Absorbing Fixed Effects with estimatr
Source:../vignettes/absorbing-fixed-effects.Rmd
absorbing-fixed-effects.Rmd
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.
## 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 211.75596 238.32895 271.18582 260.50874 283.55717 466.1051
## lm_robust 71.85358 96.26083 135.23985 106.86071 143.82585 325.9432
## lm_robust + fes 43.85444 52.53533 75.71671 69.26289 74.82418 218.3125
## 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 max
## base + sandwich 211.950361 235.26475 276.48980 248.14267 272.81066 720.0010
## lm_robust 61.147077 73.33545 88.72319 83.60469 91.41788 277.8784
## lm_robust + fes 7.219422 8.30616 16.99251 10.61166 13.97496 148.5812
## neval cld
## 50 a
## 50 b
## 50 c