Precautionary Saving in a Macroeconomic Perspective: a Comparison Between New Keynesian and Post Keynesian Consumption Theory §

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 consumer theory. It shows that the New Keynesian theory of Precautionary Saving has again come to more traditional Keynesian results already highlighted by Post Keynesians during the last decades. The often neglected consumer theory in the Post Keynesian paradigm is expanded using 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]

I Conference Paper Contents J.-O. Menz Contents

1 Introduction 1

2 Precautionary Saving 2 2.1 Neoclassicals and New Keynesians ...... 2 2.2 The Model ...... 3

3 The Postkeynesian Theory of Consumption 6 3.1 Social Class Behaviour ...... 6 3.2 Risk and Uncertainty ...... 9 3.3 The Model ...... 12

4 Macroeconomic implications 15 4.1 Derivation of the New Keynesian IS-curve with precautionary saving ...... 15 4.2 Derivation of the Post Keynesian IS-curve ...... 16 4.3 A New Keynesian model using Post Keynesian insights . . . . 19

5 Summary and Outlook 20

References 22

II Conference Paper 1 Introduction J.-O. Menz

1 Introduction

This paper deals with consumption theory using a paradigmatic approach and trying to figure out similarities and differences between New Keynesian and Post Keynesian paradigms. I distinguish these two paradigms by their treatment of risk and uncertainty and their use of optimising microeconomic tools.1 The paper tries to shed some light on two main questions: Against the background of the New Consensus Model in macroeconomics, does there also exist a unifying approach to consumption theory today? And if so, what are its characteristics? Is this new consumption theory just a least common denominator, or can one even find some agreement with more fundamental Keynesian theories? Beginning with a brief review of the developments in modern consumption theory, I will show in detail the underlying theoretical ideas and postulated consequences of the newer theory of Precautionary Saving, mainly the models built upon the work by Christopher Carroll. I will then develop a critique of the precautionary saving model from a Post Keynesian perspective, concentrating on the distinction between risk and uncertainty and a general scepticism against the use of standard microeconomic tools. Given the Post Keynesian bias in favour of firms’ investment theory, I will borrow both from Behavioural Economics and Economic Sociology to clarify the underlying assumptions of the Post Keynesian consumption theory in greater detail. Moreover, I will derive the goods market equilibrium on the basis of each of the consumption theories and then compare the resulting IS-curves. The paper will further sketch some raw ideas to develop a consumption model using both New and Post Keynesian insights. Finally, I will outline some possible consequences of a greater approval of precautionary saving or Post Keynesian models which gives at the same time some directions for further research. 1For a more detailed comparison between New Keynesian and Post Keynesian theory see Hein (2005)

1 Conference Paper 2 Precautionary Saving J.-O. Menz

2 Precautionary Saving

2.1 Neoclassicals and New Keynesians As Keynes stated in his General Theory2, ”men increase their consumption as income increases, but not by as much as the increase in income”. Thus, individuals are supposed to rely mainly on current income when deciding what and how much to consume. Neoclassical theory has heavily criticized this thesis, not least due to its non-derivation from optimal microeconomic behaviour.3 Friedman (1957) replaced the current income with ”permanent income”, supposing that consumers regard mainly their expected future income, while Modigliani and Brumbergh (1955) showed that individuals try to smooth their consumption about their entire lifetime. These neoclassical criticisms changed the main Keynesian consumption hypothesis into the contrary of its traditional results: First, consumption does not depend on current disposable income but on the expected permanent lifetime income. Secondly, the marginal propensity to consume (MPC) out of current income is not close to one, but much lower, since individuals only consume if they consider income changes as permanent. And thirdly, the consumption function looses its concavity, i.e., an increase in income does not lead to a decline in the marginal propensity to consume. In what is called in this paper ”New Keynesian Consumption Theory” is based on this neoclassical ”Life-Cycle- Permanent-Income-Hypothesis”, while it incorporates at the same time several restrictions reenforcing the role of current income and leading to more Keynesian-like results. I will focus especially on one kind of restriction which I think is of the greatest importance and which is also directly linked to original Keynesian thinking namely the explicit consideration of uncertainty and risk. 4 Neoclassical economists themselves tried to make their theory more realistic: Criticizing the implicit assumption made by Friedman and others that households have perfect knowledge about their future income, Hall (1978) was the ﬁrst paying greater attention to the role of uncertainty when considering explicitly the impact of the use of rational expectations in a standard consumption model. Though his ”Certainty Equivalence Ap-

2Keynes (1936),p.96 3See 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 restrictions and myopia.

2 Conference Paper 2 Precautionary Saving J.-O. Menz proach” consisted mainly of treating uncertainty with simply assuming the problem away. Hall had used a quadratic utility function which has several drawbacks: Without a third derivation, only the average and not the variance of future income is included in the consumption function, hence one treats uncertainty as if it were not there.5The New Keynesian Theory of precautionary saving started exactly at this point, namely in criticising Hall’s use of the speciﬁc quadratic utility function through which uncertainty drops out during the optimising process. In what follows, I will demonstrate the precautionary saving theory using a simple two-period-model. This allows for both a more realistic treatment of uncertainty and an explication for the high signiﬁcance of current income in many empirical studies, which had always stood in a big contrast to the mainstream consumption model.6

2.2 The Model Deﬁning precautionary saving as the ”additional saving that results from the knowledge that that the future is uncertain” 7, the precautionary saving model can be derived as follows:8:

1 1 U = − e−ηCt + βE − e−ηCt+1 (1) η t η The household gets utility from consumption in period t and in period t + 1: while the latter is uncertain because the household does not know for sure how much it will earn in the next period. It’s worth noting that uncertainty is modeled in this approach as risk. The use of the expectations operator assumes implicitly that the agent knows the probability distribution of all his possible future income streams and thus the agent looks at the average income being calculated on his income received in the past. The difference from the older neoclassical model lies in the different definition of risk: 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 brief overview. These studies also point out that credit restrictions or myopia can only explain partly real consumption behaviour. 7Carroll and Kimball (2006),p.2 8The 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.

3 Conference Paper 2 Precautionary Saving J.-O. Menz of risk aversion defined as −u00(Y )/u0(Y ), New Keynesians included additionally non-diversifiable risk reinterpreting η as the coefficient of prudence aversion, defined as −u000(Y )/u00(Y ). Hence it follows the obvious importance that the third derivative of the utility function exists. 9 This distinction is crucial: While diversifiable risk can be reduced using appropriate insurance and 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 intertemporal budget constraint:

˜ Ct+1 = Yt+1 + R(Yt − Ct), (2) Here, R stands for the real interest rate and the tilde about the income in the second period signals that this income is risky. Thus, the household can consume in period t + 1 what he has saved in period t, R(Yt − CT ), and what he will probably earn in period t + 1. Putting this in in the utility function (1) yields

1 1 h ˜ i U = − e−ηCt − β e−ηR(Yt−Ct)E e−ηYt+1 (3) η η t To get the optimality condition, one must derive the ﬁrst order condition: h i −ηCt −ηR(Yt−Ct) −ηY˜t+1 e = βRe Et e (4) If one solves (4) for C, one gets the optimal consumption as:

R 1 1 h ˜ i C = Y − logRβ − logE e−ηYt+1 (5) t 1 + R t η(1 + R) η(1 − R) t To specify this result further, one can make the assumption that the stochastic term in the expectations operator can be described by a normal distribution. Hence one can reformulate the stochastic term with µY as 2 expected value and σY as variance of the future income:

h ˜ i 1 logE e−ηYt+1 = −ηµ + η2σ2 (6) t Y 2 Y Using this, one obtains for the optimal consumption rule

9See for this in detail Kimball (1990).

4 Conference Paper 2 Precautionary Saving J.-O. Menz

R 1 1 1 C = Y − logRβ − −ηµ + η2σ2 (7) t (1 + R) t η(1 + R) η(1 + R) Y 2 Y

and after a short manipulation R 1 1 1 C = (Y + µ ) − logRβ − η2σ2 (8) t (1 + R) t Y η(1 + R) (1 + R) 2 Y This expression shows the key features of the precautionary saving model: First, consumption depends not only on the current income Y, but also on the expected life-time income µY . The agent will spend a large amount of this income increase on consumption, only if an increase of the current income is supposed to be permanent, i.e., only if it augments the expected average income. Otherwise, if the agent expects his life-time income to be stable or even falling, an increase in current income has less impact on consumption, i.e., the marginal propensity to consume is lower as suggested in traditional Keynesian approaches. Secondly, New Keynesian models contain an additional variance term in the consumption function which leads in turn to 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 a relaxation of this (self-imposed) credit restrictions 10. Households want to spend 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 nearly totally consumed. Moreover, including the variance of future income makes the consumption function concave again, and not linear as in the neoclassical model.11 Hence, the incorporation of a precautionary savings motive does not only lead to a higher marginal propensity to consume out of current income, but also to the dependence of the MPC on the income level. With increasing income levels, people tend to spend smaller fractions of their current income. To summarise, the Precautionary Savings model derives results that have been already stated by Keynes, namely a high MPC out of current income 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.

5 Conference Paper 3 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 Keynesian research, in the following section, I will rely on the insights from Behavioural Economics and Economic Sociology.12 The crucial starting point of the Post Keynesian consumption theory can be summarised as following: ”Consump- tion is the economic activity that depends most on social and cultural context and least on either formal rationality or complex technology.”13 In other words, Post Keynesians rely mainly on two features which distinguish them from the Precautionary Savings approach, namely social class behaviour and fundamental uncertainty.

3.1 Social Class Behaviour Post Keynesians downplay the importance and relevance of individual decisions and thus, they follow an organicist methodological approach compared to the methodological individualism of the neoclassical and New Keynesians. While the latter places the individual at the center of the analysis amd claims that people are able to chose between different consumption bundles, Post Keynesians tend to see individual’s behaviour as embedded in different social contexts or systems with the latter structuring and shaping individual decisions.14 The arguments in favour of social class as the main determinate of people’s consumption behaviour are twofold15. First, both economists and so- ciologist have long been doubtful about the implicit neoclassical assumption that individuals are highly independent in their consumption decisions. The sociological criticism of the postulated independence and sovereignty of consumers 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 between 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.101 14On 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

6 Conference Paper 3 The Postkeynesian Theory of Consumption J.-O. Menz keting strategies at the other. It arises thus the question whether consumers are indeed as independent as neoclassical economists suppose them to be or whether firms play actually the dominant role. Empirically, Rehme and Weisser (2007) have found in a study at German consumers that advertising indeed Granger-causes consumption positively in the short run, thus strengthening further doubts about consumer sovereignty that neoclassicals take for granted. But consumers are not only limited by firms’ advertising but also by social norms. As Akerlof (2007) has put it: individuals’ behaviour is embedded in a social context and thus cannot be reduced to a single optimising framework. He suggested that one should incorporate into the standard utility function a loss term that becomes relevant if individual’s decisions are not in line with the social norm for this particular behaviour.16 Already Duesenberry has pointed 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 closest social 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 role conflict in sociological discussions. Since citizens in modern societies have to adopt different social roles, they have a different preference structure in each role. For example, a person can have different preferences in his role as an investment banker and as a father, leading to a role conflict and thus to the impossibility of constructing an intransitive preference order necessary for the existence of the neoclassical consumer. Furthermore, Lavoie (1994) and Lavoie (2004) downplay the role of the price mechanism for consumption decisions using the sociological consumption theory outlined so far. In his point of view it is important to distinguish between wants and needs, the latter being separated in categories subject to changes in the needs of the social peer group: ”Decisions and preferences are not made independently of those of other agents. A households pattern of consumption will reflect the lifestyle 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 neoclassical consumption smoothing. 17See Palley (2005) for an integrative approach in consumption theory using Duesen- berry. 18Lavoie (2004),p.647

7 Conference Paper 3 The Postkeynesian Theory of Consumption J.-O. Menz becomes less important, because people go from one category of needs to the next following an increase in income and neglecting price chances of goods in a higher category when the more fundamental one is not yet satisﬁed. Lavoie’s argumentation leads to a construction of lexicographic preferences.19 Given two consumption bundles x and x0, one can state the following:

0 0 0 x x ⇐⇒ {x1 > x1 or x1 = x2 and x2 ≥ x2 (9) This is only a formal way to express the argument above: In one category 0 of needs, the consumer prefers more of good x1 compared to x1. But when he has consumed a satisfying amount of x1, he only prefers the consumption 0 0 bundle x against x , if he can consume more from a second good, i.e. x2 ≥ x2. The crucial point of these lexicographic preferences is that one cannot express them through utility functions. Moreover, this criticism of the standard utility function model is even stronger than pointing to the inadequate modeling of uncertainty in these models (see above), since it does not require to refuse the neoclassical assumption of a rational consumer. Lexicographic preferences are perfectly transitive, complete and reflexive and fulfilling thus all conditions for rationality, the only ”problem” is their nonrepresentability through the use of utility functions. Neoclassical economists often deny this problematic in treating this kind of preferences as a special case being only relevant for health economics, e.g. for describing the behaviour of a drug addicted. But already Maslow has used a fairly similar concept while constructing his well-known ”pyramid of needs”, which shows that lexicographic preferences without utility functions are not a special case at all and that social norms do have a place in consumption theory. And since social norms are mainly determined through individuals’ social class, Post Keynesians use different consumption behaviour for members of different social classes as the starting point of their consumer behaviour. To do so, one replaces the idea of one single representative agent with a theory of social class where society is usually split into workers, capitalists and rentiers. If consumption is not only a rational choice aiming at maximizing individual’s utility, but also embedded in social relations, people try to express their social identity and their belonging to a social class through the goods they consume. Especially Bourdieu (1979) has highlighted this link between social classes and consumption, showing not only that individual tastes are strongly determined by their class background but also that these different tastes are

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

8 Conference Paper 3 The Postkeynesian Theory of Consumption J.-O. Menz also used to ensure class reproduction. Thus, social norms are not simply a 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) knowledge that consumer decisions are socially determined. But the importance of social rules can also be derived from a still more fundamental condition, namely the existence of uncertainty in decision-making. Post Keynesians have always highlighted the important difference between risk and fundamental uncertainty, while in New Keynesian approaches such, as the precautionary saving model presented above, the two notions are exchangeable. Generally, moments of decision-making can be described along the two following dimensions: First, the cognitive capabilities of the actor and the complexity of the situation in which he has to make the decision. Neoclassi- cal economists have for a long time assumed high computation capacities of economic actors together with a known and stable probability function of all possible outcomes in the future. Hence, New Neoclassicals simply assumed the problem of uncertainty away. From these assumptions came the well- known rational expectations theory which claims that economic actors in the present 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 which people can thus insure themselves. New Keynesian economists have changed this assumption through the introduction of non-diversifiable risk. In this approach, individuals are limited in their cognitive capacities either because of a lack of information or because of a wrongly adapted decision-making process. However, this theory still assumes that one could principally calculate the probabilities for all the possible outcomes of one’s decision. Furthermore, this theory assumes that deviations and mistakes in expectation-building can be 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 economic 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, does not 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 situation and the limited cognitive capabilities of actors. In the view of economic sociology, the simple equalisation of risk and uncertainty neglects two main problems: First, one cannot know all ”means-ends relations” in complex situations leading thus to unintended side-effects and to the impossibility to behave in the way predicted by the optimisation model, because one cannot be sure about the effects of his decisions. ”It is not the action-model of homo economicus per se that should be the focus of criticism (...), but the underlying assumption that economic actors can, even in highly contingent situations, deduce their actions from a clear preference ranking and thereby maximise their utility” 23 Decision-making can thus not be described without taking into account the particularities of each situation. If the situation is highly uncertain, the agent does not know ex ante if his behaviour is rational since he cannot precisely determine the outcome of his decision. Beckert formulates this point in the following question: ”What do we do if we do not know what is best to do?”. The crucial assumption of rational behaviour is that people know the links between their actions and the outcomes of their actions. With this assumption, the implementation of risk only slightly complicates the situation, since one only needs to consider the probabilities that can be designed per assumption to any possible means-end relation. But in the case of uncertain behaviour, this is not true. The second problem of the the equalisation of risk and uncertainty lies in the 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.214 23Beckert (1996), p.804. Additionally, Behavioural Economists such as Kahnemann and Thaler (2006) have also criticised the concept of utility maximisation for a similar reason: Agents in general, and consumers in particular do rarely know the outcome of their 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 the hedonic outcomes of potential choices.” p.222 24This notion was originally introduced by Parsons and Shils, see Beckert (1996), p.826

10 Conference Paper 3 The Postkeynesian Theory of Consumption J.-O. Menz capacities and the special conditions in which they have to decide but also must take into account the behaviour of at least one additional actor. 25 This analysis of ”double contingency” is relevant not only for investment decisions where several agents are involved, but also in consumption decisions. This comes from the fact, as was shown above, that consumers do not build up their preferences independently but with reference to their most relevant social peer group. The consequence of the distinction between risk and uncertainty is that in the case of the latter people do not behave as foreseen in the microeconomic optimisation framework that underlies both neoclassical and New Keynesian theories. Rather, the uncertainty in social action raises the problem of social order since actors try to implement social structures to overcome their uncertainty 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’s liberty (as outlined above) but also a self-imposed restriction to deal with the unknown outcomes of the individual’s own decisions. 26 Agents ”rely on social ”devices” that restrict their ﬂexibility and create a rigidity in the re- sponses to changes in an uncertain environment” (Beckert (1996) p. 819) The existence and the need for social norms and institutions can thus be directly derived from decision theory. The higher the degree of uncertainty in one situation, the higher the likelihood that the agent deviates from rational behaviour 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 not a purely theoretical subtleness but has direct consequences for the analysis of individuals’ behaviour. Post Keynesians have always been highly scepti- cal about the use of optimising frameworks of rational consumers and the incorporation of rational expectations in their models. Mostly, Keynesians use adaptive expectations in constructing models, a practice that goes back to Keynes’ remark in the General Theory27 that investors assume ”that the

25Beckert (1996) denies that game theory has so far contributed to solve this problem since it postulates that both agents behave rationally assuming again the problem of uncertainty away. 26This point has also already been highlighted by Keynes (1937),p.214: ”Knowing that our own individual judgment is worthless, we endeavor to fall back on the judgment of the rest of the world which is perhaps better informed.” 27Keynes (1936),p.

11 Conference Paper 3 The Postkeynesian Theory of Consumption J.-O. Menz existing state of affairs will continue indefinitely, except in so far as we have specific reasons to expect a change”. However, the use of adaptive expectations has also come under criticism recently. 28

3.3 The Model If consumers’ choices are determined socially and made under fundamental uncertainty, 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 social class to which households belong, consumption becomes class-dependent. This means, that the current income becomes more important for the consumption decisions: Akerlof (2007), p.13-18 recently gave some examples supporting the evidence that the crucial consumption norm is simply that people should spend what they earn and that they should not smooth consumption 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 possibility to calculate probabilities of future income paths, consumers simply spend a large part of their current income. Furthermore, treating consumption in a social class context leads to the statement that the marginal propensity to consume (MPC) out of labour income 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 of the population wealth enters directly in the utility function, which means that the rich part of capitalist societies saves large sums of money just for the sake of accumulation. This view is also supported by behavioural economics: She- frin and Thaler (1988) extended the neoclassical life-cycle-income model using psychological insights. People are characterised by inner conflicts. In the case of consumption this signifies that there exists a confrontation between the 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 through will power at the moment when the conflict arises or impose constraints on their income and consumption in advance. People prefer the second possibility because it is less costly due to its pre-committed character. These constraints can both be external (e.g. a public pension plan) and internal

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

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(self-imposed rules). This reflection led Shefrin and Thaler (1988) to the idea of ”Mental Accounting”: People are not indifferent between different income types, but divide their wealth into three components, namely current income, current assets and future income. Each income class is treated in a unique way: Consumers finance an increase in consumption first from their current income, then from current assets and then from future income. Hence, one finds support for the Post Keynesian emphasis for different MPCs: ”At a given date, the marginal propensity to consume is typically highest out of (current, A.d.A.) income (I), lowest out of future wealth (F), and somewhere in between for current assets (A).” 29 To summarise, the Postkeynesian consumption theory is characterised by different marginal propensities to consume that depend on the type of income, a large emphasis on the role of current income as main source of financing present consumption, and the denial of using an abstract mathematical framework to analyse socioeconomic subjects such as consumption. Beginning the presentation of the Post Keynesian consumption model, it is worth noting that now an intertemporal model is considered. This stands in contrast to the typical concentration of neoclassical and New Keynesian theories of finding optimality conditions for several periods. This contrast results from the different role saving plays in the two paradigms. In the New Keynesian framework saving is merely postponed consumption even if it results from precautionary motives. In the Post Keynesian approach however, saving does not at all signify consumption in a future period: ”An act of individual savings so to speak is a decision not to have dinner to-day. But it does not necessitate a decision to have a dinner or buy a pair of boots a week hence 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... it is a net diminution of such demand.” 30 This is the Keynesian ”paradox of thrift”. Even if households wish to save more, the result can be the contrary. Macroeconomically, an increase in saving today leads to a lack of effective demand tomorrow with the actual saving being lower ex post than it should have been ex ante. Thus, the consumption model presented here stays in a one-period framework and leaves questions about how aggregate saving affects output to growth theory. Furthermore, expectations play no role in this

29Shefrin and Thaler (1988),p.618 30Keynes (1936),p.210

13 Conference Paper 3 The Postkeynesian Theory of Consumption J.-O. Menz 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 consumption out of profit income Π and out of wage income W. Then, following Keynes’ statement that ”an increase in income leads to an increase in consumption, but less than one”31, one can write the propensities to consume as cΠ and cW for profit and wage income respectively.

C = CΠ + CW = cΠΠ + cW W (10) Using the deﬁnition for the proﬁt share, h = Π/Y , one can reformulate (9) further to get:

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

The recent years saw the emergence of the so-called ”finance-led capitalism” 32. Empirically this turned out into a much higher share of financial assets owned by households, which leads to the question whether these developments effect consumption behavior. One can add financial wealth to the macroeconomic consumption function as follows: Profits Π can be split further into profits out of enterprise, Πn and interest income Z, the latter resulting from the product of long-term credits B and the nominal interest rate:

Π = Πn + Z = Πn + iB (12) If one makes the assumption that proﬁt out of enterprise is saved totally in the ﬁrm, consumption is funded by wage income CW and interest income CZ .

n C = CZ + CW = cZ Z + cW W = cZ (Π − Π ) + cW (Y − Π) (13) n = cW Y − cW Π + cZ Π − cZ Π = cW Y − (cW − cZ )hY − cZ hnY

,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. Ert´ıket al. (2005).

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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 consumption, given a constant income.

3. An increase in the share of retained earnings lowers aggregate consumption.

4 Macroeconomic implications

4.1 Derivation of the New Keynesian IS-curve with precautionary saving In the New Keynesian approach the microeconomic consumption function is used to derive the goods market equilibrium, i.e. the IS-curve. Using the precautionary savings motive, one starts with the reformulated euler equation:

−η −η Ct Ct+1 = iβEt (17) Pt Pt+1

−η(logCt − logPt) = logiβ − ηEt[logCt + 1] + ηEt[logPt+1] 1 −ηlogC = logiβ − η(µ + σ2 ) + η(E [logP ] − logP ) t C 2 C t t+1 t 1 1 logC = µ − σ2 − logiβ − E [π ] t C 2 C η t t+1

33The partial derivatives can be derived as follows: ∂C = (1 − h)c + (h − h )c > 0 (14) ∂Y W n Z ∂C = (−c + c )Y − c h Y < 0 (15) ∂h W Z Z n ∂C = −cZ Y < 0 (16) ∂hn

15 Conference Paper 4 Macroeconomic implications J.-O. Menz

Following Clarida et al. (1999), p. 1665, one can then insert the equilibrium condition for the goods market into the modified Euler equation. Defining X = I + G + Ex − Im with the usual symbols one receives for the goods market: Xt Ct = Yt − Xt = 1 − Yt (18) Yt After taking logs and defining further −log 1 − Xt = D one gets Yt

logCt = logYt − logDt (19) Inserting this equation in the Euler condition yields after some manipulation:

1 1 logY = µ − σ2 − logiβ − E [π ] + logD − E [logD ] (20) t Y 2 Y η t t+1 t t t+1

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

η 1 logY gap = µgap − σ2 − logiβ − E [π ] + ε (21) t Y 2 Y η t t+1 d,t It is easy to see that the output gap depends positively on the expected income and negatively on the expected real interest rate. Additionally, the variance of the expected income has a negative eﬀect on the output gap. Due to the concavity of the consumption function, the personal income distribution 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 market equilibrium I = S. If one puts this in relation to the nominal capital stock pK, one can reformulate this equilibrium as

σ = g (22)

16 Conference Paper 4 Macroeconomic implications J.-O. Menz

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

S s Y + (s − s )hY + (1 − s )h Y σ = = W Z W Z n (23) pK pK 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-curve so far. Since consumption is considered in a sociological context, price is only one of the determinant factor of consumption. However, one can easily integrate either adaptive or rational expectations into the model through modeling peoples’ views about future price changes. The relation Y/pK can be expanded using Y v as output at full capacity utilisation: Y Y v Y Y v u = = (24) p Y v pY v K v Here, the expression u = Y/pY v stands for the degree of capacity utilisation and v = K/Y v for the capital coefficient that is assumed to be constant. Inserting this into the saving rate, together with the profit definition Π = Πn + iB, one gets:

u u Π − iB Y Y v σ = s + (s − s )h + (1 − s ) (25) W v Z W v Z Y pY v K u u Π B = s + (s − s )h + (1 − s ) − i W v Z W v Z pK pK

Furthermore, one can use the deﬁnition for the proﬁt rate Π Π Y Y v u r = = = h (26) pK pY Y v K v and for the debt ration B λ = (27) pK to calculate the savings rate:

17 Conference Paper 4 Macroeconomic implications J.-O. Menz

u u u σ = s + (s − s )h + (1 − s ) h − iλ (28) W v Z W v Z v u u u u u = s + s h − s h + h − s h − (1 − s )iλ W v Z v W v v Z v Z u = (s − s h + h) − (1 − s ))iλ v W W Z In what follows the debt ratio λ is assumed to be constant due to the short term 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 utilisation u (a proxy for expected sales) and on the profit share h (an indicator for the functional income distribution). Besides, the debt of firms affects their accumulation decisions negatively; the debt that results from the debt ratio λ multiplied with the nominal interest rate i. Putting this accumulation function into the equilibrium condition for the goods market, together with the specified saving rate and solving for capacity utilisation u yields: u (s − s h + h) − (1 − s )iλ = α + βu + τh − θλi (30) v W W Z Solution to this yields the equilibrium value for the capacity utilisation and so the Post Keynesian IS-curve:

α + τh + iλ(1 − sZ − θ) u = 1 h (31) v sW + v (1 − sW ) − β Diﬀerentiating this function for i in order to get the reactions of the goods market equilibrium to interest rate changes gives:

∂u λ(1 − s − θ) − ∂h (1 − s ) u = Z ∂i Z v (32) ∂i 1 h v sW + v (1 − sW ) − β Thus, one gets the result that the eﬀect of a change in interest rates on the output becomes ambiguous, which stands in contrast to the New Keynesian model outlined earlier in the paper. That is the case because interest rates

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

18 Conference Paper 4 Macroeconomic implications J.-O. Menz also effect the financial costs of firms and can thus alter the mark-up and consequently the profit share. Additionally, the magnitude of the different savings propensities also plays a role.35

4.3 A New Keynesian model using Post Keynesian insights Formulating a consumption model which builds both on Post Keynesian and New Keynesian insights is possible. If one wants to do so, one has to be- gin with uncertainty since this is the most fundamental concept including all forms of risk, being the reason to take into account social devices and providing the basis for a criticism of the rational expectations hypotheses. Fundamental Uncertainty- If one really takes the concept of uncertainty serious as outlined above one should overcome the temptation to force consumption theory into an abstract mathematical optimisation model. Instead it would be better to build a macroeconomic consumption model that relies on empirical, sociological and psychological studies. In doing so, one would also strengthen the analysis of institutions and aim to answer the question how these institutions can cope best with uncertain situations. But if one will not abandon standard microeconomic optimisation theory for building up macroeconomic models one can follow an idea outlined by Miao (2004) who shows a way for incorporating uncertainty in a formal mathematical model. Indeed, Miao (2004) still assumes that the individual can principally calculate and attach probabilities to all possible outcomes and thus, uncertainty is in turn redeﬁned as risk. But Miao’s approach is less restrictive since his agent does not know the true probability distribution. Instead, he has to choose one appropriate distribution out of a probability set along the degree of uncertainty he attaches subjectively to each probability function. Assuming again that all probability functions are normally distributed, the consumption function (8) derived above is then transformed into

R 1 1 1 1 √ C = (Y + µ ) − logRβ − η2σ2 − 2φσ t (1 + R) t Y η(1 + R) (1 + R) 2 Y (1 + R) Y (33)

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

19 Conference Paper 5 Summary and Outlook J.-O. Menz

Here, the last term stands for precautionary saving due to (model) uncertainty that depends both on the parameter of uncertainty aversion φ and on the standard deviation of income. Functional income distribution - As I have sketched earlier in this paper starting from uncertainty leads directly to the analysis of social norms. This makes the concept of the representative agent inadequate for dealing with consumption theory.36 Following an idea from Campbell and Mankiw (1989), Gal´ıet al. (2007) use in their model two types of consumers to estimate the effects of fiscal policy on consumption. The first group behaves as in the New Keynesian model while the second group does no intertemporal optimisation. The authors assume that this group simply consumes its current income in every period. First, one can note the obvious similarity of Gal´ıet al. (2007) so called ”rule-of-thumb” consumers with the Post Keynesian classical saving hypothesis stating that workers do not save. Secondly, though Gal´ıet al. (2007) do not explain this behaviour one could easily explain its existence in a Post Keynesian model through adding uncertainty and socially determined consumption behaviour. Third, the functional distribution becomes important again. Expectations- Finally one has to deal with the problem of an appropriate modeling of expectations. Palley (1993) has pointed to advantages and inconveniences of both adaptive and rational expectations. As I have shown above, rational expectations are nor an adequate concept for modeling consumption theory. This is especially the case when one works with at least two consumer types, since one is then confronted with the problem of ”double contingency”. 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 consumption theory it may be useful to assume for each consumer type a different kind of expectations building.

5 Summary and Outlook

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

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

20 Conference Paper 5 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 way of 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 of the personal income distribution, and the current income plays a much larger role than before. These results are quite similar to those pointed out by Post Keynesians, and also by Behavioural Economists and Economic Sociologists. However, there remain some diﬀerences, namely the question of how to deal with uncertainty and functional distribution. Three areas of future research can be sketched:

1. Since the introduction of both uncertainty or precautionary saving has put additional emphasis on the role of institutions and institutional reform, it would be worthwhile to analyse the different effects of precautionary saving in different types of capitalism. Carlin and Soskice (2007) give a first hint in this direction by arguing that the labour market reforms in Germany during the last years had devastating effects on private consumption through confronting people with more uncertainty and hence contributing to low private consumption spending. Also in this socioeconomic area falls the recent paper by Rehme and Weisser (2007) who have shown that advertising has a positive effect on consumption in Germany. It would be worthwhile to extend this king of research to different countries to try to figure out institutions that help to reduce uncertainty. 2. In the field of growth theory too, the role of consumption and savings due to uncertainty could give some further insights. This is especially true of dealing with the link between savings and investments. In neoclassical and also in New Keynesian frameworks more saving should lead, at least in the long run, to more investment and thus a higher growth rate. However, already Carroll et al. (2000) have pointed out that empirically savings result from income and not the other way round. And recently Rehme and Weisser (2007) found that consumption Granger-causes growth. It should thus be important to show that dealing with precautionary saving is also relevant for the long run, even in New Keynesian growth models. 3. Finally, consumption theory should be seen in the light of recent devel-

21 Conference Paper References J.-O. Menz

opment on financial markets and thus linked to the phenomenon called ”financialisation”. Since consumption theory in general is a neglected field in Post Keynesian theory it is similarly neglected in the financialisation literature. 37 New Keynesian authors such as Gal´ıet al. (2007) speculate that through a higher asset market participation aggregate consumption would get closer to the ideal optimising and consumption smoothing model, thus arguing against the importance of their Keynesian-like rule-of-thumb consumer. However, both Post and New Keynesian strands could come closer together in dealing with the impact of financial markets on consumption. First, if more people own financial assets they are confronted with additional risk by making their income more volatile. This raises the policy question of how to deal with this additional risk. At the same time the incorporation of financial variables in Post Keynesian models makes the effects of interest changes on the goods market equilibrium ambiguous thus pointing in the direction of New Keynesian approaches where consumption depends not only on current income but also on wealth.

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