OLS and negative binomial regression with fixed effects yielding very different result --- which one should I trust?

[Li recordyao]

I'm running difference-in-difference regression to examine some policy changes on firms' patent application. So the dependent variable is a count variable. I tried both xtreg and xtnbreg, but they produce very different results.
For the xtreg, I tried y and log(y + 1) as dependent variables and both produced significant and negative effect of the interaction treat*post (with three stars, very significant). But the xtnbreg produce insignificant results, and the coefficients are positive.
My question is, with the two yielding very different results, which one should we trust more?

[Carlo Lazzaro]

Li:
why going OLS if your deendent variable is a count one?
Poisson regression can deal with continuous regressand (https://stats.stackexchange.com/ques...ndent-variable), but I'm not sure if the opposite holds.
I addition, as per FAQ please share via CODE delimiters what you typed and what Stata gave you back. Thanks.

[Joao Santos Silva]

Dear Li recordyao,

Following up on Carlo's helpful advice, I would like to add that the negative binomial model with the fixed effects is not a real fixed effects model and should be avoided; there are several threads in the Forum about this. Also, as Carlo hinted, a linear model is unlikely to be suitable and using log(y+1) as the dependent variable is certainly not recommended. I strongly suggest that you use Poisson regression, especially if you have fixed effects. The FE Poisson regression is remarkably robust, as shown in a well-known paper by Jeff Wooldridge. If you are doing a DiD, you may also want to check:

Ciani Emanuele & Fisher Paul, 2019. "Dif-in-Dif Estimators of Multiplicative Treatment Effects," Journal of Econometric Methods, 8, pages 1-10.

Best wishes,

Joao

[Li recordyao]

Dear Carlo Lazzaro and Joao Santos Silva


Thank you for your prompt reply. Your answers are very helpful! So it doesn't matter Poisson and OLS generating conflicting results. When it comes to count variable, Poisson regression is preferred to OLS. Also very helpful recommendation of econometric paper!
But it seems, sometimes, there is a blurry line between a count variable and a continuous variable. For example, revenue is usually treated as continuous variable, but it is simply (units_sold * price). Assume the price is 1, so the revenue is numerically the same as units sold. Then, which should we use, OLS or Poisson?
Thank you again!


Best wishes,
Li

[Carlo Lazzaro]

Li:
drawing a straight line between the two is not always easy.
Days of hospitalization are counts, but are often treated as continuous (because if converted in hours they would actually be a continuous variable).
As from your picture you seem to be commited in teaching/researching, an optional hint is to take a look at the tribal rules in your research field over and above the reference literature.

[Joao Santos Silva]

Dear Li recordyao,

The choice of approach does not depend on whether the variable is continuous or not (in the limit, even time is measured in discrete units). The difference is that OLS estimates a linear model and Poisson estimates an exponential model. So, if your data is non-negative, Poisson is likely to be a more sensible option.

Best wishes,

Joao