Marginal effects in Tobit Model

[boydb]

Hi Glenn - if I have run a logistic form of a Tobit regression for the error term would I need to replace the code for @cnorm and @dnorm to @clogistic and @dlogistic respectively. This is likely to be a last question for a while. Regards, Boydb

[Girl From Ipanema]

Raupel claims that his Tobit model is highly significant. How do I interpret this from my results? I can see the Log likelihood but no pseudo R squared. Can you please help?

[EViews Glenn]

Probably with a likelihood ratio test.

Estimate with your regressors and a constant. Estimate with only the constant. The 2 times the difference in likelihoods is distributed as a chi-square(k) where k is the number of regressors.

[Girl From Ipanema]

Thank you, you're precious.

[Girl From Ipanema]

Dear Glenn,
since my chi-square is mostly significant only at a 50% level(!), I would prefer some kind of R-squared, if it is possible to obtain it for the Tobit regression in E-views. Can you help?

[EViews Glenn]

Which definition of an R2 for a Tobit would you like to compute?

There is a forum thread on this issue...

viewtopic.php?f=9&t=1335

[Girl From Ipanema]

Well, the only problem I am having currently is that my Chi-square test statistics are around few thousands (e.g. test statistic is 30 000 and the critical value is 32,3). Since I am wondering if this indeed could be true, I would like to check with some additional measure. Actually, I was noticing in a couple of similar studies a pseudo R squared. So I was wondering if this would be possible in my case as well.

[EViews Glenn]

It's certainly possible to compute various R2 measures. But you'll have to decide on the one that you want before we can compute it...

[Girl From Ipanema]

I have calculated the McFadden one, can you please confirm that the smaller ratio confirms that the model is good and viceversa (as opposed to the one in real R squared)?

[EViews Glenn]

The statistic is

1-L_full/L_restricted

where the L are the log-likelihoods. Larger values are better. When L_rest = L_full so that the full model doesn't explain anything beyond the constant, we have R_MF = 0.

The McFadden R2 should be used with caution in the Tobit model setting since the density contributions are not guaranteed to lie between 0 and 1.

[EViews Glenn]

Gareth reminds me that we have an add-in for EViews 7.1 that computes various R2 measures.. (calculates the Mcfadden, Efron, Cox & Snell, and Nagelkerke pseudo R-squareds)

http://eviews.com/cgi/ai_download.cgi?ID=PseudoR2.aipz

[Girl From Ipanema]

Thank you! Since you recommend caution in using McFadden for Tobit, would it be possible to get a tip from you on which one is the most appropriate for Tobit. I would appreciate your answer although I am aware that this goes beyond the Eviews support service!

[EViews Glenn]

I don't know that there's any one that is universally considered better. Veall and Zimmermann have a measure:

Veall, M.R. and Zimmermann, K.F. (1994b): "Goodness of fit measures in the Tobit Model",
Oxford Bulletin of Economics and Statistics, 56, pp. 485-499.

which hasn't seemed to have made its way into much statistical software [edit: it is in some of the newer SAS routines]. It is on our list of things to consider.

You might want to consider using the information criteria instead. An alternative is to simply use the LR statistic for joint significance of your explanatory variables (which you've already indicated that you don't like the results of )

[Girl From Ipanema]

[quote="EViews Glenn"]Got it...


' Next, we extract the fitted XB
eq1.fit(i) xb

' Get means of XB, adjusting for square of mean(exper) rather than mean of expersq
xb = xb - expersq*eq1.c(4)
scalar meanxb = @mean(xb) + @mean(exper)^2*eq1.c(4)

Dear Glenn,

I am getting the marginal effects for my regression, and as you can notice I am trying to use your previous instructions. Correct me if I am wrong, but for each non-dummy regressor, I can get this sort of marginal effects, if:
I use the code you mentioned
I use my variable on the places you indicate exper, and consequently mention which regressor in the equation they are, e.g. c(xx)
?
Also, can you de-confuse me Why are you using expersq in the upper equation and exper in lower, while refering to the c(4) all of the time?

[EViews Glenn]

Because the mean of a non-linear expression isn't the same as the nonlinear expression of the mean. There is a choice on how to do this calculation. What we do here is to compute the mean of all of the linear terms separately (that's why we take out the expersq term from the fitted xb), take the means and then add back in the mean of experience, squared. Alternatively, if we'd taken the means of xb, we would have used the mean of experience-squared.

The purpose of the program here was to reproduce the results in Wooldridge. You should see his textbook for this example, where he discusses this computation.