Extended two-way fixed effects (ETWFE)

The goal of etwfe is to estimate extended (Mundlak) two-way fixed effects a la Wooldridge (2021). 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. This package aims to simplify the process by providing convenience functions that do the work for you. etwfe thus provides an R equivalent of the JWDID Stata module and, indeed, shares some of the core design elements (albeit with some internal differences).

While I’ve tested ewtfe against common use cases, please note that the package is still under early development and should be considered experimental. I plan (hope) to add some more features and the documentation could also be improved. You can help by identifying any bugs and filing issues.

Installation

You can install the development version of etwfe from GitHub:

# install.packages("remotes")
remotes::install_github("grantmcdermott/etwfe")

Note: etwfe relies on the current development versions of fixest and marginaleffects. So you’ll have to compile fixest’s C++ source code on your system during installation.¹ Once these dependencies make their way to CRAN, I’ll submit etwfe to CRAN as well so that binaries are available for easy install.

Examples

To demonstrate the core functionality of etwfe, we’ll use the mpdta dataset from the did package. (You’ll need to install the latter separately.)

# 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

Now let’s see a simple example.²

library(etwfe)

mod = 
  etwfe(
    fml  = lemp ~ lpop, # outcome ~ controls
    tvar = year,        # time variable
    gvar = first.treat, # group variable (with bespoke ref. level)
    data = mpdta,       # dataset
    vcov = ~countyreal  # vcov adjustment (here: clustered)
    )
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    
#> ... 6 coefficients remaining (display them with summary() or use argument n)
#> ... 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

As you can see, the key etwfe() function is effectively a wrapper around fixest::feols(). (Nonlinear models are also supported via the family argument.) The resulting object is thus fully compatible with other fixest methods and functions like etable().

fixest::etable(mod, signif.code = NA)
#>                                                                   mod
#> Dependent Var.:                                                  lemp
#>                                                                      
#> .Dtreat x first.treat = 2004 x year = 2004           -0.0213 (0.0217)
#> .Dtreat x first.treat = 2004 x year = 2005           -0.0819 (0.0274)
#> .Dtreat x first.treat = 2004 x year = 2006           -0.1379 (0.0308)
#> .Dtreat x first.treat = 2004 x year = 2007           -0.1095 (0.0323)
#> .Dtreat x first.treat = 2006 x year = 2006            0.0025 (0.0189)
#> .Dtreat x first.treat = 2006 x year = 2007           -0.0451 (0.0220)
#> .Dtreat x first.treat = 2007 x year = 2007           -0.0459 (0.0180)
#> .Dtreat x lpop_dm x first.treat = 2004 x year = 2004  0.0046 (0.0176)
#> .Dtreat x lpop_dm x first.treat = 2004 x year = 2005  0.0251 (0.0179)
#> .Dtreat x lpop_dm x first.treat = 2004 x year = 2006  0.0507 (0.0211)
#> .Dtreat x lpop_dm x first.treat = 2004 x year = 2007  0.0112 (0.0266)
#> .Dtreat x lpop_dm x first.treat = 2006 x year = 2006  0.0389 (0.0165)
#> .Dtreat x lpop_dm x first.treat = 2006 x year = 2007  0.0381 (0.0225)
#> .Dtreat x lpop_dm x first.treat = 2007 x year = 2007 -0.0198 (0.0162)
#> Fixed-Effects:                                       ----------------
#> first.treat                                                       Yes
#> year                                                              Yes
#> Varying Slopes:                                      ----------------
#> lpop (first.treat)                                                Yes
#> lpop (year)                                                       Yes
#> ________________________________________             ________________
#> S.E.: Clustered                                        by: countyreal
#> Observations                                                    2,500
#> R2                                                            0.87321
#> Within R2                                                     0.00084

While everyone likes a nice regression table, the raw coefficients from an etwfe() estimation are not necessarily meaningful in of themselves. Instead, we probably want to aggregate them along some dimension of interest (e.g., an event study). A natural way to perform these aggregations is by calculating marginal effects. The etwfe package provides another convenience function for doing this, emfx(), which is itself a thin(ish) wrapper around marginaleffects::marginaleffects().

# Other type options incl. "simple" (default), "calendar", and "group"
emfx(mod, type = "event")
#>      Term    Contrast event   Effect Std. Error z value   Pr(>|z|)    2.5 %   97.5 %
#> 1 .Dtreat mean(dY/dX)     0 -0.03321    0.01337  -2.484 0.01297951 -0.05941 -0.00701
#> 2 .Dtreat mean(dY/dX)     1 -0.05735    0.01715  -3.343 0.00082830 -0.09097 -0.02373
#> 3 .Dtreat mean(dY/dX)     2 -0.13787    0.03079  -4.477 7.5665e-06 -0.19823 -0.07751
#> 4 .Dtreat mean(dY/dX)     3 -0.10954    0.03232  -3.389 0.00070142 -0.17289 -0.04619
#> 
#> Model type:  etwfe 
#> Prediction type:  response

Acknowledgements

Jeffrey Wooldridge for the underlying theory behind ETWFE.
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.

This means you need Rtools if you’re on Windows, and Xcode if you’re on a Mac. Linux users should be good to go without any other requirements. ↩
See the ?etwfe helpfile for information about other function arguments that can be used to customize the underlying estimation. ↩

yfnian / etwfe

Extended two-way fixed effects (ETWFE)

Installation

Examples

Acknowledgements

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Extended two-way fixed effects (ETWFE)

Installation

Examples

Acknowledgements

Footnotes

About

Languages