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
)

## Unit: milliseconds
##             expr       min        lq      mean    median       uq      max
##  base + sandwich 236.89034 242.08188 245.44228 243.49676 246.4836 322.8886
##        lm_robust  87.15559  88.78283  92.67710  90.10200  93.2310 183.1576
##  lm_robust + fes  51.59394  52.59966  55.62709  53.29675  55.3586 127.9517
##  neval
##     50
##     50
##     50

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 236.41791 241.43950 245.63215 242.42816 244.89840
##        lm_robust  73.63169  74.81918  76.94113  75.88743  79.39765
##  lm_robust + fes  10.26760  11.05924  11.79360  11.23266  11.51700
##        max neval
##  323.22776    50
##   82.31459    50
##   16.78572    50