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This article was downloaded by: [Temple University Libraries]On: 18 November 2014, At: 13:27Publisher: RoutledgeInforma Ltd Registered in England and Wales Registered Number: 1072954Registered office: Mortimer House, 37-41 Mortimer Street, London W1T 3JH,UK
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A structure of the consumptionfunctionHsiang‐Ke Chao a
a National Tsing Hua University , Taiwan E-mail:Published online: 12 Jun 2007.
To cite this article: Hsiang‐Ke Chao (2007) A structure of the consumption function,Journal of Economic Methodology, 14:2, 227-248, DOI: 10.1080/13501780701394102
To link to this article: http://dx.doi.org/10.1080/13501780701394102
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A structure of the consumption function
Hsiang-Ke Chao
Abstract It is claimed in the structural realism in philosophy of science thatscientists aim to preserve the true structure, represented by the equations in theirmodels. We reinterpret structural realism as a doctrine involving representation.Proving the existence of a representation theorem secures the problem of lackingindependent criteria for identification between structure and non-structure. Thispaper argues that a similar realist view of structure can be found in the theory ofconsumption in which the Fisherian framework of intertemporal choices isregarded as the true structure of the consumption function. Unlike the passivestrategy of inducing the structure contained in structural realism, economistsdefine structure in terms of invariance under intervention. Such a definition servesas a crucial device to examine and develop models for the adequacy ofrepresenting the structure of the consumption functions.
Keywords: consumption function, Euler-equation approach, invariance,representation, structure, structural realism
JEL Classification: B22, B41, C50, E21
1 INTRODUCTION
The ‘stylized’ history of macroeconomic theories of consumption is usually
presented as follows. In the ‘fundamental psychological law’ in his General
Theory (Keynes 1936), John Maynard Keynes argued that the level of current
consumption is determined by current income. Keynes’s absolute income
hypothesis also implies that the marginal propensity to consume is between 0
and 1, and is less than the average propensity to consume; the averagepropensity to consume falls, and the average propensity to save rises with
income, so ‘rich people save more’. While the absolute income hypothesis
accounted for short-run phenomena, it was contradicted by long-run
phenomena, such as stable average propensities to consume and to save,
equivalence of marginal and average propensities to consume, that were found
by Simon Kuznets in his (1946) empirical survey of the US time series data
since 1896. In order to reconcile these findings, James Duesenberry’s (1949)
relative income hypothesis assumed that consumptions are interdependentamong different people and for the same people at different periods.1
Journal of Economic Methodology ISSN 1350-178X print/ISSN 1469-9427 online
# 2007 Taylor & Francis http://www.tandf.co.uk/journals
DOI: 10.1080/13501780701394102
Journal of Economic Methodology 14:2, 227–248 June 2007
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In the 1950s Milton Friedman and Franco Modigliani independently
proposed a new theory of consumption. Friedman’s permanent income
hypothesis was published in his seminal 1957 book A Theory of the
Consumption Function; Modigliani’s life-cycle hypothesis was established in
a series of papers that he had written with Albert Ando and Richard
Brumberg (Modigliani and Brumberg 1954; Ando and Modigliani 1963).
Both the permanent income hypothesis and the life-cycle hypothesis were
based on Irving Fisher’s intertemporal choices theory and claim that the
level of aggregate current consumption is determined by a long-term
expected income. But after the rational expectations revolution and the
Lucas critique of traditional econometrics (Lucas 1976) – in the 1970s, bothapproaches were criticized for not dealing properly with expectations.
Robert Hall’s famous ‘random-walk’ model (Hall 1978) then incorporated
the idea of rational expectations into the intertemporal choices framework.
In recent consumption models the representative consumers do not smooth
their consumption. But since Hall, the modeling strategy of deriving
consumption functions directly from the first-order Euler equation – the
Euler-equation approach – has come to dominate the theory of consumption
in today’s macroeconomics.Although this stylized history, at least in its early years, has been criticized
for failing to represent the ‘true’ history of the consumption function (e.g.
Thomas 1989), the first half of this stylized history is cited by economic
historians as an example of Thomas Kuhn’s scientific revolutions in
economics (Mayer 1972: 7–8; Hynes 1998). They see the change from
Keynes’s consumption theory to the theories of Friedman and Modigliani as
a Kuhnian paradigm shift. Whether or not the rest of the history can also be
seen in this way, for instance, whether or not the movement that we calledthe ‘rational expectations revolution’ is really a Kuhnian scientific
revolution, the introduction of rational expectations has changed econo-
mists’ view of many fields of macroeconomics, including that of the
consumption function.
Yet, if we take a deep look into the development of the theory of the
consumption function, we find both continuity and discontinuity. In
philosophy of science, realists and anti-realists hotly debated theory change.
Anti-realists conclude from the presence of radical theory change (orparadigm shift) in the history of science that any theory will eventually be
proven false. This is the argument of ‘pessimistic meta-induction’. In
contrast, realists assert that all theories are completely or partially true or
approximately true so that the success of past theories is not accidental. This
‘no-miracles’ argument clashes with the argument of pessimistic meta-
induction. In order to solve the puzzle, philosopher of science John Worrall
(1989) accounts for both assertions in his theory of ‘structural realism’.
Philosophers and historians of science regard Worrall’s structural realism asproviding ‘the best hope for realism’ (Papineau 1996: 13).2 However, one
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major problem, as Worrall admits, is that there are only ‘limiting cases’
for structural realism. Whether or not Worrall’s account of structural
realism fully explains the history of science, it does point out scientists’undeniable concern with preserving structure in their scientific practices.
The same concern about structure, as this article is going to demonstrate,
can also be clearly found in the history of the consumption function in
macroeconomics.
This article argues that a methodological position similar to Worrall’s
structural realism can be found in the history of the consumption function.
We call this position ‘realism about structure’.3 Realism about structure
reveals two points that are pertinent to structural realism. The first is theconcept of structure that Worrall does not clearly define. Structure usually
goes beyond the formal–mathematical level that concerns Worrall, and is
particularly construed in terms of invariance in the study of consumption
function. Precisely, the notion of structure in economics is construed in
terms of invariance under intervention. The other point is the relations
between model and structure. Worrall’s structure contains two tiers of
representations. We refer to the discussions in philosophy of science and
economic methodology to demonstrate the concerns of these models, inwhich certain independent criteria are necessary for choosing between
structural and non-structural relations, since both relations could be
preserved during theory change.
2 STRUCTURAL REALISM
Realism has many faces, but the most commonly recognized one is
‘scientific realism’. According to scientific realism, the objects ofscientific knowledge exist independently of scientists’ minds or acts. In
addition, scientific theories are true to the objects. The first assertion
leads to a metaphysical claim for the independent existence of certain
entities while the second one leads to the epistemological principle that we
can know the independent existence of these entities (Papineau 1996; Fine
1998).
Scientific realism asserts that the past and present mature scientific
theories have successfully explained or predicted phenomena because theyare (approximately) true to the world. If these theories were false, then their
empirical success would be a miracle. As Hilary Putnam (1975: 73) puts it,
‘[t]he positive argument for realism is that it is the only philosophy that does
not make the success of science a miracle’. This ‘no-miracles’ argument,
however, was challenged by the historical fact that many theories which
were once successful were later proven false. From this fact, we can induce a
conclusion that presently accepted scientific theories will likewise be proven
false. Hence, this ‘pessimistic meta-induction’ argument (Laudan 1981)rejects scientific realism, and theory can by no means be regarded as true.
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To adopt the realist position and to respond to the pessimistic meta-
induction argument, Worrall (1989) appeals to the continuity of ‘structure’
across theory change. He argues that even though pessimistic meta-induction is right about the facts about radical theory changes and the
discontinuity of ‘contents’, there is still a continuity of ‘structure’ or ‘form’
between the old and new theories. Worrall proposes an account of structural
realism, originating with Henri Poincare, Bertrand Russell and Grover
Maxwell among others,4 arguing that in structural realism even though the
new theory replaced the old, the old theory was previously accepted because
it captured the true structure, expressed in mathematical terms. The
evidence of the old theory capturing the true structure is the presence of thesame mathematical equations in the superseding theories. In this way
Worrall modifies the no-miracles argument, asserting that the success of
mature theory is due to its truth to the structure. Worrall’s paradigm
example for structural realism is that of the development of the theory of
light in the nineteenth century, starting with Augustin Fresnel’s successful
re-establishment of the wave theory. Later when James Maxwell’s
electromagnetic theory replaced Fresnel’s, Fresnel’s assumption that the
luminiferous aether – the hypothetical medium for propagation of lightwaves – was rigid was overthrown in favor of James Maxwell’s
electromagnetic field. Yet the equations contained in Fresnel’s theory (also
known as ‘Fresnel’s laws’ or ‘Fresnel’s equations’) were preserved in
Maxwell’s theory (‘Maxwell’s laws or ‘Maxwell’s equations’). Thus Worrall
states:
it seems right to say that Fresnel completely misidentified the nature of
light; but, none the less, it is no miracle that his theory enjoyed the
empirical predictive success that it did; it is no miracle because Fresnel’s
theory, as science later saw it, attributed to light the right structure.
(Worrall 1989: 117; emphasis in original)
As Poincare stated: ‘if the equations remain true, it is because the relations
preserve their reality’ (quoted in Worrall 1989: 118).
However, Worrall later admitted that the Fresnel–Maxwell example was
‘unrepresentative’ because it was a rarity in the history of science for the
mathematical equations of the old theory to be ‘completely taken overintact’ into the new theory (Worrall 1989: 120). But Worrall then argued
that ‘[t]he much more common pattern is that the old equations reappear as
limiting cases of the new’; this means that ‘the old and new equations are
strictly inconsistent, but the new tends to the old as some quantity tends to
some limit’ (Worrall 1989: 120). In this sense, structural realism is concerned
with the existence of approximate rather than complete continuity during
theory change.
Worrall further argues that structural realism is meaningful not onlybecause it reconciles radical theory change with the no-miracle argument,
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but also because it can play an active role in the ‘correspondence principle’
of scientific discovery. Some philosophers see the correspondence principle
as evidence of realism (Boyd 1984; see Worrall 1989: 120), and as a heuristicdevice for developing the new theory by inferring the old, as well as the new
theory explaining the empirical success of its predecessor (Worrall 1985). An
example is the argument that Newton arguably deduced his laws from
Kepler’s (Worrall 1985: 314–18). Worrall’s structural realism paper treats
this correspondence principle as operating ‘purely at the mathematical level’
(Worrall 1989: 120; emphasis in original). This means that from the
mathematical equations that express the structure of the old theory that was
once successful, we can infer and construct a new theory, one which containssimilar equations expressing the same structure that is thought to be real.
In sum, Worrall’s account of structural realism requires (1) a preserved
mathematical equation to be passively observed; and (2) an equation that
plays an active heuristic role in developing new theories. Yet Worrall’s
characterization of scientific practices on the importance of maintaining and
using the structure can likewise be found in the history of the consumption
function. In particular, the framework of intertemporal choices is regarded
as the structure for the consumption function.
3 STRUCTURE OF THE CONSUMPTION FUNCTION
In his work on interest, Irving Fisher (1930) developed the concept of
intertemporal choices that he traced to John Rae and Eugene Bohn-Bawerk.
Fisher argues that people tend to prefer present over future goods. This
‘time preference’, also known as ‘human impatience’ or ‘impatience’ (Fisher
1930: 62), in its marginal form, determines the rate of interest as thepremium on the exchange between present and future goods (Fisher 1930:
61). In this light, Fisher’s theory sharply contrasts with Keynes’s
fundamental psychological law, or the absolute income hypothesis, which
asserts that current consumption is only determined by current income at
the aggregate level.5
After Keynes’s revolution, we have two well-known theories of the
consumption function directly derived from Fisher’s intertemporal choices
theory. Friedman referred to Fisher’s intertemporal choices as the ‘puretheory of consumer behavior’ and the building block of his permanent
income hypothesis. Modigliani also wrote that his life-cycle hypothesis was
built on the ‘received theory of consumer’s choice a la Fisher’ (Modigliani
1975: 5). Even though the aggregation problem of deriving the macro-
economic consumption function from an individual’s optimal decisions is
not addressed in either Friedman or Modigliani, the success of the
permanent income and the life-cycle hypotheses was attributed to the
application of the Fisherian framework, in addition to their empiricalsuccesses over the Keynesian theory.6
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One crucial element of the framework of intertemporal choices is the
expectations of future income when consumers face uncertainty. Friedman
adopts the theory of adaptive expectations in forming expected income as a
proxy of permanent income. But this is challenged by the hypothesis of
rational expectations, which is seen as a more appropriate account of how
consumers form their expectations. John Muth (1960) was the first to show
the adaptive expectations formula as a special case of the rational
expectations hypothesis. He argues that Friedman’s adaptive expectations
formula only coincides with the rational expectations hypothesis under some
circumstances; otherwise they are inconsistent.7 This point is taken by Lucas
(1976). Lucas, following Haavelmo (1944) and the Cowles Commission
scholars such as Marschak (1953) and Hurwicz (1962), is concerned with
invariant relationships under policy intervention. The ‘Lucas critique’
challenges the standard econometric models which do not exhibit invariant
relationships because agents’ expectations are modified in the face of policy
change. In the case of consumption function, Lucas (1976) shows that
Friedman’s permanent income hypothesis, based on the assumption of
adaptive expectations, incorrectly forecasts the consumption for any
expected policy change. Moreover, the permanent income hypothesis does
not apply to the case of unexpected policy change. Since Friedman’s
permanent income hypothesis does not yield a stable relationship between
consumption and income, Robert Hall suggests that the Lucas critique
states that ‘there is no such thing as a consumption function’ (Hall 1990:
135).
Hall’s famous ‘random walk’ paper (Hall 1978) attempts to
construct a consumption function that satisfies the Lucas critique. Hall’s
approach is compatible with the traditional permanent income and life-cycle
hypotheses, for Hall’s consumption theory contains a Fisherian framework
in which the representative consumer intertemporally allocates his/her
wealth on consumption. But what distinguishes Hall’s consumption
function from previous theories is its accommodation of the Lucas critique.
He introduces expectations to the consumer’s maximization problem in the
face of uncertainty, sets up the problem in which the consumer maximizes
expected utility, and keeps the expected marginal utility constant. Hall’s
aggregate consumption function is derived from the representative
agent’s intertemporal optimizing behavior under the assumptions of
rational expectations and a representative agent. This derivation of the
consumption model is the Euler-equation approach, which refers to the first-
order condition of the representative agent’s intertemporal choices of
consumption.
To illustrate, consider a two-period case, in which the representative
consumer maximizes his/her utility function subject to the intertemporal
budget constraint. The Euler equation is derived as
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E1u0
c2ð Þ~1zd
1zr
� �u0
c1ð Þ ð1Þ
where d is the subjective time preference rate, and r is the constant real
interest rate. E1 denotes the conditional expectation given all the
information available at period 1. When the utility function is quadratic,
and d5r, the Euler equation (1) yields:
E1c2~c1 ð2Þ
By the definition of expectations, we have the random walk consumption
c2~c1ze2 ð3Þ
where e2 is a true regression disturbance whose expectation as of period 1 iszero. Equation (3) suggests that consumption is a random walk: the
consumption in this period is only the function of the consumption in the
previous period plus an innovation.
Hall’s random-walk model, as Clive Granger claimed, is easy to state,
easy to understand and easy to test. It is like ‘manna from heaven to
macroeconometricians’ (Granger 1999: 43). Granger’s view is shared with
macroeconomists who apply the Euler-equation approach to consumption
research. The literature cites four reasons why the Euler-equation approach
is the dominant consumption theory in macroeconomics:
First of all, the Euler-equation approach is operationally simpler than the
conventional ‘solved-out’ way, which requires deriving consumption
functions by solving all period-to-period budget constraints. In contrast to
the solved-out approach, the Euler-equation approach only needs to set up a
representative-agent model, write down the Euler-equation, and use the
equilibrium relationships between the expected marginal utility of futureconsumption and the marginal utility of current consumption like equation
(1) to derive the ‘consumption function’.8 Some economists regard the
avoidance of solving the consumer’s optimization problem as the most
appealing element of the Euler-equation approach (Attanasio and Low
2004: 407).
Secondly, the Euler equation is a more useful measuring tool than the
solved-out consumption function. In many empirical studies, the standard
procedure is to log-linearize the Euler equation given that the utility
function is constant-relative-risk-averse (Hansen and Singleton 1983). In
doing so, it allows a focus on directly estimating the ‘structural parameters’
of the consumption function (Attanasio 1998: 21), for example, the elasticity
of intertemporal substitution.9
Thirdly, the random walk consumption highlights the rational expecta-
tions hypothesis and the Lucas critique in many ways. Besides the
representative consumer’s optimization setting, the random-walk modelsuggests that the consumer uses today’s consumption as the best predictor of
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future consumption because any available information has been included in
today’s consumption. Hence other variables, particularly current and past
incomes, can be excluded from the consumption function.Finally, the Euler-equation approach preserves the ‘structure’ of the
consumption function. Even though Lucas criticizes the unsustainable
relationships between consumption and income in the traditional consump-
tion function, Hall argues that there still exists something in the Euler-
equation approach that can be considered as structure:
Although Lucas was scornful of existing econometric policy evaluation
models, his message was not completely destructive of all model-building
or empirical research. There are structural relationships in the economy,
but the consumption function is not among them. For consumption, the
structural relation, invariant to policy interventions and other shifts
elsewhere in the economy, is the intertemporal preference ordering.
(Hall 1990: 135; emphasis added)
For Hall, the intertemporal preference ordering, or the Fisherian
intertemporal choices, is the structure of the consumption function because
this relation is invariant to exogenous changes. As mentioned above, theEuler equation per se is not really a consumption function but an
equilibrium condition that can be regarded as a structure of the
consumption function. The final model exhibiting the relationships between
the current consumption and other variables, such as Hall’s random walk,
depends strongly on the auxiliary assumptions that the modeler employs.
(For Hall’s random-walk model, the most crucial assumption is the
quadratic utility function.) In this sense, Hall’s random-walk model is only
a special case of the Euler-equation approach.
4 STRUCTURAL REALIST INTERPRETATION OF THE
CONSUMPTION FUNCTION
In the context of the history of the consumption function and structural
realism, we do not find that Worrall’s structural realism fits. While
Worrall’s strategy requires observing continuity in structure during theory
change, the history of the consumption function shows that thesimultaneous discontinuity in theory and continuity in structure is hard to
find. Economists are unanimous in seeing the discontinuity between
Keynesian theory and the theories of Friedman and Modigliani. But
usually, they refer to Hall’s theory as a life cycle–permanent income
hypothesis – in fact Hall himself (1978) regards his random-walk model as a
justification of the Friedman–Modigliani theory. In this sense, it seems that
no theory change was induced by the rational expectations revolution.
Yet, consider the consumption theories before and after the rationalexpectations revolutions; if we regard adaptive and rational expected
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marginal utilities of future consumptions as different substances because of
drastic changes in the nature and the formulation of expectations, then there
is the change from Friedman and Modigliani to Hall. Therefore the Eulerequation retains the structure of the consumption function during this
theory change. This interpretation is not incongruous in the sense that we
often construe the introduction of rational expectations as a ‘revolution’.
Whether or not this is parallel to Kuhn’s ‘scientific revolution’, it marks a
sea change in macroeconomics that could parallel the ‘Keynesian revolu-
tion’ which is more commonly regarded as fitting Kuhn’s account. Gilbert
(1991: 156) sees it in this way: ‘The [rational expectations hypothesis] is seen
as an improvement over adaptive expectations in the same way that the[permanent income hypothesis] was seen as an improvement over Keynes’s
‘‘fundamental psychological law’’.’ Whereas Gilbert’s ‘improvement’ is not
as strong as a ‘revolution’, he does imply the existence of the change in
consumption theory after rational expectations. Consequently, we can see
that Friedman’s and Modigliani’s theories have been replaced by Hall’s;
Worrall’s structural realism seems to be an appropriate way to depict such a
shift.
But generally in the case of consumption theory, economists tend toclassify a theory by its structure. This view is best illustrated by the title of
Thomas Kuhn’s article ‘Theory-change as structure-change’ (Kuhn 1976).
In addition to Hall’s case, note that recently there has been a vast number of
studies on consumption that ‘go beyond’ the life cycle–permanent income
hypothesis. These studies cast doubt on the appropriateness of the
assumption of consumption smoothing, arguing that the assumption is
not fulfilled because the representative consumer may not want to smooth
out consumption owing to his/her precautionary motive of saving, orbecause s/he cannot do so due to liquidity constraints (see section 6).10
Consumption may be neither smoothing according to David Laibson’s
(1997, 1998) hyperbolic Euler equation that discount rates are declining over
time, nor constant in the standard exponential Euler equation. These
consumption theories are different from the life cycle–permanent income
hypothesis, either because consumers cannot freely borrow and lend to
smooth their consumptions, or because consumers’ behavior is based on
Laibson’s more radical adoption of time-inconsistent preferences. Thisindicates that economists usually assume complete consumption smoothing,
designated by the unrestricted Fisherian intertemporal choices framework,
and the life cycle–permanent income hypothesis as the same thing – even
though the final consumption functions, such as Friedman’s distributed lag
model and Hall’s random-walk model, are different. Therefore, theories are
distinguished by the structure they impose, so we see the discontinuity
among the Keynesian theory, Friedman–Modigliani life cycle–permanent
income hypothesis, and the new hypotheses of precautionary saving andliquidity constraints. Yet, when contemporary economists regard the Euler
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equation as representing the true structure, they apply it to future theories.
So we see that the models based on these new consumption theories are
derived from Euler equations, but with auxiliary assumptions that aredissimilar to Hall’s.11 Worrall’s correspondence principle seems to fit this
description: the framework of intertemporal choices is used in developing
new models in which their Euler equations are considered as ‘limiting cases’
of the Euler equation in the random-walk model.
It seems the structural realist account only partially interprets the theory
of consumption function. However, regardless of the questions of the
existence of theory change and the possibility of a full application of
Worrall’s structural realism to the history of the consumption function,economists themselves have emphasized that the framework of intertem-
poral choices is maintained as the structure of the consumption function and
is employed for further research – exactly the ideas that Worrall stresses.
The economists’ realist attitude toward structure will be discussed in depth
in section 6. But first it needs to be pointed out that a difference between
Worrall’s structural realism and economists’ realism about structure lies in
the fact that in economics and econometrics the notion of invariance under
intervention is usually applied to identify the existence of structure, while inWorrall’s account there is no such independent criterion for identifying the
structure. This is the main criticism of Worrall’s account in the philosophy
of science literature.
5 STRUCTURAL REALISM AND REPRESENTATION
Worrall’s structural realist strategy involves an ‘optimistic induction’
concerning the discovery of mathematical structure in the history of science(Worrall 1994: 336). Stathis Psillos (2001: S23) criticizes the strategy as
being only a ‘modest epistemic thesis that emerges from looking into the
history of scientific growth’ that does not tell us what makes unchanged
mathematical equations a real structure. Elsewhere Psillos (1999: Ch. 7)
raises some unique challenges to Worrall’s account; two of them are related
to economic methodology and to the consumption function.
First, Psillos observes that apart from mathematical equations, theoretical
assumptions and principles are preserved during theory change, even inWorrall’s case of light. This point is similar to what Marcel Boumans (1999)
says about business-cycle model building. In economics, Boumans argues,
models are usually built by integrating many ingredients. He shows that
successful business cycle models integrate concepts and facts from economic
theories and practices in a mathematical mould. One of Boumans’s case
studies is Lucas’s business cycle model. He argues that Lucas’s model
inherits many ingredients from previous studies of business cycles theories.
When the model is regarded as a successful integration, its ingredients arepreserved in the later models (Boumans 1999: 89). Usually in economics,
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also indicated in Boumans’s case studies, some, maybe not all, ingredients
are relational. Since the preserved ingredients are not all relational, it is not
possible for structural realists to identify the structure merely by employingWorrall’s inductive strategy. In addition, even though relational and non-
relational ingredients can be distinguished, not all relational equations are
regarded as structure. As the previous section stated, only the equation of
intertemporal choices is regarded as structure for the consumption function.
Psillo’s and Boumans’s studies show that in the natural and social sciences,
some ingredients preserved under theory change are non-structural. Hence
structural realism’s inductive strategy is not capable of distinguishing
structure from non-structure – this strategy seems to be ‘pessimistic’ ratherthan ‘optimistic’.
Secondly, Psillos tries to see off structural realism by arguing that Worrall
does not provide an independent argument to link mathematical equations
with the structure of the world; otherwise we cannot tell whether the
mathematical equations are preserved because they represent the true
structure or because, say, it is just convenient to apply them to build a
model. This argument seems true to our example of the Euler-equation
approach in which economists adopt the Euler-equation approach becauseit is operationally convenient, easy to measure, fitting rational expectations
hypothesis and representing the structure. It seems that we equally cannot
derive the structural realist conclusion from the employment of the Euler
equation. This again indicates that Worrall’s inductive strategy is by no
means optimistic because alone it cannot reach the existence of structure.
Both objections to Worrall’s strategy show that to claim structural
realism, some independent criteria are required to distinguish structure from
non-structure. For, as van Fraassen (2006: 293) puts it, ‘if there is no non-structure, there is no structure either’. Conventionally, like just as
economists use invariance under intervention to distinguish between
structure and non-structure, scientists apply the notions of invariance, for
example, symmetry, to serve as such criteria (van Fraassen 2006). However,
it seems that such criteria are implied in Worrall’s account if his structural
realism is understood in terms of representation.
Worrall’s structural realism involves a task of representation.
Intrinsically, Worrall is concerned with the relation between models andthe real world, that is, mathematical equations represent the true structure.
Worrall does not state that a set of equations is a structure; he says that the
mathematical equations of a theory express a structure of the phenomena
(e.g. Worrall 1989: 122). Michael Redhead, Worrall’s colleague at the
London School of Economics, points out a three-tier task of representation
in structural realism to clarify Worrall’s account (Redhead 2001). The first
task is to group the physical relations of interest as concrete structures. Then
the concrete structures are related to each other up to an isomorphism.Finally, the mathematical equations are constructed as the representation of
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the abstract structure that maps the concrete structures up to the same
isomorphism (Redhead 2001: 345). Structural realism, as Redhead states, is
the claim that ‘this abstract structure associated with physical reality is whatscience aims, and to some extent succeeds, to uncover, rather than the true
physical relations of that reality’ (Redhead 2001: 345). The last step, the
mathematical representation of the abstract structure, is what Worrall is
aiming at. Redhead’s restatement also clearly presents the necessity of types
of isomorphism – a one–one mapping – between models. It can be stated that
there exists an isomorphic mapping between mathematical equations of the
old and new theories. When the isomorphism of equations is found, we can
say that such equations represent a real structure in Worrall’s sense.But if there is a representation, we must ask what makes some
mathematical equations a good representation of something – a structure
in our case. A formal account of representation can be found in Patrick
Suppes’ work on the semantic approach of theories (e.g. Suppes 2002), in
which isomorphism is a key concept. Suppes’ account of representation
suggests that representation is in mathematical form, is usually understood
in terms of models. A mathematical representation is empirically adequate
to an aspect of the world only if we prove a representation theorem formodels. The idea of representation theorems is as follows. If we want an
empirical model of the world (consisting of Redhead’s concrete structure) to
be represented by an abstract mathematical model (consisting of Redhead’s
abstract structure), we need the empirical model to satisfy a certain set of
axioms. Given that the axioms at the empirical end can in principle find
their counterparts at the mathematical end, we find the mathematical
model, and an isomorphism can be established between the empirical and
the mathematical models. In this sense a representation is made. To prove arepresentation theorem is to prove that such a type of isomorphism exists.
The role of representation theorems and isomorphic mappings is crucial
in two respects. On the one hand, isomorphism, as Suppes puts it, ‘makes
the intuitive idea of same structure precise’ (Suppes 1967: 59; emphasis in
original). This means that if a representation theorem is proven, the
mathematical model can be used to represent the empirical model with
respect to structure. In other words, the abstract structure and the concrete
structure are two of a kind. Seen in the way of representation, Worrall’sargument is compatible with Suppes’ account in the sense that a
mathematical equation of a theoretical model expresses the structure of
the world if there is an isomorphic mapping between the model and the
world. This also means, on the one hand, that if representation in Worrall’s
structural realism is regarded as or assumed to be satisfactory, a
representation theorem can always be proven to confirm the structural
representation. On the other hand, isomorphism indicates invariance under
transformation.12 When there is an isomorphic mapping between the sametypes of models, those models are said to be related by a permissible
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transformation. Examples are the symmetry of geometric figures under
certain rotations, and the uniqueness of scales of measurement up to various
transformations (see Suppes 2002). The structural realists’ observation onthe preservation of mathematical equations between old and new theories
can be interpreted as the transformation between old and new theories.
Since the models of old and new theories are isomorphically related, these
theories contain the same structure. Hence structural realism can be
understood as a proposition derived from sequential models which are
invariant under a certain transformation.
Why does the task of representation need to be stressed for structural
realism? Because the concept of invariance that consists in representationtheorems can, at least indirectly, serve as a criterion for distinguishing
between structure and non-structure that structural realism is criticized for
failing to hold. Consider two theories, T1 and T2. Each is regarded as a
mature and successful theory because each contains a structure S1 and S2,
respectively, that represent the same empirical structure SE. Therefore the
mappings between S1 and SE (S1«SE), and between S2 and SE (S2«SE) are
the same. But since S1 and S2 are the same structure, the relationships of
S1«SE and S2«SE must be the same as well. In other words, when Worrallobserves that in the history of science the mathematical equations of the new
and old theories are invariant (isomorphism among theoretical models),
given that in the successful or mature scientific theories, the theoretical
model flourishingly represents a feature of the world (isomorphism between
theoretical and empirical models), we can conclude that the represented
empirical models are also invariant under the same type of transformation
as the theoretical one.
In this interpretation the represented empirical model is invariant andtherefore can be regarded as a structure. Moreover, when this inference
from the invariance of theoretical models to the invariance of empirical
models is established, Worrall’s inductive strategy for realism is better
supported as associated with the conventional philosophical view of ‘the
invariant as the real’ (Hooker 1991; Weinert 2004: 62).13
We interpret Worrall’s structural realism as securing invariance through a
satisfactory representation. In contrast, for economists, when structure is
explicitly and (almost) unanimously construed as invariance underintervention in macroeconometrics for those who see models as structural
(e.g. the Colwes Commission) or as non-structural (e.g. the VAR
approach),14 we can secure a good representation if the model is invariant.
Hoover (1994: 65) suggests seeing the Lucas critique as a criticism of the
traditional macroeconometric models for not being ‘accurate representa-
tions of the current structure of the economy’ because the typical
macroeconometric models are not invariant under policy change.
Therefore, the traditional ‘structural’ models do not refer to any structureas their proponents claim. When seen in this way, the Lucas critique not
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only clearly asserts that the aim of econometrics is to use models to
represent the true structure of the economy, but also that econometrics
revives the notion of invariance as a criterion for an adequate representationof the structure of the world by models. When specifying models, invariance
is thought to be a necessary and sufficient condition for a model
representing the structure.15
6 REALISM ABOUT STRUCTURE
The realist attitude toward structure that economists hold can be argued as
the following. Given that the existence of structure of the consumptionfunction, namely the Euler equation, is perceived, macroeconomists accept
or reject the theory of consumption accordingly. They accept the life cycle–
permanent income hypothesis and the Euler-equation approach precisely
because they capture the right structure. To say that Keynes’s and
Duesenberry’s theories were abandoned for lack of theoretical foundation
is to say that they do not consist of the right structure. This implies a
‘realism about structure’ among economists. Realism about structure, on
the one hand, is consistent with the invariance view of reality: invariantrelations are structural and real. On the other hand, it does not subscribe to
the falsificationist account of theory testing but asserts that we accept a
theory if it yields a model containing the right structure. If a model is not
supported by empirical data when the model is considered as containing the
true structure, we do not reject the model but instead construct a new model
with the same true structure.
Methodologically, the realism about structure is compatible with two
characterizations of the new classical macroeconomics. One is argued byHoover (1994), who asserts that the new classical macroeconomists have a
strong prior belief in economic theories that are based on well-specified
optimization behavioral assumptions. Hoover labels this a ‘strong aprior-
ism’ that is similar to the position represented in Koopmans’ (1947) article
‘Measurement without theory’. The new classical economists, as also
exemplified in Hall’s model, adopt a strategy of developing an optimizing
representative-agent model taking ‘deep parameters’ as given (Hansen and
Sargent 1980; Lucas and Sargent 1979; and see Hoover 1988, 1994). Suchmodels are secured for invariance problems and can then be regarded as
accurate representations of the structure. The other is stated by John Sutton
(2000), who claims that economists usually hold ‘strong priors’ in favor of
some basic ideas. One of the examples that Sutton uses is our history of
the consumption function. Sutton, borrowing extensively from Gilbert
(1991), observes that Duesenberry’s relative income hypothesis fits
empirical data better than Friedman’s permanent income hypothesis, but
the relative income hypothesis ‘suffered primarily from its lack of atheoretical underpinning in individual maximizing behavior, rather than any
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shortcomings at the empirical level’ (Sutton 2000: 95). Similarly, he points
out that Hall’s random-walk model is not usually falsified by empirical data.
This means that when the theory is inconsistent with data, economists whohold a strong prior belief in the framework of Fisherian intertemporal
choices accept the theories which contain the structure that is thought to be
true, and reject those which do not.
Sutton’s case of holding strong prior belief in the Euler-equation
approach can be explored in more detail. Testing the new classical
consumption theory, as addressed in literature, resolves the correspondence
problem between theory and data. Theoretically, the life cycle–permanent
income hypothesis involves intertemporal choices as to the structure of theconsumption function, where the assumption of intertemporal choices
implies that the representative consumer optimally smoothes the consump-
tion over time. This motive has been pointed out by Friedman (1957: 7) that
a consumer tends to ‘straighten out’ the stream of consumption
expenditures. This assumption is known as consumption smoothing. The
life cycle–permanent income hypothesis predicts that consumption exhibits
a smooth pattern, because permanent income does not fluctuate in response
to the short-term income fluctuation; permanent income is smoother thanmeasured income. Consumption is smoother than measured income because
consumption presumably depends upon permanent income. In some cases,
the permanent income hypothesis could lead to the conclusion that the
consumption in each period equally divides the permanent income. This
outcome of consumption function can be called consumption smoothness,
which is also a stylized fact about consumption. The problem of
correspondence lies between consumption smoothing and consumption
smoothness. The existence of such a correspondence is a strong support forHall’s random-walk model. Since the random-walk model exhibits the
relationship between current and previous consumption, smoothness
can be defined as ct+1 > ct and thus is measured by the parameter on ct.
Hall’s own estimation seems to support this interpretation: the
estimate of the coefficient for ct of the random-walk model is 0.983.
Consequently, random walk consumption is an empirical justification for
the consumption smoothing assumption. This implies the following
argument: if consumption is not a random walk, i.e. consumption is notsmooth, then the correspondence between consumption smoothing and
consumption smoothness does not exist. The failure of such correspondence
is probably due to the inadequacy of the assumption of consumption
smoothing.
Macroeconomists have long been considering the empirical issues of the
Euler-equation approach. Hall (1978) used 1948(1)–1977(1) seasonally
adjusted quarterly data to test his random-walk model against four other
consumption functions, in order to see whether variables other thanprevious consumption are significant for current consumption. The results
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show that higher lag variables have no significant predictive power for
current consumption. Moreover, the F-statistics for jointly predictive
powers for variables other than ct-1 are all below critical values of the F-
distribution at 0.05 level. Thus the random walk consumption is not
rejected. But Hall also found that when stock prices are included as proxies
of wealth, they are statistically significant, hence the random walk
consumption function should be rejected. Hall’s findings inspire further
empirical studies based on the Euler-equation approach to reconcile theory
with data. In John Campbell and Gregory Mankiw’s (1989) model,
consumers are divided into two groups: one follows the assumption of
consumption smoothing, and the other follows the rule of thumb that
consumers’ decisions are based on current income. As a result, consumption
does not follow a random walk because current income is significant to the
next period’s consumption. Other studies show that the life cycle–permanent
income hypothesis fails to explain the facts of ‘excess sensitivity’ that
consumption is too sensitive in response to expected changes in income
(Flavin 1981), or of ‘excess smoothness’, meaning that consumption is too
smooth in response to unexpected changes (Campbell and Deaton 1989) of
consumption. Consequently many have attempted to explain the anomalies
(excess sensitivity and excess smoothness) by providing models with
different modifications.
However, Hall insists that since most of the predictive value of the stock
prices in his random-walk model comes from the change of the immediately
preceding quarter, it is compatible with the implication of the life cycle–
permanent income hypothesis that the change in consumption is related to
the change in permanent income (Hall 1978: 985–6). Hall also contends that
the improving predictive power by including stock prices ‘while statistically
significant, is not numerically large’ (Hall 1978: 985).
It can be argued that even though many other economists take
this empirical finding as evidence against the fundamental assumption of
complete consumption smoothing in the random-walk model, Hall
insists that the random-walk model is a reasonable approximation of
consumption because of his strong belief, as Sutton indicates, in the
fundamental assumption of consumption smoothing. Hoover’s view
provides reason for such a belief. The belief in the new classical model is
well grounded in its satisfaction of the Lucas critique on invariance. In this
vein it can be interpreted that although the correspondence between
consumption smoothing and consumption smoothness does not exist,
Hall still has reason to believe both in the random-walk model and in the
Euler-equation approach. The very reason, as the quotation above
shows, lies in the model’s inclusion of an Euler equation, a true structure
of the consumption function that characterizes an invariant relation of
consumption.
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7 CONCLUSION
For Worrall, passively retained mathematical equations are taken as evidence of
the existence of the true structure and they can play a heuristic role in developing
new theories. In a similar realism about structure, observed in the history of the
consumption function, both representation and invariance are central to
structuring the consumption function. For economists, the structure of the
consumption function is the Fisherian intertemporal choices, or the Eulerequation. Euler equations are passively observed not only as being preserved
across changes in consumption theories, but also because they satisfy the
definition of structure in macroeconomics, invariance under intervention. The
Fisherian framework of intertemporal choices is therefore conceived by
macroeconomists as the real structure and actively involved in theoretical and
empirical research. Moreover, this structure, that is thought to be real, provides
macroeconomists with grounds for accepting and rejecting a consumption
theory. Consequently, the poor correspondence between the theoretical assump-tion of consumption smoothing and the empirical fact of consumption smooth-
ness does not imperil the Euler-equation approach. Anomalies may reject the
permanent income hypothesis or the life-cycle hypothesis, but they only
motivate modelers to modify the Euler equations instead of abandoning them.
Yet Worrall’s structural realism is criticized for not involving criteria of
distinguishing between structure and non-structure. But we can understand
the structural realism as involving a task of representation in the following
way. The mathematical equations in a theory represent invariant empiricalrelations. When these equations are retained during theory change, our
belief in their truth to the world is based on their invariance across
transforming theories. Hence the notion of invariance under transformation
is embedded in the representation and can be applied to judge the existence
of structure.
Hsiang-Ke Chao
National Tsing Hua University, Taiwan
ACKNOWLEDGEMENTS
An early version of this paper was titled ‘A structural realist interpretation
of the euler-equation approach in macroeconomics’, published as a research
memorandum of the Amsterdam Research Group in the History and
Methodology of Economics, Faculty of Economics and Econometrics,
University of Amsterdam (No. 01-9). I thank Marcel Boumans and Mary
Morgan for their advice and encouragement. I am also most grateful to
Kevin Hoover and an anonymous referee for their constructive commentsand suggestions.
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NOTES
1 Modigliani (1947, 1949) has shown a Keynesian consumption function, whichconsists of the ‘highest previous income peak’, that is similar to Duesenberry’srelative income hypothesis.
2 See, inter alia, Psillos (1999, esp. Ch. 8), Votsis (2004), and papers that appearin the special issue of Synthese in 1999 on structural realist interpretations ofquantum field theory.
3 Note that some philosophers of science, for example, French and Saatsi (2004),use the terms ‘structural realism’ and ‘realism about structure’ interchangeably.
4 See Grower (2000) and Votsis (2004) for the history of structural realism.5 The contrast between Keynes’s consumption function and Fisher’s account can
be seen as early as Holden (1938). Note that in the General Theory, before heproposes the formal definition of the fundamental psychological law, Keynesdiscusses the ‘objective factors’ that he thinks would affect the marginalpropensity to consume. These objective factors include ‘changes in the rate oftime-discounting’ and ‘changes in expectations of the relation between thepresent and the future level of income’ (Keynes 1936: 93–6). But he goes on tostate that ‘ [f]or whilst the other factors are capable of varying (and this mustnot be forgotten), the aggregate income measured in terms of the wage-unit is,as a rule, the principal variable upon which the consumption-constituent of theaggregate demand function will depend.’ (Keynes 1936: 96). I thank a refereefor pointing out this to me. Also see Keynes’ (1938) reply to Holden (1938).
6 See Deaton (2005).7 See Sheffrin (1983: 105–6).8 The term ‘solved-out approach’ appears in Muellbauer (1994). In this way,
the consumption function is solved, for example, by substituting the Eulerequation (equation (1)) into the intertemporal budget constraint
c1E1c2
1zr~A0 1zrð Þzw1zE1w2
1zr , where At is the asset in period t, ct is the
consumption in period t, Et is the mathematical expectation conditional on allinformation available in period t; r is the constant real interest rate, and wt is
income in period t. c1~1
1z 1=1zrð Þ A0 1zrð Þzw1zE1w2
1zr
� �.
9 Hall (1988) measures the elasticity of intertemporal substitution.10 Discussions on the hypotheses of precautionary saving and liquidity
constraints can be seen in Carroll (2001) and the references therein.11 Laibson (1998) further shows that the standard exponential Euler equation is a
special case of his hyperbolic Euler equation.12 One major difference between invariance under intervention and invariance
under transformation is that the former account explicitly addresses theexistence of an outside force affecting the structure and hence associates itselfto the structural account of causality firmly. In modern terminology, a causalstructure consists of superexogenous relations that are invariant to interven-tions. In this way, the requirement for invariance and the Lucas critique can beunderstood as a type of statement on using models to represent a causalstructure satisfactorily. The structural account of causality in macroeconomicshas been extensively explored in Hoover (2001). Also note that causal relationsand invariant relations cannot be treated as equal. See Hoover (2001) andChen (2002).
13 Also see van Fraassen (1989, 2006) and Nozick (2001) for discussion of theontological issue of invariance in science.
14 The introduction to Hendry and Morgan (1995) provides an excellentreview on the development of the notion of structure in econometrics
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before the 1950s. Sims’s acceptance of the Cowles Commission’s definitionof structure, especially in Hurwicz (1962), can be seen in Sims (1980,1982).
15 Hendry (1995: 34) argues that invariance is only a necessary – but notsufficient – condition for structure because he requires the structuralparameters to be non-reducible: structural parameters are those which areinvariant and not derived from more fundamental parameters.
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