DiD, Parallel trend and Falsification Test

[Wali Ullah]

Hi Everyone,

I am running a panel data based diff-in-diff regression based on the following model:


pred=b0 + b1_post + b2_ppe + b3_post*ppe + industry FE + Year FE

Here, post is a dummy variable that equals 1 if after the death of a CEO, the replacement CEO is more overconfident and 0 otherwise. Unlike usual DiD cases, post occurs pretty much randomly and so there's no particular year based on which the DiD is to be performed.

Dataex example is as follows:

input double year str6 gvkey float(pred post ppe post_ppe)
2001 "003121" .17855483 0 -.030583873 0
2002 "003121" .3044268 0 -.11854684 0
2003 "003121" .5329734 0 .1626898 0
2004 "003121" .2675809 . -.018656716 .
2005 "003121" .3730394 . -.05038023 .
2006 "003121" .4977504 0 .005005005 0
2007 "003121" .13790938 0 -.027888447 0
2008 "003121" .20920193 0 -.016393442 0
2009 "003121" 1.248736 0 -.005208333 0
2010 "003121" .7652366 0 .02513089 0
2011 "003121" .6272957 0 .06128703 0
2012 "003121" .5186867 0 .04042348 0
2013 "003121" .3308406 0 -.05550416 0
2014 "003121" .06504069 0 -.043095 0
2015 "003121" .01460557 0 -.06038895 0
2016 "003121" .1246955 0 -.013071896 0
2017 "003121" .3580247 0 .02759382 0
2018 "003121" .010122395 0 .0698174 0
1992 "003144" 2.523266 0 2.476711 0
1993 "003144" 1.8261113 0 .05749405 0
1994 "003144" 1.9922253 0 .0941271 0
1995 "003144" 2.1985939 0 .0627451 0
1996 "003144" 2.9444325 1 -.18127306 -.18127306
1997 "003144" 2.8277564 1 .0543662 .0543662
1998 "003144" 1.9397168 1 -.01977024 -.01977024
1999 "003144" 1.7793707 1 .1629872 .1629872
2000 "003144" 1.0314896 1 -.023201313 -.023201313
2000 "003144" 1.0314896 1 -.023201313 -.023201313
2001 "003144" 1.0953677 1 .06837812 .06837812
2002 "003144" .5016651 1 .3274197 .3274197
2003 "003144" .5605422 1 .031466756 .031466756
2004 "003144" .47097415 1 -.0009840905 -.0009840905
2005 "003144" .464248 1 -.05007388 -.05007388
2006 "003144" .7526742 1 .1930522 .1930522
2007 "003144" .5658016 1 .23033464 .23033464
2008 "003144" .8617747 1 -.01966325 -.01966325
2009 "003144" 1.132622 1 .14833052 .14833052
2010 "003144" .3370867 1 .54032004 .54032004
2011 "003144" .4095156 1 .014395328 .014395328
2012 "003144" .23038715 1 -.030992704 -.030992704
2013 "003144" .25746492 1 .03391821 .03391821
2014 "003144" .28698075 1 -.02231576 -.02231576
2015 "003144" .3802491 1 -.14091437 -.14091437
2016 "003144" .5047393 1 -.15400524 -.15400524
2017 "003144" .7385507 1 -.2286789 -.2286789
2018 "003144" .5161983 . .003535292 .
1997 "003157" .8571199 0 .11180945 0
1998 "003157" .5426301 0 .15361165 0
1999 "003157" .48601645 0 .08565357 0
2000 "003157" .8970334 0 .14047177 0
2000 "003157" .8970334 0 .14047177 0
2001 "003157" 3.269697 0 .6428112 0
2002 "003157" 1.4753094 0 .020559434 0
2003 "003157" .8725134 1 -.14884801 -.14884801
2004 "003157" 2.1783202 1 .13425636 .13425636
2005 "003157" .13985358 1 -.06466571 -.06466571
2006 "003157" .08038747 1 -.04329235 -.04329235
2007 "003157" .356065 1 -.2980443 -.2980443
2008 "003157" .4480166 1 -.031724274 -.031724274
2009 "003157" 1.061839 1 -.02182267 -.02182267
2010 "003157" .17112525 1 -.0855636 -.0855636
2011 "003157" 1.4202826 1 .1567983 .1567983
2012 "003157" 1.0088737 1 .101355 .101355
2013 "003157" .08768988 1 -.006629254 -.006629254
2014 "003157" .11448758 1 -.06042875 -.06042875
2015 "003157" .12172931 1 -.04634908 -.04634908
2016 "003157" 1.236827 1 .24401386 .24401386
2017 "003157" .4770739 1 1.188037 1.188037
2018 "003157" .7445387 1 .11813876 .11813876
1998 "003158" .7007297 0 -.07050501 0
1999 "003158" .7252549 0 -.033895466 0
2000 "003158" 1.6917522 0 1.240068 0
2000 "003158" 1.6917522 0 1.240068 0
2001 "003158" .23122594 0 -.05950103 0
2002 "003158" .7281552 0 -.05799322 0
2003 "003158" .7424065 0 -.0914125 0
2004 "003158" .5463315 0 .014274987 0
2005 "003158" .4599173 0 .021175403 0
2006 "003158" .3742277 0 -.06903715 0
2007 "003158" .6490846 0 .007841531 0
2008 "003158" .5158396 0 .322322 0
2009 "003158" .590818 0 -.03609021 0
2010 "003158" .354026 0 .04730831 0
2011 "003158" .8227125 0 -.07092254 0
2012 "003158" .7174624 0 -.04102104 0
2013 "003158" .6528548 0 .02148656 0
2014 "003158" .8754736 0 -.12068684 0
2015 "003158" .4612469 0 -.4035286 0
2016 "003158" .7576277 0 -.04031579 0
2017 "003158" .5909077 0 .8740815 0
2018 "003158" .852203 . 1.1752311 .
1992 "003170" .12549666 0 2562.082 0
1993 "003170" .1465559 0 .10614976 0
1994 "003170" .10531158 0 .1255732 0
1995 "003170" .23465745 0 .08405011 0
1996 "003170" .1779687 0 .1269952 0
1997 "003170" .0920004 0 .00498172 0
1998 "003170" .3334314 0 .06071282 0
1999 "003170" .3689687 0 -.014714952 0
2000 "003170" .32493615 0 -.008937359 0
end


I have been asked by my supervisor to conduct a diff-in-diff with this model, with propensity score matching based on some control variables as covariates and run parallel trend analysis and falsification test. I am left with utter confusion based on all the statalist posts as to which of them are applicable to my case. Really appreciate your assistance with the coding for a proper psm match, did regression with the psm matched samples and parallel trend analysis and falsification test.

[Fei Wang]

What does matching mean when you have continuous treatment? I don't think matching is well defined in your case. If you ignore matching, the study is a typical DiD with continuous treatment and varying treatment timing. This is still an under-explored field, and so far I think the best-suited command would be did_multiplegt (from SSC).

[Wali Ullah]

Fei Wang by matching, I meant matching control and treatment firms based on the post values (firms who had a CEO death and those who didn't).

Even if we ignore the matching, I am looking for ideas on the parallel trend graph and test along with the falsification test.

[Fei Wang]

So the event is death of CEO. Treatment groups include firms whose CEO ever died, while firms whose CEO never died belong to the control group -- This is a binary treatment setting with treatment occurring at different timings. You may use csdid or did_imputation (both from SSC) where "matching" is done in some way with DiD. But what is the continuous variable "ppe"? I thought it was your (continuous) treatment.

BTW, both commands can do parallel-trend testing.

[Wali Ullah]

Fei Wang PPE is one of the main independent variable of this study. I am looking to study whether following the death event (post), higher ppe leads to increased pred?

A sample coding for parallel-trend graph and testing would be highly appreciated. Thanks!

[Fei Wang]

Please refer to help files of csdid or did_imputation. Both have post-estimation commands, including graphing. For example, you may use csdid_plot after csdid, and event_plot after did_imputation. More details and examples are in their documents.