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From |
"Brian P. Poi" <bpoi@stata.com> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: Replicating Poi's quaids command |

Date |
Wed, 04 Sep 2013 15:25:49 -0500 |

On 09/04/2013 08:26 AM, Cruz Angel Echevarria wrote:

To Whom It May Concern, I would really appreciate some help on this. Running the following commands to estimate a QUAIDS model use food.dta, clear; des; quaids w1-w4, anot(10) prices(p1-p4) expenditure(expfd) nolog; estat expenditure e*; summarize e_1-e_4; I obtain the following output for expenditure elasticities Variable | Obs Mean Std. Dev. Min Max -------------+-------------------------------------------------------- e_1 | 4039 .1742147 1.21937 -60.39818 .7226771 e_2 | 4029 .7332107 .2953817 -8.625433 .9495344 e_3 | 3996 2.008486 1.26706 1.133542 36.11684 e_4 | 4047 2.292034 2.938157 1.211376 169.9647 However, running my own code to estimate QUAIDS model, I obtain the same parameter estimates that Boid's procedure does. I interpret this as that the nlsurquaids program I have written is OK. However, when I try to compute the expenditure elasticities, I obtain different results. This makes me think that I am not translating the theoretical formulae properly into Stata code. My code follows: cscript #delimit; set more off; version 13; drop _all; clear matrix; capture log close; log using output.log, replace; set memory 500m, permanently; use food.dta, clear; rename lnexp lnm; des; scalar a_0 = 10; nlsur quaids @ w1 w2 w3 lnp1 lnp2 lnp3 lnp4 lnm, ifgnls neq(3) param(a1 a2 a3 b1 b2 b3 g11 g12 g13 g22 g23 g33 l1 l2 l3) title( Example QUAIDS) title2( 4 goods) 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 = 1 - 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); /* This produces the same estimates tan those obtained by running the aforementioned quaids command */ /* ===== */ /* FOR ELASTICITIES */ /* ===== */ /* Preliminaries */ gen lnb = b1*lnp1 + b2*lnp2 + b3*lnp3 + b4*lnp4; gen bindex = exp(lnb); gen lna = a_0 + a1*lnp1 + a2*lnp2 + a3*lnp3 + a4*lnp4 + (1/2)*( g11*lnp1*lnp1 + g12*lnp1*lnp2 + g13*lnp1*lnp3 + g14*lnp1*lnp4 + g21*lnp2*lnp1 + g22*lnp2*lnp2 + g23*lnp2*lnp3 + g24*lnp2*lnp4 + g31*lnp3*lnp1 + g32*lnp3*lnp2 + g33*lnp3*lnp3 + g34*lnp3*lnp4 + g41*lnp4*lnp1 + g42*lnp4*lnp2 + g43*lnp4*lnp3 + g44*lnp4*lnp4 ); gen aindex = exp(lna); /* INCOME ELASTICITIES */ gen mu1 = b1 + ((l1*2)/bindex)*(lnm - lna); gen mu2 = b2 + ((l2*2)/bindex)*(lnm - lna); gen mu3 = b3 + ((l3*2)/bindex)*(lnm - lna); gen mu4 = b4 + ((l4*2)/bindex)*(lnm - lna); gen em1 = (mu1/w1) + 1; gen em2 = (mu2/w2) + 1; gen em3 = (mu3/w3) + 1; gen em4 = (mu4/w4) + 1; sum em*; And this is the output that I obtain Variable | Obs Mean Std. Dev. Min Max -------------+-------------------------------------------------------- em1 | 4039 1.556595 1.060537 -1.413979 37.93764 em2 | 4029 .9256395 .1425985 -2.658406 2.997787 em3 | 3996 .4810829 1.376963 -46.75089 4.259475 em4 | 4047 5.482535 8.378185 -.6769157 437.3061 which clearly differs from the one above shown. I would really appreciate any help on this. Regards, Cruz

Cruz, I found two issues with your code, and one error in mine. First,

scalar b4 = 1 - b1 - b2 - b3;

should be scalar b4 = 0 - b1 - b2 - b3; since the betas should sum to zero, not one. Second, you have

nlsur quaids @ w1 w2 w3 lnp1 lnp2 lnp3 lnp4 lnm, ifgnls neq(3) param(a1 a2 a3 b1 b2 b3 g11 g12 g13 g22 g23 g33 l1 l2 l3) title( Example QUAIDS) title2( 4 goods) nolog;

This -nlsur- command is going to use the nlsurquaids.ado file that was shown in my 2008 Stata Journal article (assuming it was already installed). However, that file has a_0 hardcoded as equal to 5. So to get comparable results using -quaids- and your program, you must specify anot(5) and set your scalar a_0 = 5. With those two changes to your code, we get much closer results. The last error is in my code, and it only affects the computation of the expenditure elasticities. There I forgot to include the factor of 0.5 that appears in the price index term. I will get that fixed and in the "Software Update" section of the next issue of the Stata Journal. That update will also have a new feature several users requested. When you use the -estat- postestimation commands to get elasticities either at the variable means or else for a single observation in the dataset, those commands will now also return matrices containing the standard errors of the estimated elasticities. -- Brian Poi bpoi@stata.com * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/faqs/resources/statalist-faq/ * http://www.ats.ucla.edu/stat/stata/

**References**:**st: Replicating Poi's quaids command***From:*"Cruz Angel Echevarria" <cruz.echevarria@ehu.es>

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