# Different results from random effects plm (R) and xtreg (Stata)

I'm trying to convert the analysis from an old research paper from Stata to R. However, I ran into a problem that I have been unable to fix.

When I compare the coefficients from the two programs, they are not the same, even though the input is the same. I found this thread which describes a similar problem but for fixed effects: Difference between fixed effects models in R (plm) and Stata (xtreg)

However, the answer there gets a lot smaller difference than I get, accounting just for the difference in how plm and xtreg handle year effects.

For example, using the V-dem v9 Country-Year Full+Others dataset https://www.v-dem.net/en/data/data-version-9/, I ran this:

library(plm)

model2 <- plm(v2x_polyarchy ~ v2elembaut+v2elrgstry,
data = Vdemv9,
model = "random",
index = c("country_id","year"))
summary(model2)

## Results:
Coefficients:
Estimate Std. Error z-value  Pr(>|z|)
(Intercept) 0.3735057  0.0059080  63.221 < 2.2e-16 ***
v2elembaut  0.1105280  0.0020646  53.534 < 2.2e-16 ***
v2elrgstry  0.0600031  0.0023033  26.051 < 2.2e-16 ***

Stata gives me the following results:

xtset country_id year, yearly
xtreg v2x_polyarchy v2elembaut v2elrgstry

## Results
v2x_polyar~y |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
v2elembaut |   .1105945   .0020701    53.43   0.000     .1065372    .1146518
v2elrgstry |   .0601527   .0023079    26.06   0.000     .0556292    .0646761
_cons |   .3733406   .0062298    59.93   0.000     .3611304    .3855508

Am I doing something wrong? If not, is this something I need to worry about? The difference is small at only .0000665 for the coefficient for v2elembaut, but I would have expected it to not be there at all.

Best to my knowledge, plm and EViews are the only major implementations that use the formulae as given by Baltagi/Chang (1994) for the unbalanced case of Swamy-Arora per default. Stata and gretl use a slightly different implementation, also when using Stata's sa option to specifially request Swamy-Arora. However, it is possible to replicate Stata's results (using the sa option) with plm (see plm$$`$$s vignette).