CAUSALITY
AND ECONOMETRICS
Arnold
ZELLNER*
ofChicago
University
I. Introduction Although philosophical sciences
the concept literature
including
methodology exclude
of causality
and
used
econometrics,
terms like causality
econometrics
textbooks
issue of the relationship
extensively almost
of econometrics,
that
if anything,
the concepts
by taking note of the following 1.
On the opening
price the&y, prediction,
is in turn
That
knows
‘causes’ a particular
its occurrence.” defined,
Although
perhaps
because
Indeed
even about
these
the age-old
and causality.
were irrelevant
concept
to or unimportant
observations:
phenomena. what
control
indexes.
the
principles,
That such is not the case is easily established (1949,
“The important
and prediction
in many
texts to treat the fundamental
page of Stigler’s
he writes,
in the
treating
and/or
of correlation
if this concept
and econometrics.
data
theory
and cause from their subject
between
extensively
in interpreting
is, econometric
also say little,
could be excused
for economics
treated
all, if not all, textbooks
The glaring failure of econometrics of causality
has been
requires
p. 3) influential
purpose sought
of a scientific because
prediction
it permits
is self-evident,
phenomenon,
one cannot
the word causes in this quotation its meaning
is thought
textbook
on
law is to permit control
over
for unless effect
is central,
to be self-evident
one
or prevent it is not or, more
likely, because its meaning is rather controversial, hence the use of quotation marks. Be that as it may, causation is clearly a central concept in Stigler’s discussion
of the purpose
econometrics. 3I. Cowles edited ment
Commission
by T.C. Koopmans of econometrics,
of scientific
laws that appear
Monograph
14, Studies
in price theory
in .Fconometric
and W.C. Hood, a key contribution
includes
a paper by H. Simon (1953)
causal orderings. 3. In the 1950s and 196Os, controversies
regarding
and
Method,
to the developon the nature
of
the causal interpretation
of econometric models involving H.A.O. Wold, R.L. Basmann, R.H. Strotz, and others raged in the literature, giving evidence of much concern and no little confusion dependent
regarding the causal interpretation of fully recursive or simultaneous econometric models. Given confusion
*
and interabout the
Research financed in part by National Science Foundation Grant 7745662 and by income H.G.B. Alexander Endowment Fund, Graduate School of Business, University of Chicago.
9
from the
causal interpretation the relation
of econometric
of these models
models,
there was also confusion
to the scientific
regarding
laws that they were supposed
to
represent. 4.
The
papers
more
recent
in which
various
tests
startling
results.
economic
of causality
to
the
econometrics. causality
importance
of
is thus considered
the
produced
concept
for the difficulties
by statements
namely,
interventions
of causality
in economics
omission,
and
to say about
one that may be in
that some have in understanding recent
analyses
definition
of causality
of a causal relation
with the economist’s
the are
in the form of imposed
does
usual definition
that is invariant
with respect
to
changes in the processes
the causing variables.
suggests
by the following
to me that
footnote:
it is not
really
economists’
use of the word cause typically
“invariance
under
relation
with
to be tests of causality.
a relation
is accompanied
Sims
sometimes
like that of T. Sargent (1977, p. 216):
not, in general, coincide
The statement
with
In addition,
have little or nothing
in understanding
It is true that Granger’s
governing
abounds
appears.
and applied,
to be an important
difficulties
of one:
formulated
textbooks
results of recent analyses that purport Further
literature
of causality
listed above, and many more that could be added,
The fact that many
large part responsible
econometric
concept
have been
The few observations testify
and
the Wiener-Granger
an intervention”
with a strictly
side.” Certainly the concept
rather than
exogenous
variable
in the mathematics
of a causal
relation
so clear coincides
that with
“a one-sided
on the right-hand
and engineering
literature
coincides
the latter
with
one. From these statements, the only
it seems apparent
one who is at a loss to understand
that the man in the street may not be the nature
of causality
and causal
relations. Further, in his Report C.F. Ansley states:
on the NBER-NSF
10
Seminar
on Time Series (1977).
Granger said that he wanted to clarify the notion Causality
is defined
with respect
as a reduction
to a given information
to Wiener.
The various
only in the population,
stationary
series,
one should
a test. Cross-correlation
statement
that
this definition
[their
were
not in the sample. Given a
use post-sample
forecasting
as
are tests of identification
sense] only. (p.20)
may provide
It is doubtful
set; this idea dated back
methods
[in the time series analysts’ While Ansley’s
variance
tests that had been proposed
equivalent
note that Granger and Newbold
ofcausality.
in forecasting
clarification
for some, it is pertinent
to
(1977) write: philosophers
would
definition
completely
accept
, and possibly
of causality]
CUUS~is too strong a term, or one too emotionally
laden, to
be used. A better term might be temporally
but since
cause is such a simple term we shall continue
related,
to use it. (p.225)
While the five letter word cuusc is indeed a simple word, Granger and Newbold’s remarks rather
attest subtle
temporally
to the fact, and difficult
related
causality,
cause,
presented
causal
Indeed
is relevant different the
(p.51).
literature,
with definitions these definitions
with
variance with respect
relations,
reveals
that
concepts
to
of causation,
etc. have been important in economics and writes, “The most orthodox of empiricists
can use the term ‘cause,’ as we shall define As this statement
for many. definitions
above
Simon (1953)
and antideterminists conscience”
in forecasting
that cause is a synonymous
set.
discussion
econometrics.
by philosophers,
which is not completely
or with a reduction
a given information The
long appreciated concept,
However,
implies,
of them
definition
of cause
as is clear from the above discussion,
of cause, causation,
some
a satisfactory
it, with a clear
causal relation,
inconsistent
with
many
etc. have appeared
each other
in
and inconsistent
provided by philosophers. There is thus a need to reconsider and try to arrive at a better understanding of the issues involved
and how they relate to current econometric practice. In what follows, 1 will attempt to arrive at a better causation
and associated
definition
of causation
discussion
in Section
causation
that
concepts.
1 will begin
and its implications 11 will be brought
have appeared
understanding
by reviewing
in Section
11. In Section
111, the
to bear on some major definitions
in the econometric
11
literature.
of
a philosophical
In Section
of
IV, the
implications Finally,
of the preceding
in Section
sections
V, a summary
for tests of causality
of findings
will be explored.
and some concluding
remarks
will be presented. II. Review of a Philosophical
Definition
At the end of the last section, tion
of causation.
causation
is available
purpose ological
Fortunately,
The clarified of
adequately, This deceptively
according
linking
coincides part
experience
to predict
or induction” Newton’s
of causation to
is noteworthy
a
without
of our knowledge
or Einstein’s
(1967),
“consists
who
literature.
remarks
of making
the
set, that
process
is enough
of ‘prediction
causality
is very close
the important
to predict
mentions
“a high probability,”
for our purposes”
is identified
to that
As will be seen,
in appraising
various
This view
that
inferences
the
most
from
past
future
role of laws, such as experience
unobserved outcomes. With respect to causality, Jeffreys we can say with high probability that a set of circumstances by another
to this
This part may be called generalization
emphasizes
laws, in efforts
and
a law or set of laws, or as
in the econometric
experience.
(p. 1). Jeffreys
in
more
not just to predictubility
is not causation.
theory,
of Jeffreys
future
(or
to Feigl:
both for what it includes
it links causation
predictability
that
and method-
is defined law
of
with the
to a law or set of laws. According
have appeared
with
important
of the logical
to a law or set of laws is critical
that
defini-
to a set of laws). (p. 408)
according
predictability
which “was written
(n., p. 408). According
according
might put it, without
tests of causality
a need for a clear-cut
results
concept
Most importantly
definition,
econometricians
also
(purified) predictability
to predictability
philosophical
some
and Its Implications
simple and deep definition
of causation”
simple definition
what it excludes. but
succinctly
of the concept
terms
we recognized
a sophisticatedly
in a paper by H. Feigl (1953),
of summarizing analyses
of Causality
with
or as yet
(1957) writes, “lf would be followed
(p. 190). Since, for Jeffreys,
generalization,
his concept
of
presented above. Note, however, that Jeffreys while Feigl does not similarly qualify his use of
the term predictability.
Consideration
In his definition concept of causation.”
of causation, Feigl speaks of the “clarified (purified) By clarified or purified, he means a concept of causation
that
is purged
that
had traditionally
of “metaphysical,
that is logically tenable
obscured,
will be given to this point below.
i.e. in principle if not eclipsed,
and methodologically
12
unconfirmable, the only meaning
adequate
and fruitful”
connotations of causation (p. 408).
What there
Aristotle modern
are some
is the
of these
teleological
and others). concept
socalled
conception
According
of causation.
unconfirmable
(final
cause
to Feigl,
connotations?
or causes,
final cause is eliminated
In this connection,
First,
considered
it is interesting
from the to consider
J.M. Keynes’s (192 1) analysis of the issue of final causes. Keynes writes: The discussion
of find
design has suffered with theology. determined argument
causes
confusion
and of the argument from its supposed
But the logical problem
upon
formal
is in all cases simply
from
connection
is plain
and abstract
and can be
considerations.
this--an
The
event has occurred
and has been observed which would be very improbable (I priori if we did not know that it had actually happened; on the other
hand,
the event
is of such a character
might have been not unreasonably assumed the existence of a conscious are of a certain
Keynes then provides the following Let /1 be our original b u//l
the
existence
in comparison
duta, a the occurrence supposed
of (I given h]
bluh
of the event,
conscious
[the probability
agent.
Then
very
small
is assumed
with a/bh [the probability
and we require
(p. 297)
analysis of the problem:
of the
[the probability
that it
predicted if we had agent whose motives
kind and whose powers are sufficient.
of a given b and h ] ; of b given a and h] ,
the probability,
that is to say, of b after II is known.
inverse
of probability
principle
* aT,
that b/ah = a/bh in terms
of a/bh
the probability event,
unless
The
[ Bayes’s theorem 1 . . .shows
and b/uh is therefore
and a/h alone.
of the conscious we can measure
not determinate
Thus we cannot agent’s existence its probability
measure after the
before
the
event. . . .The argument tells us that the existence of the hypothetical agent is more likely after the event than before it; but, . . .unless there is an appreciable probability first, there cannot be an appreciable probability afterwards. No conclusion, therefore which is worth having, can be based on the argument from design alone; like induction, this type of argument can only strengthen for which there is something
the probability of conclusions, to be said on other grounds.
(p. 298) 13
by
Keynes subjected
has
thus
to scientific
shown logical
that
is one of degree of confirmation; Keynes’s
notation)
very small under having.”
has relevance
somc final cause or grand to enhancing
of final
the critical
is very small, the posterior
ca~~ses
design.
can
be
result that emerges
probability
(b/h in
(.!I/&) will also be
This does not lead to a “conclusion
worth
for those who argue that an unusual
event,
World War I or the (ireat
for example,
hypothesis
and that
that is, if the initial or prior probability
Keynes’s conditions.
This analysis
lcading
the
analysis
Depression
Unless there
of the 193Os, is the result of are other
the value of our prior probability,
analysis will be an inconclusive result regarding conscious agent or grand design exists.
grounds
or evidence
the result of Keynes’s
the hypothesis
that the supposed
In closing this discussion of final causes or grand design, it is important to point out that Keynes’s analysis indicates that these concepts arc not to be ruled out a priori. The concepts, deductive
and inductive
of Jeffreys’s namely,
rules governing
proposition
formally
capable
evidence”
(p. 9).
definition
ti priori:
of being
any theory
of causation
to scientific
is in accord with one learning
or induction,
“The theory must not deny any
stated empirical
.given
conception.
are amenable
finding
of scientific
any precisely
accepted.
conception
is the animistic
of causation
to Keynes,
This important
( 1967) Rule 5, which states,
Jeffrcys’s
empirical
A second
according
analysis.
proposition
a moderate
amount
must be
of relevant
that Feigl has purged from his modern He explains
that the animistic
conception
implies that:
there
is
internal
(but
unconfinnable)
anthropomorphically
in analogy
an
(conceived
compulsion to coercion
as
experienced on the Il~~rnan level when forced against our own impulses), which supposedly accounts for the invariable connection inference
of from
causes
with
their
this conception
effects.
One
fallacious of futulisnl.
is the doctrine
(p. 408) Taking
a cut‘ from Keynes’s
treatment
of final causes, I think it may be
possible to sharpen and explicate the animistic concept to render it in the form of a clear-cut empirical proposition. If this were done, it seems that an analysis similar
to Keynes’s
the hypothesis
analysis
of final causes would apply.
of the existence
hypothesis
of the existence
susceptible
to empirical
of an internal
compulsion
of a final cause. The proposition
investigation
In this case, however, would
replace
the
would then become
in accord with Jeffreys’s theory of scientific
14
induction, similar
and the application
to that
reached
animistic
concept
historical
literature
very nature
of causation
is sometimes
concept
relation
of implication
to revive a conception
entailment,
such as mistaken
was repudiated
or necessity
conceptions
The rationalistic basic principles
Traditional
provide
reduced
or deductive
method
future
Feigl says that
and that attempts
or necessity, is rejected, that
this
by Kant of logical
. . .I” (p. 408). because
distinguish
it conflicts the rules of
only three attitudes
proof, disproof,
of previous
instances
to
or blank ignorance.
of a rule [or law] will
proof that the rule [or law] will hold in
There is always the formal possibility
the negative
findings
that there is no logically
Jeffreys there
(1967)
comments
is a “tendency
in some way to deductive (1957)
with the
work. As Jeffreys (1967) puts it: logic admits
definite
embodies
is not deductive. the
of
of an
(pp. l-2)
of all: it can be done Jeffreys
of the nature
“may be said to have failed (for diverse reasons
methodology
a deductive
namely
and effect.
scientific
and
of B by the
based on conceptions
of logical identity
in scientific
a new instance. exception.
of causation
of scientific
But no number
cause
analysis
(p. 408).
of causality
any proposition:
of causality,
in the economic
consequence
the causal relation
by Hume
conception
and deduction
This statement
Since the
by Feigl is “the rationalistic
say, confuses)
(or entailment)”
and others
with
encountered
eliminated
(I should
of causation
induction
of final causes.
having an explicit
of causation
which identifies
conception identity,
would lead to a conclusion
is valuable.
The third logical
analysis
in the guise of “A is the inevitable
of the circumstances,”
such statements conception
of Keynes’s
in the case of his analysis
that in much
to claim that scientific
“. . .inference
The observations
or simply
further
of the nature
relationship
connecting writing
method
logic, which is the most fundamental
only by rejecting
also states,
of Hume’s analysis necessary
its chief feature,
induction”
from past observations
not yet made may concern
at places
not
induction. . . .There is an element considered” (p. 13).
yet
inspected.
of uncertainty
on
can be fallacy (p. 2).
to future
ones
events either in
It is technically
in all inferences
called
of the kind
The unavoidable uncertainty involved in making inferences from past data to as yet unobserved data is a basic reason for rejecting the rationalistic conception
of causality,
entailment.
which
involves
Thus, using deduction
the concept
of deductive
to prove that, according
15
logical necessity, to economic
or
theory,
or cause event B obviously
event A must produce a logical necessity
that event B will actually
A. What is needed
in such a case is an application
produce
a statement
Most important, statement.
there
yielded
probubly
occur
development the present
of a theory
idea is that
and can in consequence
Jeffreys,
rationalistic
controversial,
(1957,
of belief,
1967) in his
‘I. . .tlle essetzceof
He states,
a frequency. which
The funda-
satisfies
of these rules be formally
along with Hume, provides
conception Jeffreys’s
of probability,
illustrating
of the phrase l~ill
certain
expressed
. .” (1967, p. 401).
Thus,
concept
in such a
. .is simply
degree
occur.”
to be utilized
by Jeffreys
induction.
no probability.
of a reasonable
rules of consistency by numbers. the
of scientific
is that
logic that would in this last
of probability at length
of
logical necessity
logic and the quantification
are issues treated
theory
of inductive
of deductive
concept
by inductive
that there is
of A, B will probably
the occurrence
is no element
The appropriate
statement
mental
like “Given
does not imply
be observed given the occurrence
of
theory and
how his concept
causality.
of scientific
in his work of probability
compelling
arguments
Further,
while
induction
requires
he provides
many
can be employed
against
perhaps
more
a particular
applied
to obtain
analyses numerical
probabilities associated with alternative laws, models, or hypotheses, many of which are frequently encountered in econometrics. In summary, the deductive, rationalistic conception of causality replaced by one grounded in inductive Returning concept
to Feigl’s definition
of “laws.”
domains
It is relevant
and levels of their
is considered inappropriate rather than deductive logic. of causality,
to consider
application.
Feigl
B.
C.
Types of Laws 1.
Deterministic
2.
Statistical
Forms
of Luws
1.
Qualitative
2.
Semi-quantitative
(topological)
3.
Fully quantitative
(metrical)
Dorizuins
ofLuws
1. Temporal (sequential) 2. Coexistential (simultaneous)
16
it involves
the
the types and forms of laws and the
list of characteristics: A.
we see that
and can be
(1953)
presents
the following
D. Levels of Laws 1. Macro 2.
Micro
In addition,
he recognizes
that certain
laws may have combinations
of these
characteristics. Although
the above list may not be all inclusive,
the characteristics undertaking.
of laws.
With respect The
principle
precise
A brief discussion to deterministic
pertinent
[i.e.,
be interpreted
extremely
ideally
given the momentary
laws, and the required
may therefore hence
laws and determinism,
of determinism
predictability,
determinism.
is variously
called the principle
similar
consequences”’
precisely
Jeffreys
such form
are ever identical.
(1967)
the
techniques]
as ‘Precisely
(p.
the
similar things can usually
similar
a looser very similar
be observed,”
or the uniformity
antecedents
that no two sets of antecedents things
of absolute
such as “In
can be observed,
truth,
most
that
can be done
is to make
the same that we believe to be relevant--“the more
than
those
achieve it”
mean
“the same as far as we know”,
and usually
means a great deal less. The question
How do we know that the neglected Only
by actually
allowing
conditions
same” can never
in practice
then arises,
variables are irrelevant?
them to vary and verifying
that
there is no associated
variation
the use of significance
tests, a theory of which must therefore
in the result; but this requires
be given before there is any application of the principle, and when it is given it is found that the principle is no longer needed.
. .(p. 12)
17
or very
that “If ‘precisely
we cannot
(pp. 1 l-l 2). He also states: The
of
lead to precisely
form of determinism
with the observations
to be a matter
have definitely
“We must also reject what
determinism,
11). He explains
the same circumstances
physicists
also writes,
of causality,
He even rejects
the same’ is intended
and
(p. 4 12)
abandoned
in any
complete
concerning
He goes on to say that most of the younger-generation
nature,
is worth
Feigl writes:
conditions,
mathematical
many of
as a--to be sure, very bold and
problematic--hypothesis
order of nature.
it does contain
of these characteristics
While the existence cited
as evidence
much
deeper
logical
Neumann
argues that
and cannot
Thus,
quantum
be embedded
theory
(p. 590),
exclusively,
nondeterministic,
Next, compelling
reason
presence
to limit
or absence
involving,
of qualities
as Feigl puts
As regards
convenient
derivatives,
to be continuous.
at various
formulations
to assume stages
may coexist. The quantum
For example, theory
predictions
are “fully about
and semi-quantitative of ‘equal’
functions
or ‘greater
their
than”’
in laws, it is
first and second are not precluded.
of a subject,
Jeffreys (1967)
the laws
causality.
appearing
and perhaps
and the continuous
two
alternative
remarks that: emission
theory
for one set of facts, but each, in its existing with the facts explained
conclusion
wrong and that. But meanwhile,
if not
to be any
to laws that
However, other representations
form, was inconsistent proper
It is thus concluded
laws in defining
of the development
both accounted The
them,
it
bearing
laws.
yield
the relations
the forms of mathematical
sometimes In fact
that
as fully quantitative
is developed,
does not appear
or characteristics
it, “only
(p. 409) are just as relevant
probabilistic
relates are in the main,
of causality
laws
their
“John von
do not have much
or probabilistic
the concept
goes
(p. 589), and that “Einstein phenomena
of laws. There
Qualitative
is often
not just that
are inherently
of determinism.
of causality
statistical
(metrical).”
systems” of quantum
critique
we take up the forms
quantitative
observations
while interesting,
laws to which Feigl’s definition
theory,
of determinism
uses of systems, systems
in deterministic
on the issues raised by Jeffreys’s that
critique
Burks’s (1977)
mechanical
a complete
will be deterministic”
a probabilistic
Jeffreys’s
to the operational
structure.
that when
theory,
determinism,
and relates
deductive
believed
of quantum
against
was that
both
by the other.
explanations
were
must be sought. . . . . .some new explanation physicists based their predictions on the
laws; in types of phenomena that had been found predictable by quantum methods, they made their predictions by quantum
methods;
in
made predictions (pp. 41 l-1 2) Another verifiable
place overly tions
point
predictions
by
forms
about
as yet unobserved
in them.
of
interference
continuous
about
severe restrictions
appearing
phenomena assuming
wave
they trains.
of laws is that they be capable data. This requirement
of yielding does not
on the forms of laws or of mathematical
However,
many
18
including
G.E.P.
func-
Box, R.A. Fisher,
M. Friedman,
H. Jeffreys, of
present
the
preference
for simplicity
Parsimony,
or the Jeffreys-Wrinch
Simplicity
virtues
the
emphasize
Postulate,
simplicity
writer, in
by appealing
Jeffreys
laws.
to Ockham’s
Razor,
Simplicity
(1967)
and a number
formulating Postulate.
states
that
contrary
because it is the most likely to give correct
the Principle
a of
to the
to the widespread “. .the simplest
predictions;
that the
degree of belief. . .” (pp. 4-5). Further
choice is based on a reasonable
do
exhibit
With respect
belief that the choice of the simplest law is merely a convention, law is chosen
of others
Some
Jeffreys
(1967) writes: Precise
statement
accordance
of the prior
probabilities
with the condition
of the laws in
of convergence
requires
that
they should
actually
be put in an order of decreasing
probability.
. .A11 we have to say is that the simpler laws have
the greater
prior
probabilities.
called the Simplicity
This is what
Postulate.
He goes on to suggest a tentative
Wrinch
prior and 1
(p. 47)
numerical
rule for assessing the complexity
of
laws expressible by differential equations. Jeffreys (1957) also presents an analysis of developments in the history of science that provides support for the Simplicity
Postulate.
Thus,
if the Simplicity
valid, it involves a most important We now Feigl’s
consider
definition
temporal-spatial.
several
of causation.
ordering
Postulate
is accepted
as probably
of causal laws.
aspects
of the domains
The domains
of many
In regard to the temporal-spatial
of laws involved
in
laws are temporal
or
aspects of laws, Feigl (1953)
writes: This principle
[the homogeneity
homogeneity
of
and isotropy
time] , clearly
states the irrelevance
of absolute
formulated
and in this sense the purely
relational Leibniz
Einstein’s
already
theory
by
of relativity.
by
Maxwell,
space or time co-ordinates,
time
as seen
of space, and
character and
The place
which events occur do not by themselves
of space and
re-emphasized
in
and the time at
have any modifying
effect on these events. (p. 4 12) He goes on to say, “Differences in effects must always be accounted for in terms of differences in the coditiorw, not in terms of purely spatio-temporal location” (p. 4 12). These considerations (symmetry) of the cause-effect relation
and considerations of the reversibility in molecular processes that is assumed
19
in the work of Gibbs Brownian
motion Since
the
dynamics
basic
may indeed
ordered
state
always
higher
than
probabilistic
time.
such a requirement
events
that
From
concept
but
in the opposite
not
as “earlier
vice versa”
to physical
to think
has been
presented
important time
in a psychological the temporal
above,
physical
laws
As regards
in terms of chrono-
laws be such that causes precede
of psychological
or discrete
are
of laws in time.
their effects
it is clear that
laws. In addition,
is considered,
is no
time frame will necessarily
meet
domain
then
if
there
that cause precede effect in chronological
relate to continuous
are
. . (p. 414)
reversibility
what
issue regarding
highly
disorder)
such statements
it has been customary
is at odds with
that laws stated
Another
later
are
explana-
from a more
of time and space as they relate
time and to require
in chronological
to Boltzmann’s
for the process
as sheer tautologies.
considerations
the requirement
those
electro-
the direction
to one of lower order (greater
laws in the social sciences,
assurance
in the case of
mechanics
seem that
for a transition
can influence
an important
and
quantum
it would
. Once this is assumed,
recognized
(1966)
observed
mechanics
be reducible
[the probabilities
actions
Allais’s
of classical
of causality
direction]
logical
laws
symmetrical,
These
and empirically
as well as those of modern
temporally tion
indicate
and Boltzmann
lead Feigl to state:
time. of laws is whether
laws
time. There does not seem to be any compelling
reason to favor either continuous fact, mixed difference-differential
or discrete time formulations of laws, and, in equation formulations of laws are not only
possible but have been employed. Finally with respect to temporal matters, there is the problem of laws that causality.” As Feigl notes, ‘I. . .an involve ” simultaneity ” or “instantaneous equally
well established
to prevail
even
usage [of the crude concepts
if the two
events
(factors,
of cause and effect]
processes)
seems
are contemporaneous”
(p. 417). In terms of the discussion of temporal ordering seems clear that simultaneous or instantaneous formulations
presented above, it of laws cannot be
ruled out, provided that these laws are capable of yielding predictions about as yet unobserved data. If they can, then such laws are causal laws according to Feigl’s definition. As regards the levels, macro possible
to have laws relating
or micro, to which laws relate, it is of course
specifically
30
to macro phenomena,
specifically
to
micro
phenomena,
is a natural
micro
desire to have a consistent
phenomena, preclude
or to combined
the
fact
that
and macro
phenomena.
law applicable
While there
to both micro and macro
in some areas such a law does not exist does not
the use of laws relating
to one level until an improved,
more general
law is formulated. In the above discussion tion
of
causation,
adequately,
“according
deductive,
logical nature
on the inductive
of some characteristics
namely,
“predictability
to a set of laws”),
to the tasks of working
of causation,
scientists.
of inductive
logic plays a central
predictions.
Jeffreys
theory
to compute
This inductive In the several works literature.
role in comparing
associated
next
section
dealing
is directed
causation
that
in Section
on
appear
of
can be covered, and relevant
I for
of tests of causality.
Ordering and Identifiability essay
“Causal
Ordering
” and
Identifiability”
111 in one of the most influential For this reason Simon’s
agrees with and
that
the tests of
not all discussions
important
as chapter
purification
Because
works
leading
to which concepts
a basis for approaching
in the next section.
Literature
with or differ from those
several
Simon’s
analysis. Simon
the extent
coincide
literature
A. Simon k Tausal
builds
literature
and discussing
in the Econometric
in the econometric
methodology.
about the quality
in the econometric
have appeared
assessing the meaningfulness
(1977)
laws or hypotheses.
to reviewing
of Causation
I1 and to provide
that
metric
the
logic that involves Bayes’s
have appeared
of this review are to establish
to be considered
published
laws’
pp. 65-91) describe
with alternative
attention
with
causality
H.
that the calculus
and testing alternative
of this use of inductive
in the econometric
selected
has been placed
since this aspect seems very relevant
of various laws.
causality have
(or,
has been said about the
more emphasis
ch. 5-6) and Burks (1977,
probabilities
The objectives considered
more
Also, it must be mentioned
Review of Selected Discussions
of causation
defini-
to a law”
logical analysis is needed to provide information
of the predictability
III.
(1967,
and some applications
theorem
not much
of causal laws; rather,
logical nature
of a philosopher’s
according
and because
contribution, Feigl
clarification.
that
monographs
some recent
it is worthwhile
the concept
In fact,
Simon
21
(1953)
on econo-
work by Sims
to review
of causation mentions
was
Simon’s
is in need
‘I. . .objectionable
of
ontological
and epistemological
overtones
In view of the generally the notion
is
use in scientific about
Moreover,
metaphorical,
or
his
of “Hume’s
causal
orderings
(when
the
not
about
its
it is not easy to explain
even
as a carry-over
this usage
of
outmoded
critique
connotations
that
above, that the notion
associated
necessary
connections
of
with the term cuusutiotz among
events
are simply
points
probabilistic
out
as well
is important, and more
dctenninistic Whether
such
of the scientist’s
a notion
as deterministic
model,
prevalent
that
this last statement features
cannot
properties
be
Applicability model
to
to probabilistic is becoming
of the world
is not a
one” (p. 50).
is true or not, it is evident relating
that Simon’s notion
to models’
when
a causal ordering
of variables
characteristics,
of inductive
“It is the aim of this chapter.
or groups
that
. .” (p. 50).
be applied
that “. . .the viewpoint
the appropriate
logical concept
basis for determining
two variables
can
of the world that require statements
Simon (p. 51) states,
and rigorous
of causality
models.
since Simon believes
is a deductive
not to empirical
between
that
model but a probabilistic
of causality Indeed,
properties
to change as the model is altered to fit new observations.
He rightly
more
writing
science,
(and hence can have no empirical basis),” (p. 49), Simon opts for a concept of causality. Simon’s narrower notion of causality is “that
are subject
models
to find the
(p. 50)
In view of the impure perceived narrower
to the
status of
surprising
Thus Simon is in agreement with the view, expressed causality is in widespread use in science. and
themselves
epistemological
it is somewhat
common writing
methodology). language.
unsavory
of causality,
term in rather scientist as
that have attached
. .” (p. 49). He also notes:
concept.
ca~lsal
logic.
.to provide a clear can be said to hold
in a model
[and
not the ‘real’
world] ,” and “. . .the concepts to be defined all refer to a model--a system of equations--and not to the “real” world the model purports to describe.” Thus, Simon’s narrower notion of causality or causation is radically different from Feigl’s concept of causation, i.e., predictability according to a law or set of laws. For Feigl predictability means predictability of empirically observable outcomes, certainly not just a deductive logical property of a model or of a law. While Simon’s notion of causality can be used to describe logically the laws that Feigl mentions, outcomes.
it involves no necessary relation Obviously a law that is
to the prediction
of “real”
world
in Feigl’s; that is, the law may be incapable
of predicting
Such a law would not be termed causal in an inductive, In addition concepts concept
to this important
of causation, of causality
distinction
it is relevant
Simon explains
“real-world” empirical
between
to note
that
outcomes.
sense.
Simon’s
even within
and Feigl’s his narrower
that:
related . . .we might say that if A and B are functionally and if A precedes B in time, then A causes B. There is no logical obstacle adopt
to this procedure.
it. We shall argue that
sometimes
provide
sequence,
is the important
asymmetry, where
exclude
them
doing
we shall find
usage,
and with than
it) does not imply imply causation. Simon
garding
time sequence,
with
the
connection
this relation [among certain time, although an analysis systems
lagged
relations.
with actual
the other,
of
and easier,
(as we shall define
nor does time sequence
discussion
of a chronological
There is no necessary
dynamical
By so
of the meaning
causation
effect. While Simon agrees with this position concluding section he remarks,
that
(and sometimes
in closer accord
understanding that
a time
(p. 5 1)
is in agreement
the non-necessity
implying
we shall admit causal
appears
if we had adopted
We shall discover
A and B,
there is a time sequence).
ourselves
a better
does, indeed,
between
necessarily
no time sequence
even where
the concept
Thus,
without
we shall not
thing, not the sequence.
at the basis of our definition
orderings
course.
time sequence
a basis for asymmetry
but that asymmetry By putting
Nevertheless,
in the previous
time ordering
section
between
cause and
in the early part of his essay, in his
the asymmetry
of
variables] and asymmetry of the causal structure
between
in of
in econometrics
and physics
will show
can generally
be interpreted
as causal
relations
re-
(pp. 73-74)
Since it is not clear to what specific lagged relations Simon is referring, it is difficult to evaluate this last remark. Suffice it to say that there are many examples
of empirically
a lagged relation
cannot
fitted
dynamical
systems
in econometrics
be regarded as causal in Feigl’s sense.
23
in which
To illustrate review the simplest the following
the nature example
threeequation,
a2 1x1
of Simon’s
presented
analysis
linear, deterministic
+“22x*
of causal orderings,
in his paper. In this example,
=(1
20
we will
he considers
system (p. 58):
(2)
’
(3)
where x1 is an index measuring
the favorableness
of weather
for growing wheat;
x2 is the size of the wheat crop; xj is the price of wheat; and the a’s are parameters. Simon writes, “We suppose the weather to depend only on a parameter; the wheat crop, upon the weather (we ignore a possible dependence of supply on price); and the price of wheat, on the wheat crop. . .” (p. 58). from (1) alone, Since the value of .Y1 can be determined to substitute
this value in equations
.Y~ and x3. The substitution
it is possible
(2) and (3) to get a reduced system involving
from (1) into (2) yields a relation
determining
the
in (3) along with the value of x 1 from (l), value of .x2, which when substituted determines the value of x3. This ordering of the algebraic solution of the system in (l)-(3)
results in Simon’s writing:
(1) -
which
Simon
(2) -
interprets
(31,
as “(1) has direct
precedence
over (2), and (2) over
(3),” (p. 58) and
which
he interprets
as “s,
is the direct
24
cause of x2, and x2 of x3 ” (p. 58).
While Simon analyzes
systems more complicated
this simple system reveals well the nature
of his notions
orderings,
just
which
considered. purpose;
are, as he emphasizes,
He leaves the inductive yet, it is the inductive
for appraising of causality
logical
relevance
than that shown above, of causality properties
of the model
close to Simon’s, Causality, general
Jeffreys
as used form,
variables,
equations,
has a more
laws are expressible connecting
previous the
instances
relevant
by
continuous
“How
than those stated
determined
of
that appears
in terms
of the
which we call laws, are inferred and
then
quantities
astronomical
questions
or set of variables
is uniquely
. .The equations,
others.“.
permits
a concept
a similar point of view:
mathematics,
possibly
some variable
in the equations
where
in applied
expresses
on
that is critical
In discussing
such that in any case, given a finite number
parameters,
from
(1967)
such as: “Physical
mathematical
aside, probably
aspect of this and other models
the degree to which the model is causal.’
and causal
of the model
applied
to instances
are different.
prediction.
But
This
form
it still leaves
no other
the
do we know
that
parameters
are needed?”
“How do we know that we
need consider no variables as relevant other than those mentioned explicitly in the laws?” and “Why do we believe
the
questions actual
have until
problems.
three
answered attended
papers,
parameters
published
bring together
Basmann
models,
appearing
after
we can
these
make
any
and the principle to the
together
is
epistemological
as “a triptych
and H.O.A. Wold (1960), and extend
in Strotz and Weld, 1960) attempting of econometric
that
of the principle,
we have
is only
Wold Discussion of Causality
R.H. Strotz
Wold (1960),
been
It
(p. 12)
B. The Basmann-StrotzIn
themselves?”
application
useless
systems,”
laws
including
in models.
earlier
on
models
chain
and H.O.A.
work of Wold (See references
to clarify the causal nature
entire
causal
R.H. Strotz (1960)
and particular
and properties equations
In a paper dealing with the Strotz-Wold
and
papers,
( 1963) writes:
1 In a letter, dated May 2, 1978, to the author, S.imon emphasizes that while in earlier work he “ . . .neglected to emphasize the correspondence prmclple that connects the syntactic with the semantic dimensions of any theory,“in more recent work he does recognize this important link.
25
. . .Wold
and Strotz
definition
of causality
only
note
contrary
to
structural
show the
equations
non-triangular, causal
are
features
which
specific
causal.
that
Their
. .is not mentioned
to their
systems
what
of the classical
own notion
by them
own. It is the purpose
constructively,
Wold-Strotz
from
to the conclusion
systems
essential
alternative
to
stated
argue
the classical notion.
as a possible this
they
recursive
triangular
view lacks several of causality;
have not
by
an example,
assertion, underlie
the
of that,
hypothethical
“interdependent,”
i.e.,
can be validly given a straightforward
interpretation,
at
least
in
the
classical
sense.
. .
(pp. 441-42)2 As the quotation
reveals,
two of the basic issues in this discussion
are (a) the
definitions of causality employed by the participants in this discussion and (b) the relationship between concepts of causality and the forms of econo.metric
models.
These two aspects
of the Strotz-Wold
are considered below. With respect to the definition, Wold (1960) in defining
‘causality.’
challenge unique,
are rather
is that
of providing
states that
come up for which
or definitions,
They
write,
The term is in common
and some may
Wold (1960)
eclectic.
prefer
tion
of econometric
whether both
models”
a single definition
the natural
in a definition entertaining
different
is necessary
and empirically
present
and the only meaningful need
at all” (p. 418).
of the models
comments
be
Also,
at issue, problems
an unusual
situation
raise the issue of
such as Feigl’s, is adequate While it is recognized
of causality
writer is aware, the proposition
and rights
so with regard to the causal interpreta-
are possible, fruitful.
Strotz
of it. No explication
(p. 46 1). These
of causality,
concepts
parlance
sciences give no guidance,
and social sciences. of causality
of causality,
to use the word
in the social sciences. This is in particular
discussion
“No one has monopoly
an explication never
“. . .in the treatment
the natural
and Basmann
it would
for work in
that improvements
have to be shown
in the natural
that
and social sciences
Since this has not been done, as far as the that different
concepts
of causality
are
required is purely speculative. It is also noteworthy that Strotz and Wold adopt a definition of causality that they believe is in agreement with “common scientific
and statistical-inference
usage.” Strotz and Wold write,
2References
cited in original have been omitted.
26
For us, however, and
the word [caz~sality]
statistical-inference
meaning.
usage
by controlling
stochastically. controlling
But
in essence
its realization
z indirectly
it may
y indirectly
therefore
and symmetric
cause
a change
of one another
without
being violated.
(p. 4 18)
Strotz-Wold
definition,
z. A causal
is of
in a causal sense. These are the change in z may cause
times a controlled
in the concept
of causality
or causation
above,
of controlled
in which no variables are under control.
In addition,
apply
contain
be controlled.
be’ possible mean
that
a consistent
for example,
causality]
or
experiment” ments
into
are admissible
incorporating
the
be controlled
variation
experiments
experiments (1967),
actually
controlled
impossible
between
differs
their definition
from Feigl’s most
applied
Feigl’s
to areas of science
the Feigl definition
can also
one or more variables
that can
but
of z, then
their definition
definition
they
estimate
that
of a quantity
they
to the Strotz-Wold
is subsumed
under
are considering
appear
theory
of causality
the position
that
of causality.
in an operational
takes
be relevant
them
changes in variables.
to be admitting impossible
of scientific
induction
is a controversial “the existence
must
not
definition,
a
Whether
issue. Jeffreys of a thing
involve
(p. 8). While the issue of the admissibility
may
be
z . . .” What do they mean by ~vo~ld be? If they
by corltrolling
hypothetical
both
and Wold say, “. . .it is or ‘would
Note too that Strotz
z cannot
in y
changes independently
can be fruitfully
in cases in which laws or models
change
y and z cannot
presented
by bringing
by
relation
the causal relationship
definition
y, at least
possible
in that in any instance
controlled
markedly
actually
be
Only in special cases may it
in z, but
to simultaneous
general
it is or “would
not
a controlled
in y and at other
subjected
scientific
following
to control
may
to control
it is asymmetric.
be reversible a change
or
asymmetric,
cases in which sometimes
The
in common the
z is a cause of y if, by hypothesis,
be” possible
may
has
[e.g.,
an impossible
of impossible
experi-
it is still the case that
Feigl’s more general definition
of causation
and causal laws. In his comment following
definition
on the Strotz-Wold
The classical scientific appeal, that
papers, Basmann
(1963) presents
of causality: notion
can be expressed
[the]
meclrarzisrrl
of causality
satisfactorily
under
to which we shall as follows:
investigation
27
cm
Assume be isolated
the
from
all systemutic,
assume from
any
definite
initial condition,
following
non-random
that
of a “model
“predictability” started
up
always
tends
represents
external
with
from
a causal hypothesis
the same initial
the exception.
the mechanism
under
he remarks,
it is sufficient
Feigl’s concept that
are similar
“It is not necessary that such that they are not ruled out in principle”
of “law or set of laws” with Basmann’s
represents
Basmann’s
a mechanism,”
requirement
approximately
the
same
approximately concepts
sciences,
initial
a single realization
concept
assert that
conditions
of
“when
the mechanism
the same sequence of causality
Feigl’s concept
Feigl (1953)
and Feigl’s
that a model
from a logical point
as to whether
Indeed,
condi-
tends to run through of states, is a causal model
of states.
or causation
. . ,I’
and causal
of view. There may, however, of predictability
of causation;
to a law or set of laws, in cases in which,
nonexperimental
in isolution
and (2) asserts that,
about
same as Basmann’s, a point considered below. Feigl does not rule out the concept according
the
(p. 442)
to run through
be some question
the sume
is said to be
a mechanism
always the same sequence
we see that Feigl’s and Basmann’s laws or models
time the
writes,
influences
mechanism
be feasible;
(p. 442). If we equate concept
(1)
Basmann
to this last sentence,
experiments
every
the mechanism
up from approximately
approximately investigation.
if,
upproximately
omitted).
his definition,
model
In a footnote
then
references
Any
the
condition.
influences;
over repeatedly
it tends to run through appro.yinlately
from
when started
external
can be started
up from
of events,
causal. (p.442,
expressing
initial
is sturted
sume sequence
tions
non-rundom
that the mechanism
mechanism
Also, directly
i.e.,
is precisely
the
i.e., predictability
as is common
in mainly
of a process is the rule rather than
writes,
In the case of unrepeatable (unique) events, as described in the historical disciplines (as in the history of the inorganic, or individual-biographical organic, mental, social, cultural occurrences), the assertion of causal relations (as in statements
regarding
who or what influenced
in which
direction)
is often
events to what degree and
methodologically
i.e., only very weakly confirmable.
precarious,
But it is not meaningless.
(P. 410) Similarly
Jeffreys
nonexperimental
(1967),
who
has
applied
data from astronomy
There
must
be
hypotheses, hold
a uniform
irrespective
in different
same
decisions
standard
otherwise
we have
concept
to
much
remarks, validity
Different
but they must
will be those warranted
the result of inadequate
causal
of
of the subject.
subjects,
criteria;
his
and geophysics,
for
all
laws may
be tested
no guarantee
by the that
our
by the data and not merely
analysis or of believing
what we want
to believe. (p. 7) Thus, predictability in which
and confirmation
repetition
of outcomes
that the experiment
mentioned
appears to be superfluous. possible,
is usually
confirmation,
of predictability is impossible.
desirable,
or lack thereof,
since
for a particular
apply
that
to complete
fully recursive, can embody
economic
sense. Whether of yielding separate Basmann
models,
repetition
phenomena.
predictions
Thus,
models (1963).
That models
has not been settled, demonstration
of
are formulated
of providing
predictions
of such models be interpreted
through
by
methodologically.
or perhaps
cannot
observational
be settled equivalence
29
as
deductive
of the structures (19.53) capable
is a of and of
on the forms
This requirement
found empirically that models than models not so constructed. the
in
are capable
be built so as to have cuch equation
be justified
about
causally
Simon
in the above sense is an a priori restriction
that cannot
of causality
are all causal in a logical,
carried
of
Models in any of these forms
by a careful examination
example,
when
degree
or laws and causality, definitions
the models
and thus can, in isolation,
as, for
justified if it were better in prediction
models
fonns.
they
a greater
model.
parts or single equations
issue that can be decided
of experiments,
it provides
whether
or interdependent
particular
requirement
and Basmann’s
laws and are capable
a causal interpretation of models
Jeffreys’s,
econometric
triangular,
yet unobserved
particular
Feigl’s,
Basmann’s
“not be ruled out in principle”
On the issue of the forms of econometric it is apparent
in situations
Thus,
in his definition
Of course, however,
highly
are relevant
could be
so constructed perfonned Since this empirical issue
in view of Basmann’s of
fully
recursive
(1965) and
interdependent ncccssarily
models,
it is inappropriate
be of one fonn or another
‘4 similar conclusion
to require
that econometric
models
simply on a priori grounds.
applies to the Strotz-Wold
view, expressed
in Strotz
(1960): If a causal possible
interpretation
of an interdependent
it is to be provided
The interdependent to the recursive
system system
in tenns
This
statement
indicated alone,
or a description
Wo1d.j (p. 428)
is an a priori
view about
observational
consistent equivalence
discrimination
among
confirmation
laws that of
fully
different
procedures.
unsound assume
the former
systems
C. The Wiener-Granger Concept Granger alternative
(1969)
to those
and
forms.
as
to “true”
Aside from the
interdependent issue involving
position
as Strotz
error. . .‘I (p. 428) is unacceptable
specification
laws and,
to rule out, on a priori grounds
the Strotz-Wold involve,
of causal
particular
recursive
systems are in some sense approximations and that
paper, written
the forms
laws is an inductive
Thus,
system.
of its equilibrium
of the preceding
with Professor
above, it is methodologically
logically
of a recursive
is
is then either an approximation
state. This was the conclusion jointly
system
systems, empirical
that interdependent
underlying
recursive systems
it, I’. . .some
puts
form of
as a general proposition.
ofCausality
considers
a theory
of Simon,
Strotz,
of causality
Weld,
and
that
Basmann
he views reviewed
as an above.
Granger writes, In the alternative theory to be discussed nature of the variables and the direction will be central for
features.
nonstochastic
assumption
The theory
variables
and
that the future cannot
will
here, the stochastic of the flow of time
is, in fact, not relevant rely
entirely
on the
cause the past. This theory
will not, of course, be contradictory to previous work but there appears to be little common ground. Its origins may be found in a suggestion
by Wiener. . . (p. 428)
that his theory is (‘ontrary to what Granger says, it is apparent contradictory to previous work on causality in at least two important respects.
3
Footnote included
in original
has been omitted.
30
First, and
in the previous others,
analysis not
both
work
of Feigl, Jeffreys,
stochastic
and nonstochastic
is not limited
warranted
Second,
on
Granger,
of temporal pointed
to stochastic
either
and “effect”
in chronological
of causality
that appear in Granger
in other
or subject
are considered. matter
to previous (1977)
The
is certainly
considerations.
embeds
with succession
time. These requirements
and Newbold
Wold, Basmann,
the notion
Feigl and Simon, as explicitly
causal asymmetry
contrary
“(ii) It is sensible
processes. processes”
variables
to Feigl, Simon and Basmann,
cause the past. Strict causality or future.”
Strotz,
and such limitation
in his theory of causality.
out above, do not identify
explicitly
variables,
methodological
in contrast
asymmetry
Simon,
of “cause”
of the Granger concept
concepts
as follows:
of causality
are stated
“(i) The future
cannot
can occur only with the past causing the present to discuss causality
only for a group of stochastic
It is not possible to detect causality between two deterministic (pp. 224-25). As stated above, these restrictions, which do not appear concepts
the Granger
of causality,
concept.
definitely
If an inductive
restrict
the range of applicability
of
case could be made that such restrictions
are required, then they would be acceptable. Because, as far as the present writer is aware, no such convincing case has been made, it is questionable that the
restrictions
are required
Granger’s
restrictions
stochustic
variation
a nonstochastic variable.
regards
+ 1,.
values .
e,(AIB)
Granger
of A,. Further,
or that
trend in a second
on the forms of economic
grounds.
considers
a stationary
he lets A(k)
represent
the optimum,
the set of values B, by P,(AlB),
= A, - P,(AIB),
in a second variable
causes a nonstochastic
stochastic
process,
the set of past values of A,, and 2, the set of past and
) -1 . He also denotes
of A, using
In fact,
of his theory of causality, Granger (1969) as “. . .very general in nature” (p. 428). In
of causality
this definition,
A,. He lets 2, represent present
on inductive
restrictiveness
of causality.
laws which state that non-
above, such a priori restrictions
his definition
developing
causes variation
in one variable
laws have to be justified the
definition
to rule out economic
in one variable
trend
As discussed
Despite
for a fruitful
appear
and the variance
unbiased
the set
f Alsi, j = k, k
least squares predictor
the predictive
error
( 1969) writes, Let Ut be all the information in the universe accumulated since time t-l and let U, - Y, denote all this information apart from the specified series Y,. We then have the following definitions.
31
series by
of E~(AIB) by u2 (AIB). Then Granger
Definition that
1: Cuusulity.
If u2 (XlL’) < uz (Xlm),
Y is causing X, denoted
causing X, if we are better able information
we say
by Y, * X,. We say that
able to predict
Y, is
X, using all avail-
than if the information
apart from Y, had
been used. Definition
2: Feedbuck.
If
u2(XIU) < a*(XIU-Y) a2(YlU)
We
say
that
feedback
Y, @ X,, i.e., feedback
-
u* (Y/U-X)
<
is
)
occurring,
)
which
and also Y, is causing X,. Definition < u2 (Xl&
3:
better
Instantaneous
we say that
is occurring.
In other
“predicted”
the “prediction” Definition (integer)
if the present
variance
variable
value
Y, Q X, of X, is
value of Y, is included
in the
lag 1~ to be the least value of k such that . p-1,
Thus,
knowing
the values
will be of no help in improving
of X,. (pp. 428-29)
definition
of the forecast
stochastic
causality
current
Lug. If Y, 3 X,, we define
< u* (Xl.5Y(k+l)).
of YIJ, j = O,l, .
Granger’s
the
than if it is not.
causality
the prediction
- = If u* (Xl U. Y)
Causulity.
instantaneous
words,
4: Causality
u* (XIU-Y(k))
is denoted
is said to occur when X, is causing Y,
of causality,
his definition
error of an unbiased
1 above, states that if the
least squares predictor
X,, based on all the information
of a stationary
in the universe accumulated
since time t-l, is smaller than the variance of the forecast error of an unbiased least squares predictor of X,, based on all the information in the universe since time t-l except for the past values of Y,, then “Y is causing X.” Several important
characteristics
of this
definition
Granger (1969), “The one completely the use of the series U,, representing fact,
this
violation
requirement
makes
of one of Jeffreys’s
the (1967)
follow.
First,
as recognized
by
unreal aspect of the above definitions all available information” (p. 429).
Granger
definition
rules for theories
32
nonoperational of scientific
is In
and in induction.
namely,
“Any
unless
rule given must be applicable
the thing
defined
occurs. The existence an impossible replacing making
(p. 429).
Second, unbiased
predictor
criteria
definition
confirmatory
does not
predictor.
processes,
from
finite
sets
laws or theory,
is often not available.
the
in that embedded
criterion
is not applicable
whose
an unbiased
least
in
error of an
Also, for most processes,
parameters
Recognizing
gives the causality.
of the forecast
This confirmatory involve
Granger
in defining
is unusual
the variance
of data,
of
mention
the set of “all relevant information.”
of causality
which
explicitly
can be employed
criterion,
of “all relevant
is a step in the direction
that do not possess finite moments.
stationary
estimated
with the concept
Granger
laws in defining
statistical
least squares
to processes
in the universe”
the role of economic
Granger’s
it is a particular
when it
Granger suggests
operational,
that purely
of the definition
(p. 8). In dealing with this problem,
role of economic
By not mentioning
is useless
must not involve
While this modification
his definition
impression
in terms
A definition
of a quantity
“all the information
important
just
can be recognized
of a thing or the estimate
experiment”
information”
in practice.
values
squares
even
must
be
“optimum”
some of these difficulties,
Granger
(1969) writes, In practice optimum
it will not usually predictors,
be normally be nonlinear only
linear
unless
distributed,
all sets of series are assumed
Even in the case of linear systems sets of data, an “optimum”
will not always be available.
predictors
ways. It seems natural
and the above definitions
be used under this assumption
finite
to use completely
since such optimum
in complicated predictors
be possible
of linearity.
with parameters
to use
may again
(p. 429) that must be estimated
(in finite samples)
In fact, the restriction
to may
linear unbiased that
a predictor
from
predictor be linear
and unbiased can result in an inadmissible predictor relative to a quadratic loss function even in linear normal models, given the results of Stein. Thus, it is not clear that causality
the confirmatory are entirely
Third, unbiased
as regards
predictors
procedures
embedded
in the Granger
definition
of
satisfactory. the implied
quadratic
criterion
and variance of forecast or prediction
involved
in the use of
errors, Granger (1969)
writes: It can be argued that the variance to use to measure
the closeness
33
is not the proper criterion
of a predictor
Pt to the true
value X,. Certainly possible
if some other criteria were used it may be
to reach
different another.
natural
to use in connection
criterion
as it is mathematically in mean.”
the confirmatory
as a matter
of convenience.
Further,
Granger’s
in practice
Fourth, Newbold
procedures
with
of variances
notes,
depart
laws that
problems
in
from those based
are adopted
of applying
is viewed
it is not applicable
by Jeffreys concept it must
it to a number
of be
of cases
have been solved. on the general
concept
of causality,
Granger
and
(1977) write,
definition.
as it stands
definition
simplification
inadvertently, entirely to those in
this the
and more
of statistical
that and
and Newbold in defining
that the concept
considerations, Basmann,
Granger not
have been mentioned
of Granger
and
of the
kind
X and Y arc not considered whether
within
34
causality.
They, can be
of view that
is
The simplifications
Newbold
discuss
involved
in the
the context
the modified,
above.
to recognize
of causality
a point
and others,
Simplicity Postulate that deals with the forms of laws. Fifth, Granger’s definitions 2.4 are also subject up in connection with his definition 1. In addition, it is hard to determine
to
in so doing,
acceptable
laws or theories
of Feigl, Jeffreys,
nature
that,
and particularizations
give the impression
in terms
particularizations
only by imposing
particularization
less intuitively
is the failure
the role of economic
perhaps
to be testable.
(p. 225)
though,
defined
definition
and
be recognized
will become
Some of the simplifications Most important,
is far too general
to reach a testable It must
error-prone.
and
to comparisons
confirmation
in commenting
It is possible
statistical
name might be “causality
and others. The posterior probability more general than Granger’s; however,
considerable
contrary
one
with linear predictors
as Granger
associated
The definition
explicitly
procedure
that not all technical
encountered
a better
However,
probabilities
(1967), Burks (1977), confirmation is much recognized
whether
does seem to be a
(p. 430)
Thus linking
on posterior
about
The variance
easy to handle and simple to interpret.
If one uses this criterion,
general.
conclusions
series is causing
appear
to
be
Jeffreys-Wrinch
to the criticisms brought since the two processes
of particular
operational
economic
Granger
concepts
laws, are
indeed
applicable
Granger
(1969)
introduced
and
lead
himself
points
constructed
this point,
examples
can be resolved (p. 431).
Perhaps
out economic Last,
out,
silly answers”
which seem to produce
while
satisfactory
position
latter
point,
(p. 430). After analyzing be found
to common
which causality
would
have, in terms of predictability Granger
causality,
. .although definitions
sense
is defined”
be to define
according
that
causality,
to well-thought-
there will
occurring. effect,
intervals.
to
suggest certain
that
causality, such
relevant
the
causality
is
information,
the
in the data, have not been used. Due to this suggest that in many
instantaneous variables
causality
were
economic
would
recorded
and what has been presented asymmetrical
such a view is not compatible component
In summary, is a nonoperational
situations
disappear
at more
frequent
if the time
setting.
or otherwise.
above reveal that Granger generally
view of cause and effect. As mentioned with certain
of a definition
Granger’s definition
special confirmatory the suggestions
rule out the concept
(p. 430)
a temporal
is not a necessary
completely
is no real instantaneous
appear
one might
economic
does not
This is because
an apparent
This statement
(1969)
he does remark that in some cases,
missing readings
definition involving
physical
the definition
are not
could be covered if definition
covered.
and
his definition
1 above,
of predictability
in a very
does not involve mention surrounding
operational
Perhaps
1 were broadened.
of laws,
the definition
have important
nonstochastic
of laws for which least squares unbiased optimal
science considerations
consideration
The definition
In fact, the conditions
for making
earlier,
of causality. of causality,
tions for the forms of laws. For example, approximately
this
series, the definitions
results contrary
the set of data within
a more
On
laws.
of instantaneous
and forms
results.
“Even for stochastic
he goes on to say, “It will often
by widening
as Feigl and others
economic
unambiguous
above may give apparently
a case illustrating
adopts
to
variables
and
implica-
are excluded,
predictors
are not at least
in principle
such variables
However,
if definition
1 is so
broadened, it appears to the present writer that it may as well be broadened to coincide with Feigl’s definition of causality, namely predictability according to a law or set of laws. Given careful attention
to the formulation
of such laws,
confirmatory procedures that are appropriate for them can be applied. Indeed, this last approach seems very similar to that employed traditionally in econometrics.
35
IV.
In this section preceding
sections
that employ
recent
with standard
employing
issues discussed
in the
will be given to studies econometric
Granger-Wiener
concept
it will be assumed
of
that
readers
in Cowles Commission
Mono-
terminology.
early paper,
an econometric
economics
the
In the discussion,
macroeconomic
introductory
involving
to above as the “traditional
econometric
(1947)
14, involves
Keynesian
studies
First, consideration
studies
will be reviewed.
Haavelmo’s graph
several empirical
will be analyzed.
Then
are familiar
Tests of Causality
what has been referred
approach.” causality
Empirical
reprinted formulation
model
that
textbooks.
and estimation
appeared
and
of a simple
appears
The simple model that Haavelmo
in
many
considered
is given by:
C,
=
p
+
uy, +
(4)
U*
T
t= 1,2,..., y, = Ct + zt .
Equation
(4)
is a consumption
(a) consumption parameters
(5)
in period
with unknown empirical
on consumers’
expenditures
income
will be given adopted,
“investment
work, he employs
here
dollars
dollars
per capita,
to the adequacy
expenditures,
in
random
income
and consumers’
expenditure,
private
net
minus
of Commerce to measure
to measure
condition
involving
data
c,, and
yt. No attention
measures.
which
corporate
Haavelmo
savings
If they are
aggregate
demand
points
plus
While much more could be said about the interpretation
of an equilibrium
disturbance.
by the data with zt equal to the difference between dollars,”
constant
investment
variables,
t, y,. p and a are
satisfied
equal deficits.
endogenous
per capita
of these empirical
(5) is an identity
disposable to
two
in period
U.S. Department
in constant
in constant
then equation
relating
values, and uI is an unobservable
In Haavelmo’s disposable
function
t, C, and (b) income
out is
government
of (5) in terms
and supply with special
assumptions regarding aggregate supply, this matter will not be pursued. Haavelmo then completes his model by assuming (u) that the 14~‘s have zero means,
constant
common
variance,
the time series zt is autonomous fulfilled
if the sequence
and are serially in relation
Z, is a sequence
36
uncorrelated
and (0) that
to zlr and y,, a condition
of given numbers,
that is
or if each zt is a
random
variable
which is stochastically
that sample variance
independent
of the zl’s converges,
nonstochastic
zt’s or in a weak probability
to a positive,
finite constant.
a causal model, may
the disturbance the
several
are errors term’s
autonomous
possible
and future
z,‘s) future
z,‘s) the future
very well if there Thus,
logical sense, Haavelmo’s predictions
if it is difficult
values of the zt’s or to predict
in specifying
properties,
the consumption
or if it is assumed assumption
for the model’s
possible
zt’s,
model is
values of c, sense,
to obtain
zt’s very well. Also, the model
or exogenous
reasons
of future
values of z,. In an inductive
not yield good predictions
case of nonstochastic of stochastic
In a deductive
estimates
he assumes
in the case of
sense in the case of stochastic
since it allows us to obtain
and y, given parameter the model
of ut. Further,
either mathematically
(in the
(in the case
may not predict
function’s
form or
that z1 is autonomous.
regarding
zI is just
poor performance
one of
in actual
prediction. In his paper,
Haavelmo
Z, is autonomous model
gives special
or exogenous.
to provide
two alternative
models
His third model involves the following
Ct = p+ uy, + Ut
rt
=
yt
= ct+xt-rt
IJ
+p*(c,+x,)+w,
to the assumption
involves
elaborating
that
his simple
in which z1 is no longer autonomous.
equations:
9
(6)
(
(7)
(8)
Xt = an autonomous
variable
in which ct, y,, and rt are endogenous and ut and wt are disturbance
attention
His approach
(9)
variables,
(7) is a business saving equation,
terms, not necessarily
uncorrelated
but with zero
means, constant covariance matrix, and serially uncorrelated. Note from (5) and (8) that zt = .xt - rl so that if rf is endogenous, z* will be also. Given future values of xt and parameter can
be employed
estimates, to generate
it is clear that the expanded
model
in (6)-(9)
predictions
future
values
c,,Y,, andr,.
37
of corresponding
of
In his analysis 1968)
points
covariance model
out
that
between
collapses
autonomous
of Haavelmo’s
or
if the parameter
the disturbance to
expanded
become
exogenous.
model,
p in (7) has a zero value and if the
the
original
Thus
a test
model
shown
of the joint
the traditional
models.
In
this
information seriously,
approach,
to formulate the initial
equations) diagnostic as
in
Haavelmo’s
prediction
economic
in the econometric
it is most including
employ
the Granger
leading
examples,
(1977).
Sims (1972)
that
causality
formulations.
theory,
more generally,
writes,
is unidirectional
to model-building
account
attention Feige
role of
in developing
causal
matter
from money
tests
of causality
obtained
relations
between
in several
other
“Results
important studies.
finding
to income
38
and Pierce
is that the hypothesis agrees with the postwar from income who analyzed
of this type [independence
economic
Using
a similar
that
will be given to just three
U.S. data, whereas the hypothesis that causality is unidirectional to money is rejected” (p. 540). On the other hand, Pierce (1977), of causal
considera-
is not taken of this
and Pearce (1976),
“The main empirical
similar data for the U.S., concludes,
literature.
the central
subject
all reported
of causality,
Sims (1972),
and
role in developing causal models in as obvious, as several empirical tests
to consider
concept namely
After
to diagnostic
to emphasize
below will show, adequate
“obvious” point. Since it is impossible
of
considerations,
the model may have to
is subjected
economic
of
to a number
and in the statistical
important
To state this point
considered
is taken
SLICKsimplicity
economic
broader
version
tions, including theory, play an important science. While some may regard this point of causality
Postulate
single-equation
it is subjected
certain
the reformulated
both
purposes,
models.
outside
with the size (number
checks have been performed,
considerations,
economic
other
simple.
In this connection, suggest
in other
of what migllt
and
and so on. Various aspects of this approach
discussed
For present
may
p = 0 and
causal econometric
theory
relationship
z1
or exogenous
some elements to building
If the Simplicity
model,
with
if it is not defective
economic
model.
entertained
case, Then
checks,
hypothesis
will be sophisticatedly
checks.
and prediction
have been
(4)-(5)
Clearly, it is possible to have complicated
the initially
be reformulated.
uses
a tentative
and prediction
diagnostic
provides approach
stand in a one-to-one
of a model. Given
one
formulation
does not necessarily models.
models
econometric
in
that zt is autonomous
and that the original model (4)-(5) may be adequate respects. The review of Haavelmo’s
(1966,
terms II, and 1.~‘~ is zero, then the expanded
COV(U,,M~~) = 0 is a test of the hypothesis
be called
(6)-(9), Chetty
variables]
have
methodology,
or lack also been Feige
and
. .have found
Pearce.
little or no association
monetary
base) and gross national
it appears
that the findings
Pearce (1976) First,
an empirical
specification
terms,
the patterns
without
between
empirical
old or new economic
cited
theories.
time series. The data
to suggest,
at least in general
that do or do not exist”
“measurement
without
as useless; his approach
results
(p. 11). Thus,
as one that involves
The phrase meusurement
Pierce’s approach
important
economic
as feasible,
quite frankly
theory.”
used to condemn generating
insofar
is described
[economic]
tests of causality
when he writes, “The present study centers around
of interrelationships
Pierce’s approach
opposite.
in what follows.
what Feigl would call a law or set of laws,
of relations
are permitted,
and of Feige and
are considered
the three empirical
resembling
Pierce (1977) is most explicit themselves
on the one hand,
of these tests of causality
anything
supply (or the
data” (p. 19). Thus,
on the other hand, are diametrically
on the issue of whether
above embody
the money
using quarterly
of Sims (1972),
and Pierce (1977),
This and other features
between
product,
theory
is not
may be capable
that can then, perhaps,
be explained
Until this latter task is accomplished,
of by
however,
by not incorporating
economic
law or laws, his analysis
is not causal according
to Fe&l’s definition,
presented
in Section
Sims (1972)
and Pearce (1976), (1977),
while not as explicit
do not develop
a detailed
about
the relationships
specification
of economic
11. Similarly,
relevant
economic
theory
is not considered,
variables
rather
than
variables
in these
analyses
has been
p. 18) and by Sims (1977, described
the problem
in regression theory, variables performed. theory
Because
they
Thus,
the attempt
do not
to establish
to realize employed
of the post hoc ergo propter’ hoc
4Newbold
(1978),
problem
by Pierce (1977,
specific
statistical
Personal communication.
39
Newbold4
of left-out
variables
to subject
matter
that, in each case, the two without
for the analyses use of economic
of causal laws in the
this fact when
he writes,
“The
here does rest on a sophisticated
principle”
(p. 543).
or just “obscure” will not be argued here. to make Granger’s definition of causality
introduce
e.g.,
or relevant
with the author,
causality
appears
version
studies
of variables,
more than two variables
pay attention
causal direction
of identifying
all three
forms
from investigation
method
version is “sophisticated” Second, in order
if
and/or the only two relevant
laws is a departure
sense of Feigl. Sims (1972)
of
to the problem
offer little assurance
are appropriate
or economic
as a serious
analogous
in the context
As is well-known,
be included,
Failure to include
recognized
considered
examined
may
p. 40). In a conversation
as simply
models,
the studies
incorrect
real variables,
may be excluded.
of theory as Pierce
they examine
laws or theories.
nominal economic
the omission
that
and Feige
operations
Whether
the
operational,
and assumptions
that
have
implications
particular
of economic
laws
and,
Sims (1972)
probably,
for the
states some of these
“We will give content to Granger’s definitions by to be jointly covariance-stationary, by considering
all time-series
linear
predictors,
and
for predictive
tions have already that
forms
quite cryptically,
assuming only
the
results of these and similar studies.
assumptions
criterion
for
most
time
covariance-stationary.
in Section
series
variables
used
squared
forecast
that
error
not,
to emphasize
as Sims
he will consider
as our
of these assump-
Ill. Here it is relevant
are nonstationary,
Sims may mean
In fact, he mentions
all
expected
(p. 544). Some implications
been discussed
economic
are stationary.
by taking
accuracy”
filtered
assumes, series that
that
in
[his]
regressions
were
measured
as
natural logs and prefiltered using the filter 1 - 1 SL + 0.5625L’ [where L is the lag operator] . . . .This filter approximately flattens
the spectral
and the hope
density
was that
of most
regression
economic
residuals
nearly white noise with this prefiltering. It is very questionable
that this specific
time-series,
would
be very
(p. 545)
filter does what Sims claims (or should
do what he claims in terms of producing
flat spectra).
Further,
if his regression
error terms were generated by a particular AR(2) process, zlt - 1.521,_, + 0.5625 ~~~~~= et, where et is white noise, his procedure would produce white noise errors. throw there
The results
considerable
of his empirical
doubt
on the adequacy
may be some filter
variables, following
tests for disturbance of his filtering
or filters that, when applied
autocorrelation
procedure.
However,
to highly nonstationary
render them stationary. Feige and Pearce (1976) and Pierce (1977), Box and Jenkins, employ differencing to render series approximately
stationary; that is, their filters are ( l-L)a, where a assumes an integer value, usually 1 or 2, and need not be the same for different variables. Then relationships
to be studied
variables,
certainly
are formulated an important
in terms restriction
of the transformed
or filtered
on the forms of economic
laws.
It might be asked, “Why filter? ” and “What are the possible effects of filtering?” On the question “Why filter? ” it appears that forms of laws are being thereby restricted so that stationary. statistical theory can be applied. In terms one can employ autocorrelation functions. crossof stationary variables, correlation
functions,
law or model or trending to
estimate
etc. However,
in terms
stochastic parameters’
if it makes economic
of nonstationary variables, values
variables,
it is not necessary and
to predict
40
sense to formulate
e.g., nonstochastic to filter variables
from
such estimated
a
variables in order models.
Thus,
it can be seen that the filtering
are covariancestationary nonstochastic stationary
is not
variables.
variables
considerations
This is not
in terms
of analyses
stochastic
changes
using a money
variable,
that
“What are the possible whether
example
illustrating
that controlled
can produce
stationary
effects of filtering?”
it must be
or by use of more
to justify
Friedman’s
phrase5 “throwing the baby out with the bath.” Also, Friedman’s his letter regarding an earlier draft of the Pierce (1977) paper the following
of causality
example
of the type
to dramatize
carried
through
Consider
the nonstationary
processes
measured
real consumption
and income,
lnY,
where Cr respectively. with
and Y r are real permanent
k assumed
stationary
to the Sims regression
techniques
consumption
and found
is a confirmation
function;
or independent
and YT and/or
underlying economic filtering. In addition,
(1975),
respectively.
consideration. C, and
Y, are
Assume that
and real permanent
income,
the same filter can be employed) to produce the or subjected ut and vt. If uI and vt are cross-correlated
uncorrelated
‘Friedman
under
on tests
assume that In C, and In Yt are each filtered (if CT = kY r,
consumption
Cr
of filtering
In Ct and In Y,, where
in
led me to
constant,
innovations,
is being obtained
in the papers
remarks
,
= lnYy+v,
Further,
the effects
non-
a series that is
by filtering.
by differencing
general filters, can be drastic enough in some circumstances
formulate
to
use of prefiltered,
(1977, p. 196). In addition,
it is obvious
of money
to be made covariance
that the effects of filtering,
that
it is to say that subject matter
by Hendry
in the rate of growth
On the question remarked
Rather,
variables
and is inapplicable
in this regard. An excellent
is provided
if not impossible,
to produce
in general
to say, however,
is never appropriate.
are very relevant
some of these considerations
difficult,
of variables
necessary
to be totally
uncorrelated,
of one form of Friedman’s
the conclusion
that filtered
says nothing
the causal relation
about
between
theory
what of the
In C, and filtered
In Y, are
the causal relation
between
C, and Y,. The nature
of the
theory is critical in interpreting results based on premeasurement considerations are relevant, since 14~ and vy
Personal communication.
41
contain
errors in measuring
filtering
is not
p. 429)
definition
how
important
consumption
and income.
in a “nonstationary”
required
of causality. economic
laws are in defining
procedure
possibly
too much
In general
then,
a mechanical,
results.
The
to employ,
e.g., seasonal fruitfully
filtering
resolved
results
adequately. 5 percent
(Sims,
in relation
to interpret
Feige
filtering
procedure to filter
to specific money
Sims
and
Pierce (1977)
that
economic
that necessarily
produces
and what
of filters
kinds
adjusted
economic
writes,
and either and
(1976)
Pierce
do
GNP or the rate of
seem supply
it will show up as unrelated to interest
impact
(1977)
not
“Thus if the money
over the sample period,
mention
control
design
has probably
considerations]
insofar
been operative
macroeconomic
to anything
[in terms of as closed-loop
such instruments
as money, interest rates and government spending such targets as inflation, unemployment and inCome. the context x
[the input
of the dynamic variable]
regression
has been
model.
adjusted
and If in
. . ,suppose
to keep _V [the
output or dependent variable] on a desired path according to a control strategy xI = C(B)y, [where C(B) is a polynomial in the backshift or lag operator B]. Then it can be shown that not only is the lag distribution [ V(B) in y, = V(B)x, + ~~1 unidentifiable, but that identical residuals and model forecasts
can result from
42
it else,
etc., might
over the sample period
series, including
this
grows by exactly
rates, reserves, income,
The data may be even worse than happenstance
on the
to appreciate
be” (p. 18). He also explains:
for many
data),
laws or theories
policy and its possible
(1972)
Pearce
what its actual relationship
experimental
time
considerations.
involving
of causality. but
Thus, it is difficult
1972, uses seasonally
is the issue of monetary
of tests
complication,
despite
of analyses
there
neutral
issues of whether
and other serious subject matter inflation,
theory.
it has to be recognized
series is not usually
In terms
While Pierce (1977)
detrending/deseasonalization
or “too little.”
satisfactory are most
(1969,
illustrates
out of the series” (p. 19), he does not link
with any economic
what is “too much”
example
causality.
in a special case that ‘I. .the deterministic
up this possibility
of the Granger
This consumption-income
recognizes
took
It is also the case that
version
it
1.
model
with
V(B) chosen
so that
the disturbances
[the zlt ‘s] will be white noise; ii.
a “model”
. ..
only to its own past; an infinite number of intermediate
111.
with
V(B) = 0 so that y is fonnally
Perhaps this is not surprising; and past y then, nothing
new.
strategies
over
in the short
they have existed.
control sample
indicate,
unambiguously
panaceas,
regarding
the nature
policies
analyzed.
Without
mechanical
tests
(p. 20)6 effects
tests highlight
the
have been pursued such study,
of
causality
in
as Pierce’s cannot
be
as it may be to those who seek purely
of policy control
requires
laws and testing
appreciated,
past
the possible
of causality
of
Irritating
tells us the
run and shifting
being
results
causal economic
a problem
results
of what monetary
period
the
remarks
on the
study
interpreted.
in formulating econometric
and insightful policies
of serious
the particular
if not
detailed
consideration
their performance
completely
solved,
in the
in predictraditional
approach.
To return nonoperational
to some definition
on the nature (1972)
control
from present
x in addition
in the long run; but certainly
importance
tion,
if x is determined
y, knowing
Certainly
Pierce’s thoughtful
statistical
models.
30 years have been imprecise
of monetary
remarks
knowing
related
other
of economic
analysis
aspects
of causality
of money,
of how
“operationalizing”
leads to restrictions,
laws and some specific test results, X,, and income,
Y,, variables.
Granger’s
some of them severe, consider
Sims’s
Since these variables
are nonstationary, as mentioned above, Sims prefilters the natural logarithms of these variables to obtain xt and y,, assumed stationary. He then considers the following
linear autoregressive
representation
of the assumed stationary
variables
X, and yt:
(10)
where b&j mutually
is a polynomial
uncorrelated
in the lag operator
white noise errors.
6References cited in original have been omitted.
43
L. i, j = 1, 2, and ~1, and vf are
As Sims (1972, autoregressive
p. 5443 mentions,
representation
in the (iranger
as given
sense, running
Granger in (lo),
has shown that if there is an then
the uhsence
from y, to xt is equivalent
b, 2(L) f 0. Given this condition,
of causality,
to the condition
that
(10) reduces to
(Ila)
Since [lt and I)~ are mutually
uncorrelated
terms,
fonn
(1 1) is an extreme
and non-serially
of a fully recursive
correlated
model,
disturbance
extreme
since no
lagged values of y, appear in (1 la), u/z utlded restrictiorz
to the usual definition
of a fully
to write
regression
recursive
model.
From
the dynamic
for y, as
b,,(L) _Y, =
--
b, CL)
x*+---
2
with
(I 1b), it is possible
I
v
b,,(L)
t
(12)
’
V(L) E - b, 1 (L)/h, *(L). As can be seen from (12), the disturbance
term
is in the form of an infinite moving average, 0,: (L)v,, and hence will in general be autocorrelated. Under the special assumption that b, 2 (L) is of degree zero in L, the disturbance nonstationary common
variables
term will not be autocorrelated. Y, and X,
filter, C’(L), is applied
are related
by
On the other Y, = V(L)X,
to both sides, C(L)Y, = V(L)C(L)X,
hand,
if
+ NJ,, and a + C(LW,,
or I’, = V(,!,)s, + C(L)W,. Then if M’* = v,/C(L), J‘~ = V(L)s, + vt. The disturbance term, vt , in this last equation differs from that in ( 12), namely, hi 1 (Z,)vt. Thus, in terms of the system (1 1) with X, = C’(L)Y, and J’, = C(L)Y,, the result in (12) indicates that disturbance terms will generally be autocorrelated. Y, = V(L)X, + \I’~ is viewed as a starting point, it is clearly not derived from (1 1), and on filtering both sides using C(L), it will generally have aut.ocorrelated disturbances, except in very special cases. Indeed, Sims
If the relationship
44
(1972)
reports
results
(11) and concludes, sive tests can only F-tests
be that
on regression
has pointed
out
can be produced
of tests for serial correlation
“The conclusion
explicitly
that
serial
correlation
of relevant
implementation
the form
to approximate
about
(1957,
in the error
terms
in (10)
distributed
to make assump-
distributed
lag. Sims (1972)
lag term by a finite distributed
lag term and explains ‘I. . .the length of the estimated lag distributions generous” (p. 545). Keeping the length “generous” is understandable of avoiding involve
a misspecification
a finite truncation
an important
of the lag pattern. when
only
his data. A basic result of this approach errors associated Table current
coefficient
estimates
of quarterly
values of filtered
while his smallest
is 0.276.
to 0.300
in absolute
is quite
overlooked.
coefficient
value. These results indicate
low even when
possible
monetary
in estimation
is noted
as a statistical
values of his
base range from
standard
estimates
errors range
range from 0.105
that the precision
of estima-
of disturbance
The same can be said of his other two-sided
of precision
standard in Sims’s
base, his largest
The absolute
autocorrelation
in
GNP on eight past,
for the four future values of the monetary
to 0.3 18, while the future
are available
lag coefficients
filtered
does
lag parameters,
from the reported
to 0.65. In the case of GNP on Ml, his coefficient
from 0.294 tion
quarterly
error is 0.338,
78 degrees of freedom is evident
was kept in terms
this approach
of many
of the distributed
In his regression
and four future
standard 0.088
with the estimates
4 (p. 547).
However,
of the lag and introduction
consideration
of the
pp. 43-44)
variables.
of (12), it is necessary
of V/(L)x:, an infinite
this infinite
terms in
or inconclu-
the accuracy
(p. 549). Also, Quenouille
by the omission
regarding
chooses
is room for doubt
coefficients”
For the empirical tions
there
of disturbance
from this list of approximate
terms is
regressions.
This lack
caveat by Sims (1972)
in
about the middle of his paper: Though the estimated distribution looks like what we expect from a one-sided true distribution, the standard errors on the future
coefficients
just
what
a unidirectional
but
they
bidirectional In other point
words,
the F-tests
causality
high. These results are believer
are not such as to necessarily causality
Sims is saying
of view, have yielded
inconclusive
are relatively
would
expect,
force a believer
in
to change his mind. (p. 547) that his analyses,
inconclusive
viewed
from an estimation
results. The results would be even more
if one were to do a detailed analysis of the validity and power of it must in the paper. In view of these considerations,
employed
45
bc stated
that Sims’s strong conclusions
at the opening empirical
and end
analyses.
of his paper,
As pointed
tests are not very powerful, errors,
seasonal
of monetary becomes
of money,
his estimates
even when no consideration effects of filtering,
supported
stated by his
are imprecise
and his
isgiven to autocorrelated
leftaut
variables,
When these latter points are considered,
and forms
Sims’s conclusion
even more uncertain.
Unlike
Sims, Feige and Pearce (1976)
estimate
a dynamic
variables
stationary,
models
the exogeneity
are not convincingly
out above,
complications,
policies.
about
regression. (b)
autoregressive-moving
variables,
cross-correlations
and Pierce (1977)
from
Enough
has been said above about the possible important filtering
associated
with
techniques policy
(h) of the process,
on results
control,
there
errors
is often
(ARMA)
contemporaneous
innovations
for the pairs of variables under consideration
to make their
average
and (c) then compute
the estimated
schemes or other
do not directly
they (u) use differencing
construct
for their differenced
and lagged
Instead,
of their ARMA
and test their significance. effects of differencing
of analyses
as well as complications
of measurement,
etc. As regards
some difficulty
in determining
step
the forms of
ARMA schemes from data. Any errors in this operation would be carried over to affect the operation in (c). Finally, in step (c,), a large sample x2 test is employed As lucidly not exactly
to test the hypothesis explained
that population
by Pierce (1977,
the same as, analyzing
crosscorrelations
p. 15), step CC) is closely
a dynamic
regression
directly,
are all zero. related
to, but
as Sims (1972)
does. In the one explicitly he investigates circulation.
After
completing k=lO
statistics’
reported
the relationship
A2
value,
example
between steps
in Pierce’s (1977,
weekly
(u)-(c)
retail
above,
p. 15) paper,
sales and currency
he obtains
a sample
in test
(2 1) = 38.1. Thus, at the 1 percent
= 39.1 >&,,
x_$2 level of significance, his large sample x2 test, using the estimated correlations of the innovations, the t,‘s, yields a “significant” result.
cross-
Pierce
comments, One could tentatively causality from retail tion
concerning
conclude that there is unidirectional sales to currency (although the situa-
feedback
is somewhat
unclear):
evidently
a
rise in retail sales results in a somewhat greater demand for . .The explanatory power of this relationship is currency. quite
small, however,
as the cross correlations
(p. 16)
46
arc not large.
-
These remarks test yields doubts
are quite
confusing
“significant”
about
to the uninitiated
results at the 1 percent
reader. Pierce’s statistical
level of significance;
the results of the test. A similar methodological
yet, he has
statement
is made
by Sims (1972): In applying preceding
the F-tests section,
for causal direction
size of the coefficients
is important
It is a truism
too often
“large”
the
from
ignored
economic
that coefficients
which are
of view should
how statistically
Pierce and Sims are pointing
not
to a defect of mechanical
procedures
be
“insignificant”
tests. The information
in the testing
information.
is what Sims suggests is reasonable
Nowhere
in the
regardless of the F value.
point
casually set to zero no matter they are. (p. 545) Apparently,
suggested
one should bear in mind that the absolute
significance
does not reflect all the relevant done by Pierce or by
Feige and Pearce; that is, Pierce and Feige and Pearce do not look at the absolute sizes of the individual simple
regression
dynamic
the correlation
coefficient
not necessarily
imply
crosscorrelations of uncertainty
and dynamic
crosscorrelations
coefficients
regression
and/or
coefficient
regression
coefficients.
an analysis of causality
and standard
Feige and Pearce, without
significance
adequate
specified alternative
their sum. In a
is /3 = crXY/oz, while Clearly, a small p need carry over to apply to
is p = uXY/u.xuy = (ox /u,,)p. a small /3. Similar considerations
regarding
to precisely
regression
of y on x, the
Thus, there is an element
that relies only on the estimated
tests,
as employed
by Pierce and
concern
for the power of these tests relative
hypotheses.
This point was raised by the author
in connection
with the FeigePearce
the University
of Chicago Money Workshop.
analysis
several years ago in a meeting
of
From this review of three papers in which tests of causality have been applied, it is concluded that for a variety of reasons the tests’ results are inconclusive of the
with respect
results
extensively
may,
to the basic issues considered.
in part,
by the authors,
particularly
goes deeper than just “technical considerations the
and theory
inconclusive
models,
which
nature take
economic
theory,
definition
of causality.
be due to technical
of subject attempted
This operation
quite
the problem
at the heart of
Instead
of formulating
sophisticated
matter
considerations
and relevant
to operationalize
led to consideration
47
nature
lack of subject matter
in these studies is probably
of the results.
account
discussed
Pierce and Sims. However,
issues.” The fundamental
exhibited
the authors
The inconclusive problems
a nonoperational of an extreme
form
of a fully recursive to economically
model
as the null hypothesis
to have been tested
appears
an economic
in the testing, causality,”
according
appears
mentioned
from
Given such a broad range of alternatives,
are as inconclusive
as they are. Further,with
laws and other subject
it is questionable
It is indeed
paid
The very special null hypothesis
against a very wide range of loosely specified,
that results
in the way of economic
with little or no attention
alternatives.
point of view, alternatives.
it is no wonder
Pierce
specific
motivated,
matter
that the analyses
considerations
are properly
little involved
termed
“tests of
to Feigl’s definition.
surprising
sensitive
that, of the authors
to the important
in the previous
paragraph.
considered,
role
only the statistician
of economic
Pierce (1977)
laws or theory
writes in his concluding
paragraph, Considering that by
all of these problems,
incompatible the same data,
that
a variable
variables. we
analysis
economic
situations that that
the proposition
bears
mathematical
is related
of result,
econometric
limited
theory
contained
as valid statistical statistical
is in such
past--it
be available concerning
assume
within
this
relationships--
“relationships”
to its own
[i.e.,
use in ascertaining
since we cannot
relationships
only
of other
this type
Economic
important:
is, as more valid than
that prior information
out that
is of rather relationships.
can be established
a variable
be “confirmed”
in particular
conclude
all the more
the
theory
can often
to any of a number
research
justifiably
statistical] certain
including
is not related
If future
might
it is perhaps small wonder
propositions
where
is imperative these relation-
ships. (p. 2 1) Recognizing “theory
sophisticated successful. with
the failure
without
what
econometric
of “measurement
measurement,”
economic
theory
This approach has
been
and
if not
approach.
48
theory”
the hope
relevant
is in line with
preached,
without
Pierce offers
statistical
Feigl’s always
and the failure
that intelligent
definition practiced,
techniques
may
of causation in the
of
use of be and
traditional
V. Summary In the preceding reflects
philosophers’
has been reviewed been
published
given
From
a philosophical
of causation,
of the concept
with several definitions
econometric
literature.
applications
of “causality
this review
and comparison
analysis of causality
definition
and clarification
and compared
in the
to several
literature.
sections, thinking
and Conclusions
tests, the following
of causation
In addition,
tests”
that
which
of causation, that have
consideration
have appeared
of definitions
major conclusions
was in the
of causation
and
have been reached:
The philosophical definition of causality, reviewed above, is adequate 1. for work in econometrics and other areas of science, a conclusion considered to be fortunate, “unity
given the importance
of science”
that the present
writer
attaches
to the
principle.
The philosophical definition of causality, reviewed above, is an opera2. tional definition in contrast to the Wiener-Granger “population” definition of causality,
a fact
methodological 3. tion
Basmann’s provided
respects
that would
grounds
definition
recursive,
as Strotz
are placing
and laws that
grounds
definition
Insofar
they
definition
is very close to the philosophical
differs from the latter
in cases in which only data relating
narrow.
models
of causality
by Feigl. The former
are available. The Strotz-Wold 4. rather
lead some to dismiss the latter
on
alone.
cannot
and is not required
to a single realization
of causality
is subsumed
and Wold require
an a priori
of a process
in Feigl’s
on the forms
on purely
by Fe&l’s, Jeffreys’s,
deductive
Basmann’s
defini-
in certain
that the world
restriction
be justified
slightly
and is
be “truly” of economic
methodological
and Simon’s defini-
tions of causality. 5. not
Simon’s definition an inductive
consideration
of causality
property
embedded
rowing the concept Thus,
of causality,
predictions. Simon’s 6. between ment
a model
Simon
by causation
definition
namely
view of Strotz and Wold and with views expressed
49
a fundamental
the quality
require
temporal
time. Simon’s definition
of view, but in conflict
a
By narof predic-
sense and yet yield worthless
does not
in chronological
of models,
predictability,
definitions.
and others have omitted
or causality,
of causality
property
of models’
and others’
can be causal in Simon’s
cause and effect
with Feigl’s point
the quality
in Fe&l’s, Jeffreys’s
part of what is meant tions.
is a formal, deductive
involving
asymmetry is in agree-
with the “true recursive model” by Granger.
7.
The
Wiener-Granger
embedded
a particular in a variety
not mention
any particular
but
no mention
others’
confirmatory
of economic
is unusual
that
in that
in it is
is not very general
In contrast,
and is
Fiegl’s definition
does
procedure.
definition
including
definitions,
criterion
of circumstances.
The Wiener-Granger
considerations,
of causality
confirmatory
inapplicable 8.
definition
involves
a special
form of predictability
laws. In this regard it is devoid of subject
subject
including
matter
Feigl’s,
theory,
that
and thus
do mention
both
matter
is in conflict
with
predictability
and
laws. 9.
In “operationalizing”
a priori
restrictions
definition. tion
of
the WienerCranger
are imposed
It is concluded causality,
predictability
definition
on the class of economic
of causality,
various
laws covered
by the
that it is preferable to employ a more general definiwhich imposes only the restriction of
such
as Feigl’s,
on forms of economic
laws.
From the review of applied “causality tests, ” it is concluded that results 10. of these tests are inconclusive. The specific reasons for this conclusion can perhaps
be summarized
matter
considerations,
examples matter
by saying that there was inadequate or to put
of measurement considerations.
it slightly
without
Where
much
subject
bear, they were not satisfactorily
differently,
economic
matter
integrated
attention
to subject
the studies
represent
theory
and other
considerations
were
with the statistical
subject
brought
to
analyses.
In the tests of causality involving linear stationary processes, a particularly 11. extreme form of a fully recursive model is regarded as defining the condition under
which
extreme
“one variable
restriction
causes another”
on the form of models
tion of a causal model linking
in the WienerGranger is not required
sense. This
by a broader
defini-
the two variables.
Sims’s use of “forward and backward” regressions and Feige, Pearce, 12. and Pierce’s use of cross-correlations of estimated innovations involve consideration of forms of stationary
single-equation
eters.
of the Principle
This is in violation
Postulate.
Practically,
consideration
the result
of regressions
with limited relative
data resulted alternative to
independence. Mechanical 13. causality
filtering
models involving of Parsimony
of such a violation
with many
many, many paramand the Simplicity
in the present
free parameters,
instance
is
which when analyzed
in rather imprecise estimates and tests with low power hypotheses involving serious departures from of
series
tests of the kind considered
can
above.
50
exert
a substantial
influence
on
In summary, available. offering
it can be said that
Departures
from
this
little in the way of dependable
application
of causality perhaps motivated
without
the
and subject
matter
definition produced
and convincing form
and difficult
considerations
work
of causality problems,
of integrating
will be able to produce naive and misguided
is
while
results. The mechanical
of “measurement
by the hope that application
results. That this hope is generally econometricians
have
tests is an extreme
theory,”
delicate
an adequate
definition
of statistical statistical
without techniques techniques
useful and dependable has been recognized
for a long time and is a reason that reference
by
is made to laws
In establishing and using these laws in in Feigl’s definition of causation. econometrics, there seems to be little doubt but that economic theory, data, and
other
subject
matter
considerations
as well as econometric
techniques,
including modern time series analysis, will all play a role. “Theory without measurement” and “measurement without theory” are extremes to be avoided.
51
References Allais,
M. (1966), American
Ansley,
C.F.
(1977),
Graduate Basmann,
“A
“Report
R.L. (1963),
the
Quantity
“The Causal
Interpretation
Econometrica,
A.W. (1977).
Seminar
Association,
Chunce,
Evidence.
of Non-Triangular
Testability
of ‘Explicit
Models,”
University
36:
“Bayesian
582602,
An Inquiry
Causal of the
into the Nature
Analysis
of Haavelmo’s
in
in
reprinted
Studies
Models,”
Bayesiun
of
Econometric University
of
North-Holland,
Econometrica,
Econometrics
in Honor of Leonard J. Savage, eds. S.E. Fienberg
Amsterdam: Feige,
Journal
at Madison.
(1968), Statistics
Systems
of Chicago Press.
Models.”
Wisconsin
Series,”
60: 1080-93.
Cause, Reason:
Chicago:
on Time
V.K. (1966), “Bayesian Analysis of Some Simultaneous Ph.D. dissertation, Department of Economics,
Chetty,
of Money,”
3 1: 439-48.
the Class of ‘Interdependent’
Statistical
Theory
of Chicago. Mimeographed.
“A Note on the Statistical
against
American
Scientific
of
56: 1123-57.
on the NBER-NSF
Relations,”
(1965), Chains’
Review,
School of Business, University
of Economic
Burks,
Restatement
Economic
und
and A. Zellner.
1975.
Rational Expectations: E.L., and Pearce, D.K. (1976), “Economically Are Innovations in the Rate of Inflation Independent of Innovations in Measures of Monetary and Fiscal Policy ?” Journal of Political Economy, 84: 499-552.
Feigl, H. (1953), “Notes on Causality,” Readings in the Philosophy of Science, eds. H. Feigl and M. Brodbeck. New York: Appleton-Century-Crofts, Inc. Friedman,
M. (1975),
Personal communication.
52
Granger,
C.W.J. (1969),
“Investigating
and Cross-spectral Granger,
Methods,”
C.W.J., and Newbold,
New York: Academic Haavelmo,
Causal Relations
Econometrica,
P. (1977).
by Econometric
Models
37: 424-38.
Economic Time Series.
Forecasting
Press.
T.
(1947), “Methods of Measuring the Marginal Propensity to Journal of the American Statistical Association, 42: 105-22, Consume,” reprinted
in
Monograph
Studies
No.
in
Econometric
14, eds. W.C. Hood
Method,
Cowles
Commission
and T.C. Koopmans.
New York:
John Wiley & Sons, Inc., 1953. Hendry,
D.F. (1977),
to
“Comments
Econometric
Modeling
on Granger-Newbold’s
Model
Building’
and
‘Time Series Approach
Sargent-Sims’
‘Business
Cycle
Without Pretending to Have Too Much A Priori Economic New Methods in Business Cycle Research: Proceedings from
Theory,“’
a Conference,
ed. C.A.
Sims.
Minneapolis:
Federal
Reserve
Bank
of
Minneapolis. Jeffreys;
H. (1957).
Scientific
(1967). University Keynes,
Theory
Inference. of
2nd ed. Cambridge:
Probability.
3rd
rev.
ed.
University London:
Press. Oxford
Press.
J.M. (1921).
A Treatise on Probability.
London:
Macmillan
and Co.,
Ltd. Newbold, Pierce,
P. (1978)
Personal
D.A. (1977), Time
Series,
communication
“Relationships-and with
Special
Journal of the American Quenouille,
M.H. (1957).
Hafner Publishing Sargent,
T.J.
Business
(1977),
Reference
to Money
Statistical Association,
The Analysis
and
Economic
Interest
Rates,”
72: 1 1-21.
of Multiple
Time Series.
New York:
Company. “Response
Cycle Research:
Minneapolis:
the Lack Thereof-Between
Federal
to Gordon
Proceedings
and
Ando,”
Reserve Bank of Minneapolis.
53
New
from a Conference,
Methods
in
ed. C.A. Sims.
Simon,
H. (1953), metric
“Causal
Method,
Sims,
C.A. Review,
and
Cowles Commission
and T.C. Koopmans. (1978),
Ordering
Identifiability,” Monograph
Studies
No. 14, eds. W.C. Hood
New York: John Wiley & Sons, Inc. .
Personal communication.
(1972),
itz Econo-
“Money,
Income
and
Causality,”
Atncricutt
Economic
62: 540-52.
(1977), “Exogeneity and Causal Ordering in Macroeconomic New Methods in Business Cycle Research: Proceedings ed.
Conference,
C.A.
Sims.
Minneapolis:
Federal
Models,” from a
Reserve
Bank
of
Minneapolis. Stigler, Strotz,
G.J.
(1949).
R.H. (1960),
The Theory
of Price.
“Interdependence
New
York:
as a Specification
Macmillan Error,”
Company.
Ecottottzetricu,
28: 42842. Strotz,
R.H., and Wold, H.O.A. An Attempt
Wold,
H.O.A.
at Synthesis,”
( 1960),
“Recursive
(1960),
Ecottometrica,
“A Generalization
tnetricu, 28: 443-63,
54
vs. Nonrecursive
Systems:
28: 4 17-27.
of Causal
Chain
Models,”
b’cotto-