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  • Cannot manually set reference category for an interaction term in a high dimensional fixed effects model using the reghdfe command

    Hi there - this is my first post so hope I'm following the guidelines properly.

    I'm running a temporal model (code and output attached below) using the reghdfe command in Stata and my region fixed effects (absorbed) are perfectly colinear with no10, which is a continuous, time invariant variable defined at the region level. Therefore, there needs to be a reference category on c.no10#i.year, as including all interaction terms would reconstruct no10 which would be perfectly colinear with region fixed effects.

    For some reason, the command omits 2023 for the no10. I want it to omit the interaction for the first year, 2012, to be consistent with the i.year reference category. I've tried iterations with ib2012.year ib2012.year#c.no10 etc, but it keeps omitting 2023. Is this a default reghdfe setting to omit the final year, or am I missing something econometrics-wise?

    additional note: when i drop the region fixed effects it estimates a model with a simpler interpretation, with 2012 omitted only for i.year and included for the rest, which makes sense as no10 is no longer colinear in the model.

    Here is the command and output:

    Code:
     reghdfe outcome ib2012.year c.no10#ib2012.year c.no10#i.year#i.group if outcome>=0, a(i.region)

    Code:
    (MWFE estimator converged in 1 iterations)
    note: 2023.year#c.no10 omitted because of collinearity
    
    HDFE Linear regression                            Number of obs   =    174,981
    Absorbing 1 HDFE group                            F(  34, 174619) =      95.88
    Prob > F        =     0.0000
    R-squared       =     0.0386
    Adj R-squared   =     0.0366
    Within R-sq.    =     0.0183
    Root MSE        =    17.4918
    
    
    outcome  Coefficient  Std. err.      t    P>t     [95% conf. interval]
    
    year 
    2013    -.6430878   .9695935    -0.66   0.507    -2.543469    1.257294
    2014    -1.603839   .9730478    -1.65   0.099     -3.51099    .3033134
    2015    -.8338722   .9750366    -0.86   0.392    -2.744922    1.077178
    2016    -1.497623   .9581186    -1.56   0.118    -3.375514     .380268
    2017    -1.245818   .9719537    -1.28   0.200    -3.150825    .6591894
    2018    -1.107834    .977889    -1.13   0.257    -3.024474    .8088066
    2019    -1.497494   .9760138    -1.53   0.125    -3.410459    .4154711
    2020    -5.111335    .977514    -5.23   0.000     -7.02724   -3.195429
    2021    -5.100234   .9978856    -5.11   0.000    -7.056067     -3.1444
    2022    -3.418208   1.021382    -3.35   0.001    -5.420095   -1.416322
    2023    -2.677439    1.03587    -2.58   0.010    -4.707721   -.6471563
    
    year#c.no10 
    2012     .0957184   .3394871     0.28   0.778    -.5696687    .7611056
    2013     .3320111   .3420725     0.97   0.332    -.3384433    1.002466
    2014     .5165182   .3432691     1.50   0.132    -.1562815    1.189318
    2015     .1656705   .3438548     0.48   0.630    -.5082773    .8396182
    2016     .2775079    .338472     0.82   0.412    -.3858897    .9409055
    2017      .224865   .3428359     0.66   0.512    -.4470856    .8968156
    2018     .0349294   .3442548     0.10   0.919    -.6398023    .7096611
    2019     .0623301   .3438025     0.18   0.856    -.6115151    .7361754
    2020     .7712322   .3441665     2.24   0.025     .0966736    1.445791
    2021     .6356324   .3500851     1.82   0.069    -.0505265    1.321791
    2022      .266529   .3571284     0.75   0.455    -.4334346    .9664926
    2023            0  (omitted)
    
    year#group#c.no10 
    2012 1    -1.847835   .2332402    -7.92   0.000    -2.304981    -1.39069
    2013 1    -1.823049   .2332893    -7.81   0.000    -2.280291   -1.365807
    2014 1    -2.360965   .2308371   -10.23   0.000    -2.813401    -1.90853
    2015 1    -2.789325    .224443   -12.43   0.000    -3.229228   -2.349422
    2016 1    -3.111973   .2115982   -14.71   0.000      -3.5267   -2.697245
    2017 1    -3.235186   .2152065   -15.03   0.000    -3.656986   -2.813387
    2018 1    -3.016327   .2135707   -14.12   0.000    -3.434921   -2.597734
    2019 1    -3.213313   .2091915   -15.36   0.000    -3.623323   -2.803302
    2020 1    -3.682523   .2019657   -18.23   0.000    -4.078372   -3.286675
    2021 1    -3.748953   .2120809   -17.68   0.000    -4.164627   -3.333279
    2022 1    -3.223094   .2201608   -14.64   0.000    -3.654604   -2.791584
    2023 1    -2.973004   .2218493   -13.40   0.000    -3.407824   -2.538184
    
    _cons    74.41839   1.022906    72.75   0.000     72.41352    76.42327
    
    
    Absorbed degrees of freedom:
    
    Absorbed FE  Categories  - Redundant  = Num. Coefs 
    -
    region        328           0         328





  • #2
    reghdfe is from https://github.com/sergiocorreia/reghdfe (FAQ Advice #12).

    This behavior of factor variables has been discussed previously on the forum; see, e.g.,
    https://www.statalist.org/forums/for...nuous-variable. The issue is that specifying a base level in an interaction makes sense only if all elements constituting the interaction term are present in your model, which is not the case with what you have. Nonetheless, you can achieve the desired result by using the omission operator for factor variables.

    Code:
    reghdfe outcome ib2012.year c.no10#i.year o.n10#o2012.year c.no10#i.year#i.group o.no10#o2012.year#o1.group if outcome>=0, a(i.region)

    Comment


    • #3
      Andrew Musau Thanks so much!

      Comment

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