country fixed effects or cluster standardised errors for cross-country analysis

[Lynn Al Ghazzi]

Hello,
i am doing a master thesis on the factors associated with help-seeking behavior of domestic violence victims. I have an appended dataset of 10 countries (cross-sectional datasets) and i want to run one regression for all. I have to use a logisitc regression due to the binary nature of the dependent variable. I was initially running the regression using i.country for country fixed effects to control for unobserved heterogeneity across countries. However, i was wondering if cluster standardized errors (vce (cluster country)) should be used instead in this case.
thank you

[Carlo Lazzaro]

Lynn:
you can use them both.

[Lynn Al Ghazzi]

Thank you for your answer. if i use i.country for country fixed effects, how can i represent it in the regression equation? Is putting the subscript i next to the explanatory variables correct? such as
Logit (HS)_i = β₀ + β₁ age_i + β₂ age diff_i + β₃children under 5_i + β₄edu_i + .......

[Carlo Lazzaro]

Lynn:
it should be something like

β5countryi 

[Ana ML]

Carlo Lazzaro Dear Carlo,

In the same type of model explained above (cross-national, cross-sectional), can I add country-level variables? (i.e. a cross-national multilevel model with cross-sectional data)

One comment I received said: "If you are using a country-level fixed-effects model, and if you include a time-invariant country level covariate, that covariate will fall out of the model, since country-level fixed effects make it such that you are comparing individuals within a country to each other, and therefore there will be no variation on this time-invariant characteristic. Either I am misunderstanding the model (e.g., if country level variable is time-varying) or the analysis was not conducted correctly."

When I run my model in Stata such as

 reg outcomevar covariates_individual_level covariates_country_level i.country [pweight=individual_level_weight], cluster(country)

the country level covariates don't fall out the model.

To me it was clear I could add country-level variables in such a case, but after that comment I'm wondering whether my initial understanding is correct.

Thank you so much. Really appreciated.

Ana

[Carlo Lazzaro]

Ana:
1) it may be that the reviewer is wondering whether it makes sense to include a predictor such -i.country- that, in all likelihood, is time-invariant if there are in/outflows of individuals. At the same time, it seems that reviewer is assuming that you have run a fixed effect model. However, from your code I would say that you've run a cross-sectional regression (not a panel data fixed effect regression) and, if, my intuition is correct, it makes sense to include -i.country-.
Usually this kind of confusion arises when the Methods section of your paper is not that clear. Hence, I would recommend you to double-check it, perhaps with the help of an experienced colleague.
2) that said, if you have a multilevel design with citiziens nested within countries, why not following that road?

[Ana ML]

Dear Carlo,
Thank you very much for your response - very helpful re multilevel design suggestion.
Best wishes,
Ana