Help with panel data regression, year and region FE and panel corrected standard erros

[Teuta Toth]

Dear Statalists,

I am writing my dissertation on the impact of foreign direct investment (FDI) on labour rights. For this study, I have an unbalanced panel dataset with N = 140 countries and T = 17 (from 1994 to 2010). I aim at replicating the literature's methods but with new data. My independent var is FDI, the dependent one is an index of labour rights, and I add controls for GDP x capita, trade, population, democractic status, and government ideology. My first model is a two-way fixed effects (time and country) that, however, gives me no significant results. The other model employed in published papers is a time-fixed effects panel data regression with regional dummies and panel corrected standard errors clustered at the country level. I am quite unsure how to proceed command-wise for this model. Is xtreg dep var ind var controls i.year i.region, r correct? Thank you!

[Carlo Lazzaro]

Teuta:
welcome to this forum.
The issue is not about the statistical significance of your coefficients, but the correctness of the estimator that fits your data better than its counterpart
In addition, you describe a fixed effect model, but your code refers to a -re- specification.
As per FAQ, please provide more details, that should include what you typed and what Stata gave you back, along with an example/excerpt of your dataset, that you can share via -dataex-.

[Andrew Musau]

xtreg with the -fe- option for the fixed effects model and

help xtpcse

for the second model. For xtpcse, you have to include the fixed effects using indicators.

[Carlo Lazzaro]

Teuta:
as an aside to Andrew's helpful reply, consider using cluster-robust standard errors when available.

[Teuta Toth]

Dear Carlo and Andrew, thank you for your suggestions!

For the two-way fixed effect I did in fact run: xtreg labright (dep var) FDI (ind var) controls i.year, fe r
As far as I understood, this is the same as running: xtreg labright (dep var) FDI (ind var) controls i.year, fe vce (cluster country), is that correct?

For the second model, I have looked in the forum for information on the xtpcse command, but I have seen that it is not the best option for large N small T studies. Is my interpretation correct? Is perhaps the forum-contributed xthybrid of any help in this case?

[Carlo Lazzaro]

Teuta:
1) correct. Under -xtreg-, both -robust- and -vce(cluster panelid)- options invoke cluster-robust standard errors;
2) -xtpsce- is for T>N panel data regressions;
3) the community-contributed module -xthybrid- "estimates hybrid and correlated random-effects and Mundlak mixed-effects models for linear and nonlinear outcomes" (as per its helpfile). I cannot figure out from your post if -xthybrid- is what you're looking for as far as your second model is concerned.

[Teuta Toth]

Dear Carlo,

Thank you once again for your answers. For my second model, I would like to estimate the relationship through a time-fixed effects panel data regression with regional dummies and panel-corrected standard errors clustered at the country level. The issue is that my first model, a two-way fixed effects, is considered too rigid for a part of the literature on FDI and labour rights, given that fixed effects would be collinear with certain controls such as democratic status that are fairly constant over time. A random effect model is also not adequate, due to the assumption that unit-specific errors do not correlate with the model's independent variables. As such, perhaps an estimation à la Beck & Katz (1995, 2004) would be a solution.

Do you perhaps know how I could implement it in Stata? Thank you

[Carlo Lazzaro]

Teuta:
thanks for clarifying.
rifyingI'm not familiar with the articles you (presumably; full reference, please, as per FAQ. Thanks) refer to, as they focus on time-series, if I'm not mistaken.
That said, I'd give -xthybrid- a shot.

[Andrew Musau]

I am a little unsure what you want. On the one hand, you appear to want to replicate something that you have seen in the literature:

The other model employed in published papers is a time-fixed effects panel data regression with regional dummies and panel corrected standard errors clustered at the country level. I am quite unsure how to proceed command-wise for this model.

On the other hand, you seem to want to decide what is the best model to estimate given your research questions and data:

For the second model, I have looked in the forum for information on the xtpcse command, but I have seen that it is not the best option for large N small T studies.

As I said in #2, xtpcse implements pooled OLS with Beck-Katz standard errors (which are what are referred to as panel corrected standard errors or PCSE). You do not have unit dummies (otherwise this becomes a fixed effects model), but you may add time dummies (strictly a one-way time fixed effects model as you describe).

[Jeff Wooldridge]

I believe what you’d like to do is test whether you need country-specific fixed effects if you’ve already included regional FEs. My recent paper in Empirical Economics with Leslie Papke shows how to do that. Of course, you’ll want to include the time effects.

[Carlo Lazzaro]

Teuta:
this is the link to the interesting paper coauthored by Prof. Papke & Jeff: A simple, robust test for choosing the level of fixed effects in linear panel data models | SpringerLink

[Teuta Toth]

Thank you everyone! You have been super helpful.