63
T H E O R I A
eISSN 0495-4548 – eISSN 2171-679X
Theo ia, 2022, 37(1), 63-74
h ps://doi.o g/10.1387/ heo ia.22691
* Co espondence o: Jiji Zhang. Depa men o Religion and Philosophy, Hong Kong Bap is Uni e si y, Kowloon Tong, Kowloon, Hong
Kong–[email p o ec ed]–h ps://o cid.o g/0000-0003-0684-2084
How o ci e: Zhang, Jiji (2022). «On he uni y be ween obse a ional and expe imen al causal disco e y»; Theo ia. An In e na ional Jou nal o
Theo y, His o y and Founda ions o Science,37(1), 63-74. ( h ps://doi.o g/10.1387/ heo ia.22691).
Recei ed: 2021-04-06; Final e sion: 2021-06-21.
ISSN0495-4548 - eISSN2171-679X / © 2022 UPV/EHU
This wo k is licensed unde a
C ea i e Commons A ibu ion-NonComme cial-NoDe i a i es 4.0 In e na ional License
On he uni y be ween obse a ional and expe imen al causal disco e y
(Sob e la unidad en e el descub imien o causal obse acional y expe imen al)
Jiji Zhang*
Hong Kong Bap is Uni e si y
ABSTRACT: In “Flagpoles anyone? Causal and explana o y asymme ies”, James Woodwa d supplemen s
his celeb a ed in e en ionis accoun o causa ion and explana ion wi h a se o new ideas abou causal and ex-
plana o y asymme ies, which he ex ac s om some cu ing-edge me hods o causal disco e y om obse a-
ional da a. Among o he hings, Woodwa d d aws in e es ing connec ions be ween obse a ional causal dis-
co e y and in e en ionis hemes ha a e inspi ed in he i s place by expe imen al causal disco e y, alluding
o a so o uni y be ween obse a ional and expe imen al causal disco e y. In his pape , I make explici wha
I ake o be he implica ed uni y. Like expe imen al causal disco e y, obse a ional causal disco e y also elies
on in e en ions (o exogenous a ia ions, o be mo e accu a e), albei in e en ions ha a e no ca ied ou
by in es iga o s and hence need o be de ec ed as pa o he in e ence. The obse a ional pa e ns appealed o
in obse a ional causal disco e y a e no only su oga es o would-be in e en ions, as Woodwa d some imes
pu s i ; hey also se e o ma k ele an in e en ions ha ac ually happen in he da a gene a ing p ocess.
KEYWORDS: causal disco e y; exogenous a ia ion; in e en ion; in e en ionism; in a iance; obse a io-
nal da a.
RESUMEN: En “Flagpoles anyone? Causal and explana o y asymme ies”, James Woodwa d complemen a su
celeb ada eo ía in e encionis a de la causación y la explicación con nue as ideas sob e asime ías causales y expli-
ca i as, ex aídas de ecien es mé odos de descub imien o causal a pa i de da os obse acionales. En e o as cosas,
Woodwa d es ablece in e esan es conexiones en e el descub imien o causal obse acional e ideas in e encionis-
as inspi adas inicialmen e en el descub imien o causal expe imen al, aludiendo a cie a unidad en e el descub i-
mien o causal obse acional y expe imen al. Al igual que el descub imien o causal expe imen al, el descub imien o
causal obse acional ambién se apoya en in e enciones (o a iaciones exógenas, pa a se más p ecisos), aunque
sean in e enciones que no son ealizadas po in es igado es y po an o ienen que se de ec adas como pa e de la
in e encia. Los pa ones obse acionales a los que se apela en el descub imien o causal obse acional no son los sus i-
u os de posibles in e enciones, como Woodwa d algunas eces sugie e; ambién si en pa a ma ca in e enciones
ele an es que de hecho ienen luga en el p oceso de gene ación de da os.
PALABRAS CLAVE: descub imien o causal; a iaciones exógenas; in e ención; in e encionismo; in a iancia;
da os obse acionales.
Jiji Zhang
64 Theo ia, 2022, 37/1, 63-74
1. In oduc ion
Fo se e al decades now, how o disco e causal ela ions be ween a iables using s a is ical
me hods has been a igo ous esea ch p og am pu sued in se e al ields. One o he main
goals is o in en p incipled and eliable ways o in e which a iable has a (di ec ) causal
in luence on o is (di ec ly) causally ele an o which a iable in a mul i a ia e sys em,
om obse a ional da a and wi hou p io knowledge o assump ion abou he causal o -
de . The e m ‘obse a ional’ is used o indica e he absence o any ac i e con ol o manip-
ula ion by in es iga o s o he da a gene a ing p ocess unde in es iga ion; obse a ional
da a a e, so o speak, gene a ed by he sys em o in e es unning i s na u al cou se. By con-
as , expe imen al da a a e gene a ed by a p ocess ha includes ac i e con ol o manipu-
la ion by in es iga o s. A pa adigma ic example is a andomized con olled ial, whe e he
alloca ion o ea men s is designed and adminis e ed by he in es iga o s (wi h a andomi-
za ion scheme). Causal in e ence based on expe imen al da a is ega ded as by and la ge
mo e eliable han ha based on obse a ional da a, bu he impo ance and po en ial o
he la e a e ge ing inc easingly acknowledged and app ecia ed, due on he one hand o
he ela i e abundance o obse a ional da a, especially in he e a o big da a, and on he
o he hand o signi ican me hodological ad ances in ecen yea s (Pe e s e al., 2017).
James Woodwa d’s ich and illumina ing a icle (Woodwa d, 2022) amply demon-
s a es ha he cu ing-edge me hods o causal disco e y om obse a ional da a (o
obse a ional causal disco e y as I will hence o h call i ) ha e no el implica ions o
philosophical heo izing abou causal and explana o y asymme ies. A champion o he in-
luen ial in e en ionis app oach o causa ion and explana ion, Woodwa d d aws in e -
es ing connec ions be ween obse a ional causal disco e y and in e en ionis hemes ha
a e inspi ed in he i s place by expe imen al causal disco e y, alluding o, as I unde s and
i , a so o uni y be ween obse a ional and expe imen al causal disco e y. In his pape I
ollow up on his issue and make he implica ed uni y mo e explici . My main hesis is ha
like expe imen al causal disco e y, obse a ional causal disco e y, when applicable, also e-
lies on in e en ions (o exogenous a ia ions, o be mo e accu a e), albei in e en ions
ha a e no ca ied ou by in es iga o s and hence need o be iden i ied as pa o he in e -
ence. Obse a ional causal disco e y is epis emologically mo e challenging in la ge pa be-
cause o he addi ional need o in e he loci o in e en ions.
To p oceed, I will i s e iew in Sec ion 2 some dis inc i e ea u es o Woodwa d’s
(2003) no ion o an in e en ion, and wo ways in which his no ion is used o cha ac e -
ize he p esence o a causal ela ion. I sugges ha he essen ial elemen in Woodwa d’s no-
ion o in e en ion is a no ion o exogenous a ia ion, and ha al hough Woodwa d p e-
e s no o build a condi ion o in a iance o mechanism-p ese a ion in o he no ion o an
in e en ion, he kind o in e en ion o exogenous a ia ion ha ma e s in causal in e -
ence mus sa is y some condi ion o in a iance. This makes salien he possibili y o some-
imes de ec ing exogenous a ia ion h ough in a iance, which is ela ed o Woodwa d’s
la es discussion o a alue- ela ionship independence/in a iance p inciple o causal dis-
co e y. Then, in Sec ion 3, I b ie ly ecall Richa d Scheines’s (2005) a gumen ha he in-
e ence o he p esence o a causal ela ion using obse a ional condi ional dependence and
independence ela ions is essen ially he same as he in e ence based on expe imen al da a.
I sugges ha he essen ial common elemen is ha hey bo h in e he p esence o a causal
ela ion be ween wo a iables om hei co a ia ion in which one a iable’s a ia ion is
h ps://doi.o g/10.1387/ heo ia.22691 65
On he uni y be ween obse a ional and expe imen al causal disco e y
(known o assumed o in e ed o be) exogenous wi h espec o he o he . I apply his idea,
in Sec ion4, o examine he mo e ecen and powe ul me hods o obse a ional causal dis-
co e y discussed by Woodwa d (2022), sugges ing sub le modi ica ions o some o his in-
e p e a ions while endo sing his main poin s. I close in Sec ion5 wi h b ie concluding e-
ma ks.
2. Woodwa d’s concep ion o in e en ion
In his seminal wo k, Woodwa d (2003, p. 98) p esen ed a ca e ul de ini ion o wha coun s
as an in e en ion on one a iable wi h espec o ano he . Fo p esen pu poses, we need
no go in o mo e de ails han no ing a ew ea u es o he accoun . Fi s , Woodwa d ex-
plici ly ela i izes an in e en ion on a a iable wi h espec o ano he a iable, so we alk
abou an in e en ion on a iable X wi h espec o a iable Y a he han an in e en ion
on X simplici e . Second, an in e en ion on X wi h espec o Y is ep esen ed as an in e -
en ion a iable aking a alue, and he co e equi emen o an in e en ion a iable o
X wi h espec o Y is ha i in luences Y, i a all, only h ough X and is s a is ically inde-
penden o all o he a iables ha in luence Y wi hou going h ough X.1 Thi d, and e y
impo an o my hesis, an in e en ion does no necessa ily in ol e a human ac ion; any
ga den- a ie y a iable may se e as an in e en ion a iable o X wi h espec o Y as long
as i s ands in he igh causal ela ions wi h X and Y. Fou h, an in e en ion is no e-
qui ed o be mechanism-p ese ing; ha is, i is possible ha an in e en ion on X wi h e-
spec o Y changes how Y is a ec ed by X ( hough by de ini ion, his e ec o he in e en-
ion canno be a esul o he in e en ion a ec ing causes o Y whose in luences do no go
h ough X.)
The es ic ion o single ons in he i s ea u e is no essen ial. Woodwa d’s de ini ion
can be easily ex ended o co e in e en ions on a se o a iables wi h espec o ano he
se o a iables, bu o his main pu poses he e sion o single ons is su icien . The hi d
ea u e Woodwa d e e s o as nonan h opomo phism. A s aigh o wa d implica ion o
his ea u e is ha e en hough no in e en ion is ca ied ou by in es iga o s in an obse -
a ional s udy, an in e en ion on a a iable o in e es wi h espec o ano he may none-
heless ha e aken place. The e o e, i is a leas cohe en o say ha obse a ional causal
disco e y also elies on in e en ions.
The ou h ea u e is p obably he mos dis inc i e and con o e sial. As is no ed by
Woodwa d, many o he in luen ial accoun s o in e en ions o manipula ions, such as
hose o Spi es e al. (2000) and Pea l (2009), build in some e sion o a mechanism-p es-
e a ion o in a iance condi ion. Woodwa d’s main wo y ega ding hose accoun s is ha
1 In Woodwa d (2003), ano he equi emen pu down o an in e en ion a iable o X is ha he e
a e some possible alues o he a iable such ha when he a iable akes hese alues, X ceases o de-
pend on i s o he causes and depends solely on he in e en ion a iable. These alues implemen wha
a e some imes e e ed o as “ha d” o “su gical” in e en ions. Howe e , in he subsequen de ini ion
o an in e en ion, he e does no seem o be any equi emen ha hese alues be aken by he in e -
en ion a iable in an in e en ion. In any case, Woodwa d (2022) also alks abou “so ” in e en ion
a iables, so I will assume in his pape ha his equi emen is no imposed on an in e en ion a i-
able.
Jiji Zhang
66 Theo ia, 2022, 37/1, 63-74
he no ion o in e en ion on X wi h espec o Y would hen al eady in oke he causal e-
la ionship be ween X and Y, and o use such a no ion as he does o cha ac e ize he causal
ela ionship be ween X and Y would smell o a po en ially objec ionable kind o ci cula i y.
This is an in e es ing poin , bu mo e ele an o my p esen pu pose is an appa en di i-
cul y wi h he mo e libe al no ion o an in e en ion. To see he di icul y, le us compa e
wo ways a causal ela ion be ween X and Y may be cha ac e ized in Woodwa d’s ame-
wo k.
One way is o say ( oughly) ha
(1) X is a ( ype-le el) cause o Y i and only i he e is an in e en ion on X wi h e-
spec o Y ha would change he alue o X, unde which he alue (o p obabili y
dis ibu ion) o Y would also change.
Woodwa d (2003, p. 108) conside ed he possibili y ha i an in e en ion is no e-
qui ed o be mechanism-p ese ing, hen some in e en ions may end up des oying he
causal in luence o X on Y and no changing he alue o Y. As he igh ly poin ed ou , his
possibili y does no h ea en (1), whose igh hand side is exis en ially quan i ied. How-
e e , I wo y abou he possibili y o a “ alse posi i e”: an in e en ion on X wi h espec
o Y ha is no mechanism-p ese ing may change he alue o Y, in which case X is de-
cla ed a cause o Y by (1), bu in ui i ely a mechanism-al e ing in e en ion is no a good
es o he p e-in e en ion causal ela ion be ween X and Y. This issue becomes mo e sali-
en i we compa e (1) o ano he way o cha ac e izing he causal ela ionship be ween X
and Y, which goes h ough a no ion o in a iance. Al hough Woodwa d does no equi e
e e y in e en ion on X wi h espec o Y o p ese e wha e e causal mechanism he e
is be ween X and Y, in a iance unde some such in e en ions is ega ded as a necessa y
condi ion o a gene aliza ion ela ing X and Y o be causal (wi h he causal di ec ion go-
ing om X o Y).2 Since, as I hink i is sa e o assume, X is a ( ype-le el) cause o Y only i
hey a e ela ed by a ue gene aliza ion ha is causal (wi h he di ec ion om X o Y), we
can also say ha
(2) X is a ( ype-le el) cause o Y only i he e is a ue gene aliza ion ela ing X and Y
and an in e en ion on X wi h espec o Y such ha he gene aliza ion emains
ue unde he in e en ion.
Call an ins ance ha makes an exis en ially quan i ied s a emen ue a wi nessing in-
s ance. A wi nessing in e en ion o he igh hand side o (2) is equi ed o sa is y a kind
o in a iance o mechanism-p ese a ion, whe eas a wi nessing in e en ion o ha o
(1) is appa en ly no . Gi en how cen al he no ion o in a iance is in Woodwa d’s ac-
coun o causal and explana o y gene aliza ions, his appa en disc epancy be ween (1) and
(2)should p obably be esol ed o accoun ed o in a o o (2). This does no mean ha
(1) mus be ex ensionally inadequa e wi hou an explici equi emen o in a iance, be-
cause i may be a gued ha only a mechanism-p ese ing in e en ion can sa is y he p op-
2 The e is a small echnical ca ch in ega ding i as a su icien condi ion, and Woodwa d in oduces a
u he quali ica ion called a es ing in e en ion o ende he necessa y condi ion also su icien (see
also Woodwa d and Hi chcock, 2003). Since I can make my poin wi hou en e ing ha complica-
ion, I will jus wo k wi h an “only i ” s a emen he e.
h ps://doi.o g/10.1387/ heo ia.22691 67
On he uni y be ween obse a ional and expe imen al causal disco e y
e y s a ed in he igh hand side o (1), o ha whene e he e is a wi nessing in e en ion
ha is no mechanism-p ese ing, he e is also a wi nessing in e en ion ha is. Bu i sug-
ges s s ongly ha he kind o in e en ion ha ma e s o causal in e ence in he spi i o
(1) needs o sa is y some condi ion o mechanism-p ese a ion. Mo eo e , al hough he
addi ional equi emen o en amoun s o jus ano he assump ion, i also c ea es he op-
po uni y o some imes de ec ing he p esence o an in e en ion by checking in a iance
o some su oga e p ope y o a hypo hesized causal gene aliza ion. We will e u n o his
poin in Sec ion 4.
Finally, i we look back a he second ea u e no ed ea lie o Woodwa d’s cha ac e i-
za ion o an in e en ion, oge he wi h he cha ac e iza ion o a causal ela ion be ween X
and Y gi en in (1), i is clea ha he ele an ole o an in e en ion on X wi h espec o Y
in he con ex o causal in e ence is o c ea e a change o a ia ion in X ha is no due o a
change in Y no associa ed wi h any a ia ion in a cause o Y whose in luence on Y does no
go h ough X. Call such a a ia ion an exogenous a ia ion o X wi h espec o Y. I suspec
ha mos i no all o he insigh s o in e en ionism can be ecas in e ms o a no ion o
exogenous a ia ion. I will no explo e he e how easible and desi able i is o e o mula e
in e en ionis heo ies in e ms o exogenous a ia ion, bu a po en ial ad an age is wo h
no ing: he no ion o exogenous a ia ion, unlike he no ion o in e en ion-induced a i-
a ion, accommoda es he possibili y o spon aneous and uncaused a ia ions o a a iable
ha a e none heless exogenous wi h espec o ano he a iable and a e he e o e as good as
in e en ion-induced a ia ions o he pu pose o p obing he causal ela ion be ween he
a iables.
This ad an age is pe haps me ely heo e ical. I is plausible o hink ha in p ac ical
causal in e ence, exogenous a ia ions always esul om some in e en ions. E en so, as I
will s ess la e , obse a ional causal disco e y elies hea ily on de ec ing in e en ions (as
opposed o in e en ions known in ad ance, as in expe imen al causal disco e y), bu in
many cases, no in e en ion a iable is explici ly loca ed, and i is, s ic ly speaking, only he
exogenei y o a ia ion ha is de ec ed.
3. Scheines on he simila i y be ween obse a ional and expe imen al causal disco e y
In addi ion o Woodwa d (2022), ano he inspi a ion o he main hesis o his pape is
he insigh o Scheines (2005). Scheines compa ed he basic a ionale o expe imen al in-
e ence o a causal ela ion be ween wo andom a iables and ha o obse a ional in e -
ence o a causal ela ion based on g aphical modelling, whe e a di ec ed g aph is aken o
ep esen bo h a causal s uc u e and a s a is ical model de ined by a se o s a is ical condi-
ional independence cons ain s (Pea l, 1988, 2009; Spi es e al., 2000). The simila i y be-
ween hem highligh ed by Scheines is depic ed in Figu e 1. In Figu e 1(a), he p esence o
a causal in luence o X on Y ( ep esen ed by he a ow om X o Y) is in e ed based on an
expe imen al in e en ion on X, whe e he p obabili y dis ibu ion o X is known (o as-
sumed) o be de e mined by an in e en ion a iable (say, a andomizing de ice) IX, and
he s a is ical dependence be ween X and Y unde his in e en ion is aken o be e idence
o he causal in luence o X on Y. In Figu e 1(b), he p esence o a causal in luence o X on
Y is in e ed om passi e obse a ions on X and Y as well as some o he a iables such as Z1
and Z2. Suppose he obse a ions u n ou o wa an he s a emen ha Z1 is s a is ically
Jiji Zhang
68 Theo ia, 2022, 37/1, 63-74
independen o Z2 (condi ional on he emp y se ) and he s a emen ha hey a e s a is i-
cally independen o Y condi ional on X, oge he wi h a numbe o condi ional depend-
ence s a emen s.3 Unde wo assump ions known as he causal Ma ko condi ion and he
Fai h ulness o S abili y condi ion (Spi es e al., 2000; Pea l, 2009), i ollows om hese
condi ional independence and dependence s a emen s ha X does no ha e a causal in lu-
ence on ei he Z1 o Z2 (as ep esen ed by he a owheads a X on he edges be ween Z1
and X, and be ween Z2 and X), and ha X has a causal in luence on Y (as ep esen ed by
he a ow om X o Y).
Scheines calls a a iable such as Zi (ei he Z1 o Z2) in Figu e 1(b) a de ec ible ins u-
men ( o X wi h espec o Y) and s esses he ollowing simila i y be ween such a de ec -
ible ins umen and he in e en ion a iable IX in Figu e 1(a): bo h a e adjacen o X bu
no adjacen o Y in he espec i e causal g aph, and nei he is in luenced by X. As Scheines
akes some ca e o explain, ha ing a a iable wi h hese ea u es allows an in e ence om
ce ain obse ed s a is ical ela ions o he p esence o a causal a ow om X o Y. Tha is
why he calls such a a iable an ins umen ( o causal in e ence conce ning X and Y). In
obse a ional causal disco e y such a a iable is no known in ad ance o be an ins umen
bu i s s a us as an ins umen is some imes de ec ible om da a, as he simple example in
Figu e 1(b) illus a es.
Figu e 1
Scheines’s (2005) compa ison be ween expe imen al causal disco e y and (a p ominen app oach o)
obse a ional causal disco e y: (a) expe imen al in e ence o a causal a ow om X o Y based
onin es iga o s’ in e en ions on X wi h espec o Y; (b)obse a ional in e ence o a causal a ow
om X o Y based on de ec ing Z1 o Z2 as an ins umen .
A di e ence be ween Zi in Figu e 1(b) and IX in Figu e 1(a) is also no ed by Scheines.
The o me is no necessa ily a cause o X, as indica ed by he ci cle a Zi on he edge be-
ween Zi and X,4 whe eas he la e is a cause o X. In o he wo ds, Zi could be bu is no
3 Namely, Z1 and X a e dependen condi ional on any subse o he o he a iables, and so a e Z2 and
X, and a e X and Y, which is why each o hese pai s o a iables has an edge be ween hem in Fig-
u e1(b).
4 In he amewo k Scheines (2005) wo ks wi h, Zi o® X means oughly ha i could be Zi ® X, in which
case Zi is a cause o X, o Zi « X, in which case Zi is no a cause o X bu he e is a common cause o Zi
and X.
h ps://doi.o g/10.1387/ heo ia.22691 69
On he uni y be ween obse a ional and expe imen al causal disco e y
necessa ily a (so ) in e en ion a iable o X wi h espec o Y.5 One way o iew he ole
o Zi in his simple example is ha e en i i is no i sel an in e en ion a iable o X wi h
espec o Y, i is a su oga e o an unobse ed in e en ion a iable o X wi h espec o
Y (namely, an unobse ed common cause o X and Zi). F om his pe spec i e, he exam-
ple illus a es he idea o de ec ing in e en ions in obse a ional causal in e ence, in e -
en ions ha a e no ca ied ou by in es iga o s. Ano he , closely ela ed bu on my iew
mo e ap concep ion is ha he de ec ed ea u es o Zi se e o show ha some a ia ion o
X is exogenous wi h espec o Y, and he accompanying co a ia ion o Y implies ha X has
a causal in luence on Y. As explained by Scheines, he in e ence in his case is no jus ha
X is a cause o Y, bu mo eo e ha he e is no unobse ed common cause o X and Y (see
also he no ion o “ isibili y” in Zhang, 2008). Since his simple example does no con ain
any obse ed common cause ei he , i is, so o speak, he whole a ia ion o X ha is de-
ec ed o be exogenous wi h espec o Y. In mo e complex cases, i will be he a ia ion o
X condi ional on o adjus ed o some obse ed a iables ha is de ec ibly exogenous wi h
espec o Y. Such exogenous a ia ions a e pe haps mos plausibly in e p e ed as esul ing
om ce ain (so ) in e en ions on X wi h espec o Y, bu concep ually hey do no ha e
o be. In any case, only a su oga e o an in e en ion a iable may be de ec ed in such in-
e ences.
4. Mo e ecen ad ances in obse a ional causal disco e y
The kind o obse a ional causal disco e y discussed by Scheines (2005) emains a majo
app oach o in e ing causal s uc u es om obse a ional da a. Howe e , since 2006, a
ple ho a o o he me hods o obse a ional causal disco e y ha e been p oposed and e-
ined, some o which a e mo e powe ul a leas in he ollowing espec : unde sui able
assump ions, hey can eliably in e he causal ela ion be ween wo a iables wi hou ap-
pealing o any de ec ible ins umen in Scheines’s sense. These mo e ecen ad ances in ob-
se a ional causal disco e y igu e cen ally in Woodwa d’s (2022) new accoun s o causal
and explana o y asymme ies. I submi ha al hough hese me hods do no p oceed by
iden i ying an obse ed a iable as an in e en ion a iable o a su oga e he eo , he de-
ec ion o exogenous a ia ions s ill plays a pi o al ole in hem.
Conside i s he class o me hods ha employ he se up o noisy unc ional causal
models. Fo simplici y, I will ollow Woodwa d (and Scheines) o ocus a en ion on he
ask o in e ing he causal ela ion be ween wo a iables X and Y. The basic se up o
many o hese me hods is o assume ha he e ec a iable is a unc ion o he cause a ia-
ble and a noise o e o e m ha is s a is ically independen o he cause a iable. Thus, as-
suming wi hou loss o gene ali y ha he causal a ow goes om X o Y, hen i is assumed
ha he causal gene aliza ion ela ing X and Y can be p ope ly ep esen ed as Y= (X,N),
o some unc ion (o a ce ain o m) and some noise e m N (o a ce ain ype) such ha
5 To epea he cla i ica ion s a ed in oo no e 1, I am ollowing Woodwa d (2022) o allow in e en-
ion a iables o be “so ”, in ha hey a e no equi ed o elie e he a ge a iable o dependence on
o he causes, bu only equi ed o sa is y he o he condi ions in Woodwa d’s (2003) de ini ion o an
in e en ion a iable.
Jiji Zhang
70 Theo ia, 2022, 37/1, 63-74
X and N a e s a is ically independen . As is obse ed by Woodwa d (2022, p. 34), one con-
sequence o such an assump ion is ha he noise e m N can be iewed as a (so ) in e en-
ion a iable o Y wi h espec o X. This way o hinking o he noise e m is wa an ed
i he noise e m is in e p e ed as ep esen ing omi ed causes o Y, an in e p e a ion ha
seems commonly adop ed in p ac ice. Bu again, e en i he noise e m is no in e p e ed
as a cause o Y, bu is ins ead ega ded as ep esen ing a genuinely s ochas ic componen in
he gene a ion o a alue o Y om a alue o X (S eel, 2005), i can s ill be iewed as pick-
ing ou a pa o he a ia ion o Y ha is exogenous wi h espec o X.
Mo e impo an o my p esen pu pose is he ollowing poin alluded o by Wood-
wa d. I he causal mechanism be ween X and Y is co ec ly ep esen ed as Y= (X,N),
wi h X and N being s a is ically independen , hen wha e e gene a e he alues o X “op-
e a e so as o change he alue o X in a way ha is independen o he o he causes o Y”
(Woodwa d, 2022, p. 34), and so may be ega ded as in e en ions on X wi h espec o
Y, o a any a e as exogenous a ia ions o X wi h espec o Y (e en i hey a e somehow
spon aneous and uncaused). F om his iewpoin , i is use ul o hink o he i ing o a
noisy unc ional causal model as po en ial e idence o de ec ing in e en ions o exog-
enous a ia ions: i da a suppo he hypo hesis o a unc ional ela ionship Y= (X,N)
wi h s a is ical independence be ween X and N, hen i may be e idence ha he obse ed
a ia ion o X is exogenous wi h espec o Y.
I is no necessa ily e idence because i is some imes possible o i such a model come
wha may, e en when X does no cause Y. The bes known example is ha i X and Y ol-
low a bi a ia e Gaussian dis ibu ion, hen i always i s Y= (X, N) o some linea unc-
ion and some Gaussian noise N ha is independen o X. On he o he hand, i no e-
s ic ion is pu down on o N, hen i is always possible o i a noisy unc ional causal
model o any wo andom a iables wi h con inuous suppo (Hy ä inen and Pajunen,
1999; Zhang e al., 2014). Howe e , unde some es ic ions, such as linea non- Gaussian
acyclic models (LiNGAM, Shimizu e al., 2006), addi i e noise models (ANM, Hoye
e al., 2009), o pos -nonlinea models (PNL, Zhang and Hy ä inen, 2009), i becomes
non i ial o sa is y he equi emen o s a is ical independence be ween he noise e m
and he hypo hesized cause. I has been shown ha ei he always ( o LiNGAM) o ge-
ne ically ( o ANM and PNL), his equi emen can be me o a mos one causal di ec-
ion: i he join p obabili y dis ibu ion o X and Y is compa ible wi h a gene aliza ion
Y= (X,N) sa is ying he model es ic ions such ha X and N a e s a is ically independ-
en , hen i is no compa ible wi h any gene aliza ion X=g(Y,N’) sa is ying he model
es ic ions such ha Y and N’ a e s a is ically independen . Mo eo e , i is clea ha o
LiNGAM models, i X and Y a e con ounded by an unobse ed common cause, hen unde
a sui able ai h ulness assump ion, he equi emen o s a is ical independence be ween he
noise e m and he hypo hesized cause can be me in nei he di ec ion (En ne and Hoye ,
2010). I suspec ha his is also gene ically he case o ANM and PNL models.
Wi h such model es ic ions, a s anda d p ocedu e o in e a causal ela ion om an
obse ed co a ia ion be ween X and Y is based on checking whe he a noisy unc ional
causal model (sa is ying he model es ic ions) is wa an ed by da a in ei he di ec ion. I
i is wa an ed in one di ec ion bu no in he o he , hen he o me di ec ion is in e ed
o be he causal di ec ion. Such a p ocedu e is usually aken o assume in he i s place ha
he e is no unobse ed con ounding and he ask is o decide be ween wo hypo heses: ha
X causes Y (wi hou con ounding) o ha Y causes X (wi hou con ounding). Howe e ,
h ps://doi.o g/10.1387/ heo ia.22691 71
On he uni y be ween obse a ional and expe imen al causal disco e y
we may also hink o he p ocedu e as ying o de ec in e en ions o exogenous a ia-
ions, using he asymme ic possibili y o i ing a sui able model as a c i e ion. Viewed his
way, he p ocedu e may o may no e u n an in o ma i e answe , depending on whe he
he c i e ion is o is no me o judging a a iable o ha e an exogenous a ia ion wi h e-
spec o he o he a iable in hei co a ia ion. I an unin o ma i e answe o suspension o
judgemen is allowed, i is unnecessa y o assume away la en con ounding and o ce a se-
lec ion be ween wo hypo heses o an uncon ounded causal ela ion. When we canno i
a noisy unc ional causal model in ei he di ec ion, an op ion is o emain silen abou he
causal ela ion be ween X and Y (and sugges ha he e is p obably a la en con ounde ),
because no sui able exogenous a ia ion is de ec ed.
Mo eo e , e en when he e is con ounding and he a ia ion o ei he a iable is no
en i ely exogenous wi h espec o he o he , i may be possible o iden i y pa s o he a i-
a ions ha a e exogenous and exploi hem o d aw in o ma i e causal in e ence. As men-
ioned ea lie , he se up o noisy unc ional causal models ende s he noise e ms a so o
in e en ion a iables o p oxies o exogenous a ia ions. Some imes hey may be eco e -
able om da a o a su icien ex en e en when he e is la en con ounding, and be used o
in e causal ela ions. A case in poin is he app oach o in e ing LiNGAM models based
on independen componen analysis (ICA). E en when la en con ounding is p esen , how
obse ed a iables depend on he exogenous noise e ms can be su icien ly eco e ed un-
de a ai h ulness assump ion using he so-called o e comple e ICA, so ha he acyclic
causal s uc u e among he obse ed a iables can s ill be in e ed (Hoye e al., 2008; Sale-
hkaleyba e al., 2020).
In addi ion o he me hods based on noisy unc ional causal models, Woodwa d
(2022) discussed a class o me hods ha exempli y wha he calls he alue- ela ionship in-
dependence/in a iance (VRI) p inciple. As I unde s and i , he VRI p inciple is a u he
elabo a ion o en ichmen o Woodwa d’s cha ac e iza ion o causal and explana o y gen-
e aliza ions in e ms o in a iance unde in e en ions (as we empha ically e iewed in Sec-
ion2). An impo an new elemen is ha in a iance unde in e en ions can some imes
be indica ed by o in e ed om a so o “independence” be ween a ia ions in hypo h-
esized cause a iables and he hypo hesized gene aliza ion ela ing he cause a iables o an
e ec a iable. The la e , in u n, may be in e ed om obse a ional da a in a ious ways.
Conside again he basic ask o in e ing he causal ela ion be ween wo a iables X and Y
o illus a ion. The idea is ha a hypo hesized gene aliza ion ela ing X o Y, ei he ep e-
sen ed by a unc ional ela ionship Y= (X) (as in, e.g., Janzing e al., 2012) o ep esen ed
by he condi ional p obabili y unc ion P(Y|X) (as in, e.g., Zhang e al., 2015), may be
judged o be “independen ” o a ia ions o X, acco ding o a ious c i e ia o “independ-
ence” ha can be checked based on obse a ional da a. This “independence”, acco ding
o Woodwa d, is a “su oga e o o indica o o ” he no ion o in a iance unde in e en-
ions.
I ind his iewpoin compelling, bu would like o highligh a poin ha is no su i-
cien ly s essed in Woodwa d’s discussion. In he cases whe e we de ec he desi ed “inde-
pendence” be ween a ia ions o X and a hypo hesized gene aliza ion ela ing X o Y (and
no such “independence” in he o he di ec ion), and on his basis in e ha X is a cause
o Y, we a e also commi ed o in e ing ha wha e e gene a es he obse ed alues o
X amoun s o a Woodwa dian in e en ion on X wi h espec o Y, o a any a e cons i-
u es exogenous a ia ions o X wi h espec o Y (e en i hey a e somehow spon aneous
