Estimation methods using panel data with a time-invariant variable as main explanatory variable

[Stijn van Heesch]

Dear Statalist users,

After reading many topics on this forum, I still haven't found a solution to my problem, so here goes:

I'm trying to estimate the effect of private equity funding on financial flexibility using an unbalanced panel dataset consisting of approximately 13000 firms over 25 years. In my dataset private equity funding is represented by a dummy variable (1 if backed by PE, 0 if not). Financial flexibility is measured on a continuous 0 to 1 scale. The basic model I'm trying to estimate is:

reg finflex pedummy <set of continuous control variables>

The problem is that I'm not sure which estimation method to apply. The Hausman test tells me to use fixed effects, however, this method omits the PE dummy because it's time-invariant. Since I do need to estimate the effect of PE, I'll have to use another method. However, I do not know which one to use.

Does anyone here have a suggestion on which method to apply? If my post misses any crucial information, I'm happy to elaborate.

Kind regards,
Stijn

[Mareen Tarigan]

Hi Stijn,
I had the same problem on my last paper. The teacher (specialised in economectrics) told me to do the Hausman test but then to say that I do a random effect because I need the invariant to be considered in my estimation. This is what I did.
Kind regards,
Mareen

[Stijn van Heesch]

Thank you for your reply Mareen! That is indeed a choice I could make, but the estimates will be biased then. Another possibility I thought of is to use a simple regression, in which I fix the year and industry effect (using i.fyear and i.industry), although I'm not sure if that's the most elegant solution.

[Clyde Schechter]

There is no perfect solution to this dilemma. If you use random effects, then you may have biased estimation, that is true. Using fixed effects with the industry as the fixed effect rather than the firm will create the illusion of having solved the problem, but not the reality. The problem with industry fixed effects is that this ignores the firm-level variation and leaves you with omitted variable bias as a result.

Another approach is to use -xtreg, be-.

For what it's worth, in my field, epidemiology, we do not care all that much about unbiased estimation: it's nice if you can get it, but not critical. The random effects model offers the advantage of providing greater efficiency, which is to say higher precision in the estimates. An estimate that has a small bias and high precision is often more useful and more accurate than an unbiased estimate with poor precision. So you really need to consider just how much bias you get by going to -re-.

As I say, there is no perfect solution here, they all have drawbacks. As they say, you pay your money and you make your choice.

[Stijn van Heesch]

Hi Clyde,

Thanks for your reply.

The between effects model is also something I considered. However, it yielded mostly insignificant results which made me doubt its applicability. And how do you feel about pooled OLS with clustered id's (id's being unique firms). I figured it does the same as the between effects, do you agree?

Regarding your edit; I guess that's something I'll have to accept here too, since using random effects does indeed increase the significante of my estimates. Just was not sure if there was some method I didn't find out about yet.

Anyhow, thank you for clarifying that there is no perfect solution. Saves me time on my hunt for one.

[Phil Bromiley]

You might look at the Mundlak appraoch - http://blog.stata.com/2015/10/29/fix...dlak-approach/

[Clyde Schechter]

And how do you feel about pooled OLS with clustered id's (id's being unique firms). I figured it does the same as the between effects, do you agree?

No they're not the same at all. And the results can be quite different.

I am disquieted by your repeated references to whether a particular approach gives you "significant" results or not. Hunting for a model that gives you statistically significant results is not science. If anything, it borders on scientific misconduct. The choice of the model should be made based on your understanding of the structure of the data. Tradeoffs between bias and efficiency can also be made based on an understanding of the goals of your research and the uses to which they are intended to be put. Ideally, the choice of model should be made before you even gather the data, let alone look at it, and certainly let alone run analyses on it. I realize that in the real world that level of purity is sometimes difficult to sustain, as when the originally planned model can't converge or something like that. But what you describe sounds like you are just fishing for a model that sustains your hoped-for conclusions.

[Stijn van Heesch]

Thank you Phil, I'm going to have a look at it!

Clyde, I understand your concern. The thing is that I lack knowledge in the field of econometrics/statistics, hence I'm not sure which model to use in this specific case that doesn't meet the conditions of the examples I was taught. Therefore I'm asking for help here. What I'm merely looking for is a model that helps me to tell whether private equity influences financial flexibility (and if it does: how). What the exact result will be is of less importance to me. In fact, I might consider a result that contradicts my hypothesis even more interesting. But again, I understand this could come across as data mining.