Running Poi’s Quaids manually with nlsur. Problem with computing price elasticity

[sami farook]

Dear All

I would really appreciate some help on this. I am using Stata 13. I need to run quaids model manually using nlsur for a four good model to estimate income and price elasticity. Following is how I ran my codes to estimate QUAIDS model, compute expenditure elasticities from it and own price elasticity for good1. The expenditure elasiticities matches exactly with the outputs when using POI’s built-in quaids suite, but the own price elasticity does not (slight mismatch on second decimal figure). Can anyone help me with this? Thanks a lot.

Sami


#delimit;

* lnexptot= ln of total expenditure on the four goods;
*lnprice= ln of prices;
*w = expenditure shares;

scalar a_0 = 5;
nlsur quaids @ w1 w2 w3 lnprice1-lnprice4 lnexptot, ifgnls nequations(3) param(a1 a2 a3 b1 b2 b3 g11 g12 g13 g22 g23 g33 l1 l2 l3) nolog;

matrix B = e(b)';
matrix list B;

nlcom (a1:_b[/a1]) (a2:_b[/a2]) (a3:_b[/a3])
(a4:1-_b[/a1]-_b[/a2]-_b[/a3])
(b1:_b[/b1]) (b2:_b[/b2]) (b3:_b[/b3])
(b4:-_b[/b1]-_b[/b2]-_b[/b3])
(g11:_b[/g11]) (g12:_b[/g12]) (g13:_b[/g13])
(g14:-_b[/g11]-_b[/g12]-_b[/g13])
(g22:_b[/g22]) (g23:_b[/g23])
(g24:-_b[/g12]-_b[/g22]-_b[/g23])
(g33:_b[/g33]) (g34:-_b[/g13]-_b[/g23]-_b[/g33])
(g44:-(_b[/g11]-_b[/g12]-_b[/g13]) -
(_b[/g12]-_b[/g22]-_b[/g23]) -
(_b[/g13]-_b[/g23]-_b[/g33]))
(l1:_b[/l1]) (l2:_b[/l2]) (l3:_b[/l3])
(l4:-_b[/l1]-_b[/l2]-_b[/l3]);

/* Scalars for parameter estimates */;

scalar a1 = _b[/a1];
scalar a2 = _b[/a2];
scalar a3 = _b[/a3];
scalar a4 = 1 - a1 - a2 - a3;
scalar b1 = _b[/b1];
scalar b2 = _b[/b2];
scalar b3 = _b[/b3];
scalar b4 = 0 - b1 - b2 - b3;
scalar g11 = _b[/g11];
scalar g12 = _b[/g12];
scalar g13 = _b[/g13];
scalar g14 = 0 - (g11 + g12 + g13);
scalar g21 = g12;
scalar g22 = _b[/g22];
scalar g23 = _b[/g23];
scalar g24 = 0 - (g12 + g22 + g23);
scalar g31 = g13;
scalar g32 = g23;
scalar g33 = _b[/g33];
scalar g34 = 0 - (g13 + g23 + g33);
scalar g41 = g14;
scalar g42 = g24;
scalar g43 = g34;
scalar g44 = 0 - (g14 + g24 + g34);
scalar l1 = _b[/l1];
scalar l2 = _b[/l2];
scalar l3 = _b[/l3];
scalar l4 = 0 - (l1 + l2 + l3);

predict eshare*

/* This produces the same estimates tan those obtained by running the
aforementioned quaids command */;
* FOR ELASTICITIES;
* Preliminaries;

gen lnb = b1*lnprice1 + b2*lnprice2 + b3*lnprice3 + b4*lnprice4;

gen bindex = exp(lnb);

gen lna = a_0 + a1*lnprice1 + a2*lnprice2 + a3*lnprice3 + a4*lnprice4 +
(1/2)*(g11*lnprice1*lnprice1 + g12*lnprice1*lnprice2 + g13*lnprice1*lnprice3 + g14*lnprice1*lnprice4 +
g21*lnprice2*lnprice1 + g22*lnprice2*lnprice2 + g23*lnprice2*lnprice3 + g24*lnprice2*lnprice4 +
g31*lnprice3*lnprice1 + g32*lnprice3*lnprice2 + g33*lnprice3*lnprice3 + g34*lnprice3*lnprice4 +
g41*lnprice4*lnprice1 + g42*lnprice4*lnprice2 + g43*lnprice4*lnprice3 + g44*lnprice4*lnprice4);

gen aindex = exp(lna);


/* INCOME ELASTICITIES */
gen mu1 = b1 + ((l1*2)/bindex)*(lnexptot - lna);
gen mu2 = b2 +((l2*2)/bindex)*(lnexptot - lna);
gen mu3 = b3 + ((l3*2)/bindex)*(lnexptot - lna);
gen mu4 = b4 + ((l4*2)/bindex)*(lnexptot - lna);
gen em1 = (mu1/w1) + 1;
gen em2 = (mu2/w2) + 1;
gen em3 = (mu3/w3) + 1;
gen em4 = (mu4/w4) + 1;

sum em*;

*calculating own price elasticity for "good 1";
gen muu1=((l1*b1)/bindex)*(lnexptot - lna)^2;
gen mm1=a1+(g23*lnprice2)+(g33*lnprice3);
gen pe1= g11-((b1+mu1)*mm1)-muu1;
gen ope1=-1+(pe1/w1);
sum ope1;

#delimit cr
exit

[sami farook]

Hi people

No worries, I have sorted the problem out. There was a small error in my price elasticity calculation earlier. It is fixed now, and the entire set of commands is given below, so anyone else having trouble with similar work can gain from this. Hope this helps.

Cheers
Sami

*****************************
#delimit;

scalar a_0 = 5;
nlsur quaids @ w1 w2 w3 lnprice1-lnprice4 lnexptot, ifgnls nequations(3) param(a1 a2 a3 b1 b2 b3 g11 g12 g13 g22 g23 g33 l1 l2 l3) nolog;

matrix B = e(b)';
matrix list B;

* Scalars for parameter estimates */;

scalar a1 = _b[/a1];
scalar a2 = _b[/a2];
scalar a3 = _b[/a3];
scalar a4 = 1 - a1 - a2 - a3;
scalar b1 = _b[/b1];
scalar b2 = _b[/b2];
scalar b3 = _b[/b3];
scalar b4 = 0 - b1 - b2 - b3;
scalar g11 = _b[/g11];
scalar g12 = _b[/g12];
scalar g13 = _b[/g13];
scalar g14 = 0 - (g11 + g12 + g13);
scalar g21 = g12;
scalar g22 = _b[/g22];
scalar g23 = _b[/g23];
scalar g24 = 0 - (g12 + g22 + g23);
scalar g31 = g13;
scalar g32 = g23;
scalar g33 = _b[/g33];
scalar g34 = 0 - (g13 + g23 + g33);
scalar g41 = g14;
scalar g42 = g24;
scalar g43 = g34;
scalar g44 = 0 - (g14 + g24 + g34);
scalar l1 = _b[/l1];
scalar l2 = _b[/l2];
scalar l3 = _b[/l3];
scalar l4 = 0 - (l1 + l2 + l3);

predict eshare*

gen lnb = b1*lnprice1 + b2*lnprice2 + b3*lnprice3 + b4*lnprice4;

gen bindex = exp(lnb);

gen lna = a_0 + a1*lnprice1 + a2*lnprice2 + a3*lnprice3 + a4*lnprice4 +
(1/2)*(g11*lnprice1*lnprice1 + g12*lnprice1*lnprice2 + g13*lnprice1*lnprice3 + g14*lnprice1*lnprice4 +
g21*lnprice2*lnprice1 + g22*lnprice2*lnprice2 + g23*lnprice2*lnprice3 + g24*lnprice2*lnprice4 +
g31*lnprice3*lnprice1 + g32*lnprice3*lnprice2 + g33*lnprice3*lnprice3 + g34*lnprice3*lnprice4 +
g41*lnprice4*lnprice1 + g42*lnprice4*lnprice2 + g43*lnprice4*lnprice3 + g44*lnprice4*lnprice4);

gen aindex = exp(lna);


/* INCOME ELASTICITIES */
gen mu1 = b1 + ((l1*2)/bindex)*(lnexptot - lna);
gen mu2 = b2 +((l2*2)/bindex)*(lnexptot - lna);
gen mu3 = b3 + ((l3*2)/bindex)*(lnexptot - lna);
gen mu4 = b4 + ((l4*2)/bindex)*(lnexptot - lna);
gen em1 = (mu1/w1) + 1;
gen em2 = (mu2/w2) + 1;
gen em3 = (mu3/w3) + 1;
gen em4 = (mu4/w4) + 1;

*uncompensated own price elasticity;
gen muu1=((l1*b1)/bindex)*(lnexptot - lna)^2;
gen mm1=a1+(g11*lnprice1)+(g12*lnprice2)+(g13*lnprice3 )+(g14*lnprice4);
gen pe1= g11-(mu1*mm1)-muu1;
gen ope1=-1+(pe1/w1);

gen muu2=((l2*b2)/bindex)*(lnexptot - lna)^2;
gen mm2=a2+(g21*lnprice1)+(g22*lnprice2)+(g23*lnprice3 )+(g24*lnprice4);
gen pe2= g22-(mu2*mm2)-muu2;
gen ope2=-1+(pe2/w2);

gen muu3=((l3*b3)/bindex)*(lnexptot - lna)^2;
gen mm3=a3+(g31*lnprice1)+(g32*lnprice2)+(g33*lnprice3 )+(g34*lnprice4);
gen pe3= g33-(mu3*mm3)-muu3;
gen ope3=-1+(pe3/w3);

gen muu4=((l4*b4)/bindex)*(lnexptot - lna)^2;
gen mm4=a4+(g41*lnprice1)+(g42*lnprice2)+(g43*lnprice3 )+(g44*lnprice4);
gen pe4= g44-(mu4*mm4)-muu4;
gen ope4=-1+(pe4/w4);

sum em*;
sum ope*;n
#delimit cr
exit
**************************************************
*the above work gives the exact same output as when using POI's built-in quaids suite, the command of which is as following:

** same work with quaids built-in command**
quaids w1-w4, anot(5) lnprices(lnprice1-lnprice4) lnexpenditure(lnexptot) nolog

predict eshare*
estat expenditure ee*
estat uncompensated upe*
sum ee_1-ee_4
sum upe_1_1 upe_2_2 upe_3_3 upe_4_4