This contains code that implements methods and analysis of the effects of L15
Stefano Cabras
2024
DATA collected at Osservatorio Economico della Sardegna
Enterprises are sorted by score (p variable)
source("read-dat.R")
head(dat)## i1 i2 i3 i4 p z d ey0 ey3 py0 py3 dy0
## 276/99 0.3000000 0.000000000 1.000000 19 -4.645011 0 0 10 NA 3616 NA NA
## 343/99 0.3000000 0.002730963 1.000000 21 -3.606017 0 0 NA NA NA 315 NA
## 257/99 0.3000000 0.006521739 1.000000 23 -3.293505 0 0 NA NA NA NA NA
## D1500264 0.3000344 0.001377885 1.000000 22 -3.237792 0 1 18 21 7983 9409 NA
## 307/99 0.3214286 0.011127107 1.176471 21 -3.173211 0 0 1 NA 484 NA NA
## D1500228 0.3227699 0.003129890 1.052632 23 -3.114608 0 0 2 NA 269 257 NA
## dpy3
## 276/99 NA
## 343/99 NA
## 257/99 NA
## D1500264 NA
## 307/99 NA
## D1500228 NAX.plus and X.minus estimator
These Functions returns the + (.plus) and - (.minus) in alpha.hat formula
minimi.plus=function(X,S,K,Z){
A=sum(K*Z*X)
B=sum(K*Z)
C=sum(Z*K*S)
D=sum(Z*K*S*X)
E=sum(K*Z*(S^2))
b.plus=(A*C-B*D)/(C^2-B*E)
x.plus=(A-b.plus*C)/B
return(c(x.plus,b.plus))}
minimi.minus=function(X,S,K,Z){
A=sum(K*(1-Z)*X)
B=sum(K*(1-Z))
C=sum((1-Z)*K*S)
D=sum((1-Z)*K*S*X)
E=sum(K*(1-Z)*(S^2))
b.minus=(A*C-B*D)/(C^2-B*E)
x.minus=(A-b.minus*C)/B
return(c(x.minus,b.minus))}The Bootstrap
This function returns Calibrated BootStrap CI that is, the nominal coverage correspond to actua coverage
bootci=function(y,p,K,z,d,M=1000,init.seed=NULL){
if(!is.null(init.seed)) set.seed(init.seed)
alpha.hat=function(bdat){
y=bdat$y
p=bdat$p
K=bdat$K
z=bdat$z
d=bdat$d
alpha.hat=(minimi.plus(y,p,K,z)[1]-minimi.minus(y,p,K,z)[1])/
(minimi.plus(d,p,K,z)[1]-minimi.minus(d,p,K,z)[1])
return(alpha.hat)
}
bdat=data.frame(y=y,p=p,K=K,z=z,d=d)
res=suppressWarnings (bcajack(x = bdat, B = M, func = alpha.hat, mr = 40,
alpha = c(0.005,0.025,0.05),verbose = FALSE))
return(c(res$lims[c(1,7),1],res$lims[c(2,6),1],
res$lims[c(3,5),1]))
}Analysis with the Boostrap
Here we provide the results in the paper.
attach(dat)
p.bar=-0.41067715 # Threshold selection
n=length(p);n # Sample size used to estimate the weithing function## [1] 215p=p-p.bar # Centered score
dens=density(p) # kernel density
K=rep(NA,n)
for(i in 1:n) K[i]=mean(c(dens$y[dens$x==min(dens$x[dens$x>=p[i]])],dens$y[dens$x==max(dens$x[dens$x<=p[i]])]))
K=K/sum(K)
# Analysis of production value
usable=!apply(cbind(py3,py0,z,d),1,function(x) any(is.na(x))) # usable data
y.p=log(py3/py0)[usable] # Response variale: log-ratio
z.p=(p>0)[usable] # Mandated status for the available sample
p.p=p[usable] # Score for available sample
d.p=d[usable] # Effective status for available sample
K.p=K[usable] # Weight for available sample
table(z.p,d.p) # Tables 1 and 2## d.p
## z.p 0 1
## FALSE 26 13
## TRUE 9 45ypiu=minimi.plus(y.p,p.p,K.p,z.p) # y+ estimate
ymeno=minimi.minus(y.p,p.p,K.p,z.p) # y- estimate
dpiu=minimi.plus(d.p,p.p,K.p,z.p) # d+ estimate
dmeno=minimi.minus(d.p,p.p,K.p,z.p) # d- estimate
cat("Estimated proportion of Compliers: ",dpiu[1]-dmeno[1],"\n")## Estimated proportion of Compliers: 0.5822672alpha.hat.p=(ypiu[1]-ymeno[1])/(dpiu[1]-dmeno[1]) # alpha.hat
alpha.hat.p## [1] 0.4444406exp(alpha.hat.p)## [1] 1.559618# Boot Confidence Interval for effect on Production Value
bootci(y=y.p,p=p.p,K=K.p,z=z.p,d=d.p,M=100000,init.seed=17)## 0.005 0.995 0.025 0.975 0.05 0.95
## -0.44523722 3.66504896 -0.19506843 1.77800637 -0.08995075 1.40215145# Analysis of Employement
usable=!apply(cbind(ey3,ey0,z,d),1,function(x) any(is.na(x))) # usable data
y.e=log(ey3/ey0)[usable] # Response variale: log-ratio
z.e=(p>0)[usable] # Mandated status for the available sample
p.e=p[usable] # Score for available sample
d.e=d[usable] # Effective status for available sample
K.e=K[usable] # Weight for available sample
table(z.e,d.e) # Tables 1 and 2## d.e
## z.e 0 1
## FALSE 22 13
## TRUE 8 39ypiu=minimi.plus(y.e,p.e,K.e,z.e) # y+ estimate
ymeno=minimi.minus(y.e,p.e,K.e,z.e) # y- estimate
dpiu=minimi.plus(d.e,p.e,K.e,z.e) # d+ estimate
dmeno=minimi.minus(d.e,p.e,K.e,z.e) # d- estimate
cat("Estimated proportion of Compliers: ",dpiu[1]-dmeno[1],"\n")## Estimated proportion of Compliers: 0.5589882alpha.hat.e=(ypiu[1]-ymeno[1])/(dpiu[1]-dmeno[1]) # alpha.hat
alpha.hat.e## [1] 0.5667232exp(alpha.hat.e)## [1] 1.762482# Boot Confidence Interval for effect on Employement
bootci(y=y.e,p=p.e,K=K.e,z=z.e,d=d.e,M=100000,init.seed=17)## 0.005 0.995 0.025 0.975 0.05 0.95
## -6.51126505 4.41135983 -0.18208744 2.23276228 -0.05752017 1.72723005# Figure 1
#pdf(file="results.pdf")
hl=-4
par(mfrow=c(2,1),mar=c(5, 5, 4, 2)-1)
# Figure Results for Employement
plot(p.e+p.bar,y.e,pch=21-d.e*2,xlab="p",ylab="y",main="(a) Effect on Occupation",ylim=c(hl,5),xlim=c(-3,4))
abline(v=p.bar,lty=2)
abline(h=0)
legend(2,5,c("Treated","Non-treated"),pch=c(19,21))
lines(p.e[p.e>0]+p.bar,ypiu[1]+ypiu[2]*( p.e[p.e>0]+p.bar),lwd=2)
lines(p.e[p.e<0]+p.bar,ymeno[1]+ymeno[2]*( p.e[p.e<0]+p.bar),lwd=2)
tonalita.grigio= grey(1-K.e/max(K.e))
for(i in 1:(length(p.e)-1)) lines(c(p.e[i]+p.bar, p.e[i+1]+p.bar),c(hl,hl),col= tonalita.grigio[i],lwd=12)
tonalita.grigio= grey(K/max(K))
for(i in c(seq(1,length(p.e),by=8), length(p.e))) text(p.e[i]+p.bar,hl,round(K[i],2),col=tonalita.grigio[i],cex=0.6)
# Figure Results for Production Value
plot(p.p+p.bar,y.p,pch=21-d.p*2,xlab="p",ylab="y",main="(b) Effect on Production Value",ylim=c(hl,5),xlim=c(-3,4))
abline(v=p.bar,lty=2)
abline(h=0)
legend(2,5,c("Treated","Non-reated"),pch=c(19,21))
lines(p.p[p.p>0]+p.bar,ypiu[1]+ypiu[2]*( p.p[p.p>0]+p.bar),lwd=2)
lines(p.p[p.p<0]+p.bar,ymeno[1]+ymeno[2]*( p.p[p.p<0]+p.bar),lwd=2)
tonalita.grigio= grey(1-K.p/max(K.p))
for(i in 1:(length(p.p)-1)) lines(c(p.p[i]+p.bar, p.p[i+1]+p.bar),c(hl,hl),col= tonalita.grigio[i],lwd=12)
tonalita.grigio= grey(K/max(K))
for(i in c(seq(1,length(p.p),by=8), length(p.p))) text(p.p[i]+p.bar,hl,round(K[i],2),col=tonalita.grigio[i],cex=0.6)
#dev.off()Bootstrap simulation study for assessing interval calibration under the null
nrep=100
sim.res=data.frame(inf=1,sup=1,lev=0.9,n=20,gamma.shape=1,prop.compliers=0.2,nrep=nrep)
for(nsim in c(20,50,100,200,300)){
for(gamma.shape in c(0.5,1,2,5,10)){
for(prop.compliers in c(0.2,0.3,0.5,0.6,0.7)){
for(i in 1:nrep){
psim=rnorm(nsim)
zsim=psim>0
denssim=density(psim) # kernel density
Ksim=rep(NA,nsim)
for(i in 1:nsim) Ksim[i]=mean(
c(denssim$y[denssim$x==min(denssim$x[denssim$x>=psim[i]])],
denssim$y[denssim$x==max(denssim$x[denssim$x<=psim[i]])]))
Ksim=Ksim/sum(Ksim)
ysim=rgamma(nsim,shape=gamma.shape,rate=1)
dsim=rep(0,nsim)
while(sum(dsim)<=1){dsim[zsim]=rbinom(sum(zsim),1,p=prop.compliers)}
rr=bootci(y=ysim,p=psim,K=Ksim,z=zsim,d=dsim,M=1000)
intres=rbind(
data.frame(inf=rr[1],sup=rr[2],lev=0.99),
data.frame(inf=rr[3],sup=rr[4],lev=0.95),
data.frame(inf=rr[5],sup=rr[6],lev=0.90))
intres=cbind(intres,data.frame(n=nsim,
gamma.shape=gamma.shape,
prop.compliers=prop.compliers,nrep=nrep))
sim.res=rbind(sim.res,intres)
}
cat(prop.compliers,gamma.shape,nsim,"\n")
}
}
}
sim.res=sim.res[-1,]
save(sim.res,file="simulres4.RData")Analysis of simulations
load(file="simulres4.RData")
sim.res = sim.res %>% mutate(inside=(inf<0)&(sup>0),int.wide=sup-inf) %>% na.omit()
res=sim.res %>% group_by(lev,n,gamma.shape,prop.compliers) %>% summarise(cov=mean(inside),wide=mean(int.wide)) %>% ungroup()## `summarise()` has grouped output by 'lev', 'n', 'gamma.shape'. You can override
## using the `.groups` argument.res1= sim.res %>%
group_by(lev,n) %>%
summarise(cov=mean(inside),
sdcov=sqrt(mean(inside)*(1-mean(inside))/length(inside)),
wide.mean=mean(int.wide),wide.sd=sd(int.wide)/sqrt(length(inside))) %>%
mutate(min.cov=cov+qnorm(0.025)*sdcov,max.cov=cov-qnorm(0.025)*sdcov,
min.wide=wide.mean+qnorm(0.025)*wide.sd,max.wide=wide.mean-qnorm(0.025)*wide.sd) %>%
ungroup()## `summarise()` has grouped output by 'lev'. You can override using the `.groups`
## argument.res2= sim.res %>%
group_by(gamma.shape,prop.compliers) %>%
summarise(cov=mean(inside),
sdcov=sqrt(mean(inside)*(1-mean(inside))/length(inside)),
wide.mean=mean(int.wide),wide.sd=sd(int.wide)/sqrt(length(inside))) %>%
mutate(min.cov=cov+qnorm(0.025)*sdcov,max.cov=cov-qnorm(0.025)*sdcov,
min.wide=wide.mean+qnorm(0.025)*wide.sd,max.wide=wide.mean-qnorm(0.025)*wide.sd) %>%
ungroup()## `summarise()` has grouped output by 'gamma.shape'. You can override using the
## `.groups` argument.totab1=round(res1 %>% select(lev,n,cov) %>% reshape2::dcast(data=.,lev~n),2)## Using cov as value column: use value.var to override.rownames(totab1)=NULL
totab2=round(res2 %>% select(gamma.shape,prop.compliers,cov) %>% mutate(gamma.shape=2/sqrt(gamma.shape)) %>% reshape2::dcast(data=.,gamma.shape~prop.compliers),2)## Using cov as value column: use value.var to override.rownames(totab2)=NULL
print(xtable::xtable(totab1,caption="Coverage of Bootstrap C.I. by sample size $n$ (columns) and nominal levels (rows)."),include.rownames=FALSE)## % latex table generated in R 4.3.3 by xtable 1.8-4 package
## % Wed Mar 20 14:19:14 2024
## \begin{table}[ht]
## \centering
## \begin{tabular}{rrrrrr}
## \hline
## lev & 20 & 50 & 100 & 200 & 300 \\
## \hline
## 0.90 & 0.82 & 0.86 & 0.88 & 0.88 & 0.88 \\
## 0.95 & 0.91 & 0.92 & 0.93 & 0.94 & 0.93 \\
## 0.99 & 0.97 & 0.98 & 0.98 & 0.98 & 0.98 \\
## \hline
## \end{tabular}
## \caption{Coverage of Bootstrap C.I. by sample size $n$ (columns) and nominal levels (rows).}
## \end{table}print(xtable::xtable(totab2,caption="Coverage of Bootstrap C.I. by proportion of compliers (columns) and asimmetry in $Y$ (rows)."),include.rownames=FALSE)## % latex table generated in R 4.3.3 by xtable 1.8-4 package
## % Wed Mar 20 14:19:14 2024
## \begin{table}[ht]
## \centering
## \begin{tabular}{rrrrrr}
## \hline
## gamma.shape & 0.2 & 0.3 & 0.5 & 0.6 & 0.7 \\
## \hline
## 0.63 & 0.94 & 0.94 & 0.94 & 0.94 & 0.95 \\
## 0.89 & 0.91 & 0.93 & 0.95 & 0.93 & 0.94 \\
## 1.41 & 0.93 & 0.92 & 0.93 & 0.92 & 0.92 \\
## 2.00 & 0.94 & 0.93 & 0.92 & 0.92 & 0.92 \\
## 2.83 & 0.92 & 0.91 & 0.90 & 0.92 & 0.91 \\
## \hline
## \end{tabular}
## \caption{Coverage of Bootstrap C.I. by proportion of compliers (columns) and asimmetry in $Y$ (rows).}
## \end{table}Other analysis
Regression Tree Analysis
library(rpart)
library(rpart.plot)
library(rattle)## Caricamento del pacchetto richiesto: tibble## Caricamento del pacchetto richiesto: bitops## Rattle: A free graphical interface for data science with R.
## Version 5.5.1 Copyright (c) 2006-2021 Togaware Pty Ltd.
## Type 'rattle()' to shake, rattle, and roll your data.regtree <- rpart(z ~ i1+i2+i3+i4)
regtree## n= 215
##
## node), split, n, deviance, yval
## * denotes terminal node
##
## 1) root 215 53.7395300 0.50697670
## 2) i1< 0.3978639 141 30.2695000 0.31205670
## 4) i4< 27.5 123 22.1626000 0.23577240
## 8) i3< 1.212522 76 6.3552630 0.09210526
## 16) i1< 0.3241837 47 0.9787234 0.02127660 *
## 17) i1>=0.3241837 29 4.7586210 0.20689660
## 34) i3>=1.081113 18 0.9444444 0.05555556 *
## 35) i3< 1.081113 11 2.7272730 0.45454550 *
## 9) i3>=1.212522 47 11.7021300 0.46808510
## 18) i4< 24.5 28 4.1071430 0.17857140
## 36) i2< 0.005782026 18 0.9444444 0.05555556 *
## 37) i2>=0.005782026 10 2.4000000 0.40000000 *
## 19) i4>=24.5 19 1.7894740 0.89473680 *
## 5) i4>=27.5 18 2.5000000 0.83333330 *
## 3) i1>=0.3978639 74 7.9054050 0.87837840
## 6) i4< 25.5 32 6.4687500 0.71875000
## 12) i1< 0.4254474 10 2.1000000 0.30000000 *
## 13) i1>=0.4254474 22 1.8181820 0.90909090 *
## 7) i4>=25.5 42 0.0000000 1.00000000 *summary(regtree)## Call:
## rpart(formula = z ~ i1 + i2 + i3 + i4)
## n= 215
##
## CP nsplit rel error xerror xstd
## 1 0.28963083 0 1.0000000 1.0117439 0.003804685
## 2 0.10433477 1 0.7103692 0.7900188 0.061002975
## 3 0.09221072 2 0.6060344 0.8192376 0.072555246
## 4 0.03709767 4 0.4216130 0.7324996 0.078362684
## 5 0.01586190 6 0.3474176 0.6302829 0.077891653
## 6 0.01419250 8 0.3156938 0.6312773 0.076160895
## 7 0.01000000 9 0.3015013 0.6348525 0.077110544
##
## Variable importance
## i1 i4 i3 i2
## 49 29 14 7
##
## Node number 1: 215 observations, complexity param=0.2896308
## mean=0.5069767, MSE=0.2499513
## left son=2 (141 obs) right son=3 (74 obs)
## Primary splits:
## i1 < 0.3978639 to the left, improve=0.28963080, (0 missing)
## i3 < 1.162948 to the left, improve=0.12175900, (0 missing)
## i4 < 24.5 to the left, improve=0.11420310, (0 missing)
## i2 < 0.01909164 to the left, improve=0.03893459, (0 missing)
## Surrogate splits:
## i3 < 1.40873 to the left, agree=0.665, adj=0.027, (0 split)
## i2 < 0.02380738 to the left, agree=0.660, adj=0.014, (0 split)
##
## Node number 2: 141 observations, complexity param=0.1043348
## mean=0.3120567, MSE=0.2146773
## left son=4 (123 obs) right son=5 (18 obs)
## Primary splits:
## i4 < 27.5 to the left, improve=0.1852327, (0 missing)
## i3 < 1.162948 to the left, improve=0.1219094, (0 missing)
## i2 < 0.01982193 to the left, improve=0.0399378, (0 missing)
## i1 < 0.3007355 to the left, improve=0.0366842, (0 missing)
##
## Node number 3: 74 observations, complexity param=0.03709767
## mean=0.8783784, MSE=0.1068298
## left son=6 (32 obs) right son=7 (42 obs)
## Primary splits:
## i4 < 25.5 to the left, improve=0.18173080, (0 missing)
## i1 < 0.4186274 to the left, improve=0.16624200, (0 missing)
## i3 < 1.087085 to the left, improve=0.09042496, (0 missing)
## i2 < 0.004128366 to the left, improve=0.05160640, (0 missing)
## Surrogate splits:
## i2 < 0.005751243 to the right, agree=0.635, adj=0.156, (0 split)
## i3 < 1.03652 to the left, agree=0.608, adj=0.094, (0 split)
## i1 < 0.712 to the right, agree=0.595, adj=0.063, (0 split)
##
## Node number 4: 123 observations, complexity param=0.09221072
## mean=0.2357724, MSE=0.1801838
## left son=8 (76 obs) right son=9 (47 obs)
## Primary splits:
## i3 < 1.212522 to the left, improve=0.18523140, (0 missing)
## i4 < 24.5 to the left, improve=0.09953909, (0 missing)
## i2 < 0.0004058315 to the left, improve=0.03962522, (0 missing)
## i1 < 0.3229234 to the left, improve=0.03217129, (0 missing)
## Surrogate splits:
## i1 < 0.3571322 to the left, agree=0.732, adj=0.298, (0 split)
## i4 < 23.5 to the right, agree=0.642, adj=0.064, (0 split)
## i2 < 0.0294965 to the left, agree=0.626, adj=0.021, (0 split)
##
## Node number 5: 18 observations
## mean=0.8333333, MSE=0.1388889
##
## Node number 6: 32 observations, complexity param=0.03709767
## mean=0.71875, MSE=0.2021484
## left son=12 (10 obs) right son=13 (22 obs)
## Primary splits:
## i1 < 0.4254474 to the left, improve=0.39429070, (0 missing)
## i2 < 0.004236634 to the left, improve=0.27085350, (0 missing)
## i3 < 1.162948 to the left, improve=0.18411160, (0 missing)
## i4 < 24.5 to the right, improve=0.01449275, (0 missing)
##
## Node number 7: 42 observations
## mean=1, MSE=0
##
## Node number 8: 76 observations, complexity param=0.0158619
## mean=0.09210526, MSE=0.08362188
## left son=16 (47 obs) right son=17 (29 obs)
## Primary splits:
## i1 < 0.3241837 to the left, improve=0.09722950, (0 missing)
## i2 < 0.002904424 to the left, improve=0.06616257, (0 missing)
## i4 < 26.5 to the left, improve=0.06283366, (0 missing)
## i3 < 1.081113 to the right, improve=0.01247863, (0 missing)
## Surrogate splits:
## i3 < 1.058231 to the left, agree=0.645, adj=0.069, (0 split)
##
## Node number 9: 47 observations, complexity param=0.09221072
## mean=0.4680851, MSE=0.2489814
## left son=18 (28 obs) right son=19 (19 obs)
## Primary splits:
## i4 < 24.5 to the left, improve=0.49610730, (0 missing)
## i1 < 0.3037437 to the right, improve=0.09123339, (0 missing)
## i2 < 0.004423548 to the right, improve=0.06321258, (0 missing)
## i3 < 1.360607 to the left, improve=0.05204644, (0 missing)
## Surrogate splits:
## i2 < 0.004423548 to the right, agree=0.723, adj=0.316, (0 split)
## i1 < 0.3430486 to the right, agree=0.702, adj=0.263, (0 split)
## i3 < 1.547619 to the left, agree=0.638, adj=0.105, (0 split)
##
## Node number 12: 10 observations
## mean=0.3, MSE=0.21
##
## Node number 13: 22 observations
## mean=0.9090909, MSE=0.08264463
##
## Node number 16: 47 observations
## mean=0.0212766, MSE=0.0208239
##
## Node number 17: 29 observations, complexity param=0.0158619
## mean=0.2068966, MSE=0.1640904
## left son=34 (18 obs) right son=35 (11 obs)
## Primary splits:
## i3 < 1.081113 to the right, improve=0.22840730, (0 missing)
## i2 < 0.002785339 to the left, improve=0.13729980, (0 missing)
## i4 < 24.5 to the left, improve=0.13729980, (0 missing)
## i1 < 0.3412005 to the right, improve=0.09528515, (0 missing)
## Surrogate splits:
## i1 < 0.3556962 to the left, agree=0.793, adj=0.455, (0 split)
## i2 < 0.01772197 to the left, agree=0.690, adj=0.182, (0 split)
## i4 < 23.5 to the right, agree=0.655, adj=0.091, (0 split)
##
## Node number 18: 28 observations, complexity param=0.0141925
## mean=0.1785714, MSE=0.1466837
## left son=36 (18 obs) right son=37 (10 obs)
## Primary splits:
## i2 < 0.005782026 to the left, improve=0.18570050, (0 missing)
## i4 < 23.5 to the left, improve=0.15108110, (0 missing)
## i3 < 1.37012 to the left, improve=0.14202900, (0 missing)
## i1 < 0.3701228 to the left, improve=0.02608696, (0 missing)
## Surrogate splits:
## i1 < 0.3222502 to the right, agree=0.75, adj=0.3, (0 split)
##
## Node number 19: 19 observations
## mean=0.8947368, MSE=0.09418283
##
## Node number 34: 18 observations
## mean=0.05555556, MSE=0.05246914
##
## Node number 35: 11 observations
## mean=0.4545455, MSE=0.2479339
##
## Node number 36: 18 observations
## mean=0.05555556, MSE=0.05246914
##
## Node number 37: 10 observations
## mean=0.4, MSE=0.24pdf(file="results-rt.pdf")
fancyRpartPlot(regtree,main="Regression Tree: z ~ I1+I2+I3+I4",sub = "")
dev.off()## png
## 2Analysis With BART
#pdf(file="results-bart.pdf")
par(mfrow=c(2,1))
# Analysis of Employement
usable=!apply(cbind(ey3,ey0,z,d),1,function(x) any(is.na(x))) # usable data
y.e=log(ey3/ey0)[usable] # Response variale: log-ratio
z.e=(p>0)[usable] # Mandated status for the available sample
p.e=p[usable] # Score for available sample
d.e=d[usable] # Effective status for available sample
x.insample=as.matrix(data.frame(z.e,d.e,p.e))
x.outsample=x.insample
x.outsample[,1]=1-x.outsample[,1] # Changing the Effective Status
y.e=as.double(y.e)
bartFit = bart(x.train=x.insample,y.train=y.e,x.test=x.outsample,ndpost=10000,nskip=1000)##
##
## Running BART with numeric y
##
## number of trees: 200
## Prior:
## k: 2.000000
## degrees of freedom in sigma prior: 3
## quantile in sigma prior: 0.900000
## power and base for tree prior: 2.000000 0.950000
## use quantiles for rule cut points: 0
## data:
## number of training observations: 82
## number of test observations: 82
## number of explanatory variables: 3
##
##
## Cutoff rules c in x<=c vs x>c
## Number of cutoffs: (var: number of possible c):
## (1: 100) (2: 100) (3: 100)
##
##
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##
## Tree sizes, last iteration:
## 2 2 2 3 2 2 3 2 2 2 2 2 1 2 2 2 2 2 4 3
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## 1 2 2 1 2 2 2 3 2 2 2 1 2 2 2 2 2 2 2 3
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## 2 2 2 2 2 2 2 3 2 1 2 3 3 3 3 2 2 3 1 2
## 2 2 2 1 2 2 2 2 3 3 2 2 2 2 3 2 3 4 2 2
## Variable Usage, last iteration (var:count):
## (1: 61) (2: 76) (3: 102)
## DONE BART 11-2-2014yest=cbind(bartFit$yhat.train,bartFit$yhat.test)
factual=which(d.e==1)
cfactual=length(y.e)+which(d.e==0)
post.effect.marg=apply(yest,1,function(x) mean(x[factual])-mean(x[cfactual]))
hist(post.effect.marg,nclass=50,prob=TRUE,main="(a) Posterior Effect on \n Occupation",xlab="log(y2003/y2000)",ylab="Density")
mean(post.effect.marg>0)## [1] 0.9292mean(post.effect.marg)## [1] 0.4207876qe=quantile(post.effect.marg,p=c(0.025,0.975))
qe## 2.5% 97.5%
## -0.1428711 0.9954635exp(qe)## 2.5% 97.5%
## 0.8668658 2.7059782abline(v=qe,lty=2)
quantile(post.effect.marg,p=c(0.005,0.995))## 0.5% 99.5%
## -0.3218183 1.1744883exp(quantile(post.effect.marg,p=c(0.005,0.995)))## 0.5% 99.5%
## 0.7248299 3.2364863quantile(post.effect.marg,p=c(0.025,0.975))## 2.5% 97.5%
## -0.1428711 0.9954635exp(quantile(post.effect.marg,p=c(0.025,0.975)))## 2.5% 97.5%
## 0.8668658 2.7059782quantile(post.effect.marg,p=c(0.05,0.95))## 5% 95%
## -0.0519006 0.9042703exp(quantile(post.effect.marg,p=c(0.05,0.95)))## 5% 95%
## 0.9494232 2.4701288# Analysis of production value
usable=!apply(cbind(py3,py0,z,d),1,function(x) any(is.na(x))) # usable data
y.p=log(py3/py0)[usable] # Response variale: log-ratio
z.p=(p>0)[usable] # Mandated status for the available sample
p.p=p[usable] # Score for available sample
d.p=d[usable] # Effective status for available sample
x.insample=as.matrix(data.frame(z.p,d.p,p.p))
x.outsample=x.insample
x.outsample[,1]=1-x.outsample[,1] # Changing the Effective Status
y.p=as.double(y.p)
bartFit = bart(x.train=x.insample,y.train=y.p,x.test=x.outsample,ndpost=10000,nskip=1000)##
##
## Running BART with numeric y
##
## number of trees: 200
## Prior:
## k: 2.000000
## degrees of freedom in sigma prior: 3
## quantile in sigma prior: 0.900000
## power and base for tree prior: 2.000000 0.950000
## use quantiles for rule cut points: 0
## data:
## number of training observations: 93
## number of test observations: 93
## number of explanatory variables: 3
##
##
## Cutoff rules c in x<=c vs x>c
## Number of cutoffs: (var: number of possible c):
## (1: 100) (2: 100) (3: 100)
##
##
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##
## Tree sizes, last iteration:
## 2 2 2 2 2 2 3 3 4 2 4 3 2 2 3 3 1 2 3 3
## 2 1 2 2 2 1 1 2 2 2 2 2 3 2 2 3 2 2 2 2
## 2 2 2 3 2 2 2 2 2 2 3 1 3 2 2 3 2 3 3 2
## 1 3 3 4 2 2 2 2 2 2 3 3 2 2 2 3 2 2 3 1
## 2 3 2 2 3 2 2 2 2 2 2 2 2 2 2 3 2 2 2 3
## 2 2 2 2 2 3 4 1 3 2 3 2 2 3 2 2 2 2 3 2
## 3 1 3 2 2 2 3 3 4 2 1 2 2 1 4 2 3 2 2 4
## 2 2 2 2 3 2 2 2 4 2 2 2 2 2 2 2 1 2 3 2
## 2 2 1 2 3 1 2 2 2 2 2 2 2 2 2 3 2 2 3 2
## 3 2 2 1 2 2 3 2 2 2 2 2 4 2 2 2 2 2 2 2
## Variable Usage, last iteration (var:count):
## (1: 75) (2: 77) (3: 93)
## DONE BART 11-2-2014yest=cbind(bartFit$yhat.train,bartFit$yhat.test)
factual=which(d.p==1)
cfactual=93+which(d.p==0)
post.effect.marg=apply(yest,1,function(x) mean(x[factual])-mean(x[cfactual]))
hist(post.effect.marg,nclass=50,prob=TRUE,main="(b) Posterior Effect on \n Production Value",xlab="log(y2003/y2000)",ylab="Density")
mean(post.effect.marg>0)## [1] 0.8402mean(post.effect.marg)## [1] 0.3466506qe=quantile(post.effect.marg,p=c(0.025,0.975))
qe## 2.5% 97.5%
## -0.3371866 1.0448165abline(v=qe,lty=2)
quantile(post.effect.marg,p=c(0.005,0.995))## 0.5% 99.5%
## -0.5636381 1.2728543exp(quantile(post.effect.marg,p=c(0.005,0.995)))## 0.5% 99.5%
## 0.5691347 3.5710307quantile(post.effect.marg,p=c(0.025,0.975))## 2.5% 97.5%
## -0.3371866 1.0448165exp(quantile(post.effect.marg,p=c(0.025,0.975)))## 2.5% 97.5%
## 0.7137756 2.8428769quantile(post.effect.marg,p=c(0.5,0.95))## 50% 95%
## 0.3480397 0.9306671exp(quantile(post.effect.marg,p=c(0.05,0.95)))## 5% 95%
## 0.787031 2.536200#dev.off()Analysis with Causal Forests
usable=!apply(cbind(ey3,ey0,z,d),1,function(x) any(is.na(x))) # usable data
Y=log(ey3/ey0)[usable] # Response variale: log-ratio
W=d[usable] # Effective status for available sample
p.e=p[usable] # Score for available sample
X=as.matrix(data.frame(p.e))
crf.e=causal_forest(X=X,Y=Y,W=W,
num.trees = 10000,honesty = TRUE)
ate.e=average_treatment_effect(crf.e, target.sample = "overlap")
usable=!apply(cbind(py3,py0,z,d),1,function(x) any(is.na(x))) # usable data
Y=log(py3/py0)[usable] # Response variale: log-ratio
W=d[usable] # Effective status for available sample
p.p=p[usable] # Score for available sample
X=as.matrix(data.frame(p.p))
crf.p=causal_forest(X=X,Y=Y,W=W,
num.trees = 10000,honesty = TRUE)
ate.p=average_treatment_effect(crf.p, target.sample = "overlap")
inf=round(ate.e[1]+qnorm(c(0.005,0.025,0.05))*ate.e[2],2)
sup=round(ate.e[1]-qnorm(c(0.005,0.025,0.05))*ate.e[2],2)
cbind(inf,sup)## inf sup
## [1,] -0.28 0.97
## [2,] -0.13 0.82
## [3,] -0.05 0.74inf=round(ate.p[1]+qnorm(c(0.005,0.025,0.05))*ate.p[2],2)
sup=round(ate.p[1]-qnorm(c(0.005,0.025,0.05))*ate.p[2],2)
cbind(inf,sup)## inf sup
## [1,] -0.28 0.91
## [2,] -0.13 0.76
## [3,] -0.06 0.69