group fixed effects as group dummies or xtreg?

[Jonathan Marin]

Suppose you have a list of hospitals with patients nested in the hospital. You observe each hospital multiple times over a period of time but with different patients in each period. The variable of interest varies within the hospitals.

Since the same hospital is observed multiple times and the variable of interest varies within hospital it would be possible to do a within-hospital transformation. As far as i am concerned this could be done in two ways in Stata

reg dependent_variable independent_variable i.hospital

or

xtset hospital
xtreg dependent_variable independent_variable, fe

Would these two specifications produce the same results?

In a panel data were we observe the same individual over time including a dummy for each individual (LSDV) produces the same results as FE. But for such a data set it is only possible to include a dummy for each individual if you observe the same individual more than once over time. In a specification as the one above where I seek to control for a hospital fixed effect. However, If we just observed a cross-section of hospitals (and thus not observed the same hospital more than once) it would still be possible to include a dummy for each hospital in a regression.

How then does a dummy for each hospital control for fixed effects when we observe the same hospital multiple times compared to a cross-section of hospitals with a dummy for each hospital?

Best regards,
Jonathan

[Carlo Lazzaro]

Jonathan:
since patients are nested within hospitals, -regress- and -xtreg, fe- would probably underestimate the between-hospital variance.
I find difficult to envisage that the fixed effect is the relevant resarch goal there, unless each hospital manages a different case-mix of patients/disases (and/or an interaction between those items).
You may easily check whether this is true or not by comparing -regress- with -mixed- (as per your post details, I assume that your dependent variable is continuous).
As a closing-out remark, please note that using -regress- with panel data is rarely the way to go.

[Jonathan Marin]

I find difficult to envisage that the fixed effect is the relevant resarch goal there, unless each hospital manages a different case-mix of patients/disases (and/or an interaction between those items).

There are two reasons for including fixed effects. First, the one you state above. Second, to control for any cluster level component that may cause correlation between patients within each hospital (there are very few hospitals so i cannot cluster std errors by hospital).

[Carlo Lazzaro]

Jonathan:
thanks for your clarifications.
Interesting reasearch issue. I've never come across something similar during more than 23 years in the health economic research field (but that is only relevant for me).
However, if you have a handful of hospitals (as this should be, since it is really hard to spot hospitals dealing with pretty different diseases and patienst), clustered standard errors may hamper more than help your regression model.

[Jonathan Marin]

Yes, my point. Clustered std errors wont work. That is why my best chance to capture some of the possible clustering by hospital would be to estimate a fixed effect for the hospitals. Then i could further cluster patients by each hospitals treatment unit (intensive care, peadeatric etc.) as this might capture some of the clustering (this yields far more clusters). I then assume that there is no correlation between these units, but i can hope most of the correlation between them has been removed by the fixed effects.

Of course, I assume there is no correlation across clusters.

[Carlo Lazzaro]

Jonathan:
I'm not cleat with your main research goal: patients nested within different hospital wards nested in different hospitals or hospitals per se?

[Jonathan Marin]

To clarify things. I used hospitals a general example, but in my research i am dealing with dental clinics:

I have a range of clinics observed multiple times with different patients in each period. The clinics are treated in some of the period and not in others. I want to estimate the effect of treatment on patient outcomes. Since i observe each clinic more than once i can estimate a within clinic model.

Estimating an individual level modle requires to take account of clustering. Since i have few clinics i cannot cluster std errors by clinic. It would be wrong. Instead i will try to use a fixed effects model to transform away the clinic fixed effect ASSUMING this is causing patients within clinics to correlate.

If patients are further correlated within periods in each clinic i can cluster patients by clinic*period (where i have far more clusters). Assuming the clinic fixed effect is what causes patients between periods to correlate this would yield something that takes account of clustering.

makes more sense?

[Carlo Lazzaro]

Jonathan:
thanks for further clarifications.
However, I still suspect that the between-hospital heterogeneity can play a role in your model.
You may want to consider interacting clinic with period (see -fvvarlist- for an efficient notation).

[Jonathan Marin]

Thanks for replying Carlo!

Yes, I'm considering that too since period effects could vary across clinics.

However, since this kind of specification seem to be used very little in general I'm wondering if it makes sense. Does it make sense to estimate a fixed effect to transform away cluster effects and then cluster over clinic*periods (assuming the fixed effects remove between period correlation)? Usually studies have enough clusters to just cluster std errors by cluster which would effectively take into account all correlation within clusters. My case is a little unusual since i have to take account of clustering by other means.

[Jesse Wursten]

You might be interested in the following paper by Cameron & Miller which discusses clustering, fixed effects and what to when you don't have a lot of clusters: cameron.econ.ucdavis.edu/research/Cameron_Miller_JHR_2015_February.pdf (available freely).

Some points to note (but see the paper for clearer explanations):
- fixed effects generally don't solve the issue you'd want to ideally tackle by clustering
- clustering on clinic x period is rarely ever a satisfactory solution. While it allows for within-cluster correlation per period, your standard errors will still be incorrect if there's serial correlation. It might be interesting to do some serial correlation tests though, maybe it's not an issue. E.g. xtserial, xtqptest
- there are methods to deal with small numbers of clusters to some extent

[Jonathan Marin]

That looks like a very nice paper. I can see it addresses almost all issues i am dealing with. Exactly what i was looking for THANKS!

In general, serial correlation is not really an issue since different patients are observed in each period. I cannot say that no serial correlation exists (can't imagine how it would look like) but i can certainly argue that there is not given the details of the design used.