RE: st: Censored Least Absolute Deviation and Probit

[Cameron McIntosh <cnm100@hotmail.com>]

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

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> 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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