storage display value
variable name type format label variable label
-------------------------------------------------------------------------------
county int %9.0g county identifier
year byte %9.0g 81 to 87
crmrte float %9.0g crimes committed per person
prbarr float %9.0g 'probability' of arrest
prbconv float %9.0g 'probability' of conviction
prbpris float %9.0g 'probability' of prison sentenc
avgsen float %9.0g avg. sentence, days
polpc float %9.0g police per capita
density float %9.0g people per sq. mile
taxpc float %9.0g tax revenue per capita
west byte %9.0g =1 if in western N.C.
central byte %9.0g =1 if in central N.C.
urban byte %9.0g =1 if in SMSA
pctmin80 float %9.0g perc. minority, 1980
wcon float %9.0g weekly wage, construction
wtuc float %9.0g wkly wge, trns, util, commun
wtrd float %9.0g wkly wge, whlesle, retail trade
wfir float %9.0g wkly wge, fin, ins, real est
wser float %9.0g wkly wge, service industry
wmfg float %9.0g wkly wge, manufacturing
wfed float %9.0g wkly wge, fed employees
wsta float %9.0g wkly wge, state employees
wloc float %9.0g wkly wge, local gov emps
mix float %9.0g offense mix: face-to-face/other
pctymle float %9.0g percent young male
d82 byte %9.0g =1 if year == 82
d83 byte %9.0g =1 if year == 83
d84 byte %9.0g =1 if year == 84
d85 byte %9.0g =1 if year == 85
d86 byte %9.0g =1 if year == 86
d87 byte %9.0g =1 if year == 87
lcrmrte float %9.0g log(crmrte)
lprbarr float %9.0g log(prbarr)
lprbconv float %9.0g log(prbconv)
lprbpris float %9.0g log(prbpris)
lavgsen float %9.0g log(avgsen)
lpolpc float %9.0g log(polpc)
ldensity float %9.0g log(density)
ltaxpc float %9.0g log(taxpc)
lwcon float %9.0g log(wcon)
lwtuc float %9.0g log(wtuc)
lwtrd float %9.0g log(wtrd)
lwfir float %9.0g log(wfir)
lwser float %9.0g log(wser)
lwmfg float %9.0g log(wmfg)
lwfed float %9.0g log(wfed)
lwsta float %9.0g log(wsta)
lwloc float %9.0g log(wloc)
lmix float %9.0g log(mix)
lpctymle float %9.0g log(pctymle)
lpctmin float %9.0g log(pctmin)
clcrmrte float %9.0g lcrmrte - lcrmrte[_n-1]
clprbarr float %9.0g lprbarr - lprbarr[_n-1]
clprbcon float %9.0g lprbconv - lprbconv[_n-1]
clprbpri float %9.0g lprbpri - lprbpri[t-1]
clavgsen float %9.0g lavgsen - lavgsen[t-1]
clpolpc float %9.0g lpolpc - lpolpc[t-1]
cltaxpc float %9.0g ltaxpc - ltaxpc[t-1]
clmix float %9.0g lmix - lmix[t-1]
Estimoi lineaarinen malli FE-estimaattorilla käyttäen kaikkia vuosia 81-87. Mallissa vastemuuttuja on log(crmrte) ja selittävät muuttujat ovat log(prbarr), log(prbconv), log(prbpris), log(avgsen) ja log(polpc).
file<-"http://cc.oulu.fi/~jklemela/panel/cornwell.raw"
data<-read.table(file=file)
# haetaan muuttujat
y<-log(data[,3])
x1<-log(data[,4])
x2<-log(data[,5])
x3<-log(data[,6])
x4<-log(data[,7])
x5<-log(data[,8])
# muunetaan data matriisimuotoon
y<-matrix(y,length(y),1)
K<-5
x<-matrix(1,length(y),K)
x[,1]<-x1
x[,2]<-x2
x[,3]<-x3
x[,4]<-x4
x[,5]<-x5
# tehdaan time demeaning
ydots<-y # y 2 pistetta = y- aikakeskiarvot
xdots<-x # x 2 pistetta = x- aikakeskiarvot
county<-data[,1]
year<-data[,2]
uc<-unique(county)
uy<-unique(year)
N<-length(uc)
T<-length(uy)
jT<-matrix(1,T,1)
QT<-diag(T)-jT%*%t(jT)/T
for (i in 1:N){
now<-uc[i]
ind<-(county==now)
yi<-y[ind]
xi<-x[ind,]
ydots[ind]<-yi-mean(yi)
#xdots[ind,]<-xi-t(matrix(colMeans(xi),K,T))
xdots[ind,]<-QT%*%xi
}
---------------------------------------------------
# lasketaan estimaattori
C<-t(xdots)%*%xdots
I<-diag(1,K)
D<-solve(C,I)
betahatFE<-D%*%t(xdots)%*%ydots
betahatFE
[,1]
[1,] -0.38353400
[2,] -0.30597508
[3,] -0.19545208
[4,] 0.03566462
[5,] 0.41377048
--------------------------------------------------
# tehdaan t-testi: Robusti
A<-matrix(0,K,K)
B<-matrix(0,K,K)
for (i in 1:N){
now<-uc[i]
ind<-(county==now)
yi<-ydots[ind]
xi<-xdots[ind,]
ui<-yi-xi%*%betahatFE
A<-A+t(xi)%*%xi
B<-B+t(xi)%*%ui%*%t(ui)%*%xi
}
I<-diag(1,K)
invA<-solve(A,I)
Avar<-invA%*%B%*%invA
Avar
[,1] [,2] [,3] [,4] [,5]
[1,] 0.0035210340 0.0016180157 0.0011140222 -3.889292e-04 -1.634012e-03
[2,] 0.0016180157 0.0025620783 0.0002199664 -2.205612e-04 -1.803734e-03
[3,] 0.0011140222 0.0002199664 0.0019760221 4.590546e-04 -3.776503e-04
[4,] -0.0003889292 -0.0002205612 0.0004590546 1.040595e-03 9.444035e-05
[5,] -0.0016340121 -0.0018037338 -0.0003776503 9.444035e-05 7.243734e-03
sdhats<-matrix(0,K,1)
tstats<-matrix(0,K,1)
pvals<-matrix(0,K,1)
for (k in 1:K){
sdhats[k]<-sqrt(Avar[k,k])
tstats[k]<-betahatFE[k]/sdhats[k]
pvals[k]<-2*(1-pnorm(abs(tstats[k])))
}
sdhats
tstats
pvals
> sdhats
[,1]
[1,] 0.05933830
[2,] 0.05061698
[3,] 0.04445247
[4,] 0.03225826
[5,] 0.08511013
> tstats
[,1]
[1,] -6.463515
[2,] -6.044910
[3,] -4.396878
[4,] 1.105597
[5,] 4.861589
> pvals
[,1]
[1,] 1.022984e-10
[2,] 1.494933e-09
[3,] 1.098191e-05
[4,] 2.689011e-01
[5,] 1.164471e-06
--------------------------------------------------
# tehdaan t-testi: Epärobusti
A<-matrix(0,K,K)
sigma0<-0
for (i in 1:N){
now<-uc[i]
ind<-(county==now)
yi<-ydots[ind]
xi<-xdots[ind,]
ui<-yi-xi%*%betahatFE
A<-A+t(xi)%*%xi
sigma0<-sigma0+sum(ui^2)
}
sigma2<-sigma0/(N*(T-1)-K)
sigma2.ols<-sigma0/(N*T-K)
I<-diag(1,K)
invA<-solve(A,I)
Avar<-sigma2*invA
sigma2
sigma2.ols
sqrt(sigma2)
sqrt(sigma2.ols)
Avar
> sigma2
[1] 0.0215554
> sigma2.ols
[1] 0.01845142
> sqrt(sigma2)
[1] 0.1468176
> sqrt(sigma2.ols)
[1] 0.135836
> Avar
[,1] [,2] [,3] [,4] [,5]
[1,] 1.120042e-03 0.0004393709 2.924350e-04 3.766651e-05 -2.899575e-04
[2,] 4.393709e-04 0.0004777594 1.866242e-04 1.980380e-05 -3.087283e-04
[3,] 2.924350e-04 0.0001866242 1.113133e-03 -2.370097e-05 -1.122500e-04
[4,] 3.766651e-05 0.0000198038 -2.370097e-05 6.824951e-04 2.204673e-05
[5,] -2.899575e-04 -0.0003087283 -1.122500e-04 2.204673e-05 7.545205e-04
sdhats<-matrix(0,K,1)
tstats<-matrix(0,K,1)
pvals<-matrix(0,K,1)
for (k in 1:K){
sdhats[k]<-sqrt(Avar[k,k])
tstats[k]<-betahatFE[k]/sdhats[k]
pvals[k]<-2*(1-pnorm(abs(tstats[k])))
}
sdhats
tstats
pvals
> sdhats
[,1]
[1,] 0.03346702
[2,] 0.02185771
[3,] 0.03336365
[4,] 0.02612461
[5,] 0.02746854
> tstats
[,1]
[1,] -11.460058
[2,] -13.998498
[3,] -5.858233
[4,] 1.365174
[5,] 15.063434
> pvals
[,1]
[1,] 0.000000e+00
[2,] 0.000000e+00
[3,] 4.678167e-09
[4,] 1.721985e-01
[5,] 0.000000e+00
---------------------------------------------
# kaytetaan lm-funktiota
reg.model<-lm(ydots ~ 0+xdots)
summary(reg.model)
Call:
lm(formula = ydots ~ 0 + xdots)
Residuals:
Min 1Q Median 3Q Max
-0.68349 -0.07548 -0.00337 0.07792 0.53094
Coefficients:
Estimate Std. Error t value Pr(>|t|)
xdots1 -0.38353 0.03096 -12.387 < 2e-16 ***
xdots2 -0.30598 0.02022 -15.130 < 2e-16 ***
xdots3 -0.19545 0.03087 -6.332 4.63e-10 ***
xdots4 0.03566 0.02417 1.476 0.141
xdots5 0.41377 0.02541 16.281 < 2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 0.1358 on 625 degrees of freedom
Multiple R-squared: 0.359, Adjusted R-squared: 0.3539
F-statistic: 70.01 on 5 and 625 DF, p-value: < 2.2e-16
Estimoi lineaarinen regression kun indikaattorimuuttujat d1_i,...,dN_i ovat mukana.
file<-"http://cc.oulu.fi/~jklemela/panel/cornwell.raw"
data<-read.table(file=file)
county<-data[,1]
year<-data[,2]
uc<-unique(county)
uy<-unique(year)
N<-length(uc)
T<-length(uy)
y<-log(data[,3])
x1<-log(data[,4])
x2<-log(data[,5])
x3<-log(data[,6])
x4<-log(data[,7])
x5<-log(data[,8])
# muodostetaan dummy-muuttujat
dummy<-matrix(0,N*T,N-1)
for (i in 1:(N-1)){
now<-uc[i]
dummy[,i]<-as.numeric(county==now)
}
# lasketaan estimaatti
reg.model<-lm(y ~ x1+x2+x3+x4+x5+dummy)
summary(reg.model)
Call:
lm(formula = y ~ x1 + x2 + x3 + x4 + x5 + dummy)
Residuals:
Min 1Q Median 3Q Max
-0.68349 -0.07548 -0.00337 0.07792 0.53094
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -2.29884 0.19533 -11.769 < 2e-16 ***
x1 -0.38353 0.03347 -11.460 < 2e-16 ***
x2 -0.30598 0.02186 -13.998 < 2e-16 ***
x3 -0.19545 0.03336 -5.858 8.18e-09 ***
x4 0.03566 0.02612 1.365 0.172772
x5 0.41377 0.02747 15.063 < 2e-16 ***
dummy1 0.71877 0.08279 8.682 < 2e-16 ***
dummy2 0.20074 0.07987 2.513 0.012257 *
dummy3 -0.12264 0.08403 -1.459 0.145015
dummy4 0.45215 0.08210 5.507 5.66e-08 ***
dummy5 0.01904 0.08376 0.227 0.820253
dummy6 -0.28616 0.08708 -3.286 0.001082 **
dummy7 0.72226 0.08100 8.916 < 2e-16 ***
dummy8 0.40550 0.08312 4.879 1.41e-06 ***
dummy9 0.33337 0.08180 4.076 5.29e-05 ***
dummy10 -0.03758 0.08036 -0.468 0.640283
dummy11 0.56061 0.08476 6.614 9.09e-11 ***
dummy12 0.37061 0.08255 4.490 8.75e-06 ***
dummy13 0.55657 0.08309 6.698 5.35e-11 ***
dummy14 0.50751 0.08254 6.149 1.53e-09 ***
dummy15 0.37737 0.08175 4.616 4.90e-06 ***
dummy16 0.62482 0.08490 7.359 7.00e-13 ***
dummy17 0.23738 0.08041 2.952 0.003296 **
dummy18 -0.07266 0.07952 -0.914 0.361267
dummy19 0.33432 0.08374 3.992 7.46e-05 ***
dummy20 0.63680 0.08153 7.811 3.02e-14 ***
dummy21 0.42068 0.08130 5.174 3.24e-07 ***
dummy22 0.58413 0.08160 7.159 2.70e-12 ***
dummy23 0.99676 0.08531 11.685 < 2e-16 ***
dummy24 0.07231 0.07935 0.911 0.362575
dummy25 0.52989 0.09197 5.762 1.41e-08 ***
dummy26 0.51547 0.07996 6.447 2.56e-10 ***
dummy27 0.18807 0.07950 2.366 0.018350 *
dummy28 0.30638 0.08092 3.786 0.000170 ***
dummy29 0.87921 0.08965 9.807 < 2e-16 ***
dummy30 1.05238 0.08186 12.855 < 2e-16 ***
dummy31 0.82415 0.08687 9.488 < 2e-16 ***
dummy32 0.16994 0.08197 2.073 0.038637 *
dummy33 0.79746 0.08700 9.166 < 2e-16 ***
dummy34 0.54242 0.08355 6.492 1.94e-10 ***
dummy35 0.06023 0.08070 0.746 0.455808
dummy36 0.78050 0.08844 8.825 < 2e-16 ***
dummy37 0.66854 0.08263 8.091 4.00e-15 ***
dummy38 0.74178 0.08134 9.119 < 2e-16 ***
dummy39 0.29362 0.08202 3.580 0.000375 ***
dummy40 0.48591 0.08036 6.047 2.77e-09 ***
dummy41 0.65052 0.08157 7.975 9.29e-15 ***
dummy42 0.78201 0.08089 9.667 < 2e-16 ***
dummy43 0.77688 0.08040 9.662 < 2e-16 ***
dummy44 -0.24379 0.08204 -2.971 0.003097 **
dummy45 0.63081 0.07991 7.894 1.67e-14 ***
dummy46 0.96522 0.08286 11.648 < 2e-16 ***
dummy47 0.78585 0.08295 9.474 < 2e-16 ***
dummy48 0.14479 0.07968 1.817 0.069749 .
dummy49 0.20042 0.08017 2.500 0.012722 *
dummy50 -0.61259 0.08534 -7.178 2.38e-12 ***
dummy51 -1.56860 0.11027 -14.225 < 2e-16 ***
dummy52 0.62097 0.08324 7.460 3.52e-13 ***
dummy53 1.12999 0.08818 12.815 < 2e-16 ***
dummy54 0.58878 0.08409 7.002 7.61e-12 ***
dummy55 0.35909 0.08163 4.399 1.31e-05 ***
dummy56 0.93649 0.08095 11.569 < 2e-16 ***
dummy57 1.12363 0.08513 13.200 < 2e-16 ***
dummy58 0.43654 0.08603 5.074 5.38e-07 ***
dummy59 0.73649 0.08271 8.905 < 2e-16 ***
dummy60 0.56242 0.09005 6.246 8.61e-10 ***
dummy61 0.17278 0.08015 2.156 0.031549 *
dummy62 0.58196 0.08424 6.909 1.40e-11 ***
dummy63 0.78323 0.09087 8.619 < 2e-16 ***
dummy64 0.41371 0.08245 5.018 7.13e-07 ***
dummy65 0.56072 0.08166 6.867 1.83e-11 ***
dummy66 0.84451 0.08367 10.093 < 2e-16 ***
dummy67 -0.07902 0.08013 -0.986 0.324520
dummy68 0.34919 0.08009 4.360 1.56e-05 ***
dummy69 0.73344 0.08122 9.031 < 2e-16 ***
dummy70 0.79528 0.08130 9.782 < 2e-16 ***
dummy71 0.49296 0.08245 5.979 4.11e-09 ***
dummy72 0.51435 0.08227 6.252 8.28e-10 ***
dummy73 0.31134 0.08158 3.816 0.000151 ***
dummy74 0.28536 0.08018 3.559 0.000405 ***
dummy75 0.97623 0.08225 11.869 < 2e-16 ***
dummy76 0.25042 0.08289 3.021 0.002637 **
dummy77 0.03507 0.08069 0.435 0.664033
dummy78 0.28336 0.07996 3.544 0.000429 ***
dummy79 -0.83737 0.08805 -9.511 < 2e-16 ***
dummy80 -0.06260 0.08221 -0.761 0.446746
dummy81 0.47113 0.08167 5.768 1.36e-08 ***
dummy82 1.01393 0.08264 12.269 < 2e-16 ***
dummy83 0.72637 0.08570 8.475 2.28e-16 ***
dummy84 -0.21126 0.09918 -2.130 0.033615 *
dummy85 0.67601 0.07949 8.505 < 2e-16 ***
dummy86 0.08485 0.08562 0.991 0.322134
dummy87 0.69076 0.08100 8.528 < 2e-16 ***
dummy88 0.39635 0.08118 4.883 1.38e-06 ***
dummy89 0.63100 0.08461 7.458 3.57e-13 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 0.1468 on 535 degrees of freedom
Multiple R-squared: 0.9441, Adjusted R-squared: 0.9343
F-statistic: 96.16 on 94 and 535 DF, p-value: < 2.2e-16