Macrodynamic Model Research Articles

Stability Analysis of a High-Dimensional Macrodynamic Model of Real-Financial Interaction: A Cascade of Matrices Approach

This paper analyzes a high-dimensional macrodynamic model of the real-financial interaction. Regarding the financial sector it focuses on the stock market dynamics, whilst for the real sector it details goods market disequilibrium and two Phillips curves for prices as well as wages. The central link between the two sectors is constituted by Tobin's (average) q. The integrated dynamics of the model constitute a seven-dimensional system of differential equations, the stability analysis of which is the main contribution of the paper. The analysis proceeds by constructing a cascade of stable matrices and thus demonstrating that the long-run equilibrium is locally stable if certain adjustments are sufficiently sluggish. Large values of some reaction parameters, on the other hand, can destabilize the economy, while a Hopf bifurcation analysis shows the potential for cyclical motion in such circumstances.

Output, Financial Markets and Growth

In this paper we reconsider a macrodynamic model of Blanchard, which integrates output and stock market dynamics in a fundamental way. We add budget equations (and their implications) to all sectors of the economy, and also capital accumulation and growth (but not yet proper wage-price dynamics) and obtain a model of the real-financial interaction with quite different steady state characteristics as compared to the Blanchard approach. We furthermore allow for somewhat sluggish adjustment of share prices and capital gain expectations in place of perfect substitutes and perfect foresight. This brings our approach closer to completion and also makes it much more involved. Instead of the originally only 2D dynamics we now obtain a 4D dynamical system with two real and two financial variables and specific stability properties. However, by setting certain secondary expressions equal to their trend values, we can regain the mathematical form of the original 2D dynamics of Blanchard type. This form is now based on variables that allow for stationarity, when estimated, that therefore permit to estimate the model to get information about the magnitude of its adjustment speeds, the size of which is crucial for the stability of instability of this dynamical system.

An elementary information macrodynamic model of a market economic system

Information represents a common and universal substance, actively participating in a diversity of physical or virtual interactions, including various forms of economic interaction. The information regularities of economical dynamics and the mathematical evaluation of the economical system’s processes are studied by building the information systemic models, based on Informational Macrodynamics. Study focuses on an elementary production–organization, the production’s interaction and management, and different market dynamics, with modeling an organization by the hierarchical structure of information, cooperative, dynamic space-distributed network. The system’s cooperative dynamics coordinate and mutually connect the micro- and macroeconomical processes, which include both the dynamics within each basic economic element and the cooperative integration between the system’s elements. The models use a common mathematical formalism and the information as a universal equivalent of money and a common models’ language. The found formalized information mechanisms govern market’s cooperative dynamics and the information restrictions on these processes. The considered systemic mechanisms of self-control, adaptation, and evolution, represent a general attribute of an economical system.

MODELING STABILIZATION POLICIES IN A FINANCIALLY UNSTABLE ECONOMY

A non-linear macrodynamic model is presented here to study possible stabilization policies in a financially unstable economy. Three policy rules will be considered, namely the interest rate rule (also called Taylor rule), the money supply rule and the fiscal policy rule. It will be shown that the interest rate rule can be used to stabilize a financially unstable economy on a ‘desired’ growth path. However, when the economy falls into a ‘liquidity trap’, the interest rate rule is ineffective, and therefore the fiscal policy rule should be employed. We also find a rule of money supply that can deal with the problem of government debt while the rest of the economy can still be stabilized on the ‘desired’ growth path.

A re-evaluation of adaptive expectations in light of global nonlinear dynamic analysis

We undertake an analysis of the dynamic behaviour of a discrete time nonlinear monetary dynamics model with adaptive expectation that is a basic mechanism in a broad class of descriptive macrodynamic models. We consider in particular a variety of ways in which the adaptive expectations mechanism may be formulated. These differ in the degree of rationality of the economic agents that inhabit the model. We study in detail the local and global properties of the maps determining the price dynamics.

Investimento direto externo, acumulação de capital produtivo e distribuição de renda: uma abordagem pós-keynesiana

It is developed a macrodynamic model in the post-keynesian tradition of political economy of the productive capital accumulation and income distribution to analyze some of the impacts of the (flow of) foreign direct investment and the (stock of) foreign productive capital on capital accumulation, economic growth and functional income distribution in a stylized economy. Alongside a usual demand effect, the impacts of such an internationalization of local capital through labor productivity and market concentration are taken into account as well.

AN INTERVIEW WITH PAUL A. SAMUELSON

AN INTERVIEW WITH PAUL A. SAMUELSON

Um modelo macrodinâmico de abertura comercial, utilização da capacidade produtiva e crescimento econômico

É desenvolvido um modelo macrodinâmico pós-keynesiano para analisar o efeito de variações quantitativas nas tarifas de importação sobre a utilização da capacidade e a taxa de crescimento da economia. Mostra-se que mesmo quando a redução tarifária promove um aumento na produtividade da mão-de-obra e/ou uma queda no mark-up, seu impacto sobre a utilização da capacidade e/ou a taxa de crescimento pode vir a ser negativo.

A stability analysis of the perfect foresight map in nonlinear models of monetary dynamics

We undertake an analysis of the dynamic behaviour of a discrete time nonlinear monetary dynamics model under perfect foresight expectations. The model derives its interest from the fact that it is a basic mechanism in a broad class of descriptive macrodynamic models. Our analysis makes transparent the multivalued nature of the nonlinear perfect foresight map governing price dynamics. This results in a number of possible discontinuous maps, all of whose dynamics we analyze in response to an unanticipated monetary shock.

Taux de change et soutenabilité extérieure

<titre>R&#233;sum&#233;</titre> L&#8217;article &#233;tudie la politique de change qu&#8217;une &#233;conomie doit adopter en pr&#233;sence de d&#233;s&#233;quilibres ext&#233;rieurs susceptibles d&#8217;affecter la soutenabilit&#233; de sa dette ext&#233;rieure. Un mod&#232;le macro-dynamique de croissance contrainte par la balance des paiements, dans lequel les revenus et les flux de capitaux internationaux jouent un r&#244;le fondamental, est pr&#233;sent&#233;. L&#8217;article montre que les &#233;volutions des actifs ext&#233;rieurs nets sont non lin&#233;aires et sensibles &#224; l&#8217;environnement &#233;conomique dans lequel les dettes sont contract&#233;es. Ainsi, le probl&#232;me de la soutenabilit&#233; ext&#233;rieure de pays ayant des engagements exc&#233;dant leurs avoirs appelle des solutions au cas par cas. Une politique d&#8217;appr&#233;ciation ou de d&#233;pr&#233;ciation du change doit &#233;minemment tenir compte des valeurs prises par les &#233;lasticit&#233;s du commerce ext&#233;rieur.

A Two-regional Model of Business Cycles with Fixed Exchange Rates: A Kaldorian Approach

In this paper, we investigate a nonlinear macrodynamic model of business cycles which describes the dynamic interaction of two regions which are connected through inter-regional trade and inter-regional capital movement with fixed exchange rates. Our model is formulated as a five-dimensional system of nonlinear differential equations, which is a two-regional extension of the Kaldorian business cycle model. We study the local stability/instability and the condition for the existence of the cyclical fluctuation analytically, and we also present some numerical examples which support our analytical results.

Endogenous Banking Markup, Distributional Conflict and Capacity Utilization

We develop a post‐Keynesian macrodynamic model of productive capacity utilization and income distribution in which the supply of credit‐money is endogenous. Nominal interest rate is set by banks as a markup over the base rate, which is exogenously determined by the monetary authority. Over time, banking markup falls with firms’ profit rate on physical capital and rises with the rate of inflation, whereas the base rate remains unchanged. The dynamic behaviour of the system is analysed for both cases regarding capacity utilization, namely full utilization and excess capacity, which then makes for the possibility of multiple equilibria for the state variables real wage and nominal interest rate.

Mark-up bancário, conflito distributivo e utilização da capacidade produtiva: uma macrodinâmica pós-keynesiana

Elabora-se um modelo macrodinâmico pós-keynesiano de utilização da capacidade, distribuição e inflação por conflito, no qual a oferta de moeda de crédito é endógena. A taxa nominal de juros é determinada pela aplicação de um mark-up sobre a taxa básica fixada pela autoridade monetária. Ao longo do tempo, o mark-up bancário varia com a taxa de lucro sobre o capital físico, enquanto a taxa básica varia com excessos de demanda que não são acomodáveis pela utilização da capacidade. São analisados os casos em que a demanda é suficiente ou não para gerar a plena utilização da capacidade.

KNIFE-EDGE CONDITIONS AND THE MACRODYNAMICS OF SMALL OPEN ECONOMIES

Macrodynamic models of small open economies are inevitably characterized by “knife-edge conditions,” meaning that certain parameters are constrained for a viable equilibrium to exist. This paper examines the macrodynamic structure of such an economy and considers the role played by various standard knife-edge conditions. The dynamic model presented is sufficiently general so as to provide a unifying framework within which alternative models can be embedded. We identify three important models as special cases of this generic structure: (i) The traditional stationary Ramsey model, (ii) the endogenous growth model, and (iii) the nonscale growth model. We consider three margins along which knife-edge conditions are imposed. These include (i) preference parameters, (ii) production and employment characteristics, and (iii) openness of international financial markets. These restrictions are shown to play key roles in determining the equilibrium dynamics, and how the economy responds to various shocks. The existence of trade-offs between these knife-edge conditions is discussed.

An Interregional Dynamic Model: The Case of Fixed Exchange Rates

In this paper, we consider a nonlinear macrodynamic model which describes the economic transaction between two regions. We suppose that the economic structures of both regions are characterized by the Kaldorian business cycle model with money, and two regions are connected through interregional trade and interregional capital movement. We study the dynamic behavior of such a system under fixed exchange rates by means of analytical method and numerical simulations.

An alternative model of a nonlinear business cycle

The purpose of this paper is to develop a piecewise linear model to understand complex dynamics that arise out of sophisticated nonlinear macrodynamic models developed by Hicks and Goodwin. This piecewise analogue has several advantages: (i) it is a natural extension of a linear accelerator; (ii) it exhibits all the qualitative results of Goodwin's model; (iii) it enables one to conveniently derive newer bounds on output; and (iv) students find its representation appealing and understandable. The use of computer software is advocated for complex economic models that are described by systems of differential equations. To this end, the usefulness of STELLA (a Macintosh-based software) in verifying the qualitative predictions of the analysis, is illustrated.

Dynamic complexity in a Keynesian growth-cycle model involving Harrod's instability

This paper develops a Keynesian macrodynamic model, where some recent reinterpretations of Harrod's dynamics are embodied. Its main purpose is to prove that Harrod's “instability principle” may give rise to a chaotic motion (specifically a Šil'nikov scenario) around two equilibrium points: a steady-state unstable equilibrium, whose value depends on parameters defining the technical-progress dynamics, and a stationary state of zero growth. Furthermore, since it allows for a variable growth rate of labor productivity and assigns a key role to expectations, this model comes closer to modern theories of economic growth and endogenous business cycle.

Micro/Macro Dynamic Characteristics of Mechanism with a Harmonic Speed Reducer and Precision Rotational Positioning Control Using Disturbance Observer.

This paper describes the dynamic characteristics and precision rotational positioning of the mechanism with a harmonic speed reducer. The harmonic speed reducer is the reduction gear that is often used for precision robots because they can be made very compact and lightweight without backlash. However they have the friction and the low stiffness which make the positioning performance low. The purpose of this research is to clarify the suitable control method for the rotational positioning mechanism with the reduction gear and to realize high speed and high precision rotational positioning over a wide range. For this purpose, first, the characteristics of the mechanism are examined experimentally. The experimental results show that the mechanism can be represented by two kinds of models, those are micro and macro dynamic models. Then, by using the controller including a disturbance observer, the mechanism has the positioning accuracy better than 1" on the working range more than 4.0×105"

Stability, instability and complex behavior in macrodynamic models with policy lag

We construct simple macrodynamic models with policy lag by means of mixed difference and differential equations, and study how lags in policy response affect the macroeconomic (in)stability. Local dynamics of the prototype model are studied analytically, and the global dynamics of the prototype and the extended models are studied by means of numerical simulations. We show that the government can stabilize the intrinsically unstable economy if the policy lag is sufficiently short, but the system becomes locally unstable when the policy lag is too long. We also show the existence of cycles and complex behavior in some range of the policy lag.

Towards Applied Disequilibrium Growth Theory: VI. Substitution, Money-Holdings, Wealth-Effects and Further Extensions

In this paper we present a theoretical disequilibrium growth model of an open economy with a full set of markets and sectors and with heterogeneous agents in the household sector. This model allows, on the one hand, for basic consistency checks, such as fully specified bedget identities and a well-defined steady state refernce path and is therefore carefully specified from the theoretical point of view. On the other hand, the model is already fairly close to applied modern structural model building and thus is rich in descriptive detail. The model exhibits five real and five financial markets. Consumption behavior is formulated by way of the life cycle hypothesis and savings of worker households are allocated to money and short-term bonds, while savings of pure asset holders concern all financial assets considered (equities and long-term bonds, domestic and foreign ones). Firms use three inputs (labor, capital and imports) to produce two outputs (domestic goods and export commodities) by way of a nested CES/CET technology and they produce in a cost-minimizing way subject to a domestic demand constraint, also formulating medium run targets that guide their investment and pricing decision. The government sector is described in a very detailed way, including a variety of taxation schemes in particular and also a debt target according to which taxes are adjusted. We consider sluggishly adjusting wages and prices, coupled with heterogeneous expectations formation, and have on this basis fluctuating rates of capacity utilization on the labor market as well as on the market for goods. Financial markets, finally, are described by delayed adjustment processes towards interest rate parity conditions. The paper itself presents only the extensive form of the model with all of its details and compares it to the Murphy model for the Australian economy and also with the Multimod model, Mark III of the IMF. In subsequent papers we derive the intensive form of the model, its interior steady state solution and a 22 dimensional core dynamics which is then investigated from the theoretical and the numerical point of view, concerning the major feedback loops it contains and the stabilizing or destabilizing implications they give rise to. The main perspective of our work is to contribute to a better theoretical underpinning and understanding of modern applied macrodynamic models which nowadays also attempt to be complete with respect to budget identities and steady state reference paths, but which have not yet fully grasped the stability implications of their model buildings and basically have not yet included heterogeneity with respect to households and expectations formation.