R plm vs fixest package - different results?

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