Using dummies for unobserved heterogeneity in cross-sectional data

[sria nusrat]

Hi

I have a few questions regarding the use of dummies to capture unobserved heterogeneity in cross-sectional studies.

I understand that in panel data (*where the same entities are studied at more than one point in time*) the use of dummies for each entity capture all time-invariant unobserved heterogeneity at the level of the entity.

However, if I have cross-sectional data on hospital performance and I also know which states the hospitals are located in.

1. If I use a dummy for each state (while keeping one reference state) can I claim that I am accounting for unobserved heterogeneity (time-invariant or not) at the state level?
2. And also what would that mean for unobserved heterogeneity at the hospital level?
3. Can I use state dummies for state-specific effects/heterogeneity as well as hospital specific dummies for hospital specific unobserved heterogeneity?
4. If I use a dummy for each hospital and no state dummies, will it capture unobserved heterogeneity at the level of hospitals?

I am just starting out in Econometrics. Any guidance will be extremely useful. Thank you so much.

Sria

[Carlo Lazzaro]

Sria.
if you have, as it would seem, hospitals nested in states, you should probably leave -regress- at take a look at -mixed-.

[sria nusrat]

Dear Carlo

Thank you so much for the suggestion; I would look into mixed.
Conceptually though, does the use of dummies in cross-sectional data help with unobserved heterogeneity? Or is the use of entity-specific dummies only useful in panel data to tackle unobserved heterogeneity?
Thank you so much again!

Sincerely yours
Sria

[Carlo Lazzaro]

Sria:
first difference approach help with both unobserved and observed heterogeneity if you have a panel data set.
Another, wider remarks relates to which kind of heterogeneity you're interested in: time-invariant or time-varying: fixed effect deals with the first type of heterogeneity only.
However, the main issue there is the nested structure of your data: regardless including or not fixed effect, if hospitals are nested within state, your OLS coefficient are, in fact, biased, because hospitals nested in the same state are probably more similar than hospitals nested in another state (other things being equal). In OLS you can cluster the standard errors around -i.state- but this one may be a partial fix if your data allow a random intercept (and perhaps a random slope) for each state: that's why I suggested taking a look at -mixed-.

[sria nusrat]

Thank you so much for the reply again.
I will go with mixed.

Sincerely yours
Sria