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Toichiro Asada, Matthieu Charpe, Peter Flaschel, Christopher Malikane, Tarik Mouakil and Christian R. Proaño

We present a simple macrodynamic model of the real-financial markets inter action with a dynamic multiplier representing the goods market and a structured portfolio choice between money holdings and equities. This is contrasted with Blanchard's (1981) alternative approach, where interest-bearing bonds and equities are perfect substitutes and are subject to myopic perfect foresight, with the result that the usual saddle-point dynamics is established, and where therefore the jump-variable technique of the rational expectations approach is needed in order to tame the explosive nature of the model by assumption. We consider this latter representation a very virtual one in contrast to our descriptive treatment of the interaction of the real with the financial markets. Our implied dynamical system has three dimensions: output, share prices and capital gains expectations. We show that this model exhibits a financial accelerator mechanism that endangers the stability of its stationary solution, at least when it becomes sufficiently strong. Furthermore, we show that this type of instability can definitely be overcome if actual capital gains are taxed to a sufficient degree. This tax policy is therefore effective as compared to an interest rate policy of Taylor type, showing that monetary policy may not impact the markets for risky financial assets, unless it is interpreted as state of confidence for the current situation of the economy and may therefore be fairly overrated in the current macrodynamic literature. By contrast, all policy measures that stabilise the profit rate of the economy may add to the stability implications of the assumed Asada et al. (2010) type tax on capital gains.

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Carl Chiarella, Peter Flaschel, Reiner Franke, Ricardo Araujo, Matthieu Charpe, Christian R. Proaño and Andreas Szczutkowski

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Carl Chiarella, Peter Flaschel, Reiner Franke, Ricardo Araujo, Matthieu Charpe, Christian R. Proaño and Andreas Szczutkowski

The model in Chapter 1 goes back to the roots of business cycle theory. Fulfilling modern standards, it combines a widely known instability mechanism with Harrod's and Kaldor's old, but largely forgotten idea that firms tend to reduce investment if they have already built up high capacities. The model is estimated by the so-called method of simulated moments, which also allows a highly satisfactory assessment of its goodness-of-fit. 14 fairly ambitious summary statistics allow a detailed diagnosis of the merits and demerits of this synthesis. It can thus constitute the ore of more elaborated attempts for business cycle modelling.

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Carl Chiarella, Peter Flaschel, Reiner Franke, Ricardo Araujo, Matthieu Charpe, Christian R. Proaño and Andreas Szczutkowski

In chapter 2 we briefly present a general Keynes--Wicksell--Goodwin model based on passive inventory holdings. We know from earlier work the model's capabilities for generating complex dynamics (strange attractors, not chaos). Continuous time has much more powerful tools to prove local stability in high-order macro-dynamics as our cascade of stable matrices approach, sketched in this introductory chapter, shows. This prepares the ground for its much more detailed application in later chapters of this book.

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Carl Chiarella, Peter Flaschel, Reiner Franke, Ricardo Araujo, Matthieu Charpe, Christian R. Proaño and Andreas Szczutkowski

In chapter 3 we generalize a two_dimensional growth cycle model of Skott that is based on supply_side adjustment and a Kaldorian theory of income distribution. This model gives rise to degenerate Hopf bifurcations if behavior is linear close to the steady state. Furthermore, full capacity limits imply globally viable dynamics if the steady state is locally attracting and corridor stability with persistent fluctuations when it is repelling. This allows to sidestep the pre-Keynesian Wicksellian inflation theory of the previous chapter and is definitely a step forward towards the development of a Keynesian theory of economic growth.

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Carl Chiarella, Peter Flaschel, Reiner Franke, Ricardo Araujo, Matthieu Charpe, Christian R. Proaño and Andreas Szczutkowski

Chapter 4 generalizes a two-sector real growth model of Marglin where the steady state of capitalist economies is plagued by secular inflation. We show that this implication need not be true in more general formulations and that his approach resembles more a general Keynes-Marx-Friedman framework where money is superneutral, where inflation is solely due to excessive monetary growth, and where the private sector is stable. However, the approach leads to a steady state rate of employment differing from the NAIRU of Friedman’s monetarist theory of inflation.

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Carl Chiarella, Peter Flaschel, Reiner Franke, Ricardo Araujo, Matthieu Charpe, Christian R. Proaño and Andreas Szczutkowski

In chapter 7 we analyze theoretically and study numerically a Keynes-Metzler-Goodwin growth model with active inventory policy in manufacturing. Households, firms and the government interact across real and financial markets. The model allows for asymptotic stability in case of sluggish wage / price adjustment, moderate inventory adjustment processes on the market for goods and sufficient elasticity regarding equilibria in the asset markets. It is studied - with its intrinsic nonlinearities only - by means of our cascade of stable matrices approach. We then add extrinsic nonlinearities based on the institutional features of modern economies, such as downward money wage rigidity. The dynamic properties are then studied in detail by bifurcation diagrams, stability basins, and by distributive characteristics of key economic quantities.

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Carl Chiarella, Peter Flaschel, Reiner Franke, Ricardo Araujo, Matthieu Charpe, Christian R. Proaño and Andreas Szczutkowski

Chapter 8 argues that applicable macro is high frequency macro. Therefor the ongoing data generating process has to be modeled in continuous time. It exemplifies this with a misuse of a 2D period model of monetarist type which becomes extremely overshooting, allowing for routes to `chaos’ when iterated at low frequencies, using mathematically suitable nonlinearities to tame its low frequency explosiveness. In its first part, moreover, this critique of macro-period models is applied to the Godley-Lavoie stock - flow approach and reformulates their model in continuous time (where stocks and flows can no longer be added), in order to allow for its general analysis from the theoretical point of view. This analysis is of a preliminary nature and demands for future investigations of this continuous-time general Godley-Lavoie model.

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Carl Chiarella, Peter Flaschel, Reiner Franke, Ricardo Araujo, Matthieu Charpe, Christian R. Proaño and Andreas Szczutkowski

We extend in chapter 11 the distributive cycle of Goodwin by effective demand forces and endogenous process innovations, driven by the evolution of the employment rate of the workers in the sphere of production through control by a monitoring workforce above them. We discuss the consequences of this MKS extension for the income distribution between capital and labor. We show that these extended dynamics can create persistent fluctuations in employment, income distribution and productivity growth if their balanced growth path is surrounded by an unstable multiplier-accelerator process. Our integration of global stability through a Marxian reserve army mechanism, with locally destabilizing Keynesian effective demand processes and Schumpeterian process innovations, provides a basic model of what Goodwin 1983 described as the MKS system approach to the understanding of the evolution of capitalism, one hundred years after Marx’s death.

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Carl Chiarella, Peter Flaschel, Reiner Franke, Ricardo Araujo, Matthieu Charpe, Christian R. Proaño and Andreas Szczutkowski

In this long chapter 13 we set up an advanced model of detailed goods market dynamics, segmented labor markets, dual and cross-dual wage-price adjustment processes, as well as counter-cyclical government policies. The cyclical movements of output generate, through Okun's law, employment variations in the heterogeneous labor markets. The core of the resulting Keynesian macro-dynamics is driven by credit-financed investment behavior and loan-rate setting by creditors. The high-order dynamical framework is constructed in such way that it allows – if simplified – lower dimensional versions of the model to be studied. Starting from such low dimensional sub-dynamics, we study the local stability of the full macro-dynamic model partly again through a `cascade of stable matrices’ approach if some feedback chains are sufficiently tranquil in their transmission mechanisms. However, local stability is solely the point of departure for the numerical investigation of local explosiveness and the forces that can bound such a behavior in the full high-order dynamics.