R plm vs fixest package - different results? - r

Question

I'm trying to understand why R packages "plm" and "fixest" give me different standard errors when I'm estimating a panel model using heteroscedasticity-robust standard errors ("HC1") and state fixed effects.
Does anyone have a hint for me?
Here is the code:
library(AER) # For the Fatality Dataset
library(plm) # PLM
library(fixest) # Fixest
library(tidyverse) # Data Management
data("Fatalities")
# Create new variable : fatality rate
Fatalities <- Fatalities %>%
mutate(fatality_rate = (fatal/pop)*10000)
# Estimate Fixed Effects model using the plm package
plm_reg <- plm(fatality_rate ~ beertax,
data = Fatalities,
index = c("state", "year"),
effect = "individual")
# Print Table with adjusted standard errors
coeftest(plm_reg, vcov. = vcovHC, type = "HC1")
# Output
>t test of coefficients:
Estimate Std. Error t value Pr(>|t|)
beertax -0.65587 0.28880 -2.271 0.02388 *
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
# Estimate the very same model using the fixest package
# fixest is much faster and user friendly (in my opinion)
fixest_reg <- feols(fatality_rate ~ beertax | state ,
data = Fatalities,
vcov = "HC1",
panel.id = ~ state + year)
# print table
etable(fixest_reg)
#output
> fixest_reg
Dependent Var.: fatality_rate
beertax -0.6559** (0.2033)
Fixed-Effects: ------------------
state Yes
_______________ __________________
S.E. type Heteroskedas.-rob.
Observations 336
R2 0.90501
Within R2 0.04075
In this example, the standard error is larger when using plm compared to the fixest results (the same is true if state+year fixed effects are used). Does anyone know the reason for this to happen?

Answer 1

Actually the VCOVs are different.
In plm vcovHC defaults to Arellano (1987) which also takes into account serial correlation. See documentation here.
If you add the argument method = "white1", you end up with the same type of VCOV.
Finally, you also need to change how the fixed-effects are accounted for in fixest to obtain the same standard-errors (see details on small sample correction here).
Here are the results:
# Requesting "White" VCOV
coeftest(plm_reg, vcov. = vcovHC, type = "HC1", method = "white1")
#>
#> t test of coefficients:
#>
#> Estimate Std. Error t value Pr(>|t|)
#> beertax -0.65587 0.18815 -3.4858 0.0005673 ***
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
# Changing the small sample correction in fixest (discarding the fixed-effects)
etable(fixest_reg, vcov = list("hc1", hc1 ~ ssc(fixef.K = "none")), fitstat = NA)
#> fixest_reg fixest_reg
#> Dependent Var.: fatality_rate fatality_rate
#>
#> beertax -0.6559** (0.2033) -0.6559*** (0.1882)
#> Fixed-Effects: ------------------ -------------------
#> state Yes Yes
#> _______________ __________________ ___________________
#> S.E. type Heteroskedas.-rob. Heteroskedast.-rob.
# Final comparison
rbind(se(vcovHC(plm_reg, type = "HC1", method = "white1")),
se(fixest_reg, hc1 ~ ssc(fixef.K = "none")))
#> beertax
#> [1,] 0.1881536
#> [2,] 0.1881536