Read the excerpt of Essays in Positive Economics and answer 3 questions

Milton Friedman

Essays in Positive Economics

Part I - The Methodology of Positive Economics ∗ University of Chicago Press (1953), 1970, pp. 3 -43

CAN A HYPOTHESIS BE TESTED BY THE REALISM

OF ITS ASSUMPTIONS?

We may start with a simple physical example, the law of falling bodies. It is an

accepted hypothesis that the acceleration of a body dropped in a vacuum is a constant - g, or

approximately 32 feet per s econd per second on the earth - and is independent of the shape of

the body, the manner of dropping it, etc. This implies that the distance traveled by a falling

body in any specified time is given by the formula s = ½ gt2, where s is the distance traveled

in feet and t is time in seconds. The application of this formula to a compact ball dropped

from the roof of a building is equivalent to saying that a ball so dropped behaves as if it were

falling in a vacuum. Testing this hypothesis by its assumptions pr esumably means

measuring the actual air pressure and deciding whether it is close enough to zero. At sea

level the air pressure is about 15 pounds per square inch. Is 15 sufficiently close to zero for

the difference to be judged insignificant? Apparently i t is, since the actual time taken by a

compact ball to fall from the roof of a building to the ground is very close to the time given

by the formula. Suppose, however, that a feather is dropped instead of a compact ball.

The formula then gives wildly inacc urate results. Apparently, 15 pounds per square inch is

significantly different from zero for a feather but not for a ball. Or, again, suppose the

formula is applied to a ball dropped from an airplane at an altitude of 30,000 feet. The air

pressure at this altitude is decidedly less than 15 pounds per square inch. Yet, the actual

time of fall from 30,000 feet to 20,000 feet, at which point the air pressure is still much less

than at sea level, will differ noticeably from the time predicted by the formula - much more

noticeably than the time taken by a compact ball to fall from the roof of a building to the

ground. According to the formula, the velocity of the ball should be gt and should therefore

increase steadily. In fact, a ball dropped at 30,000 feet wil l reach its top velocity well before

it hits the ground. And similarly with other implications of the formula.

The initial question whether 15 is sufficiently close to zero for the difference to be

judged insignificant is clearly a foolish question by itself. Fifteen pounds per square inch is

2,160 pounds per square foot, or 0.0075 ton per square inch. There is no possible basis for

calling these numbers “small” or “large” without some external stand ard of comparison. And the only relevant standard of comparison is the air pressure for which the formula does

or does not work under a given set of circumstances. But this raises the same problem at a

second level. What is the meaning of “does or does not work”? Even if we could

eliminate errors of measurement, the measured time of fall would seldom if ever be precisely

equal to the computed time of fall. How large must the difference between the two be to

justify saying that the theory “does not work”? He re there are two important external

standards of comparison. One is the accuracy achievable by an alternative theory with

which this theory is being compared and which is equally acceptable on all other grounds.

The other arises when there exists a theory that is known to yield better predictions but only

at a greater cost. The gains from greater accuracy, which depend on the purpose in mind,

must then be balanced against the costs of achieving it.

This example illustrates both the impossibility of testi ng a theory by its assumptions

and also the ambiguity of the concept “the assumptions of a theory.” The formula s = ½ gt2

is valid for bodies falling in a vacuum and can be derived by analyzing the behavior of such

bodies. It can therefore be stated: under a wide range of circumstances, bodies that fall in

the actual atmosphere behave as if they were falling in a vacuum. In the language so

common in economics this would be rapidly translated into: the formula assumes a vacuum.

Yet it clearly does no such th ing. What it does say is that in many cases the existence of air

pressure, the shape of the body, the name of the person dropping the body, the kind of

mechanism used to drop the body, and a host of other attendant circumstances have no

appreciable effect on the distance the body falls in a specified time. The hypothesis can

readily be rephrased to omit all mention of a vacuum: under a wide range of circumstances,

the distance a body falls in a specified time is given by the formula s = ½ gt2. The history o f

this formula and its associated physical theory aside, is it meaningful to say that it assumes a

vacuum? For all I know there may be other sets of assumptions that would yield the same

formula. The formula is accepted because it works, not because we live in an approximate

vacuum - whatever that means.

The important problem in connection with the hypothesis Is to specify the

circumstances under which the formula works or, more precisely, the general magnitude of

the error in its predictions under various circumstances. Indeed, as is implicit in the above

rephrasing of the hypothesis, such a specification is not one thing and the hypothesis another.

The specification is itself an essential part of the hypothesis, and it is a part that is peculiarly

likely to be revised and extended as experience accumulates. In the particular case of falling bodies a more general, though still incomplete, theory

is available, largely as a result of attempts to explain the errors of the simple theory, from

which the influence of some of the possible disturbing factors can be calculated and of which

the simple theory is a special case. However, it does not always pay to use the more general

theory because the extra accuracy it yields may not justify the extra cost of using it, so the

question under what circumstances the simpler theory works “well enough” remains

important. Air pressure is one, but only one, of the variables that define these circumstances;

the shape of the body, the velocity attained, and still other variables are relevant as well.

One way of interpreting the variables other than air pressure is to regard them as determining

whether a particular departure from the “assumption” of a vacuum is or is not significant.

For example, the difference in shape of the body can be said to make 15 pounds per square

inch significantly different from zero for a feather but not for a compact ball dropped a

moderate distance. Such a statement must, however, be s harply distinguished from the very

different statement that the theory does not work for a feather because its assumptions are

false. The relevant relation runs the other way: the assumptions are false for a feather

because the theory does not work. This p oint needs emphasis, because the entirely valid use

of “assumptions” in specifying the circumstances for which a theory holds is frequently, and

erroneously, interpreted to mean that the assumptions can be used to determine the

circumstances for which a th eory holds, and has, in this way, been an important source of the

belief that a theory can be tested by its assumptions.

Let us turn now to another example, this time a constructed one designed to be an

analogue of many hypotheses in the social sciences. Consider the density of leaves around a

tree. I suggest the hypothesis that the leaves are positioned as if each leaf deliberately

sought to maximize the amount of sunlight it receives, given the position of its neighbors, as

if it knew the physical laws determining the amount of sunlight that would be received in

various positions and could move rapidly or instantaneously from any one position to any

other desired and unoccupied position. 14 Now some of t he more obvious implications of

this hypothesis are clearly consistent with experience: for example, leaves are in general

denser on the south than on the north side of trees but, as the hypothesis implies, less so or

not at all on the northern slope of a hill or when the south side of the trees is shaded in some

other way. Is the hypothesis rendered unacceptable or invalid because, so far as we know,

leaves do not “deliberate” or consciously “seek,” have not been to school and learned the relevant laws of science or the mathematics required to calculate the “optimum” position, and

cannot move from position to position? Clearly, none of these contradictions of the

hypothesis is vitally relevant; the phenomena involved are not within the “class of

phenomena t he hypothesis is designed to explain”; the hypothesis does not assert that leaves

do these things but only that their density is the same as if they did. Despite the apparent

falsity of the “assumptions” of the hypothesis, it has great plausibility because of the

conformity of its implications with observation. We are inclined to “explain” its validity on

the ground that sunlight contributes to the growth of leaves and that hence leaves will grow

denser or more putative leaves survive where there is more su n, so the result achieved by

purely passive adaptation to external circumstances is the same as the result that would be

achieved by deliberate accommodation to them. This alternative hypothesis is more

attractive than the constructed hypothesis not becaus e its “assumptions” are more “realistic”

but rather because it is part of a more general theory that applies to a wider variety of

phenomena, of which the position of leaves around a tree is a special case, has more

implications capable of being contradicted, and has failed to be contradicted under a wider

variety of circumstances. The direct evidence for the growth of leaves is in this way

strengthened by the indirect evidence from the other phenomena to which the mo re general

theory applies.

The constructed hypothesis is presumably valid, that is, yields “sufficiently” accurate

predictions about the density of leaves, only for a particular class of circumstances. I do not

know what these circumstances are or how to d efine them. It seems obvious, however, that

in this example the “assumptions” of the theory will play no part in specifying them: the kind

of tree, the character of the soil, etc., are the types of variables that are likely to define its

range of validity, not the ability of the leaves to do complicated mathematics or to move from

place to place.

A largely parallel example involving human behavior has been used elsewhere by

Savage and me. 15 Consider the problem of predicting the shots made by an expert bil liard

player. It seems not at all unreasonable that excellent predictions would be yielded by the

hypoth esis that the billiard player made his shots as if he knew the complicated mathematical

formulas that would give the optimum directions of travel, could estimate accurately by eye

the angles, etc., describing the location of the balls, could make lightning calculations from

the formulas, and could then make the balls travel in the direction indicated by the formulas.

Our confidence in this hypothesis is not based on the belief that billiard players, even expert ones, can or do go through the process describ ed; it derives rather from the belief that, unless

in some way or other they were capable of reaching essentially the same result, they would

not in fact be expert billiard players.

It is only a short step from these examples to the economic hypothesis that under a

wide range of circumstances individual firm behave as if they were seeking rationally to

maximize their expected returns (generally if misleadingly called “profits”) 16 and had full

knowledge of the data needed to succeed in this attempt; as if, that is, they knew the relevant

cost and demand functions, calculated marginal cost and marginal revenue from all actions

open to them, and pushed each line of action to the point at whic h the relevant marginal cost

and marginal revenue were equal. Now, of course, businessmen do not actually and literally

solve the system of simultaneous equations in terms of which the mathematical economist

finds it convenient to express this hypothesis, any more than leaves or billiard players

explicitly go through complicated mathematical calculations or falling bodies decide to create

a vacuum. The billiard player, if asked how he decides where to hit the ball, may say that he

“just figures it out” but then also rubs a rabbit’s foot just to make sure; and the businessman

may well say that he prices at average cost, with of course some minor deviations when the

market makes it necessary. The one statement is about as helpful as the other, and neither is

a relevant test of the associated hypothesis.

Confidence in the maximization -of-returns hypothesis is justified by

evidence of a very different character. This evidence is in part similar to that

adduced on behalf of the billiard -player hypothesis - unless the behavior of

businessmen in some way or other approximated behavior consistent with the

maximization of returns, it seems unlikely that they would remain in business for long. Let

the apparent immediate determinant of business behavior be anything at al l - habitual reaction,

random chance, or whatnot. Whenever this determinant happens to lead to behavior

consistent with rational and informed maximization of returns, the business will prosper and

acquire resources with which to expan d; whenever it does not, the business will tend to lose

resources and can be kept in existence only by the addition of resources from outside. The

process of “natural selection” thus helps to validate the hypothesis - or, rather, given natural

selection, a cceptance of the hypothesis can be based largely on the judgment that it

summarizes appropriately the conditions for survival.

An even more important body of evidence for the maximization -of-returns

hypothesis is experience from countless applications of t he hypothesis to specific problems and the repeated failure of its implications to be contradicted. This evidence is extremely

hard to document; it is scattered in numerous memo -randums, articles, and monographs

concerned primarily with specific concrete p roblems rather than with submitting the

hypothesis to test. Yet the continued use and acceptance of the hypothesis over a long

period, and the failure of any coherent, self -consistent alternative to be developed and be

widely accepted, is strong indirect t estimony to its worth. The evidence for a hypothesis

always consists of its repeated failure to be contradicted, continues to accumulate so long as

the hypothesis is used, and by its very nature is difficult to document at all comprehensively.

It tends to become part of the tradition and folklore of a science revealed in the tenacity with

which hypotheses are rather than in any textbook list of instances in which the thesis has

failed to be contradicted.