Re: st: ML-Evaluator for modelling retirement decisions

[Nick Cox <njcoxstata@gmail.com>]

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There seems to be confusion here on several levels. First, you refer
to b[,], evidently a matrix, but it is not clear how your program can
access it. Second, your -ml- program always resets alpha and gamma, so
 as you say the iteration can only repeat the same step. Third, it is
not good style to put parameters in variables. Fourth, it is not clear
why the same utility calculation needs to be repeated each time that
-ml- iterates. Fifth, this does sound like a standard model so I
wonder why you are programming it independently.

The main point about -ml- is that it does most of the work for you. It
is usually not necessary to initialise parameters explicitly unless
the model has to strain to fit the data.

I am not an economist and I don't understand this kind of model, so
you will need to look to others for further comment.

Nick

On Wed, Jan 4, 2012 at 9:29 AM, Tibor Hanappi <hanappi@ihs.ac.at> wrote:
> Im modelling retirement decisions based on an option value framework (Gruber and Wise, 2002). Up until now I have constructed a microsimulation model calculating the option value for each individual in each year. To make it short, the option value is a forward-looking variable that summarizes the future options (with regard to retirement) of an individual at a certain point in time.
>
> Based on this approach I estimate a binary probit model with retirement in the current year as dependent variable and option value (OV), social
> security wealth (SSW), age and some other variables as covariates.
>
> However, since the option value is denoted in utility terms I have to assume some exogenous parameters of the utility function. There are basically
> two parameters: GAMMA, which defines marginal utility of income, and ALPHA, which is a factor defining the utility gain through leisure in retirement (relative to work). Exogenous values taken from the literature would be: GAMMA=0.75 and ALPHA=1.36
>
> As a next step I’m writing a maximum likelihood evaluator so that I can jointly estimate those two parameters together with the binary probit model. Since I wanted to keep it simple I’m using a gf0 evaluator. Also, I had to make sure that the two parameters stay whithin their ranges (0 to 1 for GAMMA and 1 to 2 for ALPHA), so I transform parameters b[1,5] (hp_alpha) and b[1,6] (hp_gamma) through the use of the normal cdf. Though my program passes ml check, it doesn’t converge. In fact, it seems to be unable to go on to the next iteration (#1) though it keeps on repeating every step in the program. Here is a reduced version of the code.
>
> program ML_OPV
> args todo b lnfj
> tempvar alpha gamma
> quietly gen double `alpha'=1+normal(`b'[1,5])
> quietly gen double `gamma'=normal(`b'[1,6])
> *display "ALPHA: " `alpha'
> *display "GAMMA: " `gamma'
> quietly {
> forvalues j=2002(1)2012 {
>      * Calculate Utility from Retirement based on `alpha' and `gamma'
>      < CODE OMITTED >
>
>      * Calculate Utility from Labour Income based on `gamma'
>      < CODE OMITTED >
> }
> * CALC. OPTION VALUE BASED ON UTILITY VALUES FOR DIFFERENT RETIREMENTAGES
> < CODE OMITTED >
>
> * DEFINE LIKELIHOOD FUNCTION
> tempvar xb
> gen double `xb' = `b'[1,1]*SSW + `b'[1,2]*OV + `b'[1,3]*gn_age +`b'[1,4]
> replace `lnfj' = ln(normal(`xb')) if $ML_y1 == 1
> replace `lnfj' = ln(normal(-1*`xb')) if $ML_y1 == 0
> }
> end
>
> ml model gf0 ML_OPV (theta: GO = SSW OV gn_age) /hp_alpha /hp_gamma
> ml init SSW=.000004 OV=-.0008 gn_age=.16 /hp_alpha=-.001 /hp_gamma=.5
> ml max, technique(nr) trace showstep
>
> I recognize that it might be quite hard to help me out from the distance, however, it would be greatly appreciated. Especially, I’m wondering whether my approach concerning ALPHA and GAMMA is valid or whether there is any easier way to do it.

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