[R] Problem using Tobit models in R (Testing and controlling for distributional assumptions and endogeneity)

[Malte Brockmann]

Roger, thanks for your reply and especially for pointing out that quantreg does not calculate the SCLS estimator as I thought. You are also certainly right about the covariance matrices, I meant the difference to be psd.

Nevertheless, my main questions remain open: How to I test distributional assumptions and endogeneity for Tobit models? In case I cannot reject endogeneity, how do I model structural equations with censored dependent variables?





-----Ursprüngliche Nachricht-----
Von: roger koenker [mailto:rkoenker at uiuc.edu] 
Gesendet: Mittwoch, 28. November 2007 22:14
An: Malte Brockmann
Cc: r-help at r-project.org
Betreff: Re: [R] Problem using Tobit models in R (Testing and controlling for distributional assumptions and endogeneity)


url:    www.econ.uiuc.edu/~roger            Roger Koenker
email    rkoenker at uiuc.edu            Department of Economics
vox:     217-333-4558                University of Illinois
fax:       217-244-6678                Champaign, IL 61820


On Nov 28, 2007, at 2:45 PM, Malte Brockmann wrote:

>
> Dear R-Community,
>
> I am currently using Tobit models (survreg in the survival package).
>
> 1a) Does R provide a straight-forward way to test distributional  
> assumptions for tobit models?
> 1b) If not: I tried to apply the Hausman-test proposed in Newey  
> (1987), Journal of Econometrics, on the Tobit estimator and the  
> symmetrically censored least squares estimator proposed by Powell  
> (1986) (quantreg package).

This "symmetrically censored least squares estimator"  is NOT what is  
computed by the quantreg package.
What is computed is the Powell quantile regression estimator.

> Unfortunately, quantreg only provides covariance matrices based on  
> the bootstrap which are not positive semi-definite,

The bootstrapped covariance provided by quantreg is the usual sample  
covariance matrix of the bootstrapped
realizations and is therefore necessarily positive semi-definite.   
Perhaps what you meant to say was that the
difference between the two covariance matrices that you have computed  
was not psd;  this could easily happen.
Nothing ensures that the Powell QR estimate is less efficient than  
the usual (normal theory) tobit estimator,
indeed there are very plausible conditions under which this is not  
the case.

> therefore the hausman test statistic based on the difference  
> between both covariance matrices can be negative. Newey proposes 2  
> ways to calculate positive semi-definite covariance matrices: Is  
> there a way to implement any of these without manually coding (or  
> adapting) the tobit and SCLS estimation procedures to extract the  
> necessary information needed for the estimation (first derivative  
> of loglik w.r.t. theta, etc.)?
>
> 2) I apply the test for endogeneity proposed by Smith and Blundell  
> (1986), Econometrica, and one of my variables turns out to be  
> endogenous. Does R have a package for simultaneous equations with  
> censored dependent variables? As far as I know, the sem package  
> does estimate these types of equations.
>
> Thanks in advance
> Malte
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