Problems in bootstrapping Data Envelopment Analysis (DEA) results

[Patrizio Sicari]

Hi all,

I'm using DEA in Stata to compute public expenditure efficiency frontiers across a sample of 34 countries. The command's syntax is the following:

dea env tot_hexpav = le, rts(vrs)

where left-hand variables env & tot_hexpav [an environment composite indicator and total health expenditure] are input and le [life expectancy] is output.
The command is for the input-orientation and assumes variable returns to scale (vrs). The dea command just returns a matrix where all results are saved: r(dearslt).
Now, I would like to bootstrap the efficiency scores obtained from dea, which are the second column of the r(dearslt) matrix by - in simple terms - the following Stata command:


bootstrap **XXXX**, rep(200) : dea env tot_hexpav = le, rts(vrs)

My question is...how should I shape the "exp_list" XXXX to tell Stata to bootstrap the second column of the matrix of results from dea after :? I have tried various combinations, but without success. Has someone else faced the same problem or have an idea as to how to circumvent it? The DEA command can be found in Stata Journal Volume 10, Number 2 (st0193). I also attach a txt file with input data.

Your help would be much appreciated.

Patrizio

[Axel Demenet]

Would also appreciate some help on a similar issue

[karima eco]

Would also appreciate some help on a similar issue

[Axel Demenet]

So here is what I did, adapted from
http://www.ats.ucla.edu/stat/stata/faq/ownboot.htm

Without being able to return a matrix, I went through all parameters and returned them as scalars. Probably not the best way, I guess there is a shorter one (I have 25 countries and have to write them down)

Note that my output is the result of a PCA on several output measures:

score

..and my input is

liss_DIRDA_civile

*Step 1
capture program drop manualboot_init
program define manualboot_init, rclass
quietly dea liss_DIRDA_civile = score, ort(o)
    mat deascores = r(dearslt)
    mat deascores = deascores[1...,"theta"]
    svmat deascores
    egen deascores_st=std(deascores)
    replace deascores_st=-deascores_st
    mkmat deascores_st
    mat deascores_st=deascores_st'
    foreach i of numlist 1/25{
    return scalar score_`i'=deascores_st[1,`i']
    }
    end
manualboot_init
matrix deascores_st = (r(score_1), r(score_2), r(score_3), r(score_4), r(score_5), r(score_6), r(score_7), r(score_8), ///
r(score_9), r(score_10), r(score_11), r(score_12), r(score_13), r(score_14), r(score_15), r(score_16), r(score_17), ///
r(score_18), r(score_19), r(score_20), r(score_21), r(score_22), r(score_23), r(score_24), r(score_25))

*Step 2
capture program drop manualboot
program define manualboot, rclass
 preserve
  bsample 25
    dea liss_DIRDA_civile = score, ort(o)
    mat deascores2 = r(dearslt)
    mat deascores2 = deascores2[1...,"theta"]
    svmat deascores2
    egen deascores2_st=std(deascores2)
    replace deascores2_st=-deascores2_st
    mkmat deascores2_st
    mat deascores2_st=deascores2_st'
    *return matrix dea = deascores2
    foreach i of numlist 1/25{
    return scalar score_`i'=deascores2_st[1,`i']
    }
 restore
end

*Step 3 // use the simulate prefix command along with myboot to collect stats from the bootstrapped sample.
#delimit ;
simulate score_1=r(score_1) score_2=r(score_2) score_3=r(score_3) score_4=r(score_4) score_5=r(score_5) score_6=r(score_6) score_7=r(score_7) score_8=r(score_8)
score_9=r(score_9) score_10=r(score_10) score_11=r(score_11) score_12=r(score_12) score_13=r(score_13) score_14=r(score_14) score_15=r(score_15) score_16=r(score_16) score_17=r(score_17)
score_18=r(score_18) score_19=r(score_19) score_20=r(score_20) score_21=r(score_21) score_22=r(score_22) score_23=r(score_23) score_24=r(score_24) score_25=r(score_25),
 reps(100) seed(12345): manualboot ;
#delimit cr
bstat, stat(deascores_st) n(300)
estat bootstrap, all

Hope it helps

[Axel Demenet]

Besides being ugly, the above code is probably wrong; the intuiton is that there is no guarantee that country _N will systematically return the scalar score_N, because the nature of bootstrap is to draw with replacement - and thus mix each country's position.
Any thought on this?

[Axel Demenet]

Followig up : without any more insight, I would recommend switching to R for bootstraping, as all of these routines have been programmed.
shouldn't be more difficult than this:

# library(FEAR)
library(FactoMineR)
library(Benchmarking)
library(ggplot2)
library(scales)

donnees <- read.csv2("base_boot.csv",na.strings="")
y <- as.matrix(donnees$output)
x <- as.matrix(donnees$input)

e.boot <- dea.boot(x,y,NREP = 3000,ORIENTATION="out",RTS = "vrs")
e.boot$eff
write.table(e.boot$eff,"eff.csv",sep=";",dec=",")
e.boot$eff.bc
write.table(e.boot$eff.bc,"eff_bc.csv",sep=";",dec=",")
e.boot$conf.int
write.table(e.boot$conf.int,"eff_ic.csv",sep=";",dec=",")