Tobit model - Testing for heteroskedasticity

[Ash Summerfield]

Is there a way to test for heteroskedasticity once a tobit model has been predicted in Stata?

Thanks,

Ash

[Joao Santos Silva]

Dear Ash,

Indeed there are test for that, but are not particularly easy to implement. I believe the key reference in the area is:

A Chesher, M Irish (1987). Residual analysis in the grouped and censored normal linear model, Journal of Econometrics 34 (1), 33-61.

A shortcut to do it is to just estimate the probit for the 0 vs positive observations and then test heteroskedasticity in the probit. A simple RESET test can be used for that.

All the best,

Joao

[Ash Summerfield]

Joao, thanks for your reply.

If I do find heteroskedasticity is a problem with my tobit model, is there anything I can do to combat this? I'm aware you can add in -robust- with an OLS regression, is there something similar which could be used with a tobit?

Thanks,

Ash

[Joao Santos Silva]

Dear Ash,

Unfortunately there isn't much you can do about it and heteoskedasticity will all but "kill" the Tobit. A key paper in the area is this one.

All the best,

Joao

[Benjamin Krüger]

Hey guys,

I want to estimate a Tobit model with random effects and I'm not sure if I tested heteroscedasticity correctly. I tried to use the idea of Joao Santos Silva and estimate a probit model and test for heterogenity in between the probit model:

A shortcut to do it is to just estimate the probit for the 0 vs positive observations and then test heteroskedasticity in the probit. A simple RESET test can be used for that.

In the following there is my code:

xtprobit FinancialAssetMV_a_Besitz RB_fin_test Alter sex unidegree Haushaltsgröße Schule_Mutter Schule_Vater 
predict xbhat, index

xtprobit FinancialAssetMV_a_Besitz RB_fin_test Alter sex unidegree Haushaltsgröße Schule_Mutter Schule_Vater c.xbhat#c.RB_fin_test c.xbhat#c.Alter c.xbhat#c.sex  c.xbhat#c.unidegree c.xbhat#c.Haushaltsgröße c.xbhat#c.Schule_Mutter c.xbhat#c.Schule_Vater  

test c.xbhat#c.RB_fin_test c.xbhat#c.Alter c.xbhat#c.sex  c.xbhat#c.unidegree c.xbhat#c.Haushaltsgröße c.xbhat#c.Schule_Mutter c.xbhat#c.Schule_Vater

The result is:
chi2( 7) = 177.42
Prob > chi2 = 0.0000

As far as I unterstand there are heterogenity issues. My questions are the following:

1) Did I use the correct procedure?

2) If there is heterogenity, can I still use xttobit? Robust standard errors don't seem to work in my case for diffrent reasons. Do I have to use tobithetm and are there issues considering the time component?

Thanks

Ben

[Benjamin Krüger]

Hey guys,

I want to estimate a Tobit model with random effects and I'm not sure if I tested heteroscedasticity correctly. I tried to use the idea of Joao Santos Silva and estimate a probit model and test for heterogenity in between the probit model:

In the following there is my code:

xtprobit FinancialAssetMV_a_Besitz RB_fin_test Alter sex unidegree Haushaltsgröße Schule_Mutter Schule_Vater
predict xbhat, index

xtprobit FinancialAssetMV_a_Besitz RB_fin_test Alter sex unidegree Haushaltsgröße Schule_Mutter Schule_Vater c.xbhat#c.RB_fin_test c.xbhat#c.Alter c.xbhat#c.sex c.xbhat#c.unidegree c.xbhat#c.Haushaltsgröße c.xbhat#c.Schule_Mutter c.xbhat#c.Schule_Vater

test c.xbhat#c.RB_fin_test c.xbhat#c.Alter c.xbhat#c.sex c.xbhat#c.unidegree c.xbhat#c.Haushaltsgröße c.xbhat#c.Schule_Mutter c.xbhat#c.Schule_Vater

The result is:
chi2( 7) = 177.42
Prob > chi2 = 0.0000

As far as I unterstand there are heterogenity issues. My questions are the following:

1) Did I use the correct procedure?

2) If there is heterogenity, can I still use xttobit? Robust standard errors don't seem to work in my case for diffrent reasons. Do I have to use tobithetm and are there issues considering the time component?

Thanks

Ben

Do I have to use a diffrent procedure because I have panel data?

[Joao Santos Silva]

Dear Benjamin Krüger,

A Tobit is often tricky because it is very sensitive to violations of its strong assumptions, with RE it is even worse. So, I wonder whether there there is a different way to model the data you have. Can you tell us more about it?

Best wishes,

Joao

[Benjamin Krüger]

Hey Joao,

thank you for the answer. My model is about the effect of risk on diffrent investment choices. Most investment choices have a lot of values equal to zero (no investment in this area). Because of that I wanted to use a 2-step model. Firstly a Probitmodel and afterwards a leftcensored Tobit-Model (values >0). My professor recommended this kind of modelling but I've a lot of problems to implement robust standard errors and testing for heterogenity . Because I have Paneldata I want to use the xttobit-command.

The Tobit model looks like this:

xttobit FinancialAssetMV_a RB_fin_test Alter sex unidegree Haushaltsgröße Schule_Mutter Schule_Vater, ll(0) re

.

Adding vce(robust) or vce(cluster) is not allowed (r(198)) and bootstrapping and jackknifeing needs an endless amount of time.

Best wishes

Ben

[Benjamin Krüger]

Also I don't want to use fixed effects because important control variables are binary

[Joao Santos Silva]

Dear Benjamin Krüger,

Thanks for the additional details. My suggestion is that in the second part you use Poisson regression as in this famous and most elegant paper. Actually, you can use Poisson regression for the full data (not just positives) at least as a benchmark. In either case, make use you use clustered standard errors.

On the fixed effects, having binary explanatory variables is not a problem. The only problem with FE is if your variable of interest does not vary over time. If that is the case, just use a pooling estimator and not one with random effects (not-linear models with random effects rely on very strong assumptions).

Best wishes,

Joao