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From |
Tunga Kantarcı <tungakantarci@gmail.com> |

To |
statalist@hsphsun2.harvard.edu |

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

Date |
Fri, 24 Jun 2011 20:54:02 +0200 |

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/

**Follow-Ups**:**Re: st: Estimating a mixed logit model with mixlogit***From:*Arne Risa Hole <arnehole@gmail.com>

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