Re: st: Censored Least Absolute Deviation and Probit

[Reshmi Sengupta <sengupta.r12@gmail.com>]

Dear Cameron,

Thank you so much for your help and guidance. I sincerely appreciate.
Just for a final confirmation..... so if I have comprehended your
answers correctly then

(A) you believe that theoretically there is no problem in estimating a
non-parametric CLAD and a parametric Probit, simultaneously. Am I
correct?

(B) If that is the case then what shall be my assumption about the
distribution of the errors in the two models (i.e., e1 and e2)? Can I
assume that the errors are bivariate normally distributed?

Also about -cmp-:
-------------------------
 I think -cmp- is for recursive models and cannot fit models with
simultaneous causation (as is my case). Also it is based on normality
assumption (since, -cmp- is a ML estimator), therefore, would not be
appropriate in my case. Please correct me if I am wrong. Nevertheless,
I will explore more on it and will also try to contact the author for
more information.

I have few more questions, it would be very helpful if you could
provide me with your valued guidance:

(1) Can you give me any insight on the Box-Cox Tobit or the Box-Cox
Double Hurdle estimation: In Box-Cox Tobit estimation (or, Box-Cox
Double Hurdle), can I simple transform my dependent variable using the
Box-Cox transformation and then use simple -tobit- (or, -craggit-)
command for estimation? Can that take into account the change in the
likelihood function of the Tobit model (or, the Hurdle model) that is
occurring due to the Box-Cox transformation?

(2) Do you know of any STATA command for any semi-parametric methods
for binary response model (e.g., Klein and Spady's Single Index
Model). Please let me know.

Please help.

Regards,

Reshmi



On Sun, Mar 4, 2012 at 4:54 PM, Cameron McIntosh <cnm100@hotmail.com> wrote:
> Reshmi,
> Well, I thought I did help. Theoretically, it should be reasonable to estimate that 2-equation model with the link functions you describe, but I am not sure if -cmp- can invoke the CLAD estimator for a tobit model, so I would encourage you to check on that. The author of -cmp- is on the list, so he may chime in on that point. I might also suggest that you have a look at:
>
> Li, L., Simonoff, J.S., & Tsai, C.-L. (2007). Tobit model estimation and sliced inverse regression. Statistical Modelling, 7(2), 107-123.
>
> Holden, D. (2011). Testing for heteroskedasticity in the tobit and probit models. Journal of Applied Statistics, 38(4), 735-744.
>
> Newey, W.K. (1987). Specification tests for distributional assumptions in the Tobit model. Journal of Econometrics, 34(1-2), 125-145.
>
> Wilhelm, M.O. (2008). Practical Considerations for Choosing Between Tobit and SCLS or CLAD Estimators for Censored Regression Models with an Application to Charitable Giving. Oxford Bulletin of Economics and Statistics, 70(4), 559-582.
>
> Reynolds, A., & Shonkwiler, J.S. (1991). Testing and correcting for distributional misspecifications in the Tobit model: An application of the Information Matrix test. Empirical Economics, 16(3), 313-323.
>
> Holloway, G., Nicholson, C., Delgado, C., Staal, S., & Ehui, S. (2004). A revised Tobit procedure for mitigating bias in the presence of non-zero censoring with an application to milk-market participation in the Ethiopian highlands. Agricultural Economics, 31(1), 97–106.
>
> Carson, R.T., & Sun, Y. (2007). The Tobit model with a non-zero threshold. Econometrics Journal, 10, 488–502.http://econ.ucsd.edu/~rcarson/papers/TobitEJ07.pdf
>
> Barros, M., Galea, M., González, M., & Leiva, V. (2010). Influence diagnostics in the tobit censored response model. Statistical Methods & Applications, 19(3), 379-397.http://staff.deuv.cl/leiva/archivos/leiva_art/barros_galea_gonzalez_leiva_2010.pdf
>
> Sullivan, C.J., McGloin, J.-M., & Piquero, A.R. (2008). Modeling the Deviant Y in Criminology: An Examination of the Assumptions of Censored Normal Regression and Potential Alternatives. Journal of Quantitative Criminology, 24(4), 399-421.
>
> Cam
>
> ----------------------------------------
>> Date: Sun, 4 Mar 2012 16:29:14 -0600
>> Subject: Re: st: Censored Least Absolute Deviation and Probit
>> From: sengupta.r12@gmail.com
>> To: statalist@hsphsun2.harvard.edu
>>
>> Hello Cameron,
>>
>> Thank you so much for your reply. Actually, I want to relax the
>> distributional assumptions in estimating my Eq( 2 ) (the censored
>> Tobit type model), because, I have non-normality in errors (which I
>> checked using -tobcm- in STATA after a tobit estimation), and
>> therefore, I was contemplating of using CLAD.
>>
>> However, I do not know the code for any other semi or non-parametric
>> estimation for the binary response model that can estimate Eq(1),
>> except for Manski's Maximum Score estimator. But because of large N
>> (around 13000 observations), I cannot use this estimation, and instead
>> trying to estimate it using a Probit ML (normality of errors is
>> satisfied using Probit ML).
>>
>> Since, CLAD satisfies asymptotic normality of the distribution of the
>> error term, so I was wondering whether estimating the equations using
>> CLAD and Probit simultaneously, would be a reasonable and
>> statistically correct choice.
>>
>> Please help.
>>
>> Thank you.
>>
>> Regards,
>>
>> RSG
>>
>> On Sun, Mar 4, 2012 at 3:34 PM, Cameron McIntosh <cnm100@hotmail.com> wrote:
>> > Hi,
>> >
>> > I think -cmp- would be your best bet. It does allow for simultaneous equations with a mix of link functions for accommodating a variety of particular response variable types:
>> >
>> > Roodman, D. (2011). Fitting fully observed recursive mixed-process models with cmp. The Stata Journal, 11(2), 159-206.http://www.stata-journal.com/article.html?article=st0224http://ideas.repec.org/c/boc/bocode/s456882.html
>> >
>> > Cam
>> >> Date: Sun, 4 Mar 2012 10:58:15 -0600
>> >> Subject: st: Censored Least Absolute Deviation and Probit
>> >> From: sengupta.r12@gmail.com
>> >> To: statalist@hsphsun2.harvard.edu
>> >>
>> >> Dear Friends,
>> >>
>> >> I need your help on the following question:
>> >>
>> >> Can I estimate a CLAD (Censored Least Absolute Deviation) and a Probit
>> >> model simultaneously?
>> >>
>> >> I have the following 2 equations:
>> >>
>> >> (1) Y1*=a0 + a1*Y2* + a2*X1 + e1
>> >>
>> >> where Y1=1 if Y1*>0
>> >>  and   Y1=0 if otherwise
>> >>
>> >> (2) Y2*=b0 + b1*Y1*+ b2*X2+e2
>> >>
>> >> where Y2=Y2* if Y2*>0
>> >>   and  Y2=0  if otherwise
>> >>
>> >> I am trying to estimate equation (1) using Probit Maximum Likelihood
>> >> (ML) and equation (2) using CLAD.
>> >>
>> >> Please let me know.
>> >>
>> >> I will sincerely appreciate any help.
>> >>
>> >> Best Regards,
>> >>
>> >> R. Sengupta
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