tobit with vce (cluster clustervar) or xttobit

[Erwin van Kooten]

Dear all,

I'm working with a unbalanced panel data set with 208500 observations from 3371 firms in the period 2011-2019.
My variable of interest is a measure of overconfidence, a dummy variable which takes the value of 0 and 1, and is almost time-invariant. My dependent variable is a ratio of the amount of shares repurchased divided by the total amount of shares outstanding.


I want to run a xttobit regression due to the fact that I work with panel data, however xttobit doesn't allow vce(cluster clustervarname), therefore I'm considering running a normal tobit which does allow clustering at firmlevel. Is their a command which controls for the panel data structure and allows vce cluster? or should I still go for xttobit?

I really hope somebody could help me out!

Kind regards,
Erwin van Kooten

[Carlo Lazzaro]

Erwin:
when a given Stata command does not have an option available, there's always a sound technical reason for that.
That said, you can go -xttobit- with -boostrap- standard errors.
In An Introduction to the Bootstrap. New York: Chapman & Hall/CRC, 1993 (page 47) Efron, B., and R. J. Tibshirani state that 25-200 bootstrap replications are enough for standard errors (in most researches you'll find 200).

[Erwin van Kooten]

Dear Carlo,

First of all I would really like to thank u for taking the time to help me out, it is much appreciated.
I've tried your advice and used bootstrap on the standard errors, however i've ran into an error which is new for me:

xttobit percentage_repurchases dividend_payout_w holder67 prior_six_month_market_return_w analystcoverage_w cash_to_assets_w market_to_book_w leverage_w net_insider_trading_w ROA_w volatility_w relative_spread_w amihud_w lntotalassets_w I.SIC I.year, vce(bootstrap) ll(0)
(running xttobit on estimation sample)
cannot compute an improvement -- discontinuous region encountered
an error occurred when bootstrap executed xttobit
r(430);

Is there a way to resolve this error?

Kind regards,
Erwin van kooten

[Carlo Lazzaro]

Erwin:
does Stata give you back the same error message with default standard errors?

[Erwin van Kooten]

Dear Carlo,

I do not remember having seen the error before. But I just ran the regression with default standard errors to be sure and stata gave the same error message with the default standard errors.

Kind regards,
Erwin van Kooten

[Carlo Lazzaro]

Erwin:
hence the issue should rest on your model specification.
The usual diagnostic approach recommends to add one predictor at time and see when Stata starts gasping.

[Jeff Wooldridge]

I strongly recommend that, before using any Stata command, you find out what the command is actually doing. Then, look up a reputable source to determine the assumptions under which the estimator is consistent.

The xttobit command estimates a random effects Tobit model using joint MLE. Consistency requires very strong assumptions on the idiosyncratic shocks. Namely, if u(i,t) are the time-varying errors, these must be independent across time. This is not true for a linear model. So, unlike linear RE estimation, RE Tobit adds a very strong assumption. I assume this is why Stata does not allow a vce(cluster id) option: If you need to use it, you're admitting your model is wrong and that your estimators are inconsistent. (In my view, this is not a good reason. Stata should still allow it, but it is up to researchers to understand what they are implicitly admitting.) I discuss these issues in Chapter 17 of my 2010 MIT Press book.

Using tobit with vce(cluster id) is more robust because it allows any kind of serial correlation. Even better, use the correlated random effects version of Tobit to allow the heterogeneity, c(i), to be correlated with the time-varying covariates. I discuss the balanced case in my MIT Press book and the unbalanced case in my 2019 Journal of Econometrics paper on Correlated Random Effects with Unbalanced panels.

I wish Stata were more consistent in when it does and does not allow vce(cluster id). It allows it with xtprobit, but this estimator has exactly the same problem as the xttobit: xtprobit with the re option computes a joint MLE which is inconsistent if the idiosyncratic errors are serially correlated. If it allows it with xtprobit it should with xttobit, with a warning that the resulting estimators are inconsistent of clustering is needed. How inconsistent is an empirical question.

Finally, I should add that, in my experience, with xtprobit, re, the cluster-robust standard errors are often missing for some coefficients. I'm not sure why. I would use the CRE version of pooled Tobit (tobit) with the cluster option.

JW

[Erwin van Kooten]

Erwin:
hence the issue should rest on your model specification.
The usual diagnostic approach recommends to add one predictor at time and see when Stata starts gasping.

After a long running time, I found out that It gasped at the (, ll(0)) part of the regression, this wasn't a problem in the normal tobit regression.

Kind regards,
Erwin van Kooten

[Erwin van Kooten]

I strongly recommend that, before using any Stata command, you find out what the command is actually doing. Then, look up a reputable source to determine the assumptions under which the estimator is consistent.

The xttobit command estimates a random effects Tobit model using joint MLE. Consistency requires very strong assumptions on the idiosyncratic shocks. Namely, if u(i,t) are the time-varying errors, these must be independent across time. This is not true for a linear model. So, unlike linear RE estimation, RE Tobit adds a very strong assumption. I assume this is why Stata does not allow a vce(cluster id) option: If you need to use it, you're admitting your model is wrong and that your estimators are inconsistent. (In my view, this is not a good reason. Stata should still allow it, but it is up to researchers to understand what they are implicitly admitting.) I discuss these issues in Chapter 17 of my 2010 MIT Press book.

Using tobit with vce(cluster id) is more robust because it allows any kind of serial correlation. Even better, use the correlated random effects version of Tobit to allow the heterogeneity, c(i), to be correlated with the time-varying covariates. I discuss the balanced case in my MIT Press book and the unbalanced case in my 2019 Journal of Econometrics paper on Correlated Random Effects with Unbalanced panels.

I wish Stata were more consistent in when it does and does not allow vce(cluster id). It allows it with xtprobit, but this estimator has exactly the same problem as the xttobit: xtprobit with the re option computes a joint MLE which is inconsistent if the idiosyncratic errors are serially correlated. If it allows it with xtprobit it should with xttobit, with a warning that the resulting estimators are inconsistent of clustering is needed. How inconsistent is an empirical question.

Finally, I should add that, in my experience, with xtprobit, re, the cluster-robust standard errors are often missing for some coefficients. I'm not sure why. I would use the CRE version of pooled Tobit (tobit) with the cluster option.

JW

Dear Jeff,

Thank u for your extensive explanation, it is much appreciated.

I understand why I can't use the xttobit version if I want to combine it with vce(cluster id).

As soon as I found how to run a tobit with the correlated random effects, I will give it a try.

Kind regards,
Erwin van Kooten

[Pia Pico]

Dear all,

I have a related issue. I want to use the xttobit command and cluster the standard errors at the individual level. However, we know that the vce(cluster id) option is not available with xttobit. Bootstrapping can bypass this limitation if I’m working with a simple long format, where the panel variable is the individual ID. But now, I’m working with a long-long format, and my panel variable is no longer the individual ID. My question is: is it possible to specify the variable for clustering standard errors when using vce(bootstrap)?

I am grateful for any help!

Kind regards,
Pia Pico

[Carlo Lazzaro]

Pia:
welcome to this forum.
No, because -bootstrap- standard errors do not have such an option.
That said, you may want to consider -tobit- with -cluster()- standard errors.