# Re: st: Defining variables for the ml procedure

 From bpersson@bu.edu To statalist@hsphsun2.harvard.edu Subject Re: st: Defining variables for the ml procedure Date Mon, 10 Oct 2005 17:02:18 -0400

```Ed,

Thank you very much for your message, your code does accomplish what I
want to do in principle.

Unfortunately, however, the regression equation I want to estimate is
actually in logarithms:

log(consumption) = a + b*(log(c*income[_n-1] + invest))

(I am sorry, I should have mentioned this). In this case, I guess I
cannot use this method since it is no longer possible to retrieve the
parameter c, right? Would you have any ideas on an alternative method?

Thanks again for all your help!

Best Regards
Bjorn

Quoting Ed Blackburne <blackburne@shsu.edu>:

```
```Bjorn,

I am perhaps misunderstanding your model.

Here is a code snippet you can paste into to Stata and run.

****************Begin do file********************

webuse lutkepohl

*** Estimate consumption=a+b*(c*income[_n-1]+invest)
*** The reduced form is consumption=a + d*l.income + b*investment
*** This is what we will estimate with Stata

regress consu l.income invest

*** From these estimates, we can recover parameter c.
*** Since d=b*c, we have c=d/b
*** In Stata speak this is _b[l.income]/_b[investment]

nlcom (_b[l.income]/_b[investment])

*************End do file

Let me know.

Ed

On Mon, 2005-10-10 at 13:47 -0400, bpersson@bu.edu wrote:
```
```Hi Ed,

would be very grateful for any hints and advice you might have on how
to use it.

(As I understand it, I cannot use Option 1 because the variable Z is
unobserved. Since it depends on the unknown coefficient c, the
variable Z must somehow be generated as a part of (that is,
simultaneously as) the estimation of the regression equation

y = a + b*(c*Z[_n-1] + x))

Please let me know if this is not clear, and thanks for your help!

Best Regards
Bjorn

Quoting Ed Blackburne <blackburne@shsu.edu>:

> Bjorn,
>
> My understanding is that you want to estimate an equation of the form
> (it doesn't much matter whether it is Z or Z[_N-1] for this post):
>
> y=a+b(cZ+x)
>
> Is this correct?
> If so, I see two options.
>
> Option 1: Estimate y=a+dZ+bx and use nlcom to recover c:
> 	nlcom _b[Z]/_b[x]
>
> Option 2: You can estimate via conditional likelihood (aka profile
> likelihoods) using the undocumented hold option of ml.
>
> If you would like a pointer at Option 2 let me know.
>
> -Ed
>
>
> On Sun, 2005-10-09 at 12:59 -0400, bpersson@bu.edu wrote:
>> Dear Statalist,
>>
>> I am trying to estimate a nonlinear regression equation using the ml
>> routine, and I am having problems defining one of my input variables.
>>  Specifically, I would like to use the recursively defined variable
>> Z(it):
>>
>> Z(it) = c*Z(it-1) + X(it)
>>
>> as an independent variable in my regression equation.  If the
>> coefficient "c" is known, this variable can be generated as follows:
>>
>> gen Z = X
>> bysort group (time): replace Z = c * Z[_n-1] + X if _n >= 2
>>
>> My problem is that I would like to estimate the coefficient "c" (along
>> with the other regression coefficients) and therefore I need to define
>> the variable Z(it) "within" the program itself.
>>
>> It seems, however, as if the "by" command and the "if" command are not
>> allowed when specifying variables in the ml programs.  I would be most
>> grateful if anyone would have any ideas on how to do this.
>>
>> Thank you for your help.
>>
>> Best
>> Bjorn
>>
>>
>>
>> *
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>
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```
```*
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```
```

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```