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# st: problems with nlsur aids

 From Mintewab Bezabih To "statalist@hsphsun2.harvard.edu" Subject st: problems with nlsur aids Date Mon, 31 Oct 2011 21:52:11 +0100

```Dear statalisters,

I posted a problem I had with an nlsur aids command a while ago. I had gotten tremendous help from Jorge and nick which helped me run the estimation correctly. But I have been stuck with computing the corresponding elastities for a while now. As my programming skills are not that great, I was not able to quite get to the problem so I thought of posting the problem again.
I remain grateful for any help I may get.
mintewab

**** here is the code*****

capture program drop nlsuraids

quietly: program define nlsuraids

version 10

syntax varlist(min=26 max=26) if, at(name)

tokenize `varlist'

args w1 w2 w3 w4 w5 w6 w7 w8 w9 w10 w11 w12 lnp1 lnp2 lnp3 lnp4 lnp5 lnp6 lnp7 lnp8 lnp9 ///

lnp10 lnp11 lnp12 lnp13 lnexp

// With 18 goods, there are 204 parameters that can be

// estimated, after eliminating one of the goods and

// imposing adding up, symmetry, and homogeneity

// constraints, in the QUAIDS model

// Here, we extract those parameters from the `at'

// vector, and impose constraints as we go along

tempname a1 a2 a3 a4 a5 a6 a7 a8 a9 a10 a11 a12 a13

scalar `a1' = `at'[1,1]

scalar `a2' = `at'[1,2]

scalar `a3' = `at'[1,3]

scalar `a4' = `at'[1,4]

scalar `a5' = `at'[1,5]

scalar `a6' = `at'[1,6]

scalar `a7' = `at'[1,7]

scalar `a8' = `at'[1,8]

scalar `a9' = `at'[1,9]

scalar `a10' = `at'[1,10]

scalar `a11' = `at'[1,11]

scalar `a12' = `at'[1,12]

scalar `a13' = 1 - `a1' - `a2' - `a3' - `a4' - `a5' - `a6' - `a7' - `a8' - `a9' - `a10' - `a11' - `a12'

tempname b1 b2 b3 b4 b5 b6 b7 b8 b9 b10 b11 b12 b13

scalar `b1' = `at'[1,13]

scalar `b2' = `at'[1,14]

scalar `b3' = `at'[1,15]

scalar `b4' = `at'[1,16]

scalar `b5' = `at'[1,17]

scalar `b6' = `at'[1,18]

scalar `b7' = `at'[1,19]

scalar `b8' = `at'[1,20]

scalar `b9' = `at'[1,21]

scalar `b10' = `at'[1,22]

scalar `b11' = `at'[1,23]

scalar `b12' = `at'[1,24]

scalar `b13' = - `b1' - `b2' - `b3' - `b4' - `b5' - `b6' - `b7' - `b8' - `b9' - `b10' - `b11' - `b12'

tempname g11 g12 g13 g14 g15 g16 g17 g18 g19 g110 g111 g112 g113

tempname g21 g22 g23 g24 g25 g26 g27 g28 g29 g210 g211 g212 g213

tempname g31 g32 g33 g34 g35 g36 g37 g38 g39 g310 g311 g312 g313

tempname g41 g42 g43 g44 g45 g46 g47 g48 g49 g410 g411 g412 g413

tempname g51 g52 g53 g54 g55 g56 g57 g58 g59 g510 g511 g512 g513

tempname g61 g62 g63 g64 g65 g66 g67 g68 g69 g610 g611 g612 g613

tempname g71 g72 g73 g74 g75 g76 g77 g78 g79 g710 g711 g712 g713

tempname g81 g82 g83 g84 g85 g86 g87 g88 g89 g810 g811 g812 g813

tempname g91 g92 g93 g94 g95 g96 g97 g98 g99 g910 g911 g912 g913

tempname g101 g102 g103 g104 g105 g106 g107 g108 g109 g1010 g1011 g1012 g1013

tempname g111 g112 g113 g114 g115 g116 g117 g118 g119 g1110 g1111 g1112 g1113

tempname g121 g122 g123 g124 g125 g126 g127 g128 g129 g1210 g1211 g1212 g1213

tempname g131 g132 g133 g134 g135 g136 g137 g138 g139 g1310 g1311 g1312 g1313

tempname g141 g142 g143 g144 g145 g146 g147 g148 g149 g1410 g1411 g1412 g1413

tempname g151 g152 g153 g154 g155 g156 g157 g158 g159 g1510 g1511 g1512 g1513

tempname g161 g162 g163 g164 g165 g166 g167 g168 g169 g1610 g1611 g1612 g1613

tempname g171 g172 g173 g174 g175 g176 g177 g178 g179 g1710 g1711 g1712 g1713

tempname g181 g182 g183 g184 g185 g186 g187 g188 g189 g1810 g1811 g1812 g1813

scalar `g11' = `at'[1,25]

scalar `g12' = `at'[1,26]

scalar `g13' = `at'[1,27]

scalar `g14' = `at'[1,28]

scalar `g15' = `at'[1,29]

scalar `g16' = `at'[1,30]

scalar `g17' = `at'[1,31]

scalar `g18' = `at'[1,32]

scalar `g19' = `at'[1,33]

scalar `g110' = `at'[1,34]

scalar `g111' = `at'[1,35]

scalar `g112' = `at'[1,36]

scalar `g113' = -`g11' - `g12' - `g13'- `g14'- `g15'- `g16'- `g17'- `g18'- `g19'- `g110'- `g111'- `g112'

scalar `g21' = `g12'

scalar `g22' = `at'[1,37]

scalar `g23' = `at'[1,38]

scalar `g24' = `at'[1,39]

scalar `g25' = `at'[1,40]

scalar `g26' = `at'[1,41]

scalar `g27' = `at'[1,42]

scalar `g28' = `at'[1,43]

scalar `g29' = `at'[1,44]

scalar `g210' = `at'[1,45]

scalar `g211' = `at'[1,46]

scalar `g212' = `at'[1,47]

scalar `g213' = -`g21' - `g22' - `g23'- `g24'- `g25'- `g26'- `g27'- `g28'- `g29'- `g210'- `g211'- `g212'

scalar `g31' = `g13'

scalar `g32' = `g23'

scalar `g33' = `at'[1,48]

scalar `g34' = `at'[1,49]

scalar `g35' = `at'[1,50]

scalar `g36' = `at'[1,51]

scalar `g37' = `at'[1,52]

scalar `g38' = `at'[1,53]

scalar `g39' = `at'[1,54]

scalar `g310' = `at'[1,55]

scalar `g311' = `at'[1,56]

scalar `g312' = `at'[1,57]

scalar `g313' = -`g31' - `g32' - `g33'- `g34'- `g35'- `g36'- `g37'- `g38'- `g39'- `g310'- `g311'- `g312'

scalar `g41' = `g14'

scalar `g42' = `g24'

scalar `g43' = `g34'

scalar `g44' = `at'[1,58]

scalar `g45' = `at'[1,59]

scalar `g46' = `at'[1,60]

scalar `g47' = `at'[1,61]

scalar `g48' = `at'[1,62]

scalar `g49' = `at'[1,63]

scalar `g410' = `at'[1,64]

scalar `g411' = `at'[1,65]

scalar `g412' = `at'[1,66]

scalar `g413' = -`g41' - `g42' - `g43'- `g44'- `g45'- `g46'- `g47'- `g48'- `g49'- `g410'- `g411'- `g412'

scalar `g51' = `g15'

scalar `g52' = `g25'

scalar `g53' = `g35'

scalar `g54' = `g45'

scalar `g55' = `at'[1,67]

scalar `g56' = `at'[1,68]

scalar `g57' = `at'[1,69]

scalar `g58' = `at'[1,70]

scalar `g59' = `at'[1,71]

scalar `g510' = `at'[1,72]

scalar `g511' = `at'[1,73]

scalar `g512' = `at'[1,74]

scalar `g513' = -`g51' - `g52' - `g53'- `g54'- `g55'- `g56'- `g57'- `g58'- `g59'- `g510'- `g511'- `g512'

scalar `g61' = `g16'

scalar `g62' = `g26'

scalar `g63' = `g36'

scalar `g64' = `g46'

scalar `g65' = `g56'

scalar `g66' = `at'[1,75]

scalar `g67' = `at'[1,76]

scalar `g68' = `at'[1,77]

scalar `g69' = `at'[1,78]

scalar `g610' = `at'[1,79]

scalar `g611' = `at'[1,80]

scalar `g612' = `at'[1,81]

scalar `g613' = -`g61' - `g62' - `g63'- `g64'- `g65'- `g66'- `g67'- `g68'- `g69'- `g610'- `g611'- `g612'

scalar `g71' = `g17'

scalar `g72' = `g27'

scalar `g73' = `g37'

scalar `g74' = `g47'

scalar `g75' = `g57'

scalar `g76' = `g67'

scalar `g77' = `at'[1,82]

scalar `g78' = `at'[1,83]

scalar `g79' = `at'[1,84]

scalar `g710' = `at'[1,85]

scalar `g711' = `at'[1,86]

scalar `g712' = `at'[1,87]

scalar `g713' = -`g71' - `g72' - `g73'- `g74'- `g75'- `g76'- `g77'- `g78'- `g79'- `g710'- `g711'- `g712'

scalar `g81' = `g18'

scalar `g82' = `g28'

scalar `g83' = `g38'

scalar `g84' = `g48'

scalar `g85' = `g58'

scalar `g86' = `g68'

scalar `g87' = `g78'

scalar `g88' = `at'[1,88]

scalar `g89' = `at'[1,89]

scalar `g810' = `at'[1,90]

scalar `g811' = `at'[1,91]

scalar `g812' = `at'[1,92]

scalar `g813' = -`g81' - `g82' - `g83'- `g84'- `g85'- `g86'- `g87'- `g88'- `g89'- `g810'- `g811'- `g812'

scalar `g91' = `g19'

scalar `g92' = `g29'

scalar `g93' = `g39'

scalar `g94' = `g49'

scalar `g95' = `g59'

scalar `g96' = `g69'

scalar `g97' = `g79'

scalar `g98' = `g89'

scalar `g99' = `at'[1,93]

scalar `g910' = `at'[1,94]

scalar `g911' = `at'[1,95]

scalar `g912' = `at'[1,96]

scalar `g913' = -`g91' - `g92' - `g93'- `g94'- `g95'- `g96'- `g97'- `g98'- `g99'- `g910'- `g911'- `g912'

scalar `g101' = `g110'

scalar `g102' = `g210'

scalar `g103' = `g310'

scalar `g104' = `g410'

scalar `g105' = `g510'

scalar `g106' = `g610'

scalar `g107' = `g710'

scalar `g108' = `g810'

scalar `g109' = `g910'

scalar `g1010' = `at'[1,97]

scalar `g1011' = `at'[1,98]

scalar `g1012' = `at'[1,99]

scalar `g1013' = -`g101' - `g102' - `g103'- `g104'- `g105'- `g106'- `g107'- `g108'- `g109'- `g1010'- `g1011'- `g1012'

scalar `g111' = `g111'

scalar `g112' = `g211'

scalar `g113' = `g311'

scalar `g114' = `g411'

scalar `g115' = `g511'

scalar `g116' = `g611'

scalar `g117' = `g711'

scalar `g118' = `g811'

scalar `g119' = `g911'

scalar `g1110' = `g1011'

scalar `g1111' = `at'[1,100]

scalar `g1112' = `at'[1,101]

scalar `g1113' = -`g111' - `g112' - `g113'- `g114'- `g115'- `g116'- `g117'- `g118'- `g119'- `g1110'- `g1111'- `g1112'

scalar `g121' = `g112'

scalar `g122' = `g212'

scalar `g123' = `g312'

scalar `g124' = `g412'

scalar `g125' = `g512'

scalar `g126' = `g612'

scalar `g127' = `g712'

scalar `g128' = `g812'

scalar `g129' = `g912'

scalar `g1210' = `g1012'

scalar `g1211' = `g1112'

scalar `g1212' = `at'[1,102]

scalar `g1213' = -`g121' - `g122' - `g123'- `g124'- `g125'- `g126'- `g127'- `g128'- `g129'- `g1210'- `g1211'- `g1212'

scalar `g131' = `g113'

scalar `g132' = `g213'

scalar `g133' = `g313'

scalar `g134' = `g413'

scalar `g135' = `g513'

scalar `g136' = `g613'

scalar `g137' = `g713'

scalar `g138' = `g813'

scalar `g139' = `g913'

scalar `g1310' = `g1013'

scalar `g1311' = `g1113'

scalar `g1312' = `g1213'

scalar `g1313' = -`g131' - `g132' - `g133'- `g134'- `g135'- `g136'- `g137'- `g138'- `g139'- `g1310'- `g1311'- `g1312'

// Okay, now that we have all the parameters, we can

// calculate the expenditure shares.

quietly {

// First get the price index

// I set a_0 = 5

tempvar lnpindex

gen double `lnpindex' = 5 + `a1'*`lnp1' + `a2'*`lnp2'+ `a3'*`lnp3' + `a4'*`lnp4'+ `a5'*`lnp5'+ `a6'*`lnp6' ///

+ `a7'*`lnp7'+ `a8'*`lnp8'+ `a9'*`lnp9'+ `a10'*`lnp10'+ `a11'*`lnp11'+ `a12'*`lnp12'+ `a13'*`lnp13'

forvalues i = 1/13 {

forvalues j = 1/13 {

replace `lnpindex' = `lnpindex' + ///

0.5*`g`i'`j''*`lnp`i''*`lnp`j''

}

}

// Finally, the expenditure shares for 17 of the 18

// nutrients (the equation 18 is dropped to avoid singularity)

replace `w1' = `a1' + `g11'*`lnp1' + `g12'*`lnp2' +`g13'*`lnp3' + `g14'*`lnp4' + `g15'*`lnp5' ///

+ `g16'*`lnp6' + `g17'*`lnp7' + `g18'*`lnp8' + `g19'*`lnp9' + `g110'*`lnp10' + `g111'*`lnp11' ///

+ `g112'*`lnp12' + `g113'*`lnp13'+ `b1'*(`lnexp' - `lnpindex')

replace `w2' = `a2' + `g21'*`lnp1' + `g22'*`lnp2' +`g23'*`lnp3' + `g24'*`lnp4' + `g25'*`lnp5' ///

+ `g26'*`lnp6' + `g27'*`lnp7' + `g28'*`lnp8' + `g29'*`lnp9' + `g210'*`lnp10' + `g211'*`lnp11' ///

+ `g212'*`lnp12' + `g213'*`lnp13' + `b2'*(`lnexp' - `lnpindex')

replace `w3' = `a3' + `g31'*`lnp1' + `g32'*`lnp2' +`g33'*`lnp3' + `g34'*`lnp4' + `g35'*`lnp5' ///

+ `g36'*`lnp6' + `g37'*`lnp7' + `g38'*`lnp8' + `g39'*`lnp9' + `g310'*`lnp10' + `g311'*`lnp11' ///

+ `g312'*`lnp12' + `g313'*`lnp13' + `b3'*(`lnexp' - `lnpindex')

replace `w4' = `a4' + `g41'*`lnp1' + `g42'*`lnp2' +`g43'*`lnp3' + `g44'*`lnp4' + `g45'*`lnp5' ///

+ `g46'*`lnp6' + `g47'*`lnp7' + `g48'*`lnp8' + `g49'*`lnp9' + `g410'*`lnp10' + `g411'*`lnp11' ///

+ `g412'*`lnp12' + `g413'*`lnp13' + `b4'*(`lnexp' - `lnpindex')

replace `w5' = `a5' + `g51'*`lnp1' + `g52'*`lnp2' +`g53'*`lnp3' + `g54'*`lnp4' + `g55'*`lnp5' ///

+ `g56'*`lnp6' + `g57'*`lnp7' + `g58'*`lnp8' + `g59'*`lnp9' + `g510'*`lnp10' + `g511'*`lnp11' ///

+ `g512'*`lnp12' + `g513'*`lnp13' + `b5'*(`lnexp' - `lnpindex')

replace `w6' = `a6' + `g61'*`lnp1' + `g62'*`lnp2' +`g63'*`lnp3' + `g64'*`lnp4' + `g65'*`lnp5' ///

+ `g66'*`lnp6' + `g67'*`lnp7' + `g68'*`lnp8' + `g69'*`lnp9' + `g610'*`lnp10' + `g611'*`lnp11' ///

+ `g612'*`lnp12' + `g613'*`lnp13' + `b6'*(`lnexp' - `lnpindex')

replace `w7' = `a7' + `g71'*`lnp1' + `g72'*`lnp2' +`g73'*`lnp3' + `g74'*`lnp4' + `g75'*`lnp5' ///

+ `g76'*`lnp6' + `g77'*`lnp7' + `g78'*`lnp8' + `g79'*`lnp9' + `g710'*`lnp10' + `g711'*`lnp11' ///

+ `g712'*`lnp12' + `g713'*`lnp13' + `b7'*(`lnexp' - `lnpindex')

replace `w8' = `a8' + `g81'*`lnp1' + `g82'*`lnp2' +`g83'*`lnp3' + `g84'*`lnp4' + `g85'*`lnp5' ///

+ `g86'*`lnp6' + `g87'*`lnp7' + `g88'*`lnp8' + `g89'*`lnp9' + `g810'*`lnp10' + `g811'*`lnp11' ///

+ `g812'*`lnp12' + `g813'*`lnp13' + `b8'*(`lnexp' - `lnpindex')

replace `w9' = `a9' + `g91'*`lnp1' + `g92'*`lnp2' +`g93'*`lnp3' + `g94'*`lnp4' + `g95'*`lnp5' ///

+ `g96'*`lnp6' + `g97'*`lnp7' + `g98'*`lnp8' + `g99'*`lnp9' + `g910'*`lnp10' + `g911'*`lnp11' ///

+ `g912'*`lnp12' + `g913'*`lnp13' + `b9'*(`lnexp' - `lnpindex')

replace `w10' = `a10' + `g101'*`lnp1' + `g102'*`lnp2' +`g103'*`lnp3' + `g104'*`lnp4' + `g105'*`lnp5' ///

+ `g106'*`lnp6' + `g107'*`lnp7' + `g108'*`lnp8' + `g109'*`lnp9' + `g1010'*`lnp10' + `g1011'*`lnp11' ///

+ `g1012'*`lnp12' + `g1013'*`lnp13' + `b10'*(`lnexp' - `lnpindex')

replace `w11' = `a11' + `g111'*`lnp1' + `g112'*`lnp2' +`g113'*`lnp3' + `g114'*`lnp4' + `g115'*`lnp5' ///

+ `g116'*`lnp6' + `g117'*`lnp7' + `g118'*`lnp8' + `g119'*`lnp9' + `g1110'*`lnp10' + `g1111'*`lnp11' ///

+ `g1112'*`lnp12' + `g1113'*`lnp13' + `b11'*(`lnexp' - `lnpindex')

replace `w12' = `a12' + `g121'*`lnp1' + `g122'*`lnp2' +`g123'*`lnp3' + `g124'*`lnp4' + `g125'*`lnp5' ///

+ `g126'*`lnp6' + `g127'*`lnp7' + `g128'*`lnp8' + `g129'*`lnp9' + `g1210'*`lnp10' + `g1211'*`lnp11' ///

+ `g1212'*`lnp12' + `g1213'*`lnp13' + `b12'*(`lnexp' - `lnpindex')

}

end

nlsur aids @ w1 w2 w3 w4 w5 w6 w7 w8 w9 w10 w11 w12 lnp1 lnp2 lnp3 lnp4 lnp5 lnp6 lnp7 lnp8 lnp9 ///

lnp10 lnp11 lnp12 lnp13 lnexp , ifgnls nequations(12) param(a1 a2 a3 a4 ///

a5 a6 a7 a8 a9 a10 a11 a12 b1 b2 b3 b4 b5 b6 b7 b8 b9 b10 b11 b12 g11 g12 g13 g14 g15 ///

g16 g17 g18 g19 g110 g111 g112 g22 g23 g24 g25 g26 g27 g28 g29 g210 g211 g212 ///

g33 g34 g35 g36 g37 g38 g39 g310 g311 g312 g44 g45 g46 g47 g48 g49 g410 g411 g412 ///

g55 g56 g57 g58 g59 g510 g511 g512 g66 g67 g68 g69 g610 g611 g612 g77 g78 ///

g79 g710 g711 g712 g88 g89 g810 g811 g812 g99 g910 g911 g912 ///

g917 g1010 g1011 g1012 g1111 g1112 g1212)

*************************************************************************

**********************THE ELASTICITY PART**************************************

******************************************************************************

set trace on

set tracedepth 4

est store aidsminti

quietly {

foreach x of varlist w* lnp* lnexp {

sum `x'

scalar `x'mean=r(mean)

}

* Price indexes

glo asum "_b[a1]*lnp1mean"

forv i=2(1)13 {

glo asum "\${asum} + _b[a`i']*lnp`i'mean"

}

glo gsum ""

forv i=1(1)13 {

forv j=1(1)13 {

glo gsum "\${gsum} + 0.5*_b[g`i'`j']*lnp`i'mean*lnp`j'mean"

}

}

*glo ap "4.7 + \${asum} \${gsum}"

*glo bp "_b[b1]*lnp1mean"

*forv i=2(1)13 {

*glo bp "\${bp} + _b[b`i']*lnp`i'mean"

*}

*glo bp "(exp(\${bp}))"

* Mus

forv i=1(1)13 {

glo mu`i' "_b[b`i'] "

}

forv j=1(1)13 {

glo gsum2`j' ""

forv k=1(1)13 {

glo gsum2`j' "\${gsum2`j'} + _b[g`j'`k']*lnp`k'mean"

}

}

}

forv i=1(1)13 {

forv j=1(1)13 {

glo delta=cond(`i'==`j',1,0)

glo mu`i'`j' "_b[g`i'`j'] - \${mu`i'}*(_b[a`j'] \${gsum2`j'})-_b[l`i']*_b[b`j']/\${bp}*(lnexpmean - (\${ap}))^2"

* If expression is too long, split it

cap nlcom (elasgasto`i': \${mu`i'}/w`i'mean + 1)(mu`i'`j':\${mu`i'`j'}), post noheader

if _rc {

qui nlcom (elasgasto`i': \${mu`i'}/w`i'mean + 1) (mu`i'`j'f:(1e+2)*(\${mu`i'`j'})), post noheader

qui nlcom (elasgasto`i': _b[elasgasto`i']) (mu`i'`j':_b[mu`i'`j'f]/(1e+2)), post noheader

}

}

}

* Uncompensated price elasticity

nlcom (elasgasto`i': _b[elasgasto`i'])

(elpnc`i'`j':_b[mu`i'`j']/w`i'mean - \${delta}) , post noheader

* Compensated price elasticity

nlcom (elpc`i'`j': _b[elpnc`i'`j'] + _b[elasgasto`i']*w`j'mean), noheader

qui est restore aidsminti

}

}

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```