Extended Two-way Fixed Effects (ETWFE)

The goal of etwfe is to estimate extended two-way fixed effects a la Wooldridge (2021, 2022). Briefly, Wooldridge proposes a set of saturated interaction effects to overcome the potential bias problems of vanilla TWFE in difference-in-differences designs. The Wooldridge solution is intuitive and elegant, but rather tedious and error prone to code up manually. The etwfe package aims to simplify the process by providing convenience functions that do the work for you.

Documentation is available on the package homepage.

Installation

You can install etwfe from CRAN.

install.packages("etwfe")

Or, you can grab the development version from R-universe.

install.packages("etwfe", repos = "https://grantmcdermott.r-universe.dev")

Quickstart example

A detailed walkthrough of etwfe is provided in the introductory vignette (available online, or by typing vignette("etwfe") in your R console). But here’s a quickstart example to demonstrate the basic syntax.

library(etwfe)

# install.packages("did")
data("mpdta", package = "did")
head(mpdta)
#>     year countyreal     lpop     lemp first.treat treat
#> 866 2003       8001 5.896761 8.461469        2007     1
#> 841 2004       8001 5.896761 8.336870        2007     1
#> 842 2005       8001 5.896761 8.340217        2007     1
#> 819 2006       8001 5.896761 8.378161        2007     1
#> 827 2007       8001 5.896761 8.487352        2007     1
#> 937 2003       8019 2.232377 4.997212        2007     1

# Estimate the model
mod =
  etwfe(
    fml  = lemp ~ lpop, # outcome ~ controls
    tvar = year,        # time variable
    gvar = first.treat, # group variable
    data = mpdta,       # dataset
    vcov = ~countyreal  # vcov adjustment (here: clustered)
    )

# This gives us a regression model with fully saturated interactions
mod
#> OLS estimation, Dep. Var.: lemp
#> Observations: 2,500
#> Fixed-effects: first.treat: 4,  year: 5
#> Varying slopes: lpop (first.treat): 4,  lpop (year): 5
#> Standard-errors: Clustered (countyreal) 
#>                                               Estimate Std. Error   t value   Pr(>|t|)    
#> .Dtreat:first.treat::2004:year::2004         -0.021248   0.021728 -0.977890 3.2860e-01    
#> .Dtreat:first.treat::2004:year::2005         -0.081850   0.027375 -2.989963 2.9279e-03 ** 
#> .Dtreat:first.treat::2004:year::2006         -0.137870   0.030795 -4.477097 9.3851e-06 ***
#> .Dtreat:first.treat::2004:year::2007         -0.109539   0.032322 -3.389024 7.5694e-04 ***
#> .Dtreat:first.treat::2006:year::2006          0.002537   0.018883  0.134344 8.9318e-01    
#> .Dtreat:first.treat::2006:year::2007         -0.045093   0.021987 -2.050907 4.0798e-02 *  
#> .Dtreat:first.treat::2007:year::2007         -0.045955   0.017975 -2.556568 1.0866e-02 *  
#> .Dtreat:first.treat::2004:year::2004:lpop_dm  0.004628   0.017584  0.263184 7.9252e-01    
#> .Dtreat:first.treat::2004:year::2005:lpop_dm  0.025113   0.017904  1.402661 1.6134e-01    
#> .Dtreat:first.treat::2004:year::2006:lpop_dm  0.050735   0.021070  2.407884 1.6407e-02 *  
#> .Dtreat:first.treat::2004:year::2007:lpop_dm  0.011250   0.026617  0.422648 6.7273e-01    
#> .Dtreat:first.treat::2006:year::2006:lpop_dm  0.038935   0.016472  2.363731 1.8474e-02 *  
#> .Dtreat:first.treat::2006:year::2007:lpop_dm  0.038060   0.022477  1.693276 9.1027e-02 .  
#> .Dtreat:first.treat::2007:year::2007:lpop_dm -0.019835   0.016198 -1.224528 2.2133e-01    
#> ... 10 variables were removed because of collinearity (.Dtreat:first.treat::2006:year::2004, .Dtreat:first.treat::2006:year::2005 and 8 others [full set in $collin.var])
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> RMSE: 0.537131     Adj. R2: 0.87167 
#>                  Within R2: 8.449e-4

# Pass to emfx() to recover the ATTs of interest. Here's an event-study example.
emfx(mod, type = "event")
#> 
#>  event Estimate Std. Error     z Pr(>|z|)    S   2.5 %   97.5 %
#>      0  -0.0332     0.0134 -2.48    0.013  6.3 -0.0594 -0.00701
#>      1  -0.0573     0.0172 -3.34   <0.001 10.2 -0.0910 -0.02373
#>      2  -0.1379     0.0308 -4.48   <0.001 17.0 -0.1982 -0.07751
#>      3  -0.1095     0.0323 -3.39   <0.001 10.5 -0.1729 -0.04619
#> 
#> Term: .Dtreat
#> Type:  response 
#> Comparison: mean(TRUE) - mean(FALSE)
#> Columns: term, contrast, event, estimate, std.error, statistic, p.value, s.value, conf.low, conf.high, predicted_lo, predicted_hi, predicted

Acknowledgements

• Jeffrey Wooldridge for the underlying ETWFE theory.
• Laurent Bergé (fixest) and Vincent Arel-Bundock (marginaleffects) for maintaining the two wonderful R packages that do most of the heavy lifting under the hood here.
• Fernando Rios-Avila for the JWDID Stata module, which has provided a welcome foil for unit testing and whose elegant design helped inform my own choices for this R equivalent.