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 142.56229 156.97977 168.79622 163.87872 178.01253 232.8792
##        lm_robust  34.92195  38.33225  44.44786  40.76792  43.38718 105.4679
##  lm_robust + fes  22.08030  24.78397  30.28659  25.41184  27.07591 104.5249
##  neval cld
##     50 a  
##     50  b 
##     50   c

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 140.903265 143.112632 154.383706 145.361175 158.64401
##        lm_robust  28.047321  28.886673  34.141559  31.142821  32.53477
##  lm_robust + fes   2.615431   2.843514   5.171081   3.181703   3.56003
##        max neval cld
##  226.63156    50 a  
##  108.13373    50  b 
##   68.92203    50   c