Precautionary Saving in a macroeconomic perspective: A comparison between New Keynesian and Post Keynesian consumption theory x 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 ne- glected 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: x ∗∗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 consump- tion theory, I will show in detail the underlying theoretical ideas and postu- lated consequences of the newer theory of Precautionary Saving, mainly the models 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 the Post Keynesian bias in favour of firms’ investment theory, I will borrow both from 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 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 in- come, while Modigliani and Brumbergh (1955) showed that individuals try to smooth their consumption about their entire lifetime. These neoclassi- cal 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 func- tion 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 sev- eral 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 re- strictions 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 vari- ance of future income is included in the consumption function, hence one treats uncertainty as if it were not there.5The New Keynesian Theory of pre- cautionary 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 distribu- tion 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 addi- tionally 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.