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From |
Arne Risa Hole <arnehole@gmail.com> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: Estimating a mixed logit model with mixlogit |

Date |
Sat, 25 Jun 2011 13:00:31 +0100 |

Tunga You are right: you would have to write your own program to do this as the utility function U_is is non-linear in the parameters. Note that this was not the case in the model you outlined in your earlier question. Arne On 24 June 2011 19:54, Tunga Kantarcı <tungakantarci@gmail.com> wrote: > Hello, > > I would like to sketch a discrete response model and ask if I can make > use of the mixlogit package. Actually I asked in a previous thread a > similar question and Arne Hole replied my question but I now realize > that I should elaborate more on my model because it is still not clear > to me if I can estimate my model with mixlogit, or with any other > Stata package I am not aware of. The model is as follows. > > In an online survey, I provide three retirement scenarios (early, > normal and delayed retirement) where each scenario describes the labor > force and work and retirement income trajectory of a hypothetical > person at each age from 60 to 80. For example, from age 60 to 65, a > hypothetical person is working full-time and from 66 onward he is > fully retired. At each age the corresponding hypothetical work and > retirement income is indicated. I ask the respondent to choose among > the "three" retirement scenarios the one he likes the best. I want to > model the choice as follows. > > V_is = U_is + E_is > > is a random utility model where E_is is assumed to be iid normal. > > U_is = sum operator_{t=60}^{80} rho^(t-60) * U_its > > is the total life cycle utility from retirement scenario s where s = > {1,2,3}. rho is the discount rate to be estimated. > > U_its = alfa_i^0 + alfa_it^lf * L_its^f + alfa_it^lyf * L_its^f * Y_its^f > > is the within period utility: I assume that total utility is > additively separable. > > L_its^f is a dummy variable which indicates if respondent i, at age t, > in scenario s, is working full time. > Y_its^f indicates a replacement rate, to indicate retirement income, > which takes a random value among the six predetermined values (I > randomize over sub-samples in the sample). The base category is > working full time and hence omitted. > > Alfa coefficients represent preference parameters and they are assumed > to be random and depend on observed and unobserved individual > characteristics in the following way. > > alfa_i^0 = beta^0x * X_i + e_i^0 > alfa_it^lf = beta^lfx * X_i + beta^lft * t + e_i^lf > alfa_it^lyf = beta^lyfx * X_i + beta^lyft * t + e_i^lyf > > Unobserved e terms are assumed to be iid normal. X_i is a vector of > observed characteristics such as gender, education etc. t is age in > the scenario described to the respondent (takes values from 60 to 80 > as defined in U_is). > > A respondent will choose, for example, scenario 1 if U_i1 + Ei1 > U_i2 > + Ei2 and if U_i1 + Ei1 > U_i3 + Ei3. > Hence, probability of choosing first scenario is given by > P(S=1|L,Y,X,t,e) = P(E_i2 - E_i1 < U_i1 - U_i2, E_i3 - E_i1 < U_i1 - > U_i3). > > Then I write the likelihood function and then that function needs to > be integrated over all possible values of e_i^0, e_i^lf, and e_i^lyf. > This is a three dimensional integral which does not have a closed form > solution and hence needs to be simulated. > > My question is the following. I wanted to write a Matlab code to > estimate this model but I have a time constraint and hence wondering > if I can estimate this model with mixlogit. It obviously does not seem > feasible to run the mixlogit syntax right away. I could plug in the > alfa coefficients in U_its and indicate the variables as having random > coefficients in the syntax of mixlogit. However, I am not considering > U_its but U_is. So it looks like I first need to instruct Stata about > U_is. But U_is is a long expression where U_its at each age t is > multiplied by the discount factor rho. > > Is there a relatively easy way of estimating this model in Stata, for > example with mixlogit, or shall I give up and program it myself in > Matlab? > In particular, would it be feasible to estimate this model in Stata if > I figure out how to instruct Stata about my utility function U_is? > > Thanks, > Tunga > * > * For searches and help try: > * http://www.stata.com/help.cgi?search > * http://www.stata.com/support/statalist/faq > * http://www.ats.ucla.edu/stat/stata/ > * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**References**:**st: Estimating a mixed logit model with mixlogit***From:*Tunga Kantarcı <tungakantarci@gmail.com>

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