Absorbing Fixed Effects with estimatr

Whether analyzing a block-randomized experiment or adding fixed effects for a panel model, absorbing group means can speed up estimation time. The fixed_effects argument in both lm_robust and iv_robust allows you to do just that, although the speed gains are greatest with “HC1” standard errors. Specifying fixed effects is really simple.

library(estimatr)
lmr_out <- lm_robust(mpg ~ hp, data = mtcars, fixed_effects = ~ cyl)
lmr_out

##       Estimate Std. Error   t value  Pr(>|t|)    CI Lower    CI Upper DF
## hp -0.02403883 0.01503818 -1.598521 0.1211523 -0.05484314 0.006765475 28

lmr_out$fixed_effects

##     cyl4     cyl6     cyl8 
## 28.65012 22.68246 20.12927

Before proceeding, three quick notes:

• Most of the speed gains occur when estimating “HC1” robust standard errors, or “stata” standard errors when there is clustering. This is because most of the speed gains come from avoiding inverting a large matrix of group dummies, but this step is still necessary for “HC2”, “HC3”, and “CR2” standard errors.
• While you can specify multiple sets of fixed effects, such as fixed_effects = ~ year + country, please ensure that your model is well-specified if you do so. If there are dependencies or overlapping groups across multiple sets of fixed effects, we cannot guarantee the correct degrees of freedom.
• For now, weighted “CR2” estimation is not possible with fixed_effects.

Speed gains

In general, our speed gains will be greatest as the number of groups/fixed effects is large relative to the number of observations. Imagine we have 300 matched-pairs in an experiment.

# Load packages for comparison
library(microbenchmark)
library(sandwich)
library(lmtest)

# Create matched-pairs dataset using fabricatr
set.seed(40)
library(fabricatr)
dat <- fabricate(
  blocks = add_level(N = 300),
  indiv = add_level(N = 2, z = sample(0:1), y = rnorm(N) + z)
)
head(dat)

##   blocks indiv z          y
## 1    001   001 1  1.4961828
## 2    001   002 0 -0.8595843
## 3    002   003 1  0.1709400
## 4    002   004 0 -0.3215731
## 5    003   005 1 -0.3037704
## 6    003   006 0 -1.4214866

# With HC2
microbenchmark(
  `base + sandwich` = {
    lo <- lm(y ~ z + factor(blocks), dat)
    coeftest(lo, vcov = vcovHC(lo, type = "HC2"))
  },
  `lm_robust` = lm_robust(y ~ z + factor(blocks), dat),
  `lm_robust + fes` = lm_robust(y ~ z, data = dat, fixed_effects = ~ blocks),
  times = 50
)

## Warning in microbenchmark(`base + sandwich` = {: less accurate nanosecond times
## to avoid potential integer overflows

## Unit: milliseconds
##             expr       min        lq      mean    median        uq      max
##  base + sandwich 152.02927 171.93338 196.08340 186.15716 207.33405 357.9189
##        lm_robust  37.86477  42.81306  53.01016  45.75485  55.73438 173.0752
##  lm_robust + fes  23.17537  27.29411  41.56304  29.41647  39.39981 175.1639
##  neval cld
##     50  a 
##     50   b
##     50   b

Speed gains are considerably greater with HC1 standard errors. This is because we need to get the hat matrix for HC2, HC3, and CR2 standard errors, which requires inverting that large matrix of dummies we previously avoided doing. HC0, HC1, CR0, and CRstata standard errors do not require this inversion.

# With HC1
microbenchmark(
  `base + sandwich` = {
    lo <- lm(y ~ z + factor(blocks), dat)
    coeftest(lo, vcov = vcovHC(lo, type = "HC1"))
  },
  `lm_robust` = lm_robust(
    y ~ z + factor(blocks),
    dat,
    se_type = "HC1"
  ),
  `lm_robust + fes` = lm_robust(
    y ~ z, 
    data = dat,
    fixed_effects = ~ blocks,
    se_type = "HC1"
  ),
  times = 50
)

## Unit: milliseconds
##             expr        min         lq       mean     median        uq
##  base + sandwich 150.288452 162.198419 183.655957 179.340540 198.34623
##        lm_robust  28.198160  33.884122  41.277148  36.848996  40.21579
##  lm_robust + fes   2.914485   3.513003   4.574218   3.916956   4.99052
##        max neval cld
##  269.24052    50 a  
##  151.36946    50  b 
##   20.17672    50   c