Alternatives to Panel Data Fixed Effects Tobit Model

[Claire Lyng]

Dear Statalist,

I want to estimates the effect of mortgage run-offs on risky asset shares in one's liquid portfolio. Risky asset share is defined as stock investment as a percentage of total liquid wealth (bank deposit + stock investment + bond investment). So risky asset share is left censored, as one has to participate in stock market, in order to have a positive risky asset share. otherwise, risky share is equal to zero.
If I have a cross-sectional dataset, I would used a Tobit model. But I have a 4-year panel dataset. I want to allow unobserved individual heterogeneity, so I would like to use a fixed effect model. I know xttobit estimate panel data random effect tobit model. and I think theoretical studies cannot agree on whether fixed effect tobit model gives robust results. So will you please recommend an alternative to fixed effect tobit model in my case?

1. I am think about using conditional fixed effect panel data model (analog to conditional OLS using cross-sectional data).
2. I saw someone suggested to use Poisson regression, but my outcome variable (risky asset share) is not a discrete variable. So I don't think Poisson is appropriate here.
3. What should I choose, conditional fixed effect or random effect tobit?
4. Or some other alternatives you may suggest?

I appreciate your suggestions! Thank you for your time.

Best, Claire Lyng

[Phil Bromiley]

As you note, some folks like a fixed effects tobit even though it's theoretical properties are moot. I find imposing the orthogonality condition of random effects uncomfortable without any evidence for it.

One of the commentators on this list likes the poisson regression approach - search the list and you'll find his comments. I'm not sure if he recommends it for this specific problem.

An alternative would be a Mundlak approach - I think there are some papers talking about this in non-linear models. Mundlak has the added advantage of letting you differentiate between the effect of stable individual characteristics and time-varying ones.

[Joao Santos Silva]

Dear Claire,

First of all, I would say that your data is not censored; you just have a fractional variable that is bounded between 0 and 1. In view of this, I see no reason to even consider the Tobit.

In my view, the right approach here would be to use fractional regression (search for the two papers by Papke and Wooldridge on the fractional logit), but as far as I understand you cannot use fixed effects in this context. As Phil Bromiley noted, you can use the Mundlak approach and Jeff Wooldridge often recommends it. Of course, this is based on reasonably strong assumptions, but may be your best bet,

Now, if most of your data are close to zero and the you have few values above 0.5, the logit function is reasonably approximated by an exponential function and in that case Poisson regression can produce reasonable results. The advantage, of course, is that with Poisson regression you can use proper fixed effects and the fact that the variable is not discrete is not a problem at all. So, whether or not I recommend Poisson regression very much depends on what your data looks like.

Best wishes,

Joao

[Claire Lyng]

Dear Phil and Joao,

Thank you so much for your suggestions. I am sorry I didn't check back more often.

Joao Santos Silva I appreciate your view on the problem. However, I'd like to discuss a bit more on the fractional regression idea. One of Raj Chetty's paper on this exact problem did use Tobit model (cross-sectional data):
(Chetty, R., Sándor, L. and Szeidl, A., 2017. The effect of housing on portfolio choice. The Journal of Finance, 72(3), pp.1171-1212.) page 23, to study risky asset share, they describe "...two-stage Tobit speci…cation. This model is analogous to the two-stage-least-squares estimates, but corrects for the fact that some individuals are non-participants using a Tobit speci…cation where the stock share is left censored at 0."
My understanding is that fractional regression is more appropriate when the "rate/probability" variable is a natural rate bounded between 0 and 1, it should not be conditional on something in which case is left censored and Tobit is more appropriate. What do you think? Please correct me if I am wrong.

I thought Poisson regression was only appropriate with count data, thus discrete variables. Thank you so much for clearing my concern on that. here is a histogram of risky asset shares in my sample. I think I could try a Poisson regression.

Best, Claire Lyng

[Claire Lyng]

And Joao Santos Silva, do you mean I can do something like: "poisson ln(stockshare) age age^2 maritalstatus education and other covariates"?
I found an article talking about using Poisson for log models: http://blog.stata.com/2011/08/22/use...tell-a-friend/

and I just found your article which is the first to use Poisson for this sort of problem: Santos Silva, J.M.C., S. Tenreyro 2006. "The log of gravity", The Review of Economics and Statistics 88(4):641-658. That is a very nice paper. I will spend more time to read it more carefully.

I'd appreciate it if you could recommend me any publication that used this approach as a identification strategy, in application?

Best, Claire

[Joao Santos Silva]

Dear Claire,

I still think your data is not censored. The data would be censored if the shares could be below 0 but these values were reported as 0 (likewise for values above 1). As I understand it, this is not your case because the shares cannot be below 0 or above 1.

As a consequence, I would still say that fractional regression is the best approach, but there is the issue with the fixed effects. Poisson may not work well here because three is a substantial mass of observations at or close to 1.

Best wishes,

Joao

[Claire Lyng]

Dear Joao Santos Silva ,

I see. My data is not censored. you are right.
I am thinking about comparing fractional regression and conditional panel data fixed effect model (which is analogue to conditional OLS using cross-sectional data). Can I use the conditional fixed effect as my main result? I think time-invariant unobserved individual heterogeneity poses the most serious threat for my identification. Later, I also use 2SLS IV estimation to address the endogenous explanatory variable.
I aware that if I use fractional regression, I can use probit control function approach later to deal with endogeneity. So what do you suggest is a more correct way here, fractional regression+control function, or conditional fixed effect+ 2SLS IV?
(my endogenous regressor is housing value, outcome variable is stock share)

Best Wishes,
Claire

[Joao Santos Silva]

Dear Claire,

I am afraid I do not know enough about your problem to be able to help you with that decision.

Best wishes,

Joao

[Olive Bat]

Dear Joao Santos Silva and Claire,

my dependent variables are expenditure variables which are censored .. i want to run a fixed effect tobit regression ..the basic methodology which in use in my paper PSM followed by DID.. Is a fixed effect tobit regression possible.. what are its command on STATA..

[Joao Santos Silva]

Dear Olive Bat,

Why do you say that your data is censored? If you mean that it cannot be negative, that is not censoring and I would just use Poisson regression with FE.

Best wishes,

Joao

[Olive Bat]

Dear Joao Santos Silva ... my dependent variable is log of expenditure on different items and it ranges from 0-12.0 approximately ...so instead of using an OLS i was running a Tobit..as i performing PSM and thn DID... i wanted to know can tobit panel regression be performed for fixed effect..

[Jeff Wooldridge]

Olive: You probably shouldn’t be taking the log. What happens at zero expenditures?

[Olive Bat]

Jeff Wooldridge .. nothing happens at zero as some items are not consumed in a particular year and some not , it stands at zero... thus took a log..

[Jeff Wooldridge]

Then something does happen and it’s not good: taking the log of zero results in missing values. If I understand correctly, that has the result of dropping the zeroes. You don’t want that. The whole point in using Tobit or FE Poisson is to leave y in its original form and do nothing special with the zeroes.