. 88, No. 3, 450-477. The file Fertility.dta (in STATA format) contains data on 254,654 women between the age of 21 and 35. The data in Fertility are a subset of the data used in the Angrist-Evans paper. (The file Fertility_Small contains data on a 30,000 randomly selected women from the Fertility data set. This smaller dataset is provided for students with memory limitations on their computer software.)
Artikkeli loytyy osoitteista http://siteresources.worldbank.org/INTPUBSERV/Resources/Angrist_and_Evans.pdf http://siteresources.worldbank.org/INTPUBSERV/Resources/Angrist_and_Evans.pdf
(a) OLS regressio kun y-muuttuja on weeksworked ja x-muuttuja on morekids
file<-"http://cc.oulu.fi/~jklemela/econometrics/Fertility_small.csv"
data<-read.table(file,skip=1,sep=",")
y<-data[,9] # weeksmom
x<-data[,1] # morekids
reg.model<-lm(y ~ x)
summary(reg.model)
Call:
lm(formula = y ~ x)
Residuals:
Min 1Q Median 3Q Max
-21.48 -21.48 -13.48 26.52 36.53
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 21.4782 0.1592 135.0 <2e-16 ***
x -6.0082 0.2590 -23.2 <2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 21.75 on 29998 degrees of freedom
Multiple R-squared: 0.01762, Adjusted R-squared: 0.01759
F-statistic: 538.2 on 1 and 29998 DF, p-value: < 2.2e-16
(b) IV regressio kun y-muuttuja on weeksworked, x-muuttuja on morekids ja instrumenttimumuuttuja on samesex
file<-"http://cc.oulu.fi/~jklemela/econometrics/Fertility_small.csv"
data<-read.table(file,skip=1,sep=",")
y<-data[,9] # weeksworked
x<-data[,1] # morekids
z<-data[,4] # samesex
cor(x,z)
[1] 0.06891525
# IV-estimaattori
n<-length(x)
K<-2
Z<-matrix(0,n,K)
Z[,1]<-1
Z[,2]<-z
X<-matrix(0,n,K)
X[,1]<-1
X[,2]<-x
ztx<-t(Z)%*%X
invztx<-solve(ztx,diag(2))
b<-invztx%*%t(Z)%*%y
b
[,1]
[1,] 21.487634
[2,] -6.033194
# 2SLS-estimaattori
n<-length(x)
K<-2
Z<-matrix(0,n,K)
Z[,1]<-1
Z[,2]<-z
X<-matrix(0,n,K)
X[,1]<-1
X[,2]<-x
# 1. askel
ZtZ<-t(Z)%*%Z
invZtZ<-solve(ZtZ,diag(rep(1,K)))
b1<-invZtZ%*%t(Z)%*%x
b1
[1,] 0.34397853
[2,] 0.06681975
# Toinen askel
n<-length(y)
K<-2
xhat<-Z%*%b1
Xhat<-matrix(0,n,K)
Xhat[,1]<-1
Xhat[,2]<-xhat
XtX<-t(Xhat)%*%X
invXtX<-solve(XtX,diag(rep(1,K)))
b<-invXtX%*%t(Xhat)%*%y
b
[1,] 21.487634
[2,] -6.033194
# hajontakuvio
plot(x,y)
segments(0,b[1],1,b[1]+b[2])
# histogrammat
hist(y)
y0<-y[(x==0)]
hist(y0)
x11()
y1<-y[(x==1)]
hist(y1)
sum(x==0)
#[1] 18672
(c) IV regressio kun y-muuttuja on weeksworked, x-muuttuja on morekids, instrumenttimumuuttuja on samesex seka agemom, black, hispan ja othrace ovat eksogeenisia selittavia muuttujia.
file<-"http://cc.oulu.fi/~jklemela/econometrics/Fertility_small.csv"
data<-read.table(file,skip=1,sep=",")
y<-data[,9] #weeksworked
x<-data[,1] #morekids
z<-data[,4] #samesex
w1<-data[,5] #agemom
w2<-data[,6] #black
w3<-data[,7] #hispan
w4<-data[,8] #othrace
# IV-estimaattori
n<-length(x)
K<-6
Z<-matrix(0,n,K)
Z[,1]<-1
Z[,2]<-z
Z[,3]<-w1
Z[,4]<-w2
Z[,5]<-w3
Z[,6]<-w4
X<-matrix(0,n,K)
X[,1]<-1
X[,2]<-x
X[,3]<-w1
X[,4]<-w2
X[,5]<-w3
X[,6]<-w4
ztx<-t(Z)%*%X
invztx<-solve(ztx,diag(K))
b<-invztx%*%t(Z)%*%y
b
[,1]
[1,] -4.3703424
[2,] -5.7807463
[3,] 0.8234973
[4,] 11.4262797
[5,] -0.4117677
[6,] 3.3077888
# 2sls
# Ensimmainen askel
n<-length(x)
K<-6
Z<-matrix(0,n,K)
Z[,1]<-1
Z[,2]<-z
Z[,3]<-w1
Z[,4]<-w2
Z[,5]<-w3
Z[,6]<-w4
ZtZ<-t(Z)%*%Z
invZtZ<-solve(ZtZ,diag(rep(1,K)))
b1<-invZtZ%*%t(Z)%*%x
b1
[,1]
[1,] -0.17301671
[2,] 0.06786242
[3,] 0.01643797
[4,] 0.09626415
[5,] 0.14843272
[6,] 0.02352631
# Toinen askel
n<-length(y)
K<-6
xhat<-Z%*%b1
Xhat<-matrix(0,n,K)
Xhat[,1]<-1
Xhat[,2]<-xhat
Xhat[,3]<-w1
Xhat[,4]<-w2
Xhat[,5]<-w3
Xhat[,6]<-w4
XtX<-t(Xhat)%*%X
invXtX<-solve(XtX,diag(rep(1,K)))
b<-invXtX%*%t(Xhat)%*%y
b
[,1]
[1,] -4.3703424
[2,] -5.7807463
[3,] 0.8234973
[4,] 11.4262797
[5,] -0.4117677
[6,] 3.3077888
Kokeillaan sem-pakettia
library(sem)
# pieni malli
model<-tsls(y ~ x , instruments = ~ z )
model
Model Formula: y ~ x
Instruments: ~z
Coefficients:
(Intercept) x
21.487634 -6.033194
# diagnostiikka
summary(model)
2SLS Estimates
Model Formula: y ~ x
Instruments: ~z
Residuals:
Min. 1st Qu. Median Mean 3rd Qu. Max.
-21.5 -21.5 -13.5 0.0 26.5 36.5
Estimate Std. Error t value Pr(>|t|)
(Intercept) 21.488 1.425 15.083 0.0000
x -6.033 3.758 -1.605 0.1084
Residual standard error: 21.7472 on 29998 degrees of freedom
# kaikki muuttujat
model<-tsls(y ~ x+w1+w2+w3+w4 , instruments = ~ z+w1+w2+w3+w4 )
model
Model Formula: y ~ x + w1 + w2 + w3 + w4
Instruments: ~z + w1 + w2 + w3 + w4
Coefficients:
(Intercept) x w1 w2 w3 w4
-4.3703424 -5.7807463 0.8234973 11.4262797 -0.4117677 3.3077888
summary(model)
2SLS Estimates
Model Formula: y ~ x + w1 + w2 + w3 + w4
Instruments: ~z + w1 + w2 + w3 + w4
Residuals:
Min. 1st Qu. Median Mean 3rd Qu. Max.
-35.9 -17.9 -10.7 0.0 23.2 44.0
Estimate Std. Error t value Pr(>|t|)
(Intercept) -4.3703 1.2279 -3.5591 3.728e-04
x -5.7807 3.6450 -1.5860 1.128e-01
w1 0.8235 0.0700 11.7651 0.000e+00
w2 11.4263 0.6552 17.4387 0.000e+00
w3 -0.4118 0.7480 -0.5505 5.820e-01
w4 3.3078 0.5959 5.5511 2.862e-08
Residual standard error: 21.4201 on 29994 degrees of freedom
# virheellinen input
tsls(y ~ x+w1+w2+w3+w4 , instruments = ~ z)
Error in chol.default(XtZ %*% invZtZ %*% t(XtZ)) :
the leading minor of order 3 is not positive definite
Kokeillaan SAS:ia
http://support.sas.com/documentation/cdl/en/etsug/60372/HTML/default/viewer.htm#etsug_syslin_sect007.htm
FILENAME
myurl URL 'http://cc.oulu.fi/~jklemela/econometrics/Fertility_small.txt';
DATA Fertility;
INFILE myurl firstobs=2;
INPUT ind $ morekids boy1st boy2nd samesex agemom black hispan othrace
weeksworked;
RUN;
proc syslin data=Fertility 2sls;
endogenous morekids;
instruments samesex;
model weeksworked = morekids;
run;
The SAS System 12:07 Wednesday, February 12, 2014 1
The SYSLIN Procedure
Two-Stage Least Squares Estimation
Model weeksworked
Dependent Variable weeksworked
Analysis of Variance
Sum of Mean
Source DF Squares Square F Value Pr > F
Model 1 1218.844 1218.844 2.58 0.1084
Error 29998 14187255 472.9400
Corrected Total 29999 14441766
Root MSE 21.74718 R-Square 0.00009
Dependent Mean 19.20950 Adj R-Sq 0.00005
Coeff Var 113.21057
Parameter Estimates
Parameter Standard
Variable DF Estimate Error t Value Pr > |t|
Intercept 1 21.48763 1.424628 15.08 <.0001
morekids 1 -6.03319 3.758169 -1.61 0.1084
###############################################################
FILENAME
myurl URL 'http://cc.oulu.fi/~jklemela/econometrics/Fertility_small.txt';
DATA Fertility;
INFILE myurl firstobs=2;
INPUT ind $ morekids boy1st boy2nd samesex agemom black hispan othrace
weeksworked;
RUN;
proc syslin data=Fertility 2sls;
endogenous morekids;
instruments samesex agemom black hispan othrace;
model weeksworked = morekids agemom black hispan othrace;
run;
The SAS System 12:10 Wednesday, February 12, 2014 2
The SYSLIN Procedure
Two-Stage Least Squares Estimation
Model weeksworked
Dependent Variable weeksworked
Analysis of Variance
Sum of Mean
Source DF Squares Square F Value Pr > F
Model 5 361252.8 72250.56 157.47 <.0001
Error 29994 13761883 458.8212
Corrected Total 29999 14441766
Root MSE 21.42011 R-Square 0.02558
Dependent Mean 19.20950 Adj R-Sq 0.02542
Coeff Var 111.50791
Parameter Estimates
Parameter Standard
Variable DF Estimate Error t Value Pr > |t|
Intercept 1 -4.37034 1.227949 -3.56 0.0004
morekids 1 -5.78075 3.644973 -1.59 0.1128
agemom 1 0.823497 0.069995 11.77 <.0001
black 1 11.42628 0.655227 17.44 <.0001
hispan 1 -0.41177 0.748047 -0.55 0.5820
othrace 1 3.307789 0.595876 5.55 <.0001
###############################################################
Huom!
FILENAME
myurl URL 'http://cc.oulu.fi/~jklemela/econometrics/Fertility_small.txt';
DATA Fertility;
INFILE myurl firstobs=2;
INPUT ind $ morekids boy1st boy2nd samesex agemom black hispan othrace
weeksworked;
RUN;
proc syslin data=Fertility 2sls;
endogenous morekids;
instruments samesex;
model weeksworked = morekids agemom black hispan othrace;
run;
The SAS System 12:10 Wednesday, February 12, 2014 3
The SYSLIN Procedure
Two-Stage Least Squares Estimation
Model weeksworked
Dependent Variable weeksworked
Analysis of Variance
Sum of Mean
Source DF Squares Square F Value Pr > F
Model 5 361252.8 72250.56 157.43 <.0001
Error 29994 13765597 458.9450
Corrected Total 29999 14441766
Root MSE 21.42300 R-Square 0.02557
Dependent Mean 19.20950 Adj R-Sq 0.02541
Coeff Var 111.52296
Parameter Estimates
Parameter Standard
Variable DF Estimate Error t Value Pr > |t|
Intercept 1 -1.35070 1.799170 -0.75 0.4528
morekids 1 -5.87095 3.702350 -1.59 0.1128
agemom 1 0.728474 0.036624 19.89 <.0001
black 1 10.86980 0.552211 19.68 <.0001
hispan 1 -1.26982 0.520349 -2.44 0.0147
othrace 1 3.171789 0.589436 5.38 <.0001