jan-oliver menz october 22, 2007 - hans b¶ckler stiftung

Precautionary Saving in a macroeconomic perspective:A comparison between New Keynesian and Post

Keynesian consumption theory §

Jan-Oliver Menz∗

October 22, 2007

Abstract

The following paper gives a survey of the current state of consumertheory. It shows that the New Keynesian theory of PrecautionarySaving has again come to more traditional Keynesian results alreadyhighlighted by Post Keynesians during the last decades. The often ne-glected consumer theory in the Post Keynesian paradigm is expandedusing insights from both Economic Sociology and Behavioural Eco-nomics. Finally, the paper will disuss both agreement and disagree-ment between the two theoretical strands.

Keywords: Precautionary Saving, Consumption Theory, Post Key-nesianism, New Keynesianism

JEL classification:

§

∗∗University of Warwick, United Kingdom, jan [email protected]

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mailto:[email protected]

Conference PaperContents J.-O. Menz

Contents

1 Introduction 1

2 Precautionary Saving 22.1 Neoclassicals and New Keynesians . . . . . . . . . . . . . . . . 22.2 The Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

3 The Postkeynesian Theory of Consumption 63.1 Social Class Behaviour . . . . . . . . . . . . . . . . . . . . . . 63.2 Risk and Uncertainty . . . . . . . . . . . . . . . . . . . . . . . 93.3 The Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

4 Macroeconomic implications 154.1 Derivation of the New Keynesian IS-curve with precautionary

saving . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154.2 Derivation of the Post Keynesian IS-curve . . . . . . . . . . . 164.3 A New Keynesian model using Post Keynesian insights . . . . 19

5 Summary and Outlook 20

References 22

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Conference Paper1 Introduction J.-O. Menz

1 Introduction

This paper deals with consumption theory using a paradigmatic approachand trying to figure out similarities and differences between New Keynesianand Post Keynesian paradigms. I distinguish these two paradigms by theirtreatment of risk and uncertainty and their use of optimising microeconomictools.1 The paper tries to shed some light on two main questions: Againstthe background of the New Consensus Model in macroeconomics, does therealso exist a unifying approach to consumption theory today? And if so, whatare its characteristics? Is this new consumption theory just a least commondenominator, or can one even find some agreement with more fundamentalKeynesian theories?

Beginning with a brief review of the developments in modern consump-tion theory, I will show in detail the underlying theoretical ideas and postu-lated consequences of the newer theory of Precautionary Saving, mainly themodels built upon the work by Christopher Carroll. I will then develop a cri-tique of the precautionary saving model from a Post Keynesian perspective,concentrating on the distinction between risk and uncertainty and a gen-eral scepticism against the use of standard microeconomic tools. Given thePost Keynesian bias in favour of firms’ investment theory, I will borrow bothfrom Behavioural Economics and Economic Sociology to clarify the underly-ing assumptions of the Post Keynesian consumption theory in greater detail.Moreover, I will derive the goods market equilibrium on the basis of eachof the consumption theories and then compare the resulting IS-curves. Thepaper will further sketch some raw ideas to develop a consumption modelusing both New and Post Keynesian insights. Finally, I will outline somepossible consequences of a greater approval of precautionary saving or PostKeynesian models which gives at the same time some directions for furtherresearch.

1For a more detailed comparison between New Keynesian and Post Keynesian theorysee Hein (2005)

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Conference Paper2 Precautionary Saving J.-O. Menz

2 Precautionary Saving

2.1 Neoclassicals and New Keynesians

As Keynes stated in his General Theory2, ”men increase their consumptionas income increases, but not by as much as the increase in income”. Thus,individuals are supposed to rely mainly on current income when decidingwhat and how much to consume. Neoclassical theory has heavily criticizedthis thesis, not least due to its non-derivation from optimal microeconomicbehaviour.3 Friedman (1957) replaced the current income with ”permanentincome”, supposing that consumers regard mainly their expected future in-come, while Modigliani and Brumbergh (1955) showed that individuals tryto smooth their consumption about their entire lifetime. These neoclassi-cal criticisms changed the main Keynesian consumption hypothesis into thecontrary of its traditional results: First, consumption does not depend oncurrent disposable income but on the expected permanent lifetime income.Secondly, the marginal propensity to consume (MPC) out of current incomeis not close to one, but much lower, since individuals only consume if theyconsider income changes as permanent. And thirdly, the consumption func-tion looses its concavity, i.e., an increase in income does not lead to a declinein the marginal propensity to consume. In what is called in this paper ”NewKeynesian Consumption Theory” is based on this neoclassical ”Life-Cycle-Permanent-Income-Hypothesis”, while it incorporates at the same time sev-eral restrictions reenforcing the role of current income and leading to moreKeynesian-like results. I will focus especially on one kind of restriction whichI think is of the greatest importance and which is also directly linked tooriginal Keynesian thinking namely the explicit consideration of uncertaintyand risk. 4 Neoclassical economists themselves tried to make their theorymore realistic: Criticizing the implicit assumption made by Friedman andothers that households have perfect knowledge about their future income,Hall (1978) was the first paying greater attention to the role of uncertaintywhen considering explicitly the impact of the use of rational expectationsin a standard consumption model. Though his ”Certainty Equivalence Ap-

2Keynes (1936),p.963See for an overview of the historical development in consumer theory Romer (2006)

and Carroll (2001)4Other features trying to explain departures from the Life-Cycle-Model are credit re-

strictions and myopia.

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proach” consisted mainly of treating uncertainty with simply assuming theproblem away. Hall had used a quadratic utility function which has severaldrawbacks: Without a third derivation, only the average and not the vari-ance of future income is included in the consumption function, hence onetreats uncertainty as if it were not there.5The New Keynesian Theory of pre-cautionary saving started exactly at this point, namely in criticising Hall’suse of the specific quadratic utility function through which uncertainty dropsout during the optimising process. In what follows, I will demonstrate theprecautionary saving theory using a simple two-period-model. This allowsfor both a more realistic treatment of uncertainty and an explication for thehigh significance of current income in many empirical studies, which hadalways stood in a big contrast to the mainstream consumption model.6

2.2 The Model

Defining precautionary saving as the ”additional saving that results fromthe knowledge that that the future is uncertain” 7, the precautionary savingmodel can be derived as follows:8:

U = −1

ηe−ηCt + βEt

[−1

ηe−ηCt+1

](1)

The household gets utility from consumption in period t and in periodt + 1: while the latter is uncertain because the household does not knowfor sure how much it will earn in the next period. It’s worth noting thatuncertainty is modeled in this approach as risk. The use of the expectationsoperator assumes implicitly that the agent knows the probability distribu-tion of all his possible future income streams and thus the agent looks atthe average income being calculated on his income received in the past. Thedifference from the older neoclassical model lies in the different definition ofrisk: while Hall treated risk only as diversifiable and thus η as the coefficient

5See for an early criticism of this approach Blanchard and Mankiw (1988).6Many empirical studies have found strong support for consumption depending on

current income, see e.g. Campbell and Mankiw (1989) or Akerlof (2007), p.14 for a briefoverview. These studies also point out that credit restrictions or myopia can only explainpartly real consumption behaviour.

7Carroll and Kimball (2006),p.28The following section borrows from Miao (2004). I also use a CARA-utility-function

instead of the more common CRRA-function to be able to display the results analytically.

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of risk aversion defined as −u′′(Y )/u′(Y ), New Keynesians included addi-tionally non-diversifiable risk reinterpreting η as the coefficient of prudenceaversion, defined as −u′′′(Y )/u′′(Y ). Hence it follows the obvious importancethat the third derivative of the utility function exists. 9 This distinction iscrucial: While diversifiable risk can be reduced using appropriate insuranceand financial market instruments, this is not the case for systemic or non-diversifiable risk. Finally, the coefficient β stands for the discount factor mea-suring the household’s preference for utility in the present and in the future.The consumer maximises this utility function subject to his intertemporalbudget constraint:

Ct+1 = Yt+1 +R(Yt − Ct), (2)

Here, R stands for the real interest rate and the tilde about the income inthe second period signals that this income is risky. Thus, the household canconsume in period t+ 1 what he has saved in period t, R(Yt−CT ), and whathe will probably earn in period t + 1. Putting this in in the utility function(1) yields

U = −1

ηe−ηCt − β 1

ηe−ηR(Yt−Ct)Et

[e−ηYt+1

](3)

To get the optimality condition, one must derive the first order condition:

e−ηCt = βRe−ηR(Yt−Ct)Et

[e−ηYt+1

](4)

If one solves (4) for C, one gets the optimal consumption as:

Ct =R

1 +RYt −

1

η(1 +R)logRβ − 1

η(1−R)logEt

[e−ηYt+1

](5)

To specify this result further, one can make the assumption that thestochastic term in the expectations operator can be described by a normaldistribution. Hence one can reformulate the stochastic term with µY asexpected value and σ2

Y as variance of the future income:

logEt

[e−ηYt+1

]= −ηµY +

1

2η2σ2

Y (6)

Using this, one obtains for the optimal consumption rule

9See for this in detail Kimball (1990).

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Ct =R

(1 +R)Yt −

1


η(1 +R)

[−ηµY +

1

2η2σ2

Y

](7)

and after a short manipulation

Ct =R

(1 +R)(Yt + µY )− 1


(1 +R)

1

2η2σ2

Y (8)

This expression shows the key features of the precautionary saving model:First, consumption depends not only on the current income Y, but also onthe expected life-time income µY . The agent will spend a large amount ofthis income increase on consumption, only if an increase of the current in-come is supposed to be permanent, i.e., only if it augments the expectedaverage income. Otherwise, if the agent expects his life-time income to bestable or even falling, an increase in current income has less impact on con-sumption, i.e., the marginal propensity to consume is lower as suggested intraditional Keynesian approaches. Secondly, New Keynesian models containan additional variance term in the consumption function which leads in turnto a higher MPC: since households cannot be sure about their future income,they keep a buffer-stock of savings in order to insure themselves against un-foreseen income shocks. Thus, an increase in current income works like arelaxation of this (self-imposed) credit restrictions 10. Households want tospend more on consumption, but they are not able to do so due to the risk-iness of their expected income, thus every increase in income will be nearlytotally consumed. Moreover, including the variance of future income makesthe consumption function concave again, and not linear as in the neoclas-sical model.11 Hence, the incorporation of a precautionary savings motivedoes not only lead to a higher marginal propensity to consume out of currentincome, but also to the dependence of the MPC on the income level. Withincreasing income levels, people tend to spend smaller fractions of their cur-rent income. To summarise, the Precautionary Savings model derives resultsthat have been already stated by Keynes, namely a high MPC out of currentincome and the concavity of the consumption function.

10See Carroll and Kimball (2006) for this analogy.11See Carroll and Kimbal (1996) for a formal proof of the concavity of the consumption

function in the precautionary saving model.

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Conference Paper3 The Postkeynesian Theory of Consumption J.-O. Menz

3 The Postkeynesian Theory of Consumption

Since consumption theory has been a neglected field in the Post Keynesianresearch, in the following section, I will rely on the insights from BehaviouralEconomics and Economic Sociology.12 The crucial starting point of the PostKeynesian consumption theory can be summarised as following: ”Consump-tion is the economic activity that depends most on social and cultural con-text and least on either formal rationality or complex technology.”13 In otherwords, Post Keynesians rely mainly on two features which distinguish themfrom the Precautionary Savings approach, namely social class behaviour andfundamental uncertainty.

3.1 Social Class Behaviour

Post Keynesians downplay the importance and relevance of individual deci-sions and thus, they follow an organicist methodological approach comparedto the methodological individualism of the neoclassical and New Keynesians.While the latter places the individual at the center of the analysis amd claimsthat people are able to chose between different consumption bundles, PostKeynesians tend to see individual’s behaviour as embedded in different so-cial contexts or systems with the latter structuring and shaping individualdecisions.14

The arguments in favour of social class as the main determinate of peo-ple’s consumption behaviour are twofold15. First, both economists and so-ciologist have long been doubtful about the implicit neoclassical assumptionthat individuals are highly independent in their consumption decisions. Thesociological criticism of the postulated independence and sovereignty of con-sumers dates back to Adorno and Horkheimer, who showed that consumers’decisions are influenced and even manipulated by advertising. Recently, Holt(2002) has delivered a detailed discussion about the potential tensions be-tween the needs and wants of consumers on the one hand and firms’ mar-

12See also Fontana and Gerrard (2004) for a similar approach using Economic Psychol-ogy.

13Zukin (2006),p.10114On can also find this separated view in sociology, where the ”Rational-Choice-Theory”

stands in contrast to the ”systems theory” followed by Parsons and Luhmann.15See also Beckert (1996),p.827-830 for a detailed overview about four categories gov-

erning peoples’ social and economic behaviour

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keting strategies at the other. It arises thus the question whether consumersare indeed as independent as neoclassical economists suppose them to beor whether firms play actually the dominant role. Empirically, Rehme andWeisser (2007) have found in a study at German consumers that adver-tising indeed Granger-causes consumption positively in the short run, thusstrengthening further doubts about consumer sovereignty that neoclassicalstake for granted.

But consumers are not only limited by firms’ advertising but also by socialnorms. As Akerlof (2007) has put it: individuals’ behaviour is embedded in asocial context and thus cannot be reduced to a single optimising framework.He suggested that one should incorporate into the standard utility function aloss term that becomes relevant if individual’s decisions are not in line withthe social norm for this particular behaviour.16 Already Duesenberry haspointed to the importance of the social context in consumption behaviour:Extending his point of view, people want to ”keep up with the Joneses”,i.e., individuals link their consumption decisions to those of their closestsocial reference group in order to reach or keep a similar social status.17

And one can also add to these reflections the well-known problem of roleconflict in sociological discussions. Since citizens in modern societies haveto adopt different social roles, they have a different preference structure ineach role. For example, a person can have different preferences in his role asan investment banker and as a father, leading to a role conflict and thus tothe impossibility of constructing an intransitive preference order necessaryfor the existence of the neoclassical consumer. Furthermore, Lavoie (1994)and Lavoie (2004) downplay the role of the price mechanism for consumptiondecisions using the sociological consumption theory outlined so far. In hispoint of view it is important to distinguish between wants and needs, thelatter being separated in categories subject to changes in the needs of thesocial peer group: ”Decisions and preferences are not made independently ofthose of other agents. A households pattern of consumption will reflect thelifestyle of the other households that constitute its social reference group.”18 It follows that the role of prices as the determinant allocation mechanism

16Akerlof highlights for example that societies expect students to live in cheap apart-ments and not in large houses even though this would be rational in the context of neo-classical consumption smoothing.

17See Palley (2005) for an integrative approach in consumption theory using Duesen-berry.

18Lavoie (2004),p.647

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becomes less important, because people go from one category of needs to thenext following an increase in income and neglecting price chances of goods in ahigher category when the more fundamental one is not yet satisfied. Lavoie’sargumentation leads to a construction of lexicographic preferences.19 Giventwo consumption bundles x and x′, one can state the following:

x � x′ ⇐⇒ {x1 > x′1 or x1 = x2 and x2 ≥ x′2 (9)

This is only a formal way to express the argument above: In one categoryof needs, the consumer prefers more of good x1 compared to x′1. But whenhe has consumed a satisfying amount of x1, he only prefers the consumptionbundle x against x′, if he can consume more from a second good, i.e. x2 ≥ x′2.The crucial point of these lexicographic preferences is that one cannot ex-press them through utility functions. Moreover, this criticism of the standardutility function model is even stronger than pointing to the inadequate mod-eling of uncertainty in these models (see above), since it does not requireto refuse the neoclassical assumption of a rational consumer. Lexicographicpreferences are perfectly transitive, complete and reflexive and fulfilling thusall conditions for rationality, the only ”problem” is their nonrepresentabilitythrough the use of utility functions. Neoclassical economists often deny thisproblematic in treating this kind of preferences as a special case being onlyrelevant for health economics, e.g. for describing the behaviour of a drugaddicted. But already Maslow has used a fairly similar concept while con-structing his well-known ”pyramid of needs”, which shows that lexicographicpreferences without utility functions are not a special case at all and thatsocial norms do have a place in consumption theory.

And since social norms are mainly determined through individuals’ socialclass, Post Keynesians use different consumption behaviour for members ofdifferent social classes as the starting point of their consumer behaviour. Todo so, one replaces the idea of one single representative agent with a theory ofsocial class where society is usually split into workers, capitalists and rentiers.If consumption is not only a rational choice aiming at maximizing individual’sutility, but also embedded in social relations, people try to express theirsocial identity and their belonging to a social class through the goods theyconsume. Especially Bourdieu (1979) has highlighted this link between socialclasses and consumption, showing not only that individual tastes are stronglydetermined by their class background but also that these different tastes are

19See for the following Mas-Colell et al. (1995), p.46-50

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also used to ensure class reproduction. Thus, social norms are not simplya constraint of individuals’ otherwise completely rational decisions, in fact,they are also adopted voluntarily to express social and class identity.

3.2 Risk and Uncertainty

So far, I have simply assumed on the basis of common (sociological) knowl-edge that consumer decisions are socially determined. But the importanceof social rules can also be derived from a still more fundamental condition,namely the existence of uncertainty in decision-making. Post Keynesianshave always highlighted the important difference between risk and funda-mental uncertainty, while in New Keynesian approaches such, as the precau-tionary saving model presented above, the two notions are exchangeable.

Generally, moments of decision-making can be described along the twofollowing dimensions: First, the cognitive capabilities of the actor and thecomplexity of the situation in which he has to make the decision. Neoclassi-cal economists have for a long time assumed high computation capacities ofeconomic actors together with a known and stable probability function of allpossible outcomes in the future. Hence, New Neoclassicals simply assumedthe problem of uncertainty away. From these assumptions came the well-known rational expectations theory which claims that economic actors in thepresent take into account future events. This is also the case of the so called”diversifiable risk” that only affects a group of people and against whichpeople can thus insure themselves. New Keynesian economists have changedthis assumption through the introduction of non-diversifiable risk. In thisapproach, individuals are limited in their cognitive capacities either becauseof a lack of information or because of a wrongly adapted decision-making pro-cess. However, this theory still assumes that one could principally calculatethe probabilities for all the possible outcomes of one’s decision. Furthermore,this theory assumes that deviations and mistakes in expectation-building canbe solved through learning processes. 20. Though the incorporation of asym-metric information makes the calculation of probabilities more complicated,it does not deny the existence and usefulness of the rationally behaving eco-nomic agent in general.21

20See for this concept e.g. Carroll (2003)21The decisive point of criticism of the rational consumer is thus not that people can

behave irrationally or are restrained from behaving rationally. Akerlof (2007), too, doesnot want to eliminate the homo economicus but only wants to model him being limited

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This view is challenged by both Post Keynesians and Economic Sociol-ogists. As Keynes22 had put it: ”The sense in which I am using the term[uncertainty] is that...there is no scientific basis on which to form any calcu-lable probability whatever. We simply do not know”. Generally speaking,uncertainty arises out of the gap between the complexity of a given situa-tion and the limited cognitive capabilities of actors. In the view of economicsociology, the simple equalisation of risk and uncertainty neglects two mainproblems:

First, one cannot know all ”means-ends relations” in complex situationsleading thus to unintended side-effects and to the impossibility to behave inthe way predicted by the optimisation model, because one cannot be sureabout the effects of his decisions. ”It is not the action-model of homo eco-nomicus per se that should be the focus of criticism (...), but the underlyingassumption that economic actors can, even in highly contingent situations,deduce their actions from a clear preference ranking and thereby maximisetheir utility” 23 Decision-making can thus not be described without takinginto account the particularities of each situation. If the situation is highly un-certain, the agent does not know ex ante if his behaviour is rational since hecannot precisely determine the outcome of his decision. Beckert formulatesthis point in the following question: ”What do we do if we do not know whatis best to do?”. The crucial assumption of rational behaviour is that peo-ple know the links between their actions and the outcomes of their actions.With this assumption, the implementation of risk only slightly complicatesthe situation, since one only needs to consider the probabilities that can bedesigned per assumption to any possible means-end relation. But in the caseof uncertain behaviour, this is not true.

The second problem of the the equalisation of risk and uncertainty lies inthe observation that social action is characterised by a ”double contingency”24, that means that individuals do not only have to consider their cognitive

through social norms represented by a loss term in the standard utility function.22Keynes (1937),p.21423Beckert (1996), p.804. Additionally, Behavioural Economists such as Kahnemann

and Thaler (2006) have also criticised the concept of utility maximisation for a similarreason: Agents in general, and consumers in particular do rarely know the outcome oftheir decisions influencing their future utility and being though subject to various errors.Concrete, the authors question the necessary assumption for utility-maximization, namely”the ability of economic agents to make accurate, or at least unbiased, forecasts of thehedonic outcomes of potential choices.” p.222

24This notion was originally introduced by Parsons and Shils, see Beckert (1996), p.826

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capacities and the special conditions in which they have to decide but alsomust take into account the behaviour of at least one additional actor. 25 Thisanalysis of ”double contingency” is relevant not only for investment decisionswhere several agents are involved, but also in consumption decisions. Thiscomes from the fact, as was shown above, that consumers do not build uptheir preferences independently but with reference to their most relevantsocial peer group.

The consequence of the distinction between risk and uncertainty is that inthe case of the latter people do not behave as foreseen in the microeconomicoptimisation framework that underlies both neoclassical and New Keynesiantheories. Rather, the uncertainty in social action raises the problem of socialorder since actors try to implement social structures to overcome their uncer-tainty about the behaviour of other agents and to make it more predictable,thus shaping the situation by which the actor is confronted. Hence, the ori-entation on social norms is not only a punishment or limitation of consumer’sliberty (as outlined above) but also a self-imposed restriction to deal withthe unknown outcomes of the individual’s own decisions. 26 Agents ”rely onsocial ”devices” that restrict their flexibility and create a rigidity in the re-sponses to changes in an uncertain environment” (Beckert (1996) p. 819) Theexistence and the need for social norms and institutions can thus be directlyderived from decision theory. The higher the degree of uncertainty in onesituation, the higher the likelihood that the agent deviates from rational be-haviour and trusts ”all form of rules, social norms, conventions, institutions,social structures, and power-relations” (p.820).

The emphasis on the distinction between risk and uncertainty is thus nota purely theoretical subtleness but has direct consequences for the analysisof individuals’ behaviour. Post Keynesians have always been highly scepti-cal about the use of optimising frameworks of rational consumers and theincorporation of rational expectations in their models. Mostly, Keynesiansuse adaptive expectations in constructing models, a practice that goes backto Keynes’ remark in the General Theory27 that investors assume ”that the

25Beckert (1996) denies that game theory has so far contributed to solve this problemsince it postulates that both agents behave rationally assuming again the problem ofuncertainty away.

26This point has also already been highlighted by Keynes (1937),p.214: ”Knowing thatour own individual judgment is worthless, we endeavor to fall back on the judgment of therest of the world which is perhaps better informed.”

27Keynes (1936),p.

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existing state of affairs will continue indefinitely, except in so far as we havespecific reasons to expect a change”. However, the use of adaptive expecta-tions has also come under criticism recently. 28

3.3 The Model

If consumers’ choices are determined socially and made under fundamentaluncertainty, households are limited in their independence to maximise utility.In view of this becomes rational not to follow the optimisation framework.Since social norms are still mainly shaped against the background of so-cial class to which households belong, consumption becomes class-dependent.This means, that the current income becomes more important for the con-sumption decisions: Akerlof (2007), p.13-18 recently gave some examplessupporting the evidence that the crucial consumption norm is simply thatpeople should spend what they earn and that they should not smooth con-sumption when they know about a heritage in the near future, for example.Besides, if the future is uncertain in the sense that there is no possibilityto calculate probabilities of future income paths, consumers simply spend alarge part of their current income.

Furthermore, treating consumption in a social class context leads to thestatement that the marginal propensity to consume (MPC) out of labour in-come is higher than the MPC out of enterprise income or financial (rentiers)income. In his recent paper, Carroll (2006) has postulated that for a part ofthe population wealth enters directly in the utility function, which means thatthe rich part of capitalist societies saves large sums of money just for the sakeof accumulation. This view is also supported by behavioural economics: She-frin and Thaler (1988) extended the neoclassical life-cycle-income model us-ing psychological insights. People are characterised by inner conflicts. In thecase of consumption this signifies that there exists a confrontation betweenthe wish to consume as much as possible today and to save for retirement.To find a solution to this problem people can either exert self-control throughwill power at the moment when the conflict arises or impose constraints ontheir income and consumption in advance. People prefer the second pos-sibility because it is less costly due to its pre-committed character. Theseconstraints can both be external (e.g. a public pension plan) and internal

28See Palley (1993) for an attempt to integrate both advantages from rational andadaptive expectations.

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(self-imposed rules). This reflection led Shefrin and Thaler (1988) to the ideaof ”Mental Accounting”: People are not indifferent between different incometypes, but divide their wealth into three components, namely current income,current assets and future income. Each income class is treated in a uniqueway: Consumers finance an increase in consumption first from their currentincome, then from current assets and then from future income. Hence, onefinds support for the Post Keynesian emphasis for different MPCs: ”At agiven date, the marginal propensity to consume is typically highest out of(current, A.d.A.) income (I), lowest out of future wealth (F), and somewherein between for current assets (A).” 29

To summarise, the Postkeynesian consumption theory is characterisedby different marginal propensities to consume that depend on the type ofincome, a large emphasis on the role of current income as main source offinancing present consumption, and the denial of using an abstract mathe-matical framework to analyse socioeconomic subjects such as consumption.Beginning the presentation of the Post Keynesian consumption model, it isworth noting that now an intertemporal model is considered. This standsin contrast to the typical concentration of neoclassical and New Keynesiantheories of finding optimality conditions for several periods. This contrastresults from the different role saving plays in the two paradigms. In the NewKeynesian framework saving is merely postponed consumption even if it re-sults from precautionary motives. In the Post Keynesian approach however,saving does not at all signify consumption in a future period: ”An act ofindividual savings so to speak is a decision not to have dinner to-day. But itdoes not necessitate a decision to have a dinner or buy a pair of boots a weekhence or a year hence or to consume any specified thing at any specified date.Thus it depresses the business of preparing to-days dinner without stimulat-ing the business of making ready for some future act of consumption... itis a net diminution of such demand.” 30 This is the Keynesian ”paradox ofthrift”. Even if households wish to save more, the result can be the contrary.Macroeconomically, an increase in saving today leads to a lack of effectivedemand tomorrow with the actual saving being lower ex post than it shouldhave been ex ante. Thus, the consumption model presented here stays in aone-period framework and leaves questions about how aggregate saving af-fects output to growth theory. Furthermore, expectations play no role in this

29Shefrin and Thaler (1988),p.61830Keynes (1936),p.210

13


model due to its one-period formulation.Beginning with a model that relies explicitly on a functional distribution

framework explained above, one first splits aggregate consumption into con-sumption out of profit income Π and out of wage income W. Then, followingKeynes’ statement that ”an increase in income leads to an increase in con-sumption, but less than one”31, one can write the propensities to consumeas cΠ and cW for profit and wage income respectively.

C = CΠ + CW = cΠΠ + cWW (10)

Using the definition for the profit share, h = Π/Y , one can reformulate(9) further to get:

C = cΠΠ + cW (Y − Π) = cWY + (cΠ − cW )Π = cW + (cΠ − cW )hY (11)

The recent years saw the emergence of the so-called ”finance-led capital-ism” 32. Empirically this turned out into a much higher share of financialassets owned by households, which leads to the question whether these de-velopments effect consumption behavior. One can add financial wealth tothe macroeconomic consumption function as follows: Profits Π can be splitfurther into profits out of enterprise, Πn and interest income Z, the latterresulting from the product of long-term credits B and the nominal interestrate:

Π = Πn + Z = Πn + iB (12)

If one makes the assumption that profit out of enterprise is saved totallyin the firm, consumption is funded by wage income CW and interest incomeCZ .

C = CZ + CW = cZZ + cWW = cZ(Π− Πn) + cW (Y − Π) (13)

= cWY − cWΠ + cZΠ− cZΠn = cWY − (cW − cZ)hY − cZhnY

,where hn = Πn/Y defines the share of retained earnings.

31Keynes (1936),p.?32See for an analysis of financialisation putting emphasis on household behaviour e.g.

Ertık et al. (2005).

14

Conference Paper4 Macroeconomic implications J.-O. Menz

Calculating the partial derivatives, one gets three results: 33

1. An increase in income increases aggregate consumption.

2. Since cW > cZ , an increase of the profit share lowers aggregate con-sumption, given a constant income.

3. An increase in the share of retained earnings lowers aggregate consump-tion.

4 Macroeconomic implications

4.1 Derivation of the New Keynesian IS-curve withprecautionary saving

In the New Keynesian approach the microeconomic consumption functionis used to derive the goods market equilibrium, i.e. the IS-curve. Usingthe precautionary savings motive, one starts with the reformulated eulerequation:

C−ηtPt

= iβEt

[C−ηt+1

Pt+1

](17)

−η(logCt − logPt) = logiβ − ηEt[logCt + 1] + ηEt[logPt+1]

−ηlogCt = logiβ − η(µC +1

2σ2C) + η(Et[logPt+1]− logPt)

logCt = µC −1

2σ2C −

(1

ηlogiβ − Et[πt+1]

)33The partial derivatives can be derived as follows:

∂C

∂Y= (1− h)cW + (h− hn)cZ > 0 (14)

∂C

∂h= (−cW + cZ)Y − cZhnY < 0 (15)

∂C

∂hn= −cZY < 0 (16)

15


Following Clarida et al. (1999), p. 1665, one can then insert the equi-librium condition for the goods market into the modified Euler equation.Defining X = I +G+ Ex− Im with the usual symbols one receives for thegoods market:

Ct = Yt −Xt =

(1− Xt

Yt

)Yt (18)

After taking logs and defining further −log(

1− Xt

Yt

)= D one gets

logCt = logYt − logDt (19)

Inserting this equation in the Euler condition yields after some manipu-lation:

logYt = µY −1

2σ2Y −

(1


)+ logDt − Et[logDt+1] (20)

Defining Y gapt = Yt − Y pot

t as output gap and εd,t = logDt − Et[logDt+1]as demand shock yields the IS-curve with precautionary saving:

logY gapt = µgapY −

η

2σ2Y −

(1


)+ εd,t (21)

It is easy to see that the output gap depends positively on the expectedincome and negatively on the expected real interest rate. Additionally, thevariance of the expected income has a negative effect on the output gap. Dueto the concavity of the consumption function, the personal income distribu-tion effect output: Because the income variance is higher for low incomes,redistribution can augment the output gap.

4.2 Derivation of the Post Keynesian IS-curve

To derive the Post Keynesian IS-curve, one starts with the goods marketequilibrium I = S. If one puts this in relation to the nominal capital stockpK, one can reformulate this equilibrium as

σ = g (22)

16


,where σ = S/pK stands for the saving rate and g = I/pK for theaccumulation rate. Using the savings equation derived from the aggregateconsumption function (12), one gets for the saving rate:

σ =S

pK=sWY + (sZ − sW )hY + (1− sZ)hnY

pK(23)

It is worth noting that prices do not play a decisive role in the Postkeyne-sian consumption model outlined and thus in the derivation of the IS-curveso far. Since consumption is considered in a sociological context, price isonly one of the determinant factor of consumption. However, one can eas-ily integrate either adaptive or rational expectations into the model throughmodeling peoples’ views about future price changes.

The relation Y/pK can be expanded using Y v as output at full capacityutilisation:

Y

p

Y v

Y v=

Y

pY v

Y v

K=u

v(24)

Here, the expression u = Y/pY v stands for the degree of capacity utili-sation and v = K/Y v for the capital coefficient that is assumed to be con-stant. Inserting this into the saving rate, together with the profit definitionΠ = Πn + iB, one gets:

σ = sWu

v+ (sZ − sW )h

u

v+ (1− sZ)

(Π− iBY

)Y

pY v

Y v

K(25)

= sWu

v+ (sZ − sW )h

u

v+ (1− sZ)

(Π

pK− i B

pK

)

Furthermore, one can use the definition for the profit rate

r =Π

pK=

Π

pY

Y

Y v

Y v

K= h

u

v(26)

and for the debt ration

λ =B

pK(27)

to calculate the savings rate:

17


σ = sWu

v+ (sZ − sW )h

u

v+ (1− sZ)

(hu

v− iλ

)(28)

= sWu

v+ sZh

u

v− sWh

u

v+ h

u

v− sZh

u

v− (1− sZ)iλ

=u

v(sW − sWh+ h)− (1− sZ))iλ

In what follows the debt ratio λ is assumed to be constant due to the shortterm character of this analysis. For capital accumulation I use a Bhaduri-Marglin-function with monetary expansion:34

g = I/K = α + βu+ τh− θλi (29)

The accumulation rate g depends positively on the capacity utilisationu (a proxy for expected sales) and on the profit share h (an indicator forthe functional income distribution). Besides, the debt of firms affects theiraccumulation decisions negatively; the debt that results from the debt ratioλ multiplied with the nominal interest rate i. Putting this accumulationfunction into the equilibrium condition for the goods market, together withthe specified saving rate and solving for capacity utilisation u yields:

u

v(sW − sWh+ h)− (1− sZ)iλ = α + βu+ τh− θλi (30)

Solution to this yields the equilibrium value for the capacity utilisationand so the Post Keynesian IS-curve:

u =α + τh+ iλ(1− sZ − θ)

1vsW + h

v(1− sW )− β

(31)

Differentiating this function for i in order to get the reactions of the goodsmarket equilibrium to interest rate changes gives:

∂u

∂i=λ(1− sZ − θ)− ∂h

∂i(1− sZ)u

v1vsW + h

v(1− sW )− β

(32)

Thus, one gets the result that the effect of a change in interest rates on theoutput becomes ambiguous, which stands in contrast to the New Keynesianmodel outlined earlier in the paper. That is the case because interest rates

34See for this Hein (2006),p.10.

18


also effect the financial costs of firms and can thus alter the mark-up andconsequently the profit share. Additionally, the magnitude of the differentsavings propensities also plays a role.35

4.3 A New Keynesian model using Post Keynesian in-sights

Formulating a consumption model which builds both on Post Keynesian andNew Keynesian insights is possible. If one wants to do so, one has to be-gin with uncertainty since this is the most fundamental concept includingall forms of risk, being the reason to take into account social devices andproviding the basis for a criticism of the rational expectations hypotheses.

Fundamental Uncertainty- If one really takes the concept of uncertaintyserious as outlined above one should overcome the temptation to force con-sumption theory into an abstract mathematical optimisation model. Insteadit would be better to build a macroeconomic consumption model that relieson empirical, sociological and psychological studies. In doing so, one wouldalso strengthen the analysis of institutions and aim to answer the questionhow these institutions can cope best with uncertain situations. But if onewill not abandon standard microeconomic optimisation theory for buildingup macroeconomic models one can follow an idea outlined by Miao (2004)who shows a way for incorporating uncertainty in a formal mathematicalmodel. Indeed, Miao (2004) still assumes that the individual can principallycalculate and attach probabilities to all possible outcomes and thus, uncer-tainty is in turn redefined as risk. But Miao’s approach is less restrictivesince his agent does not know the true probability distribution. Instead, hehas to choose one appropriate distribution out of a probability set along thedegree of uncertainty he attaches subjectively to each probability function.Assuming again that all probability functions are normally distributed, theconsumption function (8) derived above is then transformed into

Ct =R

(1 +R)(Yt + µY )− 1


(1 +R)

1

2η2σ2

Y −1

(1 +R)

√2φσY

(33)

35See Hein (2006) for a deeper discussion with and Boyer (2000) for a model yieldingsimilar results.

19

Conference Paper5 Summary and Outlook J.-O. Menz

Here, the last term stands for precautionary saving due to (model) un-certainty that depends both on the parameter of uncertainty aversion φ andon the standard deviation of income.

Functional income distribution - As I have sketched earlier in this paperstarting from uncertainty leads directly to the analysis of social norms. Thismakes the concept of the representative agent inadequate for dealing withconsumption theory.36 Following an idea from Campbell and Mankiw (1989),Galı et al. (2007) use in their model two types of consumers to estimate theeffects of fiscal policy on consumption. The first group behaves as in the NewKeynesian model while the second group does no intertemporal optimisation.The authors assume that this group simply consumes its current income inevery period. First, one can note the obvious similarity of Galı et al. (2007)so called ”rule-of-thumb” consumers with the Post Keynesian classical sav-ing hypothesis stating that workers do not save. Secondly, though Galı et al.(2007) do not explain this behaviour one could easily explain its existencein a Post Keynesian model through adding uncertainty and socially deter-mined consumption behaviour. Third, the functional distribution becomesimportant again.

Expectations- Finally one has to deal with the problem of an appropri-ate modeling of expectations. Palley (1993) has pointed to advantages andinconveniences of both adaptive and rational expectations. As I have shownabove, rational expectations are nor an adequate concept for modeling con-sumption theory. This is especially the case when one works with at least twoconsumer types, since one is then confronted with the problem of ”doublecontingency”. Since the use of adaptive expectations has its drawbacks, too,at present there is no totally convincing way of dealing with expectations.If one follows the direction of a more sociological determined consumptiontheory it may be useful to assume for each consumer type a different kind ofexpectations building.

5 Summary and Outlook

To sum up and to come back to the questions raised in the introduction onecan restate the following results. The enlargement of traditional neoclassicalconsumption theory with the New Keynesian precautionary savings approach

36See for a critique of the representative agent also Carroll (2000).

20

Conference Paper5 Summary and Outlook J.-O. Menz

has led to a kind of consensus model in the field of consumption theory. Con-sumers still maximise their utility over their lifetime and behave in the wayof the rational-choice-theory, but the results turn out to be more Keynesian-like. One gets a high marginal propensity to consume out of current income,the consumption function becomes concave thus stressing to again the role ofthe personal income distribution, and the current income plays a much largerrole than before. These results are quite similar to those pointed out by PostKeynesians, and also by Behavioural Economists and Economic Sociologists.However, there remain some differences, namely the question of how to dealwith uncertainty and functional distribution. Three areas of future researchcan be sketched:

1. Since the introduction of both uncertainty or precautionary saving hasput additional emphasis on the role of institutions and institutionalreform, it would be worthwhile to analyse the different effects of pre-cautionary saving in different types of capitalism. Carlin and Soskice(2007) give a first hint in this direction by arguing that the labour mar-ket reforms in Germany during the last years had devastating effectson private consumption through confronting people with more uncer-tainty and hence contributing to low private consumption spending.Also in this socioeconomic area falls the recent paper by Rehme andWeisser (2007) who have shown that advertising has a positive effecton consumption in Germany. It would be worthwhile to extend thisking of research to different countries to try to figure out institutionsthat help to reduce uncertainty.

2. In the field of growth theory too, the role of consumption and savingsdue to uncertainty could give some further insights. This is especiallytrue of dealing with the link between savings and investments. In neo-classical and also in New Keynesian frameworks more saving shouldlead, at least in the long run, to more investment and thus a highergrowth rate. However, already Carroll et al. (2000) have pointed outthat empirically savings result from income and not the other wayround. And recently Rehme and Weisser (2007) found that consump-tion Granger-causes growth. It should thus be important to show thatdealing with precautionary saving is also relevant for the long run, evenin New Keynesian growth models.

3. Finally, consumption theory should be seen in the light of recent devel-

21

Conference PaperReferences J.-O. Menz

opment on financial markets and thus linked to the phenomenon called”financialisation”. Since consumption theory in general is a neglectedfield in Post Keynesian theory it is similarly neglected in the financial-isation literature. 37 New Keynesian authors such as Galı et al. (2007)speculate that through a higher asset market participation aggregateconsumption would get closer to the ideal optimising and consump-tion smoothing model, thus arguing against the importance of theirKeynesian-like rule-of-thumb consumer. However, both Post and NewKeynesian strands could come closer together in dealing with the im-pact of financial markets on consumption. First, if more people ownfinancial assets they are confronted with additional risk by making theirincome more volatile. This raises the policy question of how to dealwith this additional risk. At the same time the incorporation of finan-cial variables in Post Keynesian models makes the effects of interestchanges on the goods market equilibrium ambiguous thus pointing inthe direction of New Keynesian approaches where consumption dependsnot only on current income but also on wealth.

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