Interwar Demand and Consumer Choice
Theory: The Ordinal Revolution and
Revealed Preference
I. The Standard Story
II. Some Problems with the Standard
Story
III. Some Specific Topics
a. Integrability
b. Revealed Preference Theory
I. The Standard Story of Demand/Choice
Theory (1870s - 1970s)
Three Stages (cardinal then ordinal, psychology in then out):
1.
2.
Early Neoclassicals (Jevons, Walras, …)
a. Based on Hedonistic Cardinal Utility
b. Explicitly assumed diminishing MU
c. Only informal derivation of Demand from MU
The Ordinal Revolution (OUT) (Pareto 1927, Slutsky 1915, Hicks
& Allen 1934, Hicks 1939, Samuelson 1947, …)
a. Non-Hedonistic and Ordinal Utility
b. Assumed "observable" restrictions on indifference curves
c. Formal derivation of (now) standard demand functions:
(S ii  0,S ij  S ji i  j, x T Sx  0x  0,h.d.0)
3.
Revealed Preference Theory (RPT) (Samuelson 1938, 1948,
Houthakker 1950, …
a. Based on "consistency" with various versions of revealed
preference axioms: WARP, SARP, GARP, …
2
"At first the modern theory of value seemed almost a
branch of psychology … [but] the very bases of the
edifice constructed by this school have been shaken
by violent attacks … From this it follows that, if we
wish to place economic science upon a solid basis,
we must make it completely independent of
psychological assumptions …" (Slutsky, 1915, p.
27)
"Recognition of the ordinal nature of the valuations
implied in price is fundamental. It is difficult to
overstress its importance. With one slash of
Occam's razor, it extrudes for ever from economic
analysis the last vestiges of psychological
hedonism." (Robbins, 1952, p. 56, n. 2)
3
II. Some Problems with the Standard Story
Tensions and Problems in the Standard Story of OUT and PRT
1. Psychology was not clearly "in" in early neoclassical and
clearly "out" in OUT; cardinal was not clearly "in" early
neoclassical and ordinal "in" in OUT; OUT was not
necessarily more "empirical" than early neoclassical …
a. Robbins for example was pro-introspection and not
eliminativist about mental states (hedonism was out, but
not psychology).
b. Slutsky was working with a cardinal utility function in
most of the 1915 paper.
c. OUT was not more empirical, it was "differently"
empirical (what counted as empirical changed).
2. Samuelson started RPT in 1938 to drop "off the last
vestiges of the utility analysis" (Samuelson, 1938, p. 61)
and yet by 1950 he was arguing that RPT was just an
alternative characterization of OUT (and equivalent).
4
III a. Integrability in Demand Theory
The argument is that much of the theoretical work on
consumer choice theory during this period actually
addressed some of the same issues discussed in
contemporary behavioral economics: particularly
endowment effects, reference dependence, irreversibility of
preferences, and similar anomalies. The main reasons
these similarities have not been recognized within the
existing literature are: 1) during this period the
discussion of these issues was bound up with the socalled integrability problem, 2) the modeling framework of
the 1930s did not involve risky choice or expected utility
theory, and 3) the source of the insights was introspective
rather than experimental as it is today.
5
Endowment Effects, Reference Dependence, and the
Irreversibility of Preferences
The proposition that decision makers evaluate outcomes by the utility of
final asset positions has been retained in economic analysis for almost
300 years. This is rather remarkable, because the idea is easily shown
to be wrong; I call it Bernoulli’s error. (Kahneman, 2003, p. 1455)
Although the literature on endowment effects, reference-dependence,
prospect theory, etc. is often framed in terms of risky choice the main
point applies just as well to the standard riskless choice model from
textbook consumer choice theory.
Bernoulli’s error – the idea that the carriers of utility are final states –
is not restricted to decision-making under risk … The error of
reference-independence is built into the standard representation of
indifference maps. It is puzzling to a psychologist that these maps do
not include a representation of the decision maker’s current holdings
of various goods – the counterpart of the reference point in prospect
theory. The parameter is not included, of course, because consumer
theory assumes that it does not matter. (Kahneman, 2003, p. 1457)
6
Integrability in Pareto
(Note: not integrability as rationalizability of the postSamuelson-1950 literature)
For Pareto the primitive of consumer choice was the
differential equation of the indifference curve:
1(x,y)dx  2(x,y)dy  0
If this equation is exact, then it can be integrated to
directly obtain the solution (underlying utility function). If
it is not exact, it still may be integrable (i.e. a solution
exists, but cannot necessarily be found by direct
integration). This is Pareto's integrability problem - it is
question of the existence of the ordinal utility function. As
Voterra (1906) and many others later pointed out, the
equation is always integrable in two dimensions (though
it is not necessarily exact).
7
For Pareto the integrability issue was tied up with
the issue of the order of consumption - the
question of whether the consumer would have
the same level of utility "if he eats the soup at
the beginning of a meal and the desert at the
end, or begins with the dessert and ends with
the soup" (Pareto, p. 182). As Samuelson,
Chipman, and many others have pointed out
over the years, this mixes-up a number of
issues - most importantly the exactness of the
differential with integrability - but it also makes
clear that for Pareto the question of endowment
effects and the reversibility of preferences were
both 1) empirically important and 2) directly
related to the issue of the existence of an
underlying utility function.
8
In his 1906 reply to Volterra Pareto proposed a "pathdependent" indifference relation given by
y  f (x,  )
where µ is a particular consumption path.
This is essentially the reference-dependent indifference curve
of modern behavioral economics:
"the important notion of a stable preference order must be
abandoned in favor of a preference order that depends on
the current reference level. A revised version of preference
theory would assign a special role to the status quo,
giving up some standard assumptions of stability,
symmetry and reversibility which the data have shown to
be false. But the task is manageable. The generalization of
preference theory to indifference curves that are indexed
to reference level is straightforward" (Kahneman, Knetsch
and Thaler, 1991, p. 205).
9
But Pareto was not alone!
R. G. D. Allen (also one of the key figures in the
ordinal revolution) proposed - and thought
Hicks & Allen (1934) provided - a non-integrable
theory of consumer choice. For Allen consumer
choice theory needed to be strictly grounded in
observables, which he considered to by discrete
"movements" in the choice space (discrete
movements which in the limit became Pareto's
differential equations). For Allen, the "integrable
case" - Slutsky's case - was only a special case
where the economic theorist has assumed
(without scientific grounds) the existence of an
underlying utility function.
10
Allen's interpretation of what was going on in
Hicks & Allen (1934) - it was not the same as
what Hicks thought was going on (Hicks' view is
the standard story)
"Our theory was constructed so as to be
independent of the existence of an index of
utility and it was only in the special case, the
so-called “integrability case,” that such an
index was taken … Slutsky, on the other
hand, assumes the special integrability case
from the outset and his results are, therefore,
unnecessarily limited" (Allen, 1936, p. 127)
11
Many others during the late 1930s and early 1940s also offered
non-integrable consumer choice theories motivated by the
same endowment effect and irreversibility issues: including
Georgescu-Roegen, Frisch, Evans, Armstrong, Bernardelli,
and many others. Also note that Samuelson's original 1938
paper (what came to be called revealed preference theory) was
a non-integrable theory of consumer demand.
In addition, many who assumed integrability went to great
lengths to explain what they were assuming about
irreversibility (Schultz, Mosak, and others).
Finally, the one attempt to empirically construct indifference
curves (Thurstone 1931) did so from a particular reference
point.
12
Conclusion (i.e. some reasons why this might matter)
To HPE:
Empiricism mattered to the neoclassicals of the 1930s (it was not
experimental-based, but it was empiricism).
Integrability matters to the dominance of neoclassical theory
(stabilizing demand theory required redefining, and
technically eliminating, the integrability issues of the 1930s).
Early neoclassicism was not the same as what neoclassicism
came to be during the late 1940s and 1950s. What many
consider to be driving out psychology did not happen until
later.
It did not need to turn out as it did. For those concerned with
the issues raised by contemporary behavioral economics,
many of the key figures in 1930s demand theory were actually
on the right road.
13
For contemporary behavioral economics (and
economic theory more generally)
Many of those identified as villains were not (i.e.
one does not necessarily need to go back to
Bentham and Smith to find precursors)
Perhaps there is something in the technical nonintegrable literature from this period that could
be salvaged for use today (there were a number
of attempts to develop a formal choice theory
without the assumption of fixed, irreversible,
endowment-independent, preferences).
Theory-choice in economic science, like individual
choice, is path dependent.
14
IIIb. Revealed Preference Theory
Two main goals of this paper:
1. Distinguishing and clarifying the various subprograms
within the Revealed Preference Family. The distinctions
between the various members of the family are not
generally recognized (by theorists, practitioners, or
historians of economics) and criticism is misdirected
because it only applies to one or a few of the various
subprograms.
2. To understand Samuelson's own interpretation of RPT
and whether his views changed over time ("Das Paul
Samuelson Problem"). In particular, to try to answer the
question of whether Samuelson's views changed between
his original 1938 paper and his two important follow-up
papers in 1948 and 1950.
15
Samuelson, Paul A. (1938), "A Note on the Pure Theory of
Consumer's Behaviour," Economica, 5, 61-71.
Paul Samuelson was twenty-three
years old when the first "revealed
preference" appeared in
Economica.
This was the first paper in a broad
research program - a "family" of
theories - in consumer choice
theory. There are many different
"members" of this family, each
with shared features (family
resemblances), but each with
substantial differences: goals,
practical tools, and
methodological foundations.
16
Varieties of Revealed Preference
1.
2.
3.
4.
5.
Samuelson's original Weak Axiom (WARP) approach (1938).
This paper was eliminativist, seeking to drop "the last vestiges
of the utility analysis." (p. 62)
The second generation literature of Samuelson 1948 and
1950 as well as Hendrik Houthakker's 1950 Strong Axiom
(SARP).
The "high theory" literature (1950-1970) extending the basic
WARP and SARP results expanded and elaborated in various
ways (Hurwicz, Kihlstrom, Mas-Colell, Sonnenschein, and
others). This literature included various (aggregate) excess
versions of WARP and SARP that were used (primarily for
stability and uniqueness analysis) in Arrow-Debreu GE.
The Generalized Axiom of Revealed Preference (GARP)
introduced by Sidney Afriat in 1967 and related literature.
The Contemporary Revealed Preference Theory (CRPT) of Ken
Binmore, Faruk Gul and Wolfgang Pesendorfer, and others.
17
The original Samuelson 1938 WARP project
1. Explicitly eliminativist about "utility" and "preference":
a. To go beyond ordinalists like Hicks and Allen (1934) on this.
b. Term "revealed preference" not used in the paper.
2. Initial givens were demand functions xi = hi(p1, p2,…pn, I) assumed
continuous and satisfying the budget constraint. It was a "demand first"
rather than "preference/utility" first approach.
3. The WARP consistency condition replaced preference/utility:
4. The results of the theory were two out of the three standard ordinal
restrictions on demand functions: Negative substitution terms and Negative
Semi-definiteness. But WARP did not imply Slutsky symmetry (integrability)
which was actually a benefit for Samuelson.
5. Final sentence: "In closing I should like to state my personal opinion that
nothing said here in the field of consumer's behaviour affects in any way or
touches upon at any point the problem of welfare economics …" (p. 71).
18
Second Generation (SARP) and High Theory Literature
1.
2.
3.
Houthakker (1950) extended the weak axiom to all finite
sequences of price-quantity combinations in such a way that
the final bundle in any sequence could not be revealed
preferred to the initial bundle. Unlike WARP, SARP implied all
three of the standard restrictions on consumer demand
functions, including Slutsky symmetry (integrability).
Thus, under SARP, RPT and ordinal utility theory (OUT) were
equivalent: one could start from the consumer maximizing a
well-behaved ordinal utility function subject to a budget
constraint, or from demand functions satisfying SARP, and
the implications on the resulting demand functions would be
exactly the same.
The "high theory" literature expanded and elaborated the
WARP and SARP results in various ways (aggregate demand
and excess demand, weaker restrictions, boundary
conditions, etc.) but kept the basic "start from demand
functions" approach.
19
Afriat's Theorem, GARP, and Related Literature
1.
2.
3.
One problem with the 1st and 2nd generation of RPT is that it
provides very little to work with for empirical application: the
givens are abstract functions (not based on finite empirical
data), there is no way to recover the relevant preferences (RPT
did not "reveal" preferences in any way), and the main
attempt to link the theory up explicitly with empirical data
(Samuelson 1948) was restricted to two dimensions.
Enter Afriat's GARP, a framework that started from finite data
(not continuous demand functions) and offered a practical
technique for both i) "testing" empirical data for consistency
with RPT and ii) estimating a utility function consistent with
(i.e. could have generated) the data.
This led to an extensive literature on GARP-based empirical
demand analysis (Diewert, Varian, and others) called
"nonparametric demand analysis" that offered an alternative
to traditional econometrics-based (i.e. parametric) demand
analysis.
20
Contemporary Revealed Preference Theory (CRPT)
1.
2.
Binmore (2009), Gul & Pesendorfer (2008), and others: it is
GARP+, i.e. the empirical techniques of the GARP-based
literature + a methodological vision of how choice theory is,
should be, and must be done.
Two main features:
a) "Preferred" = "Chosen":
"Though we often speak of choice as determined from
preferences, the opposite is actually the case. Standard
economics makes no assumption about how choices are
actually made; preferences are merely constructs that
summarize choice." (Bernheim and Rangel, 2008, p. 158)
b) The Causal Utility Fallacy:
"In RPT it isn't true that Pandora chooses b rather than a
because the utility of b exceeds the utility of a. This is the
Causal Utility Fallacy … it is because Pandora chooses b
rather than a that we say that Pandora prefers b to a …
(Binmore, 2009, p. 19)
21
So what did Samuelson say about these various
interpretations of RPT in published research, unpublished
research, and correspondence? (i.e. Did, or how did,
Samuelson reveal his preferences about RPT?)
The clearest tension within published works is the statement that
he was always interested in deriving the "full empirical
implications of … the most general ordinal utility analysis"
in his 1950 paper and the eliminativism of his original 1938
paper. But additional evidence (published and archival) does
little to clarify his views on the matter.
1. Repeated the always story throughout the rest of his life in
published work and correspondence.
2. Foundations (1947, 1983) doesn't help. Reviews by Baumol,
Metzler, and Stigler are revealing.
3. Uses RPT as an example of his descriptivist methodology.
4. Correspondence with Afriat, Houthakker, Varian, and others
provides little clarity.
22
So neither the published works nor the archives provides a
clear answer to how Samuelson interpreted RPT later in his
life or Das Paul Samuelson Problem. What can be said?
1.
2.
It is very clear that Samuelson did not like being accused of
inconsistency. As early as 1948 he says in a letter to Little: "I
should not like for those few who have read it to receive the
impression from your account that I have altered my own
earlier views" (Box 48). Such remarks continue through the
1990s, and yet he never makes any effort to explain his views.
Perhaps a rational reconstruction is all that is available. It
goes like this: Given his early positivism Houtakker's
demonstration of equivalence may have elevated the scientific
status of OUT for Samuelson. The OUT that was not
operationally meaningful became so in 1950. The other details
can be explained by Samuelson's lack of interest in applied
research and/or Bourbakian formalism. Perhaps rationality
really was (consistently) consistency for Samuelson and that
explains both his resistance to the charge inconsistency and
lack of interest in providing any deeper explanation of his
views.
23
Final thoughts and Open Questions
This investigation has increased our historical understanding of RPT
as well as Samuelson's relationship with it, but there are still a
number of open questions.
1.
Why repeated insist on saying "something" about the foundations
of RPT when what was said, said so little? As Samuelson himself
said about Bertil Ohlin: he "repeatedly comes back to the point
only to leave it elusively hanging in the air … This is hardly
cricket" (Samuelson, 1948, p.167).
2.
What is the role of the difference between "observational" and
"observed" in Samuelson's work and perhaps in 20th century
economic theory more generally (i.e. "potentially observable' is
not the same as "derived from empirical data" and this may have
influenced how he saw, or didn't see, the GARP-based literature.
3.
Why have so many people be interested in criticizing, defending,
and using versions of RPT and yet there has been so little effort
to distinguish among the various versions.
24