Heckman model with present heteroskedasticity and autocorrelation

[Courtney Bass]

I have an unbalanced panel dataset (N = <6,000 and spans 1998-2014). I am dealing with a dependent variable that is censored (some firms take specified action and others do not), so I'd like to use this variable as my DV in the probit model (stage 1 of Heckman). In stage 2, my DV is a measure that captures the extent (dollars spent) to which firms participate in the activity investigated in stage 1.

My question is this -- how do I address heteroskedasticity and autocorrelation (at the same time) in this model? I am unsure as to whether the Heckman is appropriate, given the heteroskedasticity and autocorrelation that is present in the dataset. If it is not appropriate, does anyone have suggestions as to what type of model I should try using instead?

Thanks!

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[Carlo Lazzaro]

Courtney:
I'm not clear with your labelling your DV as censored if you can retruieve from your data which company did (and did not) a specific action. usually, you have censored variabke if you do not know what happened before or after a given time date.
As far as the gist of your query is concerned, does the literature in your research field report hurdle models for panel dataset?
Heteroskedasticity and autocorrelation can be dealt with -vce(cluster)- standarr errors.

[Courtney Bass]

Carlo Lazzaro -- I think you are correct with the suggestion for the Hurdle model. I have reviewed some literature in my area and have found a couple of examples of this type of methodology. However, I'm wondering if you can provide a suggestion on dealing with the issues noted above in the Hurdle model.

In the first stage, if I understand correctly, I should run a logistic regression to determine the probability (or, decision stage). However, a hausman test tells me that I should be using fixed effects. If I employ -xtlogit depvar indvars, fe- I am unable to add the "vce(cluster clustervar)" option. It seems to be available in the random effects model, but not the fixed effects. So, I'm a bit confused on how I should correct these issues in the xtlogit, fe syntax (or, perhaps, whether another command would work).

In the second stage, I have read several articles that use GLS. With the xtgls option, I could use -xtgls, panels(correlated)- to deal with both heteroskedasticity and autocorrelation if my panels were balanced (which they are not). Also, I am unsure about how I can definitively know that I should be using GLS in this stage. What is the difference in using xtreg for this second stage? Or, is it just common practice to always use GLS in the second part of the Hurdle model?

I am using stata13, so I don't have access to the -churdle- command in Stata14. This is why I'm running the two models separately.

Any suggestions would be appreciated!

[Carlo Lazzaro]

Courtney:
- for the first stage, you can try a pooled logit with vce(cluster id);
- for the second stage, since you have a large N, small T panel data set, I would go -xtreg, fe- with vce(cluster).