[Clyde Schechter]

What does the "adjusted" in that variable name mean? If that variable has already been adjusted for SIZE and FISCALYEAR then all you need to do is -ttest ΔOROAt5_adjusted = 0 -.

If the variable is not already adjusted for those things, then you need to look at the separate values in the two groups, not at the difference. Since you calculated differences, I assume these differences are coming from matched pairs (since we were working on matching before)? In that case, it's a bit more complicated. To give you specific advice I would need to see an example of the data that you are working from for this.

[Carl-Johan Andersson]

Adjusted in this case only means adjusted for the control group - SIZE and FISCALYEAR are not included.

Correct, the differences are coming from matched pairs. See example of data:

* Example generated by -dataex-. To install: ssc install dataex
clear
input long CompanyID int FISCALYEAR byte INDUSTRY double(SIZE OROA) byte(TURNOVER FORCED OUTSIDE FORCEDOUTSIDE) double(OROABencht1 ΔOROAt5 mean_ΔOROAt5) float ΔOROAt5_adjusted
  4439 2003 36 11.676217095857377  -.04915325039492575 1 1 1 1   -.07741066001215728    .16822035497415502  -.005410793361195487   .17363115
  4439 2010 36   12.2226740760276   .08991175238780026 1 0 0 0    .08267176320689994    .01218513049042734  -.026896938326069254   .03908207
  4439 2017 36  12.21256651464649  -.04200150345689208 1 1 0 0    .05170152234995411                     .   -.09022392022503123           .
 11217 2011 37 12.645510747206432   .08588490190467506 1 0 0 0    .05487186432516215                     .    .03372212157168948           .
 11217 2015 37 12.652407747006631   .05235364171994484 1 1 1 1    .03331216342012998                     .   .052490377320463445           .
 11749 2003 35 10.630480449879682   .08413924018161763 1 0 0 0    .09756216837420838    .06479133144232914  -.009060388704502348   .07385172
 11749 2015 35 11.238449144805152   .08504513774054068 1 1 0 0    .10549224549590794                     .  -.005582143196854336           .
 12368 2002 24 11.385614684158762   .08318350376446791 1 0 0 0    .11296369024242207   -.04718012827033796   -.11516162358035129    .0679815
 12368 2007 24   11.5720901981382   .06578356197208411 1 1 0 0   .059096287531430265   .001959509424053027   .042596808134388084   -.0406373
 12368 2015 24 11.655431465059884   .07974227070623513 1 1 0 0    .07816717273954116                     .   .031495315130320854           .
 14620 2002 36 11.799231591242078   .08546592268679788 1 0 0 0    .07212821775939694  -.002028746154982039                     .           .
 14620 2011 36 11.528779128893396  .041675167639177925 1 0 0 0     .0894547155276769  -.017465641478006957  -.042857141897898396    .0253915
 14620 2016 36 11.704314124402291   .07198907404966995 1 0 0 0    .05644897768649052                     .   -.09998044360290577           .
 16299 2003 99  8.335431477880796   .02916307161345988 1 0 0 0    .03138181204656656    .02078376015147078 -.0014958189068808095   .02227958
 17420 2002 35  10.76978940206521   .08354957502680362 1 0 1 0     .0993710284009856    .11907074157458222   .007599697225851927   .11147104
 17420 2009 35  11.06291268060075    .1215083428389527 1 1 0 0    .24049136059584533    -.0484466688754189   -.08336442949876516   .03491776
 17420 2017 35 11.664968210378253   .22325958651157973 1 0 0 0    .19200077662362877                     .   -.05805923966783464           .
 19591 2002 35 10.793434309070681   .11647056449171528 1 0 0 0    .13125170811697184    .08344913102052229    .05427667870784696   .02917245
 19591 2011 35 11.451943279235435    .1340014889054323 1 1 1 1    .12043680043680044                     .  -.002279173956025176           .
 19591 2015 35 11.360298623511312    .0807757785532219 1 1 1 1     .1077948914594917                     . -.0002481705340628253           .
 62557 2012 37 11.284807059564494   .10186718385494332 1 0 0 0    .15431427729632527   -.05208289312645295  -.039577675161984294 -.012505218
 64335 2002 28  4.865501616417073 -.009422287835696142 1 1 0 0   -.29009909672893097                     .     .1011230591520009           .
 64894 2001 33  9.235032984566555 -.022006028262999456 1 1 1 1  -.015997478726009807     .3855323421521378     -.275671859086543    .6612042
 64894 2008 33 10.341323040674743   .03675957548382358 1 0 1 0     .2013442756879201    -.1579572393447204   -.11837711343684262  -.03958013
 65423 2012 48   9.49822242443063   .14582040599237656 1 0 0 0    .12541065562062562   -.05094317158197936                     .           .
 65423 2017 48  9.772068213669293   .07446748403864625 1 0 0 0    .08365157301327514                     .       .03275984837442           .
100744 2001 26   9.72046575062778   .12580962531770107 1 1 0 0    .16598107774578363                     .                     .           .
100744 2004 26  9.658417870888224   .06730404431292207 1 0 0 0    .08625356917714243   -.04142957056434548   -.12773563090958046   .08630606
100744 2014 26  9.679968930891835  .039343727042690395 1 0 0 0   .023700264535982292                     .    .02736989017460522           .
100956 2004 21   9.47324295306374    .1404449741756059 1 1 0 0    .14313458924062925                     .                     .           .
100956 2008 21  9.485089169016064   .18169672678690715 1 0 0 0    .18845909955611923    .04569301233588552    .00645307155578187   .03923994
100980 2002 15 11.888453565993078   .02511709853465687 1 1 0 0   .029255904950700302    .04098965298891292    .06897853625843318  -.02798888
100980 2008 15 11.875302123198598    .0418793782698471 1 0 0 0    .07024555793961322  -.014734706236774212  .0015790642500901077  -.01631377
101048 2005 30  10.09286747369753   .08027891187669159 1 0 0 0    .05613405670283514    .01665107481820484    .05635385535433082  -.03970278
101585 2003 55   9.62990560446313   .05100634132892198 1 0 1 0   .057051574623459604  -.061879062909701264                     .           .
101585 2011 55  9.806976652155285   .09551004332414337 1 0 0 0    .10133559465762138   .011061767033050313   .019368655264897575 -.008306888
101693 2001 50   8.66561319653451  .043857946827091016 1 0 0 0    .11023804021261845    .03367158650643852   .018702708772335305  .014968878
101693 2012 50    8.9445502459405  .005179496338631898 1 0 0 0     .0666421207658321                     .   .059621953320462016           .
102009 2001 15 10.737656750807961 -.007767149047502249 1 0 1 0    .06241818808129521   .024155032132647976  -.003281523759614361  .027436556
102009 2007 15 10.975019797633829    .0903832957553181 1 0 0 0    .08657322021394319                     .   .042852108504920085           .
102009 2011 15 10.869234893122876   .06558641975308642 1 0 0 0    .07509340805978115   -.03605985646341549   .021969851203238498  -.05802971
102276 2000 56 10.323962776429454    .2652871490752349 1 0 0 0      .399898715609147    .06843276306104173   .022752517987896553   .04568024
102276 2009 56 11.526759334225725    .4223796420974572 1 0 0 0     .4825322279196818   -.09299876059524059   -.17598367543554555   .08298492
102476 2005 37  8.920789888464375   .09858429858429858 1 0 1 0    .08704115684093437   -.05270894806935271  -.011629528707320707  -.04107942
102476 2011 37  8.301521654940728  .046507025529388485 1 0 0 0    .03433220877158166                     .   .052490377320463445           .
102476 2012 37   8.27715777243181  .052484254723582924 1 0 1 0   .046507025529388485   .047702984284154204  -.007358129956519452   .05506111
102476 2017 37  8.403352374992478   .09421000981354269 1 0 0 0    .09492119089316987                     .  -.030558304882003423           .
102799 2004 35  8.374015421739909   .21368198626518753 1 0 1 0    .17867511216679863   -.12237442595344866    -.0550304904588878 -.067343935
102799 2011 35   8.85978949474541    .2426749396759738 1 1 1 1    .21729448877342736                     .   -.05285926329315852           .
102840 2002 15  9.090655529030203  .029872749844816884 1 0 0 0    .09068627450980392     .1800727071699486    .06999977120161881   .11007293
102846 2002 22  7.289610521451167 -.004719949653870359 1 1 1 1    .05719237435008666                     .                     .           .
102846 2004 22  7.072591521435072  -.10254591872916814 1 0 1 0 -.0038125287582988234                     .    .07476952197464609           .
102846 2008 22  5.989713014069176   -.2554603262372132 1 1 0 0    -.1611325229765787                     .    .02592250005280261           .
102915 2006 33 10.343482903541116    .2569660861594867 1 0 1 0    .25406005644750845     -.220564568920278                     .           .
102915 2011 33 10.706385597055192   .03349548752723044 1 0 0 0    .01585593935682484   -.00353766039301639   .020615262452183467 -.024152923
103045 2002 28 6.5131529566006785  .028633901346114578 1 0 0 0   .011259765081367947   .000767768719086015                     .           .
103045 2010 28  7.165353588924841  -.04032755581668625 1 1 1 1  -.025917341022157377                     .    .11896901593457265           .
103045 2012 28  6.885648719671672 -.015872649078888246 1 0 0 0   .013395668034402538                     .                     .           .
103051 2002 87  7.557021624869986  -.01853044505661536 1 0 1 0    .05122038876416957    .09140770837580836    .13483390064955894  -.04342619
103051 2017 87   9.44604470533525   .09906793504372058 1 0 1 0    .11531570530163655                     .   .012892278355732588           .
103219 2013 50  8.794119527763097   .07490278666254573 1 0 0 0    .08113406162834942                     .  -.000637655910241669           .
103314 2008 26  7.887208585813932  -.11476829796448679 1 0 1 0   -.04812398042414356  -.022973392064264485   .055315746124500104  -.07828914
103314 2013 26  7.236339342754344  -.07109737248840804 1 1 1 1  -.013363028953229399                     .   -.08338048685231352           .
103314 2014 26  7.344072850573066   .07838070628768304 1 1 0 0   -.07109737248840804                     .   -.00293433090457583           .
103314 2016 26  7.455876687491824    .1038961038961039 1 0 1 0    .19904837430610625                     .                     .           .
104961 2008 34    9.1942109900463   .17337662337662338 1 0 0 0    .18651971174226367   -.11031771597570789    .03135050019752336  -.14166822
104961 2013 34  8.783089671796096   .07620199576655579 1 1 1 1    .07146164531563513                     .    -.1395927454884285           .
104981 2007 73 11.049422262098634   .08607271037351832 1 0 1 0     .0772458013420151 -.0005761528354805145    .03729876489056089  -.03787492
201038 2005 34  8.972083182851925    .0870429252782194 1 1 0 0     .0774478330658106    .08277415046444361   .009382282569645989   .07339187
210970 2001 24 7.0530670101421915  -.02378023780237802 1 1 0 0   .022286821705426358                     .    .13332100817897813           .
210970 2004 24  7.235763222905484  .013805678562125554 1 0 0 0   .037031802120141344                     .  .0006673822797582107           .
210970 2006 24  7.655864017616056   .10754189944134078 1 0 1 0      .097900227363916   -.19255099397379677   -.09737385547851496  -.09517714
211788 2001 56    8.4567380552363   .03967684071319059 1 1 1 1    .16093932804937927                     .                     .           .
211788 2004 56  8.585245780976662  .036537456008516205 1 1 1 1    .11424309124081485                     .                     .           .
212346 2001 48  7.692008359187909   .04500395048129421 1 0 0 0     .2157128650814637   .035672176469782824                     .           .
212548 2009 73 7.2694398537401765   .05658064644126072 1 0 1 0    .13880331991400927  -.027842479881793863   -.08217362201704013   .05433114
212844 2005 73  8.776059035849977     .016352868381508 1 0 1 0    .07459724950884086                     .   .012460116694166157           .
212844 2009 73  8.822970552137111   .04652135079150909 1 1 1 1    .05122692411055754   .030112899184097486   .021654452982025275  .008458446
212844 2015 73   8.70807797887068   .08470115228384316 1 1 1 1    .08133982329465503                     .    .02610018399875837           .
213038 2004 73  8.000651260654138  -.10299491579281857 1 1 1 1   -.06958151521363516                     .   .041610653381825485           .
213039 2002 73 7.8308627241832145 -.024910614852587776 1 0 0 0  -.021182233401734293                     .     .2082597872059582           .
213039 2006 73  7.731053144007127  .045907531449109626 1 1 1 1    .04717914879577697                     .   .056707237474916274           .
213039 2008 73  7.618005367441745 -.026804509519577118 1 1 1 1    .01835958237480092                     .                     .           .
213044 2003 87  5.004167757933224  -.30317437176704354 1 1 1 1   -.17209841022139863   -.07575826253273876                     .           .
213044 2009 87  3.393198811550889  -.35614981898442866 1 0 0 0    -.2478566727541374                     .                     .           .
213044 2011 87 6.5490296624222655    .1829781485917813 1 1 0 0    -.6663109161793372                     .    .08594704727088343           .
213044 2014 87  7.477032247059799   1.1941414608175032 1 1 0 0    .03271618990982118                     .    .02079636308680043           .
213044 2017 87 3.6011132468570612   -.1842146486370305 1 1 0 0    -.1932739573891496                     .                     .           .
213047 2003 30  7.890208213109961   .05013192612137203 1 0 1 0   .016245487364620937    .10210696310461785   .020615262452183467    .0814917
213047 2008 30  7.945909598613133   .11835245046923878 1 0 1 0     .1142691415313225    .03873009916723483    .07456056827562114 -.035830468
213047 2016 30  8.399984990510696    .1305289205072688 1 0 0 0    .18599862731640357                     .   .019421370583221298           .
213048 2001 36  3.595502404608637   -.3985308689644906 1 1 1 1    -.5681818181818182    .38947169730216813    .13448402785571878   .25498766
213048 2007 36  6.069089719511962 .0065396495330411085 1 0 0 0   -.17871012087965013                     .   -.15331923532215092           .
213048 2010 36  6.102932126631507   .09879535306347031 1 0 1 0   .038175029596575906                     .                     .           .
213048 2013 36 6.2626570355697835   .01766700102533911 1 0 1 0    .08257960474982211                     .  -.026896938326069257           .
213048 2017 36  6.718746210546363   .06512219740572116 1 1 0 0    .07913378186052529                     .  -.012953373689297894           .
213075 2011 15 10.681412367138472  .053092820884699056 1 0 0 0   .053839136384369775                     .    .02064903383511931           .
213075 2013 15   10.6711622600815  .015714152090543446 1 1 0 0   .031229066317904876                     .    .06897853625843318           .
213323 2008 28 3.9788588856144007   -.3770876570849607 1 1 0 0    -.4383403150079693    .13833471748695342    .20444940346640741  -.06611469
213323 2017 28   3.00795724317656  -.11935331516802906 1 1 0 0   -.12265040939836241                     .   .031099912251147693           .
end

To illustrate, I only included the t+5 variables - I would want to do the same with t+1, t+2, t+3, and t+4 as well.

Thanks!

[Clyde Schechter]

I don't understand this data. There are no matched pairs here that I can see. You just have observations for one CompanyID in each YEAR. Moreover, all of the firms are TURNOVER firms in the example.

When you say ΔOROAt5_adjusted is adjusted for SIZE and FISCALYEAR, how was that calculated? And what other variables are there that you need to adjust for?

At this point I really don't understand at all what you have and what you want to do.

[Carl-Johan Andersson]

Sorry for not being clear on the data structure.

The matching is not done in pairs, but each turnover is matched to the mean performance of all controls matching the criteria (according to the procedure we discussed in the other thread).
This matching generates the mean_ΔOROAt5 variable. ΔOROAt5_adjusted is not adjusted for SIZE and FISCALYEAR but calculated as the difference between ΔOROAt5 and mean_ΔOROAt5.

Ultimately, I want to be able to test if ΔOROAt5_adjusted is different from zero controlled for SIZE and year fixed effects (FISCALYEAR).

Let me know if you want me to clarify anything else.

[Clyde Schechter]

So looking back at https://www.statalist.org/forums/for...variable/page2, I would like to assume you are referring to the calculation in #18, but the variable names are different (in that post there are no Δ characters in the variable names). So perhaps it is best that I not assume. Can you show the actual code you used to calculate mean_ΔOROAt5 so I can be sure of what I'm talking about.

[Carl-Johan Andersson]

This is the code used to do the matching and generate the variables:

//    VERIFY INDUSTRY HAS TWO DIGITS
assert length(string(INDUSTRY, "%02.0f")) == 2

//    MAKE A COPY OF THE FILE FOR JOINING
tempfile copy
save `copy'

//    ONLY FIND MATCHES FOR THE TURNOVER OBSERVATIONS
keep if TURNOVER == 1
isid CompanyID FISCALYEAR

//    SET LIMITS OF MATCHING ON OROABencht1
gen low = OROABencht1 - 0.1*abs(OROABencht1)
gen high = OROABencht1 + 0.1*abs(OROABencht1)

//    DO THE JOIN
rangejoin OROABencht1 low high using `copy', keepusing(CompanyID INDUSTRY TURNOVER ΔOROAt*)
// IF YOU WANT TO EXCLUDE SELF (ändra till att droppa om samma firm-year): drop if CompanyID == CompanyID_U
// IF YOU WANT TO EXCLUDE OTHER TURNOVERS:
drop if TURNOVER_U == 1

//    CALCULATE THE DIGIT MATCH IN SIC CODE
gen byte digits_matching = 0
replace digits_matching = 1 if floor(INDUSTRY/10) == floor(INDUSTRY_U/10)
replace digits_matching = 2 if INDUSTRY == INDUSTRY_U

//    KEEP ONLY THOSE MATCHES THAT HAVE THE MOST DIGIT-MATCHING ON SNICode
gsort CompanyID FISCALYEAR -digits_matching
by CompanyID FISCALYEAR: keep if digits_matching == digits_matching[1]

//    NOW CALCULATE MEAN OROAt* FOR THE SURVIVING MATCHES
ds CompanyID FISCALYEAR *_U, not
collapse (mean) ΔOROAt*_U (first) `r(varlist)', by(CompanyID FISCALYEAR)
rename *_U mean_*

gen ΔOROAt1_adjusted = ΔOROAt1 - mean_ΔOROAt1
gen ΔOROAt2_adjusted = ΔOROAt2 - mean_ΔOROAt2
gen ΔOROAt3_adjusted = ΔOROAt3 - mean_ΔOROAt3
gen ΔOROAt4_adjusted = ΔOROAt4 - mean_ΔOROAt4
gen ΔOROAt5_adjusted = ΔOROAt5 - mean_ΔOROAt5

[Clyde Schechter]

Thank you. So these are already matched on FISCALYEAR, so no adjustment for that is needed. But they are not matched on SIZE, so that has to be done.

The following should do it. You might want to preserve the data set before this, as the code below will eliminate most of the variables, just to simplify the -reshape- that is needed

//    STRIP THE DATA SET DOWN TO ESSENTIALS FOR THIS CALCULATION
keep ΔOROAt* mean_ΔOROAt* SIZE
gen long pair_num = _n

//    MAKE VARIABLE NAMES MORE FRIENDLY TO -reshape-
rename (ΔOROAt*) =_index
rename mean_ΔOROAt* ΔOROAt*_mean

//    DO THE -reshape- AND -encode- THE INDEX VS MEAN DISTINCTION
reshape long ΔOROAt1_ ΔOROAt2_ ΔOROAt3_ ΔOROAt4_ ΔOROAt5_, ///
    i(pair_num) j(_j) string
encode _j, gen(j)

//    DO A FIXED EFFECTS REGRESSION ON j
//    AND INCLUDE SIZE AS A COVARIATE TO ADJUST FOR IT
xtset pair_num j
forvalues i = 1/5 {
    xtreg ΔOROAt`i'_ i.j c.SIZE, fe

Note: Not tested, so there may be some typos or other glitches, but this is the gist of it, and I do believe the code is correct, even if I can't be certain.

The loop over i = 1/5 will then do this comparison for each of the 5 ΔOROAt* variables to the corresponding mean_ version. The estimated difference, adjusted for SIZE, is given by the coefficient of 2.j (which will be displayed as" mean" under the j heading) in the regression output, and, as with all regression outputs, if you are interested in statistical tests or confidence intervals, those are there as well.

[Carl-Johan Andersson]

Thanks.

First, I am not really sure how they are already matched on FISCALYEAR. Have we already taken year fixed effects into account in the matching?

The code seems to work fine, although I notice SIZE is omitted due to collinearity. What is the interpretation of that?
This is the output for ΔOROAt5:

note: SIZE omitted because of collinearity

Fixed-effects (within) regression               Number of obs     =        668
Group variable: pair_num                        Number of groups  =        404

R-sq:                                           Obs per group:
     within  = 0.0060                                         min =          1
     between = 0.0005                                         avg =        1.7
     overall = 0.0020                                         max =          3

                                                F(2,262)          =       0.78
corr(u_i, Xb)  = 0.0015                         Prob > F          =     0.4575

------------------------------------------------------------------------------
    ΔOROAt5_ |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
           j |
      index  |   .0145046   .0116189     1.25   0.213    -.0083738    .0373829
       mean  |    .006239   .0116189     0.54   0.592    -.0166394    .0291173
             |
        SIZE |          0  (omitted)
       _cons |   .0163663   .0090408     1.81   0.071    -.0014356    .0341682
-------------+----------------------------------------------------------------
     sigma_u |  .10468767
     sigma_e |  .09439265
         rho |  .55157497   (fraction of variance due to u_i)
------------------------------------------------------------------------------
F test that all u_i=0: F(403, 262) = 1.74                    Prob > F = 0.0000

This result tells me that firm performance 5 years after turnover is not different from the matched control group sample.

On an earlier note about the following hypotheses:
H2: Whether CEO succession is forced or voluntary does not affect subsequent firm performance.
H3: Whether a CEO succession candidate is appointed from inside or outside the firm does not affect subsequent firm performance.

I understand I cannot reject them using the earlier specified "non-interaction" model - but can I do two these separate regressions:

∆OROA_(t+5)= α + β1FORCED + β2SIZE + Year Fixed Effects + ε
∆OROA_(t+5)= α + β1OUTSIDE + β2SIZE + Year Fixed Effects + ε

And infer something meaningful about the hypotheses?

[Clyde Schechter]

First, I am not really sure how they are already matched on FISCALYEAR. Have we already taken year fixed effects into account in the matching?

They are matched on FISCALYEAR because the -collapse- command that calculates the mean-* variables contains FISCALYEAR in the -by()- option. So the only observations that are included in the calculation of mean are observations that have the same value of FISCALYEAR.

The code seems to work fine, although I notice SIZE is omitted due to collinearity. What is the interpretation of that?

Ah, yes, I should have foreseen that problem. The data you are starting from here (as illustrated in #17) only has SIZE information for the TURNOVER firms, and no information about SIZE in the controls. Without that, the value of SIZE from the turnover firm gets dragged along into the SIZE variable for the control observations after -reshape-. As a result, SIZE does not vary within the matched pair, and hence it is colinear with the pair-level fixed effect. It is not possible to adjust for SIZE from a data set that has no information about the size of the controls. That will need to be included as a variable, and the -reshape- will have to be modified to deal with it.

It is not obvious to me how you want to deal with size in the controls. Each turnover event has, potentially, several different firms that contribute to the calculation of mean_∆OROAt*. As the pairing of turnover events with non-turnover firms in that code in #17 does not match on or in any way restrict size, these different control firms will generally have different sizes. Since you are ultimately reducing to one observation per turnover event, you will need to decide how you want to designate a "size" for that group of controls as a whole. Do you want the mean? The median? The largest? The smallest? Something else?

Regarding H2 and H3, you need to give up on those. There is no valid way to do this. You are trying to test hypotheses about something that does not exist. Sure you can estimate those regressions. But they are garbage regressions because they don't include the interaction term, and we already know that the interaction effect is huge, so the results of those regressions is simply incorrect and misleading. Please reread what I wrote earlier (I think it was in the other thread) about the basketball coaching intervention.

[Carl-Johan Andersson]

Thanks again.

Could you say that this is the regression model that we are estimating to test if the turnover group is different from the control group?
∆OROA_(t+5)= α + β1TURNOVER + β2SIZE + Year Fixed Effects + ε

I will have to think about how the handle the SIZE control. Thanks for the insights.

I understand. I guess I keep pushing for it since they make inferences of that kind in many previous studies in the area. I will have to rethink my hypotheses.

[Clyde Schechter]

∆OROA_(t+5)= α + β1TURNOVER + β2SIZE + Year Fixed Effects + ε

This is almost right. There is no separate Year Fixed Effects term here. Rather, the Year Fixed Effects are absorbed into, a part of, the ε. That's because the unit of analysis here is the matched pair, and the fixed effect is at the matched pair level (not the firm level), and the fiscal year is the same in both the turnover and the control firm within the pair (because of the -by()- option in -collapse-).

I understand. I guess I keep pushing for it since they make inferences of that kind in many previous studies in the area. I will have to rethink my hypotheses.

Well, just because others have done it before doesn't mean they were right to do it. Also, did those people find large interaction effects? If not, then H2 and H3 are perfectly reasonable hypotheses and you can estimate those parameters.

[Carl-Johan Andersson]

Thanks.

One last question on this topic then:
What is the difference really between testing turnover vs non-turnover using this regression:
∆OROA_(t+5)= α + β1TURNOVER + β2SIZE + ε (1)
And testing forced vs non-forced using this regression:
∆OROA_(t+5)= α + β1FORCED + β2SIZE + ε (2)

If the issue with (2) is the omitted interaction with OUTSIDE, why isn't that an issue in (1)?
After all, if there is an interaction between forced and outside (which clearly exists), wouldn't we expect an interaction with turnover and outside as well?

[Clyde Schechter]

If the issue with (2) is the omitted interaction with OUTSIDE, why isn't that an issue in (1)?
After all, if there is an interaction between forced and outside (which clearly exists), wouldn't we expect an interaction with turnover and outside as well?

No, we wouldn't expect an interaction with turnover and outside. In fact, such an interaction is not even possible because when turnover = 0, the variable outside is undefinable! The variable outside only exists and only makes sense when turnover = 1.

[Carl-Johan Andersson]

I understand - very helpful!

[Carl-Johan Andersson]

Received some feedback comments from my supervisor today regarding what we have discussed here.

1. About the hypotheses:
H2: Whether CEO succession is forced or voluntary does not affect subsequent firm performance.
H3: Whether a CEO succession candidate is appointed from inside or outside the firm does not affect subsequent firm performance.

"Keep the hypotheses as they are. Discuss them in the context of different turnovers. The critical aspect of this is that your current approach (regardless of whether it is with an interaction or not) does not let you claim anything related to the level changes, only the differences in performance changes between different groups. If you want to see how the performance in different turnover groups changed, you need to run a pre-post for each subsample separately. i.e. take eg voluntary insider turnovers, calculate average ROA changes, and test whether they are significantly different from 0 (also do that in a multivariate setting with controls). Do the same for all others as well."

2. On your comments on the interpretation of the interaction coefficient:

• The coefficient of the interaction term represents either of the following (they are the same):

1. The difference between the effects of forced and unforced turnovers on outcomes if the turnover is to an outsider.
2. The difference between the effects of turnover to an outsider or an insider on outcomes if the turnover is forced.

• FORCED and OUTSIDE are effects, whereas the interaction is a difference between effects.

"Not exactly. Interaction alone here is not directly interpretable. Rather, FORCED+OUTSIDE+INTERACTION (sum of coefficients) shows the effect for the forced&outside turnover, relative to all the other. Effectively, what you see is that forced internal does not has a significant effect, but forced external does. Voluntary external has some effect (performance declines, though), whereas voluntary internal is the baseline about which you cannot say much in from this test.
These tests give you an insight to differences among turnovers. You can do simple pre-post tests (maybe simply ttests) on subsamples for:
- voluntary inside
- voluntary outside
- forced inside
- forced outside
Then you would have insight not only about the differences between groups (current results), but also changes in groups."

3. On doing a marginal effects analysis:
"I am not sure why you want to do this at all."

I have to admit I am a bit confused now as how to interpret the supervisors different way of approaching this. Would very much appreciate your input.