Parallel trends assumption test for a two way fixed effect model (omitted treatment variable)

[David Gebhard]

Hi everyone,

I want to test for the parallel trend assumption in the difference in differences. My research design is about testing the change in corporate social responisbility behaviour due to european csr regulation (in force for fiscal year 2017).

I'm trying to estimate this model with company fixed effects and year fixed effects.

reghdfe CSRW_TOT i.TREATMENT##i.MANDATE LNSALE LEVERAGE, absorb(YEAR COMP_ID) vce(cluster COMP_ID)

My panel data is yearly (xtset COMP_ID YEAR).
COMP_ID is the Company ID
CSRW_TOT is a variable that indicates the percentage of "CSR words" in company reports
MANDATE is a dummy variable that is equal to 1 for the years the regulation entered into force (YEAR 2017 & 2018) and 0 before (YEAR 2015 & 2016)
TREATMENT is a dummy variable that is equal to 1 when a Company is effected by the european "CSR Directive" (COUNTRY UK & Germany) and equal to 0 for the control group (S&P 500 companies)

How can i check for the parallel trend assumption for this fixed effect model?
I have tried several possibilities, but since the TREATMENT variable is probably collinear with the fixed effects the TREATMENT variable is always omitted.

These are some possibilities which i tried:

reghdfe CSRW_TOT i.TREATMENT##c.YEAR LNSALE LEVERAGE, absorb(YEAR COMP_ID) vce(cluster COMP_ID)

tfdiff CSRW_TOT TREATMENT LNSALE LEVERAGE, datatype(panel) model(fe) tvar(YEAR) t(2017) pvar(COMP_ID) test_pt vce(r)

xtreg CSRW_TOT i.TREATMENT#i.MANDATE LNSALE LEVERAGE, fe vce(r)
margins i.TREATMENT#i.MANDATE, noestimcheck

please let me know if you need any more information.
Thank you,
David

* Example generated by -dataex-. To install: ssc install dataex
clear
input str75 COMPANY float(COMP_ID YEAR) double(LNSALE LEVERAGE) float(CSRW_TOT TREATMENT MANDATE)
"3M Co"                            542 2017  17.22033468834878   .69  .08498428 0 1
"3M Co"                            542 2016 17.225799816304647  .682  .08498428 0 0
"3M Co"                            542 2015 17.275637007155716  .635  .08498428 0 0
"3M Co"                            542 2018  17.27046985113653  .727  .08498428 0 1
"4imprint Group PLC"               517 2018 13.408326974122144  .585      .0638 1 1
"4imprint Group PLC"               517 2017  13.15809917914767  .591      .0648 1 1
"4imprint Group PLC"               517 2015 12.869211547849371  .667      .0606 1 0
"4imprint Group PLC"               517 2016  13.06790719160827  .658 .064500004 1 0
"ADIDAS AG"                        390 2017  16.83562315144792  .537      .0606 1 1
"ADIDAS AG"                        390 2015 16.620635804820733  .555  .05610669 1 0
"ADIDAS AG"                        390 2018  17.07545769027168  .575      .0605 1 1
"ADIDAS AG"                        390 2016 16.760954558243554  .553  .05739328 1 0
"AES Corp"                         266 2017 16.424550408733385  .828      .0525 0 1
"AES Corp"                         266 2016 16.521625554431974  .817  .05081058 0 0
"AES Corp"                         266 2015 16.656983812489194  .815  .05831644 0 0
"AES Corp"                         266 2018  16.16973888411016    .8 .063096926 0 1
"ANSYS Inc"                        415 2017 13.803908513783359  .225      .0488 0 1
"ANSYS Inc"                        415 2018 13.906493205676146  .182      .0518 0 1
"ANSYS Inc"                        415 2015 13.749393191105485  .186      .0501 0 0
"ANSYS Inc"                        415 2016 13.756559597295334  .199      .0548 0 0
"AO World PLC"                     413 2016 13.537657356844537  .715      .0612 1 0
"AO World PLC"                     413 2018 13.843167552916222  .691      .0621 1 1
"AO World PLC"                     413 2017 13.620971470160084  .799      .0598 1 1
"AO World PLC"                     413 2015 13.397514767758244  .615      .0605 1 0
"ASOS PLC"                          52 2017 14.405132759460136  .655 .063599996 1 1
"ASOS PLC"                          52 2015 14.220279423751995  .503      .0621 1 0
"ASOS PLC"                          52 2016 14.324550989221905  .685      .0606 1 0
"ASOS PLC"                          52 2018 14.792408217380673  .564      .0597 1 1
"AURUBIS AG"                       299 2018 16.351779695579236   .43  .07022011 1 1
"AURUBIS AG"                       299 2016 16.308439691402608  .504      .0543 1 0
"AURUBIS AG"                       299 2015 16.349547155458584  .512      .0516 1 0
"AURUBIS AG"                       299 2017 16.131392356646437  .457      .0573 1 1
"AXEL SPRINGER AG"                 343 2015 15.055311596720092  .611 .063757695 1 0
"AXEL SPRINGER AG"                 343 2016 15.125129577132137  .588      .0504 1 0
"AXEL SPRINGER AG"                 343 2018 15.291126521280688  .551      .0514 1 1
"AXEL SPRINGER AG"                 343 2017 15.066932913954416  .561  .06430401 1 1
"Abiomed Inc"                      385 2016 12.621959920354175 -.009      .0532 0 0
"Abiomed Inc"                      385 2015 12.269924993804983  .005      .0586 0 0
"Abiomed Inc"                      385 2017 12.935023650630288  .123      .0527 0 1
"Abiomed Inc"                      385 2018 13.206691658108232  .036      .0569 0 1
"Accenture PLC"                     34 2016 17.254818389229275  .558  .07719437 0 0
"Accenture PLC"                     34 2015  17.23452690141206  .609  .08001322 0 0
"Accenture PLC"                     34 2018 17.395074100813453   .52  .07718616 0 1
"Accenture PLC"                     34 2017  17.32361956169649  .526  .07996055 0 1
"Adobe Inc"                        358 2015 15.237911413086874  .403  .05413578 0 0
"Adobe Inc"                        358 2016 15.383190829964633  .416   .0517677 0 0
"Adobe Inc"                        358 2017 15.582709197584865  .418      .0515 0 1
"Adobe Inc"                        358 2018 15.803591049253225  .501  .05274135 0 1
"Aggreko PLC"                      467 2016 14.629430522647521  .444      .0495 1 0
"Aggreko PLC"                      467 2015 14.700639567606773  .448      .0528 1 0
"Aggreko PLC"                      467 2018 14.686331008753667  .468      .0594 1 1
"Aggreko PLC"                      467 2017 14.452507933514392  .478       .053 1 1
"Agilent Technologies Inc"          76 2015  15.21817027317043  .442  .07440205 0 0
"Agilent Technologies Inc"          76 2016 15.211755249937333  .456  .07244961 0 0
"Agilent Technologies Inc"          76 2017 15.260309648456728  .426  .08055538 0 1
"Agilent Technologies Inc"          76 2018 15.345039087170072  .465  .06942448 0 1
"Air Products and Chemicals Inc"   602 2016 16.086594663896257  .596  .07937477 0 0
"Air Products and Chemicals Inc"   602 2017 15.833063397965265  .443      .0614 0 1
"Air Products and Chemicals Inc"   602 2015 16.162523934992667  .575   .0795564 0 0
"Air Products and Chemicals Inc"   602 2018 15.958126409418364  .414   .0749048 0 1
"Akamai Technologies Inc"           74 2017 14.665682427285581  .273      .0504 0 1
"Akamai Technologies Inc"           74 2016 14.602807245007792  .261  .05635711 0 0
"Akamai Technologies Inc"           74 2018 14.732998972330334  .412      .0494 0 1
"Akamai Technologies Inc"           74 2015 14.490429611052392  .254  .05631889 0 0
"Albemarle Corp"                     3 2018 14.937831560719182  .503 .063021526 0 1
"Albemarle Corp"                     3 2016 15.110603412111853  .513 .066984534 0 0
"Albemarle Corp"                     3 2017  14.80028315078173  .506 .065956555 0 1
"Albemarle Corp"                     3 2015 14.709779786656881  .643   .0659261 0 0
"Alexion Pharmaceuticals Inc"      411 2015 14.619184734906389  .371      .0569 0 0
"Alexion Pharmaceuticals Inc"      411 2018 15.082767972610094  .342      .0582 0 1
"Alexion Pharmaceuticals Inc"      411 2016 14.772577331302859  .344      .0603 0 0
"Alexion Pharmaceuticals Inc"      411 2017 14.941738013665358  .345      .0637 0 1
"Alliant Energy Corp"              658 2017  15.01547534089267  .691 .070985526 0 1
"Alliant Energy Corp"              658 2018 15.034036943297721   .69  .07658236 0 1
"Alliant Energy Corp"              658 2015 15.024560452030492  .686 .065864205 0 0
"Alliant Energy Corp"              658 2016 14.995272633575151  .696   .0712737 0 0
"Ameren Corp"                      279 2015 15.616064574873825    .7  .06809589 0 0
"Ameren Corp"                      279 2016 15.623471406530337  .707  .06604554 0 0
"Ameren Corp"                      279 2017   15.6198571426978  .718  .05003837 0 1
"Ameren Corp"                      279 2018 15.636343274678037  .714  .07125351 0 1
"American Airlines Group Inc"      804 2017 17.508879917351063  .923  .06164163 0 1
"American Airlines Group Inc"      804 2018  17.55809664202746 1.003  .06483074 0 1
"American Airlines Group Inc"      804 2015 17.568537831901963  .877  .05764483 0 0
"American Airlines Group Inc"      804 2016  17.52883869248052  .924  .04859415 0 0
"American Water Works Company Inc" 254 2018 15.026558275962172  .724  .08498428 0 1
"American Water Works Company Inc" 254 2015 14.917891735440003  .707  .08498428 0 0
"American Water Works Company Inc" 254 2017  15.01003890346221  .724      .0786 0 1
"American Water Works Company Inc" 254 2016 14.965766079784222  .718  .08498428 0 0
"AmerisourceBergen Corp"            44 2015  18.63564184614919  .977      .0566 0 0
"AmerisourceBergen Corp"            44 2017 18.814814595167743  .942  .06436231 0 1
"AmerisourceBergen Corp"            44 2018 18.861776107998942  .919  .06877332 0 1
"AmerisourceBergen Corp"            44 2016 18.750576021142535  .937    .060219 0 0
"Ametek Inc"                       745 2018  15.27416511476603   .51      .0478 0 1
"Ametek Inc"                       745 2016 15.195357931850126  .541      .0811 0 0
"Ametek Inc"                       745 2015 15.207280898503916  .512      .0467 0 0
"Ametek Inc"                       745 2017  15.16100558055726  .483      .0474 0 1
"Amgen Inc"                        805 2017 16.950613392966073  .684   .0598076 0 1
"Amgen Inc"                        805 2016  16.89107013137782  .615  .05831049 0 0
"Amgen Inc"                        805 2015 16.814387880662338  .608  .05422583 0 0
"Amgen Inc"                        805 2018  16.94441791067068  .812  .05772042 0 1
end
label values TREATMENT treatment
label def treatment 0 "Control", modify
label def treatment 1 "Treatment", modify
label values MANDATE mandate
label def mandate 0 "Pre", modify
label def mandate 1 "Post", modify

[Phil Bromiley]

You ask about the parallel lines assumption, but it seems as if you really have a much more basic problem that the treatment variable doesn't end up with a parameter estimate. If the treatment applies to all firms in the years after it is in, then obviously you cannot include year fixed effects.

Difference in difference normally includes multiple years where some of the firms have become treated in a given year and some do not get treated. If you really have a bunch of European treated and a bunch of US not treated, then you should get an estimate on the treatment variable. That you are not really worries me. It suggests something is going on with your data that you are not catching.

Since most of us are not in your area, it might be useful to explain exactly what you mean by the parallel trends assumption.

I suspect your problem in the first possibility you try is that you don't include the interaction with the mandate. I would think the parallel trends assumption would be that that interaction is the same in the mandate and non-mandate groups.

[David Gebhard]

Hi Mr. Bromiley
Thank you for your quick response. Only the european countries are effected by the regulation so the binary variable TREATMENT is 1 for german and UK firms,and 0 for the US firms over all four years. So i have a bunch of European treated and a bunch of US not treated firms. The Variable MANDATE is 0 for 2015/2016 and 1 for 2017/2018 for both the treatment and the control group.

After your response i searched the web again and found this post of the Columbia University:
"It (Parallel Trend Assumption) requires that in the absence of treatment, the difference between the ‘treatment’ and ‘control’ group is constant over time. Although there is no statistical test for this assumption, visual inspection is useful when you have observations over many time points"
https://mailman.columbia.edu/researc...nce-estimation

But as proposed in an other thread, perhaps the way to statistically test if there are parallel trends is to run a joint significance test on the interactions with years for the "pre" period.
https://statalist.org/forums/forum/g...3-time-periods

Perhaps that's the way how to do this test with the "tfdiff" command:

ssc install tfdiff
rename TREATMENT w
tfdiff CSRW_TOT w LNSALE LEVERAGE, datatype(panel) model(fe) tvar(YEAR) t(2017) pvar(COMP_ID) graph ci(5) vce(r)
tfdiff CSRW_TOT w LNSALE LEVERAGE, datatype(panel) model(fe) tvar(YEAR) t(2017) pvar(COMP_ID) test_pt vce(r)

Guess, the problem before was, that the tfdiff command need the treatment variable named as "w".
The output says the "parallel trend passed". And the graph shows the confidence intervalls.

It (the tfdiff command) assumes the availability of a panel dataset where the same treated and untreated units are observed over time

Since the group of treated companies and untreated companies in my dataset remain the same over time, the result should make sense, right?