[Jesse Tielens]

Hi Morten,

I think the advice given by Clyde and Carlo is excellent. I'm a finance master's student myself, so maybe I could chime in a little.

The choice between fixed effects and random effects here would mostly come down to whether you're interested in a between estimator or within estimator. In your case, you're interested in finding out what drives a firm's leverage ratio.
A fixed effects estimator essentially shows you a firm's leverage ratio changes when its size, profitability, etc change over time. The Random Effects model allows for the possibility that the the relationship you're modelling is different for each firm.

You are modelling the relationship between a firm's leverage ratio and several firm-specific factors. Unless, you have a reason to believe that this relationship works very different for some firms than for others, a fixed-effects model is the best choice. For example, you could say that the effect of firm size on leverage is smaller for firms in the pharmaceutical sector, because pharmaceutical firms are always highly leveraged no matter what their size (just an illustration). That would mean the relationship between leverage and size is different for different firms and a random-effects estimator could account for this difference.

Unless you have reason to believe the relationship you're documenting is different between the panels, a fixed estimator would be the best choice. My best guess as to your professor's reasoning would be that since you haven't told him of such a reason, he believes the fixed model to be best.

[Carlo Lazzaro]

Morten:
Clyde gave as usual excellent adivice.
As far as the "fixeed effect mantra" is concerned, the reason to use this specification sounds like "it is more interesting to take a look at variation within the same panel as time goes by, than taking a look at difference between different panels as time goes by".
That said, my experience tells that it is often difficult to replicate others' researches just moving from an article. Sometimes it happens that reviewers missed to spot an error in the methods that carries over to results; hence, you cannot replicate authors' findings by applying the correct methods.
This is one of the reason why Stata Press textbooks (with .dta, .do files and and examples) are an useful source for learning Stata and statistics.

[Clyde Schechter]

Well, as I indicated earlier, I don't have the knowledge to respond to your question about which model is appropriate here. There are plenty of people in the finance community who are members of this Forum, and perhaps one of them will chime in with advice.

I will, however, remark on a more general point. Unless you are actually replicating a prior study using the same data that they used, the fact that you get different results does not necessarily mean you did something wrong. The scientific literature is bristling with studies that fail to replicate when the study is carried out again with new data gathered. There is a burgeoning literature on just this topic and the reasons for it are many. And while you may or may not be "smarter" than some other people, it is still possible that your results are "right" and theirs are "wrong." Certainly, a substantial discrepancy between your own results and those of prior similar studies is good cause to stop and ask questions. But you should ask those questions with equal seriousness about the other studies as you ask them about your own. Just because it's been published in a peer reviewed journal doesn't mean it's right, and just because your results are different, do not assume they are wrong. Investigate, but do so with an open mind.

[Morten Gravesen]

Hi Clyde, thank you for your response.

It is not like I pick the one I like best. However, when people talk about Panel data, they always seem to be fixed on the idea of either fixed or random effects.

Then I read a paper by Mitchell Petersen (2009) who compared different methods, and he mentioned the method of clustering by two dimentions.

The issue is, that I am following a paper by Baker and Wurgler (2002) and they use Simple OLS with white standard errors and Fama Macbeth regressions on their dataset. However, these methods only correct for heteroskedasticity and cross-sectional correlation in the residuals. It does not correct for serial correlation. Petersen argue that this is wrong. This is why I don't want to use the same methods as they do.

However, my advisor keeps blindly saying - FIXED EFFECTS - without giving me any explanation for this. Why fixed effects? What does this model do exactly? In what circumstances should I use fixed effects rather than the method of clustering by two dimentions.

Clustering by two dimentions corrects the standard errors, however, are the coeffecients effecient at all?

By using the fixed effects model, I get completely different results than those given by Baker and Wurgler (2002) in their paper. This is why I don't like using it, because I am not smarter than those guys. Using their method of OLS with white standard errors and Fama Macbeth gives me "correct" results, but again, these are ineffecient because of serial correlation.

So again, which method should I use, if I want to correct for heteroskedasticity, cross-sectional correlation and serial correlation, providing me with unbiased standard errors AND effecient coeffecients?

Initiall I wanted to use fixed effects, but because I got results so different from those by Baker and Wurgler (2002), i decided not to. That is why I tested multiple models.

Best regards,
Morten Gravesen

[Clyde Schechter]

The answer to your first question comes from substantive finance considerations, not statistics or Stata, so you will have to await your advisor's return (or seek advice from somebody else in finance who can give you a better answer.) Suffice it to say that from a statistical perspective, you should not be running multiple models like this: that decision should have been made before you ran any analyses at all (and, ideally, before you even set eyes on the data). And you certainly should not be selecting your model based on whether you like the results it produces.

Regarding question 2, the cluster robust standard error calculation corrects the standard errors for heteroscedasticity and serial correlation. It doesn't affect the coefficients at all. In fact, the analysis when you specify -cluster(gvkey)- begins by doing the ordinary regression, and then doing adjustments to the variance-covariance matrix afterwards. The coefficients themselves are not changed by this option.

Regarding question 3, the fixed effects model estimates the within-gvkey effects of the variables. The OLS model estimates a mix of within- and between effects. When the within- and between- effects are different, the OLS and fixed-effects estimates will be different. They can be very different, even having opposite signs. The following example is very artificial, but makes the point with unmistakable clarity:

clear
set obs 5
gen panel_id = _n
expand 2

set seed 1234
by panel_id , sort: gen y = 4*panel_id - _n + 3 + rnormal(0, 0.5)
by panel_id: gen x = panel_id + _n

xtset panel_id 

xtreg y x, fe
regress y x

//    GRAPH THE DATA TO SHOW WHAT'S HAPPENING
separate y, by(panel_id)

graph twoway connect y? x || lfit y x