Causality and econometrics

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

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