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st: Delta Method after Quaids

 From Guilherme Travassos To "statalist@hsphsun2.harvard.edu" Subject st: Delta Method after Quaids Date Tue, 24 Dec 2013 01:04:12 +0000

```Dear Statalisters,

I'm using nlsur Quaids from Brian Poi (2008) to estimate a seven group demand system for meat products with some restrictions. After I estimate the model, I want to use delta method to calculate all coefficients and elasticities at the average values for budget shares, expenditure and prices. But I'm have some problemas wiht the delta method. After I run the codes, Stata give me this message: unknown function (). I don't know what it is.
Could anyone help me?
I'm sending delta method code.
* Step 1: create averages (suffix "bar")
qui summ lnp1
scalar lnp1bar=r(mean)
qui summ lnp2
scalar lnp2bar=r(mean)
qui summ lnp3
scalar lnp3bar=r(mean)
qui summ lnp4
scalar lnp4bar=r(mean)
qui summ lnp5
scalar lnp5bar=r(mean)
qui summ lnp6
scalar lnp6bar=r(mean)
qui summ lnp7
scalar lnp7bar=r(mean)

qui summ w1
scalar w1bar=r(mean)
qui summ w2
scalar w2bar=r(mean)
qui summ w3
scalar w3bar=r(mean)
qui summ w4
scalar w4bar=r(mean)
qui summ w5
scalar w5bar=r(mean)
qui summ w6
scalar w6bar=r(mean)
qui summ w7
scalar w7bar=r(mean)

qui summ F1
scalar F1bar=r(mean)
qui summ F2
scalar F2bar=r(mean)
qui summ F3
scalar F3bar=r(mean)
qui summ F4
scalar F4bar=r(mean)
qui summ F5
scalar F5bar=r(mean)
qui summ F6
scalar F6bar=r(mean)
qui summ F7
scalar F7bar=r(mean)

qui summ lnexp
scalar lnexpbar=r(mean)

qui summ lnpindex
scalar lnpindexbar=r(mean)

* Step 2: use delta method to calculate all coefficients and with the "post" option these are kept in memory (and used later)

nlcom (a1:_b[/b1])(a2:_b[/b2])(a3:_b[/b3])(a4:_b[/b4])(a5:_b[/b5])(a6:_b[/b6]) ///
(a7:1-_b[/b1]-_b[/b2]-_b[/b3]-_b[/b4]-_b[/b5]-_b[/b6]) ///
(b1:_b[/b7])(b2:_b[/b8])(b3:_b[/b9])(b4:_b[/b10])(b5:_b[/b11])(b6:_b[/b12]) ///
(b7:-_b[/b7]-_b[/b8]-_b[/b9]-_b[/b10]-_b[/b11]-_b[/b12]) ///
(g11:_b[/b13])(g12:_b[/b14])(g13:_b[/b15])(g14:_b[/b16])(g15:_b[/b17])(g16:_b[/b18]) //
(g21:_b[/b19])(g22:_b[/b20])(g23:_b[/b21])(g24:_b[/b22])(g25:_b[/b23])(g26:_b[/b24]) //
(g31:_b[/b25])(g32:_b[/b26])(g33:_b[/b27])(g34:_b[/b28])(g35:_b[/b29])(g36:_b[/b30]) ///
(g41:_b[/b31])(g42:_b[/b32])(g43:_b[/b33])(g44:_b[/b34])(g45:_b[/b35])(g46:_b[/b36]) ///
(g51:_b[/b37])(g52:_b[/b38])(g53:_b[/b39])(g54:_b[/b40])(g55:_b[/b41])(g56:_b[/b42]) ///
(g61:_b[/b43])(g62:_b[/b44])(g63:_b[/b45])(g64:_b[/b46])(g65:_b[/b47])(g66:_b[/b48]) (g67:_b[/49]) ///
(g17:((_b[/b1]+_b[/b7])/(_b[/b6]+_b[/b12]))*(_b[/b49]+_b[/b6]*(-_b[/b1]-_b[/b2]-_b[/b3]-_b[/b4]-_b[/b5]-_b[/b6]))-_b[/b1]*(-_b[/b1]-_b[/b2]-_b[/b3]-_b[/b4]-_b[/b5]-_b[/b6])) ///
(g27:((_b[/b2]+_b[/b8])/(_b[/b6]+_b[/b12]))*(_b[/b49]+_b[/b6]*(-_b[/b1]-_b[/b2]-_b[/b3]-_b[/b4]-_b[/b5]-_b[/b6]))-_b[/b2]*(-_b[/b1]-_b[/b2]-_b[/b3]-_b[/b4]-_b[/b5]-_b[/b6])) ///
(g37:((_b[/b3]+_b[/b9])/(_b[/b6]+_b[/b12]))*(_b[/b49]+_b[/b6]*(-_b[/b1]-_b[/b2]-_b[/b3]-_b[/b4]-_b[/b5]-_b[/b6]))-_b[/b3]*(-_b[/b1]-_b[/b2]-_b[/b3]-_b[/b4]-_b[/b5]-_b[/b6])) ///
(g47:((_b[/b4]+_b[/b10])/(_b[/b6]+_b[/b12]))*(_b[/b49]+_b[/b6]*(-_b[/b1]-_b[/b2]-_b[/b3]-_b[/b4]-_b[/b5]-_b[/b6]))-_b[/b4]*(-_b[/b1]-_b[/b2]-_b[/b3]-_b[/b4]-_b[/b5]-_b[/b6])) ///
(g57:((_b[/b5]+_b[/b11])/(_b[/b6]+_b[/b12]))*(_b[/b49]+_b[/b6]*(-_b[/b1]-_b[/b2]-_b[/b3]-_b[/b4]-_b[/b5]-_b[/b6]))-_b[/b5]*(-_b[/b1]-_b[/b2]-_b[/b3]-_b[/b4]-_b[/b5]-_b[/b6])) ///
(g71:-_b[/b13]-_b[/b19]-_b[/b25]-_b[/b31]-_b[/b37]-_b[/b43]) ///
(g72:-_b[/b14]-_b[/b20]-_b[/b26]-_b[/b32]-_b[/b38]-_b[/b44]) ///
(g73:-_b[/b15]-_b[/b21]-_b[/b27]-_b[/b33]-_b[/b39]-_b[/b45]) ///
(g74:-_b[/b16]-_b[/b22]-_b[/b28]-_b[/b34]-_b[/b40]-_b[/b46]) ///
(g75:-_b[/b17]-_b[/b23]-_b[/b29]-_b[/b35]-_b[/b41]-_b[/b47]) ///
(g76:-_b[/b18]-_b[/b24]-_b[/b30]-_b[/b36]-_b[/b42]-_b[/b48]) ///
(g77:-((_b[/b1]+_b[/b7])/(_b[/b6]+_b[/b12]))*(_b[/b49]+_b[/b6]*(-_b[/b1]-_b[/b2]-_b[/b3]-_b[/b4]-_b[/b5]-_b[/b6]))-_b[/b1]*(-_b[/b1]-_b[/b2]-_b[/b3]-_b[/b4]-_b[/b5]-_b[/b6]))-(((_b[/b2]+_b[/b8])/(_b[/b6]+_b[/b12]))*(_b[/b49]+_b[/b6]*(-_b[/b1]-_b[/b2]-_b[/b3]-_b[/b4]-_b[/b5]-_b[/b6]))-_b[/b2]*(-_b[/b1]-_b[/b2]-_b[/b3]-_b[/b4]-_b[/b5]-_b[/b6]))-(((_b[/b3]+_b[/b9])/(_b[/b6]+_b[/b12]))*(_b[/b49]+_b[/b6]*(-_b[/b1]-_b[/b2]-_b[/b3]-_b[/b4]-_b[/b5]-_b[/b6]))-_b[/b3]*(-_b[/b1]-_b[/b2]-_b[/b3]-_b[/b4]-_b[/b5]-_b[/b6]))-(((_b[/b4]+_b[/b10])/(_b[/b6]+_b[/b12]))*(_b[/b49]+_b[/b6]*(-_b[/b1]-_b[/b2]-_b[/b3]-_b[/b4]-_b[/b5]-_b[/b6]))-_b[/b4]*(-_b[/b1]-_b[/b2]-_b[/b3]-_b[/b4]-_b[/b5]-_b[/b6]))-(((_b[/b5]+_b[/b11])/(_b[/b6]+_b[/b12]))*(_b[/b49]+_b[/b6]*(-_b[/b1]-_b[/b2]-_b[/b3]-_b[/b4]-_b[/b5]-_b[/b6]))-_b[/b5]*(-_b[/b1]-_b[/b2]-_b[/b3]-_b[/b4]-_b[/b5]-_b[/b6]))-_b[/49])) ///
(l1:_b[/b50])(l2:_b[/b51])(l3:_b[/b52])(l4:_b[/b53])(l5:_b[/b54])(l6:_b[/b55]) ///
(l7:-_b[/b50]-_b[/b51]-_b[/b52]-_b[/b53]-_b[/b54]-_b[/b55]), post iterate(999)

scalar bofp = 0
forvalues i = 1/7 {
forvalues j = 1/7 {
scalar bofp = bofp + lnp`i'bar*_b[b`i']
}
}
scalar bofp = exp(bofp)
di bofp

scalar bofp = r(mean)
di bofp

scalar aofp = lnpindexbar

* Finally, we calculate the elasticities at the average values for budget shares, expenditure and prices

nlcom (e1: F1bar*((_b[b1]+2*_b[l1]/bofp*(lnexpbar-aofp)))/w1bar+1) ///
(e2: F2bar*((_b[b2]+2*_b[l2]/bofp*(lnexpbar-aofp)))/w2bar+1) ///
(e3: F3bar*((_b[b3]+2*_b[l3]/bofp*(lnexpbar-aofp)))/w3bar+1) ///
(e4: F4bar*((_b[b4]+2*_b[l4]/bofp*(lnexpbar-aofp)))/w4bar+1) ///
(e5: F5bar*((_b[b5]+2*_b[l5]/bofp*(lnexpbar-aofp)))/w5bar+1) ///
(e6: F6bar*((_b[b6]+2*_b[l6]/bofp*(lnexpbar-aofp)))/w6bar+1) ///
(e7: F7bar*((_b[b7]+2*_b[l7]/bofp*(lnexpbar-aofp)))/w7bar+1) ///
(eu11:(F1bar*(_b[g11]-(_b[b1]+2*_b[l1]/bofp*(lnexpbar-aofp))*w1bar-_b[b1]*_b[l1]*(lnexpbar-aofp)^2/bofp)/w1bar)) ///
(eu22:(F2bar*(_b[g22]-(_b[b2]+2*_b[l2]/bofp*(lnexpbar-aofp))*w2bar-_b[b2]*_b[l2]*(lnexpbar-aofp)^2/bofp)/w2bar)) ///
(eu33:(F3bar*(_b[g33]-(_b[b3]+2*_b[l3]/bofp*(lnexpbar-aofp))*w3bar-_b[b3]*_b[l3]*(lnexpbar-aofp)^2/bofp)/w3bar)) ///
(eu44:(F4bar*(_b[g44]-(_b[b4]+2*_b[l4]/bofp*(lnexpbar-aofp))*w4bar-_b[b4]*_b[l4]*(lnexpbar-aofp)^2/bofp)/w4bar)) ///
(eu55:(F5bar*(_b[g55]-(_b[b5]+2*_b[l5]/bofp*(lnexpbar-aofp))*w5bar-_b[b5]*_b[l5]*(lnexpbar-aofp)^2/bofp)/w5bar)) ///
(eu66:(F6bar*(_b[g66]-(_b[b6]+2*_b[l6]/bofp*(lnexpbar-aofp))*w6bar-_b[b6]*_b[l6]*(lnexpbar-aofp)^2/bofp)/w6bar)) ///
(eu12:(F2bar*(_b[g12]-(_b[b1]+2*_b[l1]/bofp*(lnexpbar-aofp))*w2bar-_b[b2]*_b[l1]*(lnexpbar-aofp)^2/bofp)/w1bar)) ///
(eu13:(F3bar*(_b[g13]-(_b[b1]+2*_b[l1]/bofp*(lnexpbar-aofp))*w3bar-_b[b3]*_b[l1]*(lnexpbar-aofp)^2/bofp)/w1bar)) ///
(eu14:(F4bar*(_b[g14]-(_b[b1]+2*_b[l1]/bofp*(lnexpbar-aofp))*w4bar-_b[b4]*_b[l1]*(lnexpbar-aofp)^2/bofp)/w1bar)) ///
(eu15:(F5bar*(_b[g15]-(_b[b1]+2*_b[l1]/bofp*(lnexpbar-aofp))*w5bar-_b[b5]*_b[l1]*(lnexpbar-aofp)^2/bofp)/w1bar)) ///
(eu16:(F6bar*(_b[g16]-(_b[b1]+2*_b[l1]/bofp*(lnexpbar-aofp))*w6bar-_b[b6]*_b[l1]*(lnexpbar-aofp)^2/bofp)/w1bar)) ///
(eu17:(F7bar*(_b[g17]-(_b[b1]+2*_b[l1]/bofp*(lnexpbar-aofp))*w7bar-_b[b7]*_b[l1]*(lnexpbar-aofp)^2/bofp)/w1bar)) ///
(eu21:(F1bar*(_b[g21]-(_b[b2]+2*_b[l2]/bofp*(lnexpbar-aofp))*w1bar-_b[b1]*_b[l2]*(lnexpbar-aofp)^2/bofp)/w2bar)) ///
(eu23:(F3bar*(_b[g23]-(_b[b2]+2*_b[l2]/bofp*(lnexpbar-aofp))*w3bar-_b[b3]*_b[l2]*(lnexpbar-aofp)^2/bofp)/w2bar)) ///
(eu24:(F4bar*(_b[g24]-(_b[b2]+2*_b[l2]/bofp*(lnexpbar-aofp))*w4bar-_b[b4]*_b[l2]*(lnexpbar-aofp)^2/bofp)/w2bar)) ///
(eu25:(F5bar*(_b[g25]-(_b[b2]+2*_b[l2]/bofp*(lnexpbar-aofp))*w5bar-_b[b5]*_b[l2]*(lnexpbar-aofp)^2/bofp)/w2bar)) ///
(eu26:(F6bar*(_b[g26]-(_b[b2]+2*_b[l2]/bofp*(lnexpbar-aofp))*w6bar-_b[b6]*_b[l2]*(lnexpbar-aofp)^2/bofp)/w2bar)) ///
(eu27:(F7bar*(_b[g27]-(_b[b2]+2*_b[l2]/bofp*(lnexpbar-aofp))*w7bar-_b[b7]*_b[l2]*(lnexpbar-aofp)^2/bofp)/w2bar)) ///
(eu31:(F1bar*(_b[g31]-(_b[b3]+2*_b[l3]/bofp*(lnexpbar-aofp))*w1bar-_b[b1]*_b[l3]*(lnexpbar-aofp)^2/bofp)/w3bar)) ///
(eu32:(F2bar*(_b[g32]-(_b[b3]+2*_b[l3]/bofp*(lnexpbar-aofp))*w2bar-_b[b2]*_b[l3]*(lnexpbar-aofp)^2/bofp)/w3bar)) ///
(eu34:(F4bar*(_b[g34]-(_b[b3]+2*_b[l3]/bofp*(lnexpbar-aofp))*w4bar-_b[b4]*_b[l3]*(lnexpbar-aofp)^2/bofp)/w3bar)) ///
(eu35:(F5bar*(_b[g35]-(_b[b3]+2*_b[l3]/bofp*(lnexpbar-aofp))*w5bar-_b[b5]*_b[l3]*(lnexpbar-aofp)^2/bofp)/w3bar)) ///
(eu36:(F6bar*(_b[g36]-(_b[b3]+2*_b[l3]/bofp*(lnexpbar-aofp))*w6bar-_b[b6]*_b[l3]*(lnexpbar-aofp)^2/bofp)/w3bar)) ///
(eu37:(F7bar*(_b[g37]-(_b[b3]+2*_b[l3]/bofp*(lnexpbar-aofp))*w7bar-_b[b7]*_b[l3]*(lnexpbar-aofp)^2/bofp)/w3bar)) ///
(eu41:(F1bar*(_b[g41]-(_b[b4]+2*_b[l4]/bofp*(lnexpbar-aofp))*w1bar-_b[b1]*_b[l4]*(lnexpbar-aofp)^2/bofp)/w4bar)) ///
(eu42:(F2bar*(_b[g42]-(_b[b4]+2*_b[l4]/bofp*(lnexpbar-aofp))*w2bar-_b[b2]*_b[l4]*(lnexpbar-aofp)^2/bofp)/w4bar)) ///
(eu43:(F3bar*(_b[g43]-(_b[b4]+2*_b[l4]/bofp*(lnexpbar-aofp))*w3bar-_b[b3]*_b[l4]*(lnexpbar-aofp)^2/bofp)/w4bar)) ///
(eu45:(F5bar*(_b[g45]-(_b[b4]+2*_b[l4]/bofp*(lnexpbar-aofp))*w5bar-_b[b5]*_b[l4]*(lnexpbar-aofp)^2/bofp)/w4bar)) ///
(eu46:(F6bar*(_b[g46]-(_b[b4]+2*_b[l4]/bofp*(lnexpbar-aofp))*w6bar-_b[b6]*_b[l4]*(lnexpbar-aofp)^2/bofp)/w4bar)) ///
(eu47:(F7bar*(_b[g47]-(_b[b4]+2*_b[l4]/bofp*(lnexpbar-aofp))*w7bar-_b[b7]*_b[l4]*(lnexpbar-aofp)^2/bofp)/w4bar)) ///
(eu51:(F1bar*(_b[g51]-(_b[b5]+2*_b[l5]/bofp*(lnexpbar-aofp))*w1bar-_b[b1]*_b[l5]*(lnexpbar-aofp)^2/bofp)/w5bar)) ///
(eu52:(F2bar*(_b[g52]-(_b[b5]+2*_b[l5]/bofp*(lnexpbar-aofp))*w2bar-_b[b2]*_b[l5]*(lnexpbar-aofp)^2/bofp)/w5bar)) ///
(eu53:(F3bar*(_b[g53]-(_b[b5]+2*_b[l5]/bofp*(lnexpbar-aofp))*w3bar-_b[b3]*_b[l5]*(lnexpbar-aofp)^2/bofp)/w5bar)) ///
(eu54:(F4bar*(_b[g54]-(_b[b5]+2*_b[l5]/bofp*(lnexpbar-aofp))*w4bar-_b[b4]*_b[l5]*(lnexpbar-aofp)^2/bofp)/w5bar)) ///
(eu56:(F6bar*(_b[g56]-(_b[b5]+2*_b[l5]/bofp*(lnexpbar-aofp))*w6bar-_b[b6]*_b[l5]*(lnexpbar-aofp)^2/bofp)/w5bar)) ///
(eu57:(F7bar*(_b[g57]-(_b[b5]+2*_b[l5]/bofp*(lnexpbar-aofp))*w7bar-_b[b7]*_b[l5]*(lnexpbar-aofp)^2/bofp)/w5bar)) ///
(eu61:(F1bar*(_b[g61]-(_b[b6]+2*_b[l6]/bofp*(lnexpbar-aofp))*w1bar-_b[b1]*_b[l6]*(lnexpbar-aofp)^2/bofp)/w6bar)) ///
(eu62:(F2bar*(_b[g62]-(_b[b6]+2*_b[l6]/bofp*(lnexpbar-aofp))*w2bar-_b[b2]*_b[l6]*(lnexpbar-aofp)^2/bofp)/w6bar)) ///
(eu63:(F3bar*(_b[g63]-(_b[b6]+2*_b[l6]/bofp*(lnexpbar-aofp))*w3bar-_b[b3]*_b[l6]*(lnexpbar-aofp)^2/bofp)/w6bar)) ///
(eu64:(F4bar*(_b[g64]-(_b[b6]+2*_b[l6]/bofp*(lnexpbar-aofp))*w4bar-_b[b4]*_b[l6]*(lnexpbar-aofp)^2/bofp)/w6bar)) ///
(eu65:(F5bar*(_b[g65]-(_b[b6]+2*_b[l6]/bofp*(lnexpbar-aofp))*w5bar-_b[b5]*_b[l6]*(lnexpbar-aofp)^2/bofp)/w6bar)) ///
(eu67:(F7bar*(_b[g67]-(_b[b6]+2*_b[l6]/bofp*(lnexpbar-aofp))*w7bar-_b[b7]*_b[l6]*(lnexpbar-aofp)^2/bofp)/w6bar)) ///
(eu71:(F1bar*(_b[g71]-(_b[b7]+2*_b[l7]/bofp*(lnexpbar-aofp))*w1bar-_b[b1]*_b[l7]*(lnexpbar-aofp)^2/bofp)/w7bar)) ///
(eu72:(F2bar*(_b[g72]-(_b[b7]+2*_b[l7]/bofp*(lnexpbar-aofp))*w2bar-_b[b2]*_b[l7]*(lnexpbar-aofp)^2/bofp)/w7bar)) ///
(eu73:(F3bar*(_b[g73]-(_b[b7]+2*_b[l7]/bofp*(lnexpbar-aofp))*w3bar-_b[b3]*_b[l7]*(lnexpbar-aofp)^2/bofp)/w7bar)) ///
(eu74:(F4bar*(_b[g74]-(_b[b7]+2*_b[l7]/bofp*(lnexpbar-aofp))*w4bar-_b[b4]*_b[l7]*(lnexpbar-aofp)^2/bofp)/w7bar)) ///
(eu75:(F5bar*(_b[g75]-(_b[b7]+2*_b[l7]/bofp*(lnexpbar-aofp))*w5bar-_b[b5]*_b[l7]*(lnexpbar-aofp)^2/bofp)/w7bar)) ///
(eu76:(F6bar*(_b[g76]-(_b[b7]+2*_b[l7]/bofp*(lnexpbar-aofp))*w6bar-_b[b6]*_b[l7]*(lnexpbar-aofp)^2/bofp)/w7bar)), post iterate (10)

nlcom (eu77: -(w7bar+_b[eu17]*w1bar+_b[eu27]*w2bar+_b[eu37]*w3bar+_b[eu47]*w4bar+_b[eu57]*w5bar+_b[eu67]*w6bar)/w7bar)

Thank you!
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