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From |
Stas Kolenikov <skolenik@gmail.com> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: System of equations, structural models and maximum likelihood in STATA |

Date |
Tue, 11 Sep 2012 13:54:32 -0500 |

You might want to look into David Roodman's -cmp-, which is very thoroughly documented in The Stata Journal article. Type -findit cmp-. On Tue, Sep 11, 2012 at 1:46 PM, Daniel Almar de Sneijder <dasneijder@gmail.com> wrote: > Dear statalist, > > How are you doing today? I have a question regarding the structure and > best method of solving a system of equations. More specific, I am > programming an option value model of retirement (has someone > experience with it?) and therefore use maximum likelihood to obtain > the parameters. As I am new to STATA I am not really sure how to > start. In the following I describe the problem. > > > First I describe the model, see also Stock and Wise (1990) for further > details, and then I will point out the exact questions. > > The objective is to find probabilities of retiring in a specific year, > and the parameters \rho, \gamma, k, \beta in: > > > [1.] Pr[retire in year t] = Pr[ gt( r^{*}_t ) / Kt( r^{*}_t ) < - v_t ], where > > [2.] v_{s} = \rho v_{s-1} + \epsilon_t, and > > [3.] gt(r_t) = \sum^{r-1}_{s=t} \beta^{s-t} \pi(s|t) Et(Ys^{\gamma}) + > \sum^{S}_{s=r} \beta^{s-t} \pi(s|t) Et( [k Bs(r)]^{\gamma} }) - > \sum^{S}_{s=r} \beta^{s-t} \pi(s|t) Et( [ k Bs(t)]^{\gamma} }), and > > [4.] Kt( r^{*}_t ) = \sum^{r-1}_{s=t} \beta^{s-t} \pi(s|t) \rho^{s-t}. > > [5.] Also v_t = (\omega_t - \xi_t ) > > > Here Ys are future wages and Bs(t) are retirement incomes with > \pi(s|t) the probability that a person will live in year s given that > she or he lives in year t. r^{*}_t is the year in which the value of > future stream of income is maximized. The value of future stream of > income if retirement is at age 'r' is given by: > > [6.] Vt(r) = \sum^{r-t}_{s=t} \beta^{s-t} Uw(Ys) + \sum^{S}_{s=r} > \beta^{s-t} Ur[Bs(r)] > > [7.] Uw(Ys) = Ys^{\gamma} + \omega_s, > > [8.] Ur(Bs) = [ k Bs(r)]^{\gamma} + \xi_s > > [9.] \omega_s = \rho \omega_{s-1} + \epsilon_{\omega,s} where E[disturbance] = 0 > > [10.] \xi_s = \rho \xi_{s-1} + \epsilon_{\xi, s} where E[disturbance] = 0 > > > > Particular points where I am struggling at are: > > - What is the structure of a nonlinear maximum likelihood estimation > with STATA, i.e. how to set up the code. > > - How can specific parameters be used in the context, such as equation > 2. where we have v_t that depends on it's lag and a disturbance term > \epsilon_t > > - How to estimate the probability such as in equation 1 > > - How to initialize and call the model. > > > > I understand that this may be a somewhat big question, but I would > definitely appreciate it if someone can answer for at least some parts > of it. Also, it would help the community a lot, I think. > > > Thank you in advance everyone. > > > > Regards, > Daniel > * > * 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/ -- -- Stas Kolenikov, PhD, PStat (SSC) :: http://stas.kolenikov.name -- Senior Survey Statistician, Abt SRBI :: work email kolenikovs at srbi dot com -- Opinions stated in this email are mine only, and do not reflect the position of my employer * * 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: System of equations, structural models and maximum likelihood in STATA***From:*Daniel Almar de Sneijder <dasneijder@gmail.com>

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