Interwar Demand and Consumer Choice Theory: The Ordinal

Revolution and Revealed Preference

I. The Standard StoryII. Some Problems with the

Standard StoryIII. Some Specific Topics

a. Integrabilityb. Revealed Preference Theory

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I. The Standard Story of Demand/Choice Theory (1870s - 1970s)

Three Stages (cardinal then ordinal, psychology in then out):

1. Early Neoclassicals (Jevons, Walras, …)a. Based on Hedonistic Cardinal Utilityb. Explicitly assumed diminishing MUc. Only informal derivation of Demand from MU

2. The Ordinal Revolution (OUT) (Pareto 1927, Slutsky 1915, Hicks & Allen 1934, Hicks 1939, Samuelson 1947, …)a. Non-Hedonistic and Ordinal Utilityb. Assumed "observable" restrictions on indifference curvesc. Formal derivation of (now) standard demand functions:

3. Revealed Preference Theory (RPT) (Samuelson 1938, 1948, Houthakker 1950, …a. Based on "consistency" with various versions of revealed preference axioms: WARP, SARP, GARP, …

(S

ii< 0,S

ij=S

ji∀i ≠ j, xTSx ≤0∀x ≠0,h.d.0)

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"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)

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II. Some Problems with the Standard Story

Tensions and Problems in the Standard Story of OUT and PRT1. 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).

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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 so-called 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.

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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)

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Integrability in Pareto (Note: not integrability as rationalizability of the post-

Samuelson-1950 literature)

For Pareto the primitive of consumer choice was the differential equation of the indifference curve:

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).

Ψ1(x,y)dx+Ψ2(x,y)dy=0

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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.

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In his 1906 reply to Volterra Pareto proposed a "path-dependent" indifference relation given by

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).

y=f(x,μ)

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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.

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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)

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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.

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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.

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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 non-integrable 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.

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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.

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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.

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Varieties of Revealed Preference

1. Samuelson's original Weak Axiom (WARP) approach (1938). This paper was eliminativist, seeking to drop "the last vestiges of the utility analysis." (p. 62)

2. The second generation literature of Samuelson 1948 and 1950 as well as Hendrik Houthakker's 1950 Strong Axiom (SARP).

3. 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.

4. The Generalized Axiom of Revealed Preference (GARP) introduced by Sidney Afriat in 1967 and related literature.

5. The Contemporary Revealed Preference Theory (CRPT) of Ken Binmore, Faruk Gul and Wolfgang Pesendorfer, and others.

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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).

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Second Generation (SARP) and High Theory Literature

1. 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).

2. 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.

3. 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.

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Afriat's Theorem, GARP, and Related Literature

1. 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.

2. 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.

3. 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.

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Contemporary Revealed Preference Theory (CRPT)

1. 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.

2. 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)

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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.

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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. 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.

2. 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.

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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.