Behavioral Foundations for Keynesian Macroeconomics: The Consumption Function

Fabio D’Orlando and Eleonora Sanfilippo∗

Preliminary Draft

AbstractThis paper aims to discuss: (i) the presence of behavioral assumptions in Keynes’s

General Theory; and (ii) the possibility of grounding a Keynesian-type consumption function on (some of) the assumptions underlying contemporary behavioral models.

Introduction In his Nobel Lecture Akerlof, emphasizing the increasing role that behavioral

principles play within contemporary macroeconomics, argues that “in the spirit of Keynes’ General Theory” behavioral macroeconomists are substituting the ‘primitive’ New Classical micro-foundations of macroeconomics with more realistic behavioral assumptions “grounded in psychological and sociological observation” (Akerlof 2002: 413).

Starting from the above statement our paper aims to discuss: (i) the presence of behavioral assumptions in Keynes’s General Theory; and (ii) the possibility of grounding a Keynesian theoretical approach on (some of) the assumptions underlying contemporary behavioral models.

To pursue the first goal we adopt a history-of-ideas perspective. We perform textual analysis of the General Theory and its preparatory works to ascertain whether behavioral rather than maximizing principles can be considered as the microeconomic foundations for Keynes’s original conception. In particular, we seek to verify, on the one hand, to what extent Keynes assumes maximizing agents and, on the other, to what extent he refers, rather, to determinants for the aggregate behavior of agents closer to contemporary behavioral principles. We argue that, although Keynes never explicitly refuses the maximizing principle as the basis of agents’ behavior, this principle plays virtually no role in the General Theory; on the contrary, he often (and in most cases exclusively) refers to determinants for individuals’ behavior that are fully coherent with the underlying assumptions of (some) contemporary behavioral models.

To pursue the second goal we adopt a theoretical perspective. We seek to determine whether the Keynesian macroeconomic model (both in Keynes’s original and in later IS-LM version) might be better founded on behavioral rather than on maximizing assumptions. In this paper, in particular, we investigate contemporary behavioral approaches to search for possible behavioral foundations for the key Keynesian function of Consumption (and, implicitly, of Saving). The behavioral principles that best seem to meet our needs are hyperbolic discounting, mental accounting and mental budgeting, although other behavioral principles do play a role. We show that adopting neoclassical foundations (maximizing agents and exponential discounting) we get results more coherent with the standard life-cycle and permanent-income models, but which are at odds with the empirical evidence. On the other hand, by adopting behavioral foundations we get results coherent with the empirical evidence and more in line with Keynesian Consumption theory. Fabio D’Orlando, Dipartimento di Scienze Economiche, Università di Cassino, e-mail fabio.dorlando@unicas.it; Eleonora Sanfilippo, Dipartimento di Scienze Economiche, Università di Roma “La Sapienza”, e-mail eleonora.sanfilippo@uniroma1.it.

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Our main conclusion is therefore that Keynesian Consumption theory can be considered consistent with contemporary models of behavioral economics and with some of the grounding assumptions of these models. Moreover, the analysis developed here can also serve another purpose. The standard critique that neoclassical economists bring against the Keynesian approach is that it lacks micro-foundations. We wish to argue that this critique could be (partially) right if we mean neoclassical micro-foundations (based on the assumption that agents maximize their utility/profit functions under constraints); but it is not if we mean that Keynes’s approach lacks any micro-foundations. Keynes’s (and the Keynesian) approach can be built on behavioral micro-foundations. Our proposal thus contrasts with that of the New Keynesians, who have tried to obtain Keynesian results by sharing the maximizing principle of the standard neoclassical theory.

Keywords: Keynes, Behavioral Economics, Keynesian Theory, Consumption, Hyperbolic Discounting, Mental Accounting JEL classifications: B22, D01, D11, D91, E12, E21

1. Utility/Profit Maximization within the General Theory Our first step is to analyze the role of maximizing behavior in Keynes’s approach, both

on consumption and production side.1

An analysis of the consumption choices by individuals in terms of the standard neoclassical consumer theory is totally absent in the General Theory. Only in this respect can be accepted the well-known criticism about the lack of micro-foundations in Keynes’s macroeconomic model. Consumption is addressed basically from an aggregate point of view (Keynes 1973a: 61-65; 91 and ff.), establishing that the level of aggregate consumption increases at a decreasing rate as the current income increases (Keynes 1973a: 96). On the other hand, it would be incorrect to derive the conclusion that nothing is possible to infer about Keynes’s theory of individual consumption. For example, Keynes shows a particular attention to ‘subjective factors’ and motivations “which lead individuals to refrain from spending out of their incomes” or to consume. The motives behind abstinence are: “Precaution, Foresight, Calculation, Improvement, Independence, Enterprise, Pride and Avarice”; and behind consumption: “Enjoyment, Shortsighted-ness, Generosity, Miscalculation, Ostentation and Extravagance” (Keynes 1973a: 108). In the same Chapter devoted to analysis of propensity to consume (Chap. 9), there is also a long discussion about the fundamental role played by social and institutional factors on determining the “strength” of these motives (Keynes 1973a: 109).

As far as the rate of time-discounting governing inter-temporal choices of consumption is concerned, Keynes put forward the following critique to the standard neoclassical analysis:

The influence of this factor on the rate of spending out of a given income is open to a good deal of doubt. For the classical theory of the rate of interest […] expenditure on consumption is cet. par. negatively sensitive to changes in the rate of interest, so that any rise in the rate of interest would appreciably diminish consumption. It has long been recognized, however, that the total effect of changes in the rate of interest on the

1 We are not interested here to the specific analysis of the labour market, in which is not difficult to find some adhesion by Keynes to the marginal productivity theory. For what concerns the concept of marginal efficiency and its interpretation as a neoclassical concept see Garegnani (1979). For an opposite view see Pasinetti (1977).

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readiness to spend on present consumption is complex and uncertain, being dependent on conflicting tendencies (Keynes 1973a: 93).2

We obtain a slightly different result if we turn our investigation to Keynes’s analysis of the production side of the economy.

The passages in the General Theory referring to profit maximization as the rule of behaviour followed by the entrepreneur in his decisions of production are very few and somewhat ambiguous. One is contained in Chapter 6 of the book, in which Keynes gives his definitions of income, saving and investment:

The entrepreneur’s income [...] is taken as being equal to the quantity, depending on his scale of production, which he endeavours to maximise, i.e. to his gross profit in the ordinary sense of this term; - which agrees with common sense. […] since it is the entrepreneur’s expectation of the excess of this quantity over his outgoings to the other factors of production which he endeavours to maximize when he decides how much employment to give to the other factors of production, it is the quantity which is causally significant for employment. (Keynes 1973a: 53-4; see also 56).

The most explicit reference to the marginal cost=marginal revenue rule is contained in the preparatory work of the General Theory, in a passage taken from one of the drafts of Chapter 3: 3

Each firm calculates the prospective selling price of its output and its variable costs in respect of output on various possible scales of production. Its variable cost per unit is not, as a rule, constant for all volumes of output but increases as output increases. Output is then pushed to the point at which the prospective selling price no longer exceeds the marginal variable cost (Keynes 1979: 98; see also 89).

The passage, perhaps significantly, was not included in the final version, even though there is no textual evidence in the whole General Theory of an explicit refuse by Keynes of profit maximization.4

What seems difficult to question is the lack of a specific part of Keynes’s widespread scientific work which is explicitly devoted to a comprehensive analysis of maximizing agents’ behaviour: in general, he seems to not have dedicated much effort and time to go deeper into this aspect of economic theory.

It appears evident that Keynes, if “adopted” the marginal language, employed it quite sparingly, as if - one is tempted to infer - it were outside the core of his model. Reliance on marginal analysis is, in fact, very limited in the General Theory, whose main message is its being other than the “classical” theory. Keynes’s criticism to the latter consisted “in pointing 2 As far as the long period is concerned the influence of changes in the rate of interest “modify social habits considerably […] in which direction it would be hard to say […]”. As far as the short period is concerned “fluctuation in the rate of interest is not likely […] to have much direct influence on spending either way” (Keynes 1973a: 93, emphasis in the text). 3 The chapter was entitled “The Characteristics of An Entrepreneur Economy” (according to the December 1933 Table of Contents of the General Theory, Keynes 1973b: 421).4 In Marcuzzo and Sanfilippo (2006) the ties between Keynes’s analysis and the Marshalllian apparatus in terms of supply and demand curves and rising marginal costs are fully examined; it has also been maintained that the influence of Kahn was crucial in persuading Keynes to introduce some elements of marginal analysis in the General Theory (Marcuzzo 2002).

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out that its tacit assumptions are seldom or never satisfied, with the result that it cannot solve the economic problems of the actual world” (Keynes 1973a: 378).

It may be possible perhaps to infer - a contrario - that the assumptions behind profit maximization appeared to Keynes as sufficiently explicit and general as to make them acceptable. Or simply that he preferred to concentrate his attack against the neoclassical theory on the determination of the aggregate level of income and employment, without opening another front also on neoclassical micro-foundations.

2. Behaviorally-Inspired Micro-foundations for the General TheoryThe main purpose of the General Theory - as it is well known - was to demonstrate the

substantial fallacy of Say’s Law, the logical flaws of the neoclassical theory of aggregate employment and the tendency of the economic system towards a condition of chronic depression. In this respect, two things are worth noticing: (i) that Keynes’s model does not depend in any essential feature or conclusion on the assumption of profit maximization; (ii) that his path-breaking views mainly concern investment decisions, the influence of expectation and uncertainty on the calculation of prospective yields and the role of speculative activity, in which no trace of maximizing behaviour can be found. On the contrary, entrepreneurs are seen not to be proceeding on the basis of a rational calculus (as it should be the case in the application of marginal cost=marginal revenue rule) but rather obeying to instincts, conventions and habits (Keynes 1973a: 152). In the General Theory, indeed, investment decisions - as opposed to the determination of the level of the output by the single firm5 - are never made on “a precise calculation of prospective profit”: they are the outcome of a sort of lottery in which

[…] even after the event no one would know whether the average results in terms of the sums invested had exceeded, equalled or fallen short of the prevailing rate of interest [...]. If human nature felt no temptation to take a chance, no satisfaction (profit apart) in constructing a factory, a railway, a mine or a farm, there might not be much investment merely as a result of cold calculation (Keynes 1973a: 150).

In the face of “fundamental” uncertainty, a way-out for the entrepreneurs is to follow some conventional rules as for example “to take the existing situation and to project it into the future, modified only to the extent that we have more or less definitive reasons for expecting a change” (Keynes 1973a: 148). Another one is trying to guess the prospective yields on the basis of a rational conjecture, taking into account the degree of ignorance on the causes influencing the results, through a proceeding similar to a “trial and error” in which – unlike neoclassical theory – a convergence towards an optimal position is never guaranteed.

Keynes’s vision of entrepreneur’s conduct as far as investment decisions are concerned is much more similar to modern behavioural principles rather than neoclassical theory. Conventional rules, myopia, inertia, conformism, just to make some examples, are much more explaining concepts of individuals’ actions than the optimization rule.

This is even more true if we turn our attention to those aspects of the General Theory in which Keynes provides an analysis of motivations behind economic agents’ behaviors, as it is the case in this famous passage of the General Theory:

5 In Keynes - as noted by Roncaglia (2006) - “there is a distinction of economic agents and decisions according to the “kind” of uncertainty involved: entrepreneurs have to be kept distinct from financiers, and both from households; among entrepreneur’s decisions, those concerning investments have to be kept separate from those concerning production levels”.

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Most, probably, of our decisions to do something positive, the full consequences of which will be drawn out over many days to come, can only be taken as a result of animal spirits – of a spontaneous urge to action rather than inaction, and not as the outcome of a weighted average of quantitative benefits multiplied by quantitative probabilities (Keynes 1973a: 161).

This quotation - which is contained in the analysis of long-term expectations and investment decisions by entrepreneurs - is a clear evidence of Keynes’s rejection of mathematical calculus to representing what is behind entrepreneurs’ choices, rather than a belief in the “irrational” nature of the entrepreneurs’ decision process – as it has been often interpreted in the literature. Keynes himself, few paragraphs later, explains very clearly how his claim should be intended:

We should not conclude from this that everything depends on waves of irrational psychology. On the contrary, the state of long-term expectation is often steady, and, even when it is not, the other factors exert their compensating effects. We are merely reminding ourselves that human decisions affecting the future, whether personal or political or economic, cannot depend on strict mathematical expectation, since the basis for making such calculations does not exist; and that is our innate urge to activity which makes wheels go round, our rational selves choosing between the alternatives as best we are able, calculating where we can, but often falling back for our motive on whim or sentiment or chance (Keynes 1973a: 162-3).

The main elements in Keynes’s analysis which are in sharp contrast with neoclassical optimizing behaviour by agents are: (i) the notion of “fundamental” uncertainty and “logical” probability (see Carabelli 1988); (ii) the role attributed to the social context and the influence of habits and conventions on individuals’ actions; (iii) the absence of any prevision of rational expectations; (iv) a notion of rationality which is different from the neoclassical one not only because of the lack of full information that economic agents experience - as it is admitted also in the New Keynesian literature - but because it explicitly considers the complexity of the mental processes and the impact of non-economic factors, like psychological, emotional and socially driven considerations, on individuals’ decisions. Keynes’s agents are not “irrational” but they are guided in their choices by a broader concept of rationality, closer to common sense and to a notion like “sensibleness”. A “rational” choice by an economic agent in this context is simply a choice that a person in the same situation, and with the same amount and kind of knowledge (and ignorance), could agree with.

Very often in the unending debate on the General Theory, these elements of contraposition with the neoclassical approach are fully recognised (see, for example, the whole Post-Keynesian literature). In the perspective of the present work, however, they are specifically viewed as a confirmation of the presence of some sort of behavioural micro-foundations in Keynes’s General Theory.

3. Maximizing Foundations for an Aggregate Consumption Function

3.1 Nobel-prize winning ideas On the neoclassical side the attempt to obtain micro-foundations for (aggregate)

consumption (and saving) function has an history that goes back to the 50s. In particular Friedman (1957) and Modigliani and Brumberg (1954) first inspired models within which

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consumption and saving functions, both for the short and for the long run, were obtained on the basis of the permanent-income and life-cycle Nobel-prize winner ideas. These models get micro-foundations for consumption/saving functions assuming intertemporal utility maximization by rational consumers.

Although neoclassical attempt to get micro-foundations for consumption and saving aggregate functions seems a success history, the consumption function that neoclassicals succeed in microfounding is very different from the Keynesian one. This would be a minor problem if the Keynesian idea that consumption tracks current income would not have a strong empirical support. But the Keynesian short-period consumption theory seemed to be more coherent with empirical data than the original neoclassical one. As a consequence neoclassicals have been forced to introduce “ad hoc” hypotheses to obtain results compatible with empirical evidence.

In this section we shortly describe the neoclassical microfounding procedure and discuss its weakness; in section 4 we propose alternative possible micro-foundations for the aggregate consumption function.

3.2 Current consumption as the result of intertemporal utility maximization: the life-cycle and permanent-income hypotheses

The standard (neoclassical) approach obtains an aggregate Consumption function on the basis of intertemporal maximizing behavior of a representative consumer. In this context the consumer will maximize intertemporal utility by solving the problem:

1)( )

( )

( ) ( )

0

0 0

1max1

01 1

T

ttt

T Tt t

t tt t

u C

C Ysubi i

γ=

= =

+ − = + +

∑

∑ ∑Where tC is consumption at time t, tY is income at time t, i is the interest rate,

( )( )

0

11

T

ttt

u Cγ=

⋅+

∑ is an intertemporal (separable6) utility function, ( )1

1 tγ+ is the discount

factor (γ is the subjective time preference: the larger γ is, the more the consumer prefers

present to future consumption) and ( ) ( )0 00

1 1

T Tt t

t tt t

C Yi i= =

− =+ +

∑ ∑ is the intertemporal budgeting

constraint. If we simplify the analysis by assuming that only two times exist, 1t = (present) and

2t = (future), and that the intertemporal utility function is a logarithmic function such as

1 21log log

1U C C

γ= +

+ , the consumer’s problem becomes:

2)( )

( ) ( )

1 2

2 21 1

1max log log1

01 1

C C

C Ysub C Yi i

γ + + + − − = + +

Solving this problem and posing 1C C= gives:

6 Separability implies that the utility of consumption at time t is independent from the consumption at other (present or future) dates.

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3) ( )2

112 1

YC Yi

γγ

+= ⋅ + + + .

For the general case (T>2 and generic utility functions) the relation is slightly more complex, but its main implications stay alive. In particular, since in this context the wealth W can be considered as the current income plus the actual value of the future income (i.e.

21 1

YW Yi

= ++

)7, the consumption function can be written as follows:

4)12

C Wγγ

+= ⋅+ .

Relation 4 is coherent with the results obtained within the life-cycle approach proposed by Modigliani and Brumberg. In this approach current consumption is a function of wealth, and not of current income alone (or mainly) as it was in the Keynesian approach.

We can also refer to relation 4 to discuss the consumption function which results on the basis of Friedman’s permanent-income hypothesis.8 Within our context permanent-income

can be defined as that constant level of income PY which solves 211 1

PP

Y YY Y Wi i

+ = + =+ +

, so

that wealth can be defined as:

5)21P

iW Yi

+=+

.

Substituting the right side of relation 5 for W in relation 4, the consumption function can be written as follows:9

6) 1 22 1 P P

iC Y k Yi

γγ

+ += ⋅ = ⋅+ + .

Neoclassical micro-foundation of the consumption function hence breaks the link between current income and current consumption that characterizes Keynes’s original function ( )C Yχ= and its later IS-LM version ( )dC C c Y= + : current consumption depends on the wealth or, as in relation 6), on the permanent-income.

According to this approach, an unpredictable change in current income (and hence in wealth) generates the so called consumption smoothing effect, i.e. a change in both current and (by means of saving) future consumption; whereas a predictable change in income should generate no change in consumption. Consumption smoothing has important implications for the representative agent’s consumption profile through time. According to Thaler (1990: 195) “[t]he heart of the life-cycle theory of saving is a hump-shaped age-saving profile. The young, whose incomes are below their permanent-income, borrow to finance consumption; the middle-aged save for retirement; the old dissave”.

7 In general wealth is the sum of a number of elements: real capital, financial capital, current labour income, future (discounted) labour income, etc. Here we have considered wealth as depending on income alone; we could extend the analysis and consider a broader concept of wealth, leaving unchanged the conclusions.8 In our highly simplified analysis we have deliberately ignored the main difference existing between the life-cycle and the permanent-income model, i.e. the circumstance that time horizon is finite for Modigliani and Brumberg, whereas it is infinite for Friedman. 9 Relation 6 is also coherent with Kuznets’s (1946) result of a constant long-period propensity to consume.

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3.4 The empirical weaknesses of the life-cycle/permanent-income hypothesis The life-cycle/permanent-income hypothesis faces a number of empirical problems.

The most interesting among these problems are the excess sensitivity of current consumption to current income, and the curious circumstance that different forms of wealth (or even gains of different amount) appear to have different effects on consumption, i.e. are not close substitutes.

The first problem comes from the empirical finding that often enough unpredictable changes in income generate variations in current consumption and only a small consumption smoothing effect, whereas predictable changes in income generate variations in consumption, two results which are at odds with the life-cycle/permanent-income hypothesis. Current consumption seems therefore strongly tracking current income and its fluctuation (predictable and unpredictable), whereas it is not sensitive enough to (expected) future income and asset price, i.e. to consumers’ wealth or permanent-income (see e.g. Flavin 1981 and 1983, Hall and Mishkin 1982, Carroll 1994, Zeldes 1989b, Singleton 1990). These empirical findings have been confirmed by other contributions, which have shown that wage cuts reduce consumption when the cut is effective and not when it is announced (Shea 1992) and that there is evidence of spending immediately after having received the check of social security monthly benefits (Stephens 2003). Similar results have been reached by studies on the effects of increasing in social security benefits (Wilcox 1989) or tax refunds (Souleles 2002).

The second problem is different and, from a theoretical viewpoint, particularly intriguing. In empirical studies subjects seem to violate fungibility of money, i.e. the notion that money is money: “The essence of the [traditional] theory is that an individual spends the annuity value of his or her wealth in each period, so an extra dollar of housing wealth, pension wealth, or current lottery winnings all generate the same increase in consumption. … this prediction of the theory is not consistent with behavior. People behave in ways that suggest that the source or location of wealth can influence the marginal propensity to spend it” (Thaler 1994, p. 188). Furthermore, people seem to have larger marginal propensity to consume on small rather than on large extra amount of income (Souleles 2002).

Neoclassical approach has mainly tried to face the first problem. Developments of the theory have been based on the hypothesis that subjects have liquidity constraints, i.e. they cannot borrow or that they do not maximize only their own utility but also the utility of their heirs. However, not even these amended versions of the theory resist empirical proof. Even if people are constrained in the sense that they cannot borrow enough, or if they care of their heirs, nothing prevents them from saving. Nonetheless, in most cases people reduce their consumption when they retire since they have not saved enough during their life (see Banks, Blundell and Tanner 1998; Bernheim, Skinner and Weinberg 1997).10

We believe that the maximizing approach can cope with the above mentioned problems only with great difficulty, and that behavioral economics might do a better job in dealing with consumption (and saving) decisions. This implies, for example, that the circumstance that people do not borrow enough should no more be studied trying to understand why people are unable to borrow, but accepting the hypothesis that they may be (or at least may also be) unwilling to borrow (Thaler 1990: 203). Apart from the relevant policy implications of such a change of perspective, the aggregate consumption function that

10 The standard approach faces other problems in deriving the explicit solution for consumption when uncertainty on future income exists. The attempt to cope with these problems has initially generated developments of the theory, such as the perfect foresight and the certainty equivalent versions, which are nonetheless special (and scarcely realistic) cases. Later, more robust solutions to these problems were provided (see e.g. Carroll 1992 and Zeldes 1989a) within models with impatient consumers and precautionary saving.

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we can build on these different microeconomic bases becomes closer to the Keynesian consumption function.

4. Behavioral Foundations for the Keynesian Consumption Function

4.1 Micro-foundations within a behavioral contextOn the behavioral side the interest in consumer’s choice was born with the birth of

behavioral economics but, in spite of the circumstance that “[a]lmost every where Keynes blamed market failures on psychological propensities (as in consumption)” (Akerlof 2002: 428), to the best of our knowledge no one has till now explicitly used behavioral economics to obtain micro-foundations for the Keynesian consumption function. Our argument is that behavioral economics can contribute to provide micro-foundations for the original Keynesian consumption function, reconciling Keynes with micro-foundations and consumers’ theoretically predicted behavior with empirical evidence.

Differently from neoclassical theory, behavioral economics does not possess a unique principle on which to theoretically base subjects’ behavior. Behavioral economics rather recognizes that a multiplicity of determinants for human behavior exists. This circumstance allows the approach to get closer to empirical data, but in most cases also makes it impossible to build models based on a unique simple principle (maximizing subjects) and a unique simple procedure (maximization under constraint). Therefore, within a behavioral context, the problem of microfounding aggregate functions changes abruptly. Within traditional approach, once given some more or less ‘ad hoc’ assumptions on the characteristics of the utility function, the maximizing procedure determines the form and the values of the parameters of the resulting aggregate function. Within a behavioral context, the lack of a unique principle and of a unique procedure implies that we can only speculate on the link among a number of generally vague principles and some general property of the aggregate function. It is hence not legitimate to derive any aggregate function on the basis of any simple mathematical procedure.

It is worth noticing that the above conclusion is perfectly coherent with the method used by Keynes. He has not based his aggregate functions on a unique principle (such as intertemporal utility maximization). Rather he has indicated a plurality of determinants and has discussed the link among these determinants and the properties of the aggregate function.11 He has hence obtained general but not punctual properties. Such a procedure has been criticized, arguing that Keynes did not microfound his aggregate function. But it is true the opposite. In the presence of a multiplicity of possible determinants it is incorrect to derive aggregate functions on a single principle and adopting a single procedure. As for the aggregate functions in Behavioral Economics, the correct microfounding procedure seems more a listing than a derivative procedure.

We understand that deriving aggregate functions by maximizing a utility function is simple and elegant. But, in general, it is worth remembering that microfounding macroeconomics does not mean obtaining macroeconomic behavior as the result of maximizing procedures undertaken by maximizing subjects. On the contrary microfounding macroeconomics means obtaining macroeconomic behavior on the basis of the most robust among available microeconomic principles. And today the maximizing principle is no more a robust microeconomic principle.

The same problem emerges when we try to propose micro-foundations for the Keynesian consumption function. In this case a multiplicity of behavioral principles are in general capable to explain, at least partially, some specific characteristics of this function. In

11 Chapters 8 and 9 of the General Theory (Keynes 1973a) are an example of this method with reference to the consumption function.

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what follows we describe only those behavioral principles that we consider as the most relevant to our purpose.

4.2 Not far from maximizing procedure: hyperbolic discountingThe first approach, hyperbolic discounting, has been the basis for a number of

contributions, generally still built within a maximizing framework. Among the behavioral foundations for the consumption function it is hence the one which less departs from the traditional theory. Nonetheless it has a number of appealing characteristics and poses serious problems to the conventional concept of rational behavior. In particular, assuming hyperbolic discounting allows one to cope with the circumstance that saving for retirement is often less than what predicted by the traditional theory (and less than what subjects need for maintaining their level of consumption when retired). Hyperbolic discounting explains this behavior by analyzing self-control problems that could prevent people from saving.

As we have discussed in section 3.2, the neoclassical procedure for obtaining an aggregate consumption function considers the utility function to be maximized as represented

by ( )( )

0

11

T

ttt

u Cγ= +

∑ . In this function is implicit an exponential discount rate. Furthermore,

this function satisfies time consistency: consumers make choices in time t for t+n that they will confirm when t+n arrives. The main problem with time consistency (and hence exponential discount) is that “[c]asual observation, introspection, and psychological research all suggest that the assumption of time consistency is importantly wrong. Our short term tendency to pursue immediate gratification is inconsistent with our long term preferences” (Rabin 1998: 38). If time consistency is not satisfied, agents make choices in time t for t+n that they won’t confirm when t+n arrives. Another empirical finding that exponential discount procedure cannot grasp is that real “agents are relatively farsighted when making tradeoffs between rewards at different times in the future, but pursue immediate gratification when it is available” (Ho, Lim and Camerer 2006: 21). The main implication of these empirical findings are self control problems (people decide to do tomorrow what they were supposed to do today, but when tomorrow arrives they decide to procrastinate to the day after tomorrow, and so on) and declining instead of constant discount rates. Hyperbolic discounting models can cope with these empirical findings without going to far from the neoclassical realm.

The first contribution on the theme of hyperbolic discounting was by Strotz (1956). He criticized the realism of the exponential discount procedure and suggested that better specifications for the discount function should imply declining discount rates. However he did not propose any specific alternative functional form. A number of specific functional forms have been proposed thereafter (for a list see Frederick, Loewenstein, O’Donoghue 2002: 360, and Angeletos, Laibson, Repetto, Tobacman and Weinberg 2001: 50, fn. 13). In general, “[h]yperbolic discount functions are characterized by a relatively high discount rate over shorts horizons and a relatively low discount rate over long horizons. This discount structure sets up a conflict between today’s preferences, and the preferences that will be held in the future” (Laibson 1997: 445).

The easiest way to model hyperbolic discounting is to write down the intertemporal

utility function as ( )01

11

T

tt

u u ut

βγ=

= ++ ⋅∑ , or even as 0

1

1T

tt

u u ut

β=

= + ⋅∑ . However, often

enough theoretical analysis uses quasi-hyperbolic or present-biased models, within which the intertemporal utility function becomes

7) ( )01

11

T

ttt

u u uβγ=

= ++

∑ ,

10

where 1β < (cfr. Laibson 1997 and Phelps and Pollak 1968). All these approaches, albeit bearing implications radically alternative to those of the standard framework, allows economists to treat hyperbolic discounting using otherwise traditional tools (see on this point Rabin 1998: 40).

The hyperbolic discount approach models subjects that, albeit following a maximizing procedure, make time inconsistent choices (see e.g. Strotz 1956; Angeletos et al. 2001: 51-52), thus behaving as real subjects do. This explains why hyperbolic discounting represents a departure from the traditional concept of rationality. Nonetheless authors exist that consider also this approach coherent with a more general formulation of the life-cycle/permanent-income approach (Browning and Crossley 2001).

The main implication of hyperbolic discounting for our analysis is that consumption smoothing fades and a stronger relation between current income and current consumption arises. In particular, saving will always be less than what predicted by the traditional approach, since “the benefits of current consumption are immediate, whereas the increased future consumption that saving allows is delayed” (Rabin 1998: 41). Hyperbolic discounting can therefore contribute to the building of a Keynesian-type consumption function but cannot solve by itself alone all the problems that we have discussed in section 3.4 above, and in particular cannot cope with the non fungibility of money critique. If real subjects adopt an hyperbolic discounting procedure and consider money as a non fungible asset, hyperbolic discount models based on utility maximization are empirically flawed. And the inconsistency is to be found in the maximizing and not in the discounting procedure, which we can instead retain. To cope with these problems we have hence to refer to behavioral principles which are totally at odds with the maximizing approach.

4.3 Far from maximizing procedure: mental accounts and mental budgeting Leaving the traditional approach, we have first to discuss the possibility that subjects

fail to behave as the traditional life-cycle/permanent-income approach predicts because they are not able to solve the complex problems involved in consumption/saving choices (Thaler 1994: 187). However, the mere acknowledgment that people do not maximize maybe enough for criticizing the validity of the standard approach, but it is not enough for building on an aggregate consumption function. To do this we have to know how people do behave, and hence to address our attention to other aspects of the behavioral approach.

We believe that the main behavioral principles which can contribute to the building of an aggregate consumption function (together with idea that subjects hyperbolically discount, that we propose to disregard only when coupled with maximizing behavior) are mental accounting and mental budgeting (Thaler 1985).

According to Heat and Soll (1996: 40) “consumers budget portions of their total resources to separate mental accounts (e.g. entertainment or household expenses) and then track expenses against the budgets. As expenses are incurred, they deplete the funds available in their account, which makes future purchases less likely”. This implies that certain amounts of money are ex-ante (before occasions of consuming arise) destined to specific types of consumption, and that the transfer of money from an account (i.e. from a type of consumption) to another (i.e. to another type of consumption) is not easily allowed.

Mental budgets have often been considered as self-control devices, and “[b]ecause budgets are set before consumption opportunities arise, they sometimes overestimate or underestimate the money required for a particular account” (Heat and Soll 1996: 40). Furthermore, some authors have argued that, when acts of payment are delayed with respect to the consumption experience (as in credit purchases) the utility deriving from actual consumption is reduced by the disutility deriving from expected payment. As a consequence, mental budgeting may generate strong debt aversion.

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Debt aversion deriving from mental accounting can explain the paradoxical circumstance, for the standard life-cycle theory, that young people with temporarily low income but high future expected income “fail to borrow sufficiently against future earnings” (Loewenstein and Prelec 1998: 15). People are not unable to borrow: they instead are unwilling to borrow due to debt aversion. Consumption smoothing is totally out of question and consumption tracks income.

Mental budgeting can also explain the non-fungibility of money argument. In this case the violation of fungibility follows from the well known circumstance that “people distinguish between wealth in categories like ‘current spendable income’ and ‘current assets’, and are more willing to consume an increase in current income […] than an increase in current assets” (Heat and Soll 1996: 41). A number of contribution have studied how different increases in different type of wealth become consumption (see e.g. Heath and Soll 1996 and Thaler 1990): for example, a typical conclusion is that small gains more likely become consumption, whereas large gains more likely become saving. Mental accounting can therefore explain what the life-cycle, the permanent-income and also the hyperbolic discount approach cannot: why people consume different fraction out of different type of income (or even out of different type of wealth).

Mental accounting and mental budgeting (together with their empirical robustness) jeopardize the traditional approach for at least two reasons: first, subjects do not borrow what they should, since they are strongly adverse to debt; second, an identical increase in future (or even current) income can become consumption or saving independently of the interest rate or the time preference, but only on reason of the mental account within which it is categorized, violating the principle of fungibility of money. If we add the insufficient level of saving deriving from the hyperbolic discount idea, behavioral considerations and their empirical robustness leave nothing alive of the traditional theory.

A more general consideration is that building inflexible budget, i.e. (ex-ante) inflexibly devoting certain amount of money to certain expenses, implies that it is impossible to re-allocate money among different accounts ex-post, so that utility cannot be maximized: “when people budget too little money, they may underconsume goods that they desire. When they budget too much, they may overconsume goods that they desire less. These predictions clearly differ from those of economic consumer theory, which assumes that people always consume an optimal quantity of each good.” (Heat and Soll 1996: 40).

On the basis of the preceding arguments, we believe that hyperbolic discount and mental accounts principles can be possible micro-foundations for a consumption function that, within a two-periods time span (t and t+1), could be written as follows:

8) 1 1, , ,

1 1 1

n n mtt t t t t t tY i i Y i i W i i

i n jC C c Y c Y c W+ +

= = == + ⋅ + ⋅ + ⋅∑ ∑ ∑

In our formalization, it exists a single propensity to consume ,tY ic for any possible type

of current income tiY , for any possible type of future discounted income 1t

iY + and for any possible type of wealth t

jW . Future incomes can be considered hyperbolically discounted and

,tW ic are small. t

C represents, as usual, the measure of our ignorance on other determinants of the consumption function. It is worth noticing that this functional relationship has not been built on a utility maximization procedure.

By averaging and aggregating all the propensity to consume, we can write down a synthetic, deterministic function which sounds like the Keynesian one:

9) C C c Y= + ⋅ .

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5. Conclusions Our analysis has shown that:(i) the optimization procedure is not at the heart of Keynes’s model;(ii) a number of behavioral principles can be detected in Keynes’s discussion of

individual choices relating to consumption and investment decisions;(iii) the traditional analysis of aggregate consumption, based on maximizing

agents, presents relevant empirical drawbacks and is not coherent with Keynes’s consumption theory;

(iv) an analysis of aggregate consumption grounded on behavioral principles is a better representation of actual reality and is more coherent with Keynes’s consumption theory;

(v) at least as far as consumption is concerned, Keynes’s theory can be better micro-founded using behavioral rather than maximizing assumptions.

Given the complexity of the real world and the decision process by individuals, we believe that the only sensible way to represent the relation between consumption and income is by using a very simple function. Exactly what Keynes did.

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