etwfe | R Documentation |

Extended two-way fixed effects

```
etwfe(
fml = NULL,
tvar = NULL,
gvar = NULL,
data = NULL,
ivar = NULL,
xvar = NULL,
tref = NULL,
gref = NULL,
cgroup = c("notyet", "never"),
fe = c("vs", "feo", "none"),
family = NULL,
...
)
```

`fml` |
A two-side formula representing the outcome (lhs) and any control
variables (rhs), e.g. |

`tvar` |
Time variable. Can be a string (e.g., "year") or an expression (e.g., year). |

`gvar` |
Group variable. Can be either a string (e.g., "first_treated") or an expression (e.g., first_treated). In a staggered treatment setting, the group variable typically denotes treatment cohort. |

`data` |
The data frame that you want to run ETWFE on. |

`ivar` |
Optional index variable. Can be a string (e.g., "country") or an
expression (e.g., country). Leaving as NULL (the default) will result in
group-level fixed effects being used, which is more efficient and
necessary for nonlinear models (see |

`xvar` |
Optional interacted categorical covariate for estimating
heterogeneous treatment effects. Enables recovery of the marginal
treatment effect for distinct levels of |

`tref` |
Optional reference value for |

`gref` |
Optional reference value for |

`cgroup` |
What control group do you wish to use for estimating treatment effects. Either "notyet" treated (the default) or "never" treated. |

`fe` |
What level of fixed effects should be used? Defaults to "vs" (varying slopes), which is the most efficient in terms of estimation and terseness of the return model object. The other two options, "feo" (fixed effects only) and "none" (no fixed effects whatsoever), trade off efficiency for additional information on other (nuisance) model parameters. Note that the primary treatment parameters of interest should remain unchanged regardless of choice. |

`family` |
Which |

`...` |
Additional arguments passed to |

A fixest object with fully saturated interaction effects.

Specifying `etwfe(..., xvar = <xvar>)`

will generate interaction effects
for all levels of `<xvar>`

as part of the main regression model. The
reason that this is useful (as opposed to a regular, non-interacted
covariate in the formula RHS) is that it allows us to estimate
heterogeneous treatment effects as part of the larger ETWFE framework.
Specifically, we can recover heterogeneous treatment effects for each
level of `<xvar>`

by passing the resulting `etwfe`

model object on to
`emfx()`

.

For example, imagine that we have a categorical variable called "age" in
our dataset, with two distinct levels "adult" and "child". Running
`emfx(etwfe(..., xvar = age))`

will tell us how the efficacy of treatment
varies across adults and children. We can then also leverage the in-built
hypothesis testing infrastructure of `marginaleffects`

to test whether
the treatment effect is statistically different across these two age
groups; see Examples below. Note the same principles carry over to
categorical variables with multiple levels, or even continuous variables
(although continuous variables are not as well supported yet).

Under most situations, `etwfe`

should complete very quickly. For its part,
`emfx`

is quite performant too and should take a few seconds or less for
datasets under 100k rows. However, `emfx`

's computation time does tend to
scale non-linearly with the size of the original data, as well as the
number of interactions from the underlying `etwfe`

model. Without getting
too deep into the weeds, the numerical delta method used to recover the
ATEs of interest has to estimate two prediction models for *each*
coefficient in the model and then compute their standard errors. So, it's
a potentially expensive operation that can push the computation time for
large datasets (> 1m rows) up to several minutes or longer.

Fortunately, there are two complementary strategies that you can use to
speed things up. The first is to turn off the most expensive part of the
whole procedure—standard error calculation—by calling `emfx(..., vcov = FALSE)`

. Doing so should bring the estimation time back down to a few
seconds or less, even for datasets in excess of a million rows. While the
loss of standard errors might not be an acceptable trade-off for projects
where statistical inference is critical, the good news is this first
strategy can still be combined our second strategy. It turns out that
collapsing the data by groups prior to estimating the marginal effects can
yield substantial speed gains of its own. Users can do this by invoking
the `emfx(..., collapse = TRUE)`

argument. While the effect here is not as
dramatic as the first strategy, our second strategy does have the virtue
of retaining information about the standard errors. The trade-off this
time, however, is that collapsing our data does lead to a loss in accuracy
for our estimated parameters. On the other hand, testing suggests that
this loss in accuracy tends to be relatively minor, with results
equivalent up to the 1st or 2nd significant decimal place (or even
better).

Summarizing, here's a quick plan of attack for you to try if you are worried about the estimation time for large datasets and models:

Estimate

`mod = etwfe(...)`

as per usual.Run

`emfx(mod, vcov = FALSE, ...)`

.Run

`emfx(mod, vcov = FALSE, collapse = TRUE, ...)`

.Compare the point estimates from steps 1 and 2. If they are are similar enough to your satisfaction, get the approximate standard errors by running

`emfx(mod, collapse = TRUE, ...)`

.

Wooldridge, Jeffrey M. (2021). Two-Way Fixed Effects, the Two-Way Mundlak Regression, and Difference-in-Differences Estimators. Working paper (version: August 16, 2021). Available: http://dx.doi.org/10.2139/ssrn.3906345

Wooldridge, Jeffrey M. (2022). Simple Approaches to Nonlinear Difference-in-Differences with Panel Data. The Econometrics Journal (forthcoming). Available: http://dx.doi.org/10.2139/ssrn.4183726

`fixest::feols()`

, `fixest::feglm()`

```
## Not run:
# We’ll use the mpdta dataset from the did package (which you’ll need to
# install separately).
# install.packages("did")
data("mpdta", package = "did")
#
# Basic example
#
# The basic ETWFE workflow involves two steps:
# 1) Estimate the main regression model with etwfe().
mod = etwfe(
fml = lemp ~ lpop, # outcome ~ controls (use 0 or 1 if none)
tvar = year, # time variable
gvar = first.treat, # group variable
data = mpdta, # dataset
vcov = ~countyreal # vcov adjustment (here: clustered by county)
)
# mod ## A fixest model object with fully saturated interaction effects.
# 2) Recover the treatment effects of interest with emfx().
emfx(mod, type = "event") # dynamic ATE a la an event study
# Etc. Other aggregation type options are "simple" (the default), "group"
# and "calendar"
#
# Heterogeneous treatment effects
#
# Example where we estimate heterogeneous treatment effects for counties
# within the 8 US Great Lake states (versus all other counties).
gls = c("IL" = 17, "IN" = 18, "MI" = 26, "MN" = 27,
"NY" = 36, "OH" = 39, "PA" = 42, "WI" = 55)
mpdta$gls = substr(mpdta$countyreal, 1, 2) %in% gls
hmod = etwfe(
lemp ~ lpop, tvar = year, gvar = first.treat, data = mpdta,
vcov = ~countyreal,
xvar = gls ## <= het. TEs by gls
)
# Heterogeneous ATEs (could also specify "event", etc.)
emfx(hmod)
# To test whether the ATEs across these two groups (non-GLS vs GLS) are
# statistically different, simply pass an appropriate "hypothesis" argument.
emfx(hmod, hypothesis = "b1 = b2")
#
# Nonlinear model (distribution / link) families
#
# Poisson example
mpdta$emp = exp(mpdta$lemp)
etwfe(
emp ~ lpop, tvar = year, gvar = first.treat, data = mpdta,
vcov = ~countyreal,
family = "poisson" ## <= family arg for nonlinear options
) |>
emfx("event")
## End(Not run)
```

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