Reconstructing Keynesian Macroeconomics Volume 1

Partial Perspectives

Carl Chiarella, Peter Flaschel, Willi Semmler

• Publisher: Routledge
• Year: 2012
• ISBN:
  9781136650369
• Edition: 1
• Topic: Business
• Subtopic: Business General
• Index: Business

This book represents the first of three volumes offering a complete reinterpretation and restructuring of Keynesian macroeconomics and a detailed investigation of the disequilibrium adjustment processes characterizing the financial, the goods and the labour markets and their interaction. It questions in a radical way the evolution of Keynesian macroeconomics after World War II and focuses on the limitations of the traditional Keynesian approach until it fell apart in the early 1970s, as well as the inadequacy of the new consensus in macroeconomics that emerged from the Monetarist critique of Keynesianism.

Professors Chiarella, Flaschel and Semmler investigate basic methodological issues, the pitfalls of the Rational Expectations School, important feedback channels in the tradition of Tobin's work, and theories of the wage-price spiral and the evidences for them. The book uses primarily partial approaches, the integration of which will be the subject of subsequent volumes. With its focus on Keynesian propagation mechanisms, the research in this book provides a unique alternative to the black-box shock-absorber approaches that dominate modern macroeconomics.

Reconstructing Keynesian Macroeconomics should be of interest to students and researchers who want to look at alternatives to the mainstream macrodynamics that emerged from the Monetarist critique of Keynesianism.

Part I

Methodological issues

Macro-frequencies
and dimensions

1 Applicable macro is
continuous time macro

1.1 Introduction

In this chapter, we reconsider the issue of the (non-) equivalence of period and continuous time analysis, first discussed in Flaschel et al. (2008, Ch.1). Period models – the now dominant model type in the macrodynamic literature – assume a single (uniformly applied) lag length for all markets, which therefore act in a completely synchronized manner. In view of this, we start in Section 1.2 from the methodological precept that period and continuous time representations of the same macrostructure should give rise to the same qualitative outcomes, in particular, that the qualitative results of period analysis should not depend on the length of the period, see Foley (1975) for an early statement of this precept, as well as Medio (1991) and Sims (1998) for related observations. A simple example where this is fulfilled is given by the conventional Solow growth model, here considered in Section 1.3, while all chaotic period dynamics of dimension less than 3 are in conflict with this precept, see however Medio (1991) for routes to chaos in such an environment.

A basic empirical fact moreover is that the actual data generating process in macroeconomics is by and large a daily one (and the data collection frequency is also much less than a year). This suggests that empirically oriented macromodels should be iterated with a short period length as far as actual processes are concerned and will then – we claim – in general provide the same answer as their continuous time analogues. Concerning expectations, the data collection process is however of importance and may give rise to certain (smaller) delays in the revision of expectations, which however may be overcome by the formulation of extrapolating expectation mechanisms and other ways by which agents smooth their expectation formation process. We do not expect here that this implies a major difference between period and continuous time analysis if appropriately modeled, a situation which may however radically change if proper delays, as they are for example considered in Invernizzi and Medio (1991), are taken into account.

We discuss in Section 1.4 a typical example from the literature (certainly not the only one), where chaos results from a “too” stable continuous time model when this model is reformulated as a “long-period” macro-model, then exhibiting a sufficient degree of locally destabilizing overshooting. Shortening the period lengths in such chaotic macro models, i.e., iterating them with a finer step size, removes on the one hand “chaos” from such model types, while it on the other hand (and at the same time) brings the model into closer contact with what happens in the data generating process of the real world.¹

Macromodels can however give rise to complex dynamics in continuous time if they are sufficiently rich in their dynamical structure and dimension. We conclude from this result that the investigation of complex dynamics is of a more fundamental and relevant type when applied to higher dimensional continuous time macrodynamics, since such approaches avoid the mixture of locally destabilizing, strongly overshooting adjustment processes (which would converge in continuous time) with the dynamics as they are typical for the larger macromodels – with interacting real and financial markets – of the advanced macrodynamics literature.

1.2 The satellite nature of macroeconomic period models

Period analysis with a single period is now the dominant form for models in the macrodynamic literature and thus of interest in its own right, independently of the consideration of the existence of more complicated lags in more advanced macrosystems. Discrete time macro modeling is of course not restricted to the assumption of a uniform and synchronized period length between all economic activities, with which this chapter is concerned. We focus in this respect on the empirical fact that the actual data generating process in macroeconomics is of much finer step size than the corresponding data collection frequency available nowadays, also in the real markets of the economy, and that the latter process is nowadays also much finer than one year.² This suggests that empirically applicable period macromodels (using annualized data) should be iterated with a much finer frequency (approximately with step size between “1/365 year” and “1/52 year” with respect to the actual performance of economy) in order to increase the likelihood of generating results that are equivalent to the ones of their continuous time analogue.

These empirically applicable period models – which take account of the fact that macroeconomic (annualized) data are generally updated each day – will then not be able to give rise to chaotic dynamics in dimensions one and two, suggesting that the literature on such chaotic dynamics is of highly questionable empirical relevance (though mathematically often demanding and of interest from this point of view). To exemplify this we consider in this chapter a one-dimensional (1-D) non-linear dynamic model that is known to be globally asymptotically stable in continuous time and that has been used in a period framework to generate from its parameters a period doubling route to chaos.

Before doing so we however consider a simple case, the Solow growth model, where period and continuous analysis give qualitatively the same answer for any length of the period between zero and infinity. The clustering of production and investment activities at possibly very distant points in time thus does not raise in this case the question of which period length is the most appropriate one, though it may still be asked whether the assumed type of clustering of economic activities really makes sense from an applied macroeconomic point of view if periods longer than one month are considered.

In concluding, this chapter therefore proposes that continuous time modeling (or period modeling with a short period length) is the better choice to approach macrodynamical issues, in particular when compared to a period model where the length of the period remains unspecified, since it avoids the empirically uninterpretable situation of a uniform period length (with a length of one quarter, year or more) and with an artificial synchronization of economic decision making. If discrete time formulations (not period analysis) are used for macroeconomic model building they should represent averages over the day as the relevant time unit for complete models of the real-financial interaction on the macroeconomic level. The stated dominance of continuous time modeling (or quasi-continuous modeling with a period length of one day) not only simplifies significantly the stability analysis for macrodynamic model building, but also questions the relevance of period model attractors that differ from their continuous time analogue.

Chiarella and Flaschel (2000) argue that a fully specified Keynesian model of monetary growth exhibits at least the six state variables, namely wage share and labor intensity (the growth component), inflation and expected inflation (the medium-run component) and expected sales and actual inventories per unit of capital (the short-run dynamics), i.e., these models easily meet the 3-D requirement for the existence of strange attractors in continuous time. They can be used for detecting routes to complex dynamics without running into the danger of synthesizing basically continuous time ideas with radically synchronized (overshooting) discrete time adjustment processes (which when appropriately bounded produce “chaos” also in dimensions one or two). This suggests that the techniques developed for analyzing non-linear dynamical systems represent unquestionably a useful stock of knowledge, to be applied now (in macroeconomics) to investigate strange attractors as they may come about in continuous time in high-order macrodynamics.

Continuous vs. discrete time modeling, in macroeconomics, was discussed extensively in the 1970s and 1980s, sometimes in very confusing ways and o...

Table of contents

• Cover Page
• Half Title page
• Series page
• Title Page
• Copyright Page
• Contents
• List of Figures
• List of Tables
• Notation
• Notes on Contributors
• Introduction Keynesian Macroeconomics
• Part I Methodological issues Macro-frequencies and dimensions
• Part II Model-consistent forecasts, determinacy and the rational expectations school
• Part III Macroeconomic adjustment processes Theory
• Part IV Macroeconomic adjustment processes Evidence
• Part V The road ahead Neoclassical syntheses and beyond
• Notes
• References
• Index