Fixed effect vs dummy variable (OLS vs FEM)

[Tivea Vorn]

My name is Tivea Vorn, and I am a master's student at Kobe University, Japan. I am using STATA SE 17.

I would like to ask about fixed effects and dummy variables in questions.
Please kindly consider the following comparison question regarding panel data as follow:

1. Are Year Fixed Effect and Year Dummy the same or different? I use i.year (year dummy or year fe) for both OLS and FEM. Can you help explain how does it work in both estimators?

2. Are Country-pair FE ( I use country-pair=id=group(contryA countryB)) and Country-pair dummy (i.id) variables same or different? I use i.id in OLS and fe in FEM. Can you help explain both terms and how does it work in STATA analysis?

Example:
FEM: xtreg no_ad_cases ln_fdi_lag1 gdp_growth3_d gdp_growth3_o lag1_lnimp lag1_lnrer treat_pta_post i.year, fe vce (robust)
OLS: reg no_ad_cases ln_fdi_lag1 gdp_growth3_d gdp_growth3_o lag1_lnimp lag1_lnrer treat_pta_post i.year i.id, vce (robust)

Notice: I got identical results and statistical significance by running both regress commands. How can I explain my result based on using a dummy in OLS and a Fixed Effect in FEM?

Thank you so much for considering my questions and helping to answer them all.

Best regard,

Tivea VORN

[Andrew Musau]

Notice: I got identical results and statistical significance by running both regress commands. How can I explain my result based on using a dummy in OLS and a Fixed Effect in FEM?

Google the Frisch-Waugh theorem or read their Econometrica paper: https://www.sv.uio.no/econ/om/tall-o...ks/rf1933f.pdf