Multiplier-accelerator Model Research Articles

Samuelson's last macroeconomic model: Secular stagnation and endogenous cyclical growth

On the occasion of the centennial of his mentor Alvin Hansen, Paul Samuelson published in 1988 a modified version of his seminal 1939 multiplier-accelerator model to address aspects of Hansen's secular stagnation hypothesis. The “Keynes-Hansen-Samuelson” model (or KHS, as he called it) was built to analyse the effects of population growth on the economy's trajectory. Several changes were then made. Instead of difference equations and a tight accelerator, as in his 1939 model, Samuelson deployed differential equations and a flexible accelerator to produce a nonlinear limit cycle. Despite Samuelson's strong claims for the analytical contributions of his 1988 paper, it has – in contrast with the 1939 model – received only scant attention by macroeconomists and historians of economics alike. Samuelson's 1988 paper was his last published macroeconomic model, based on his long-established tradition of non-optimising macro-dynamics. Our paper provides a close reading of that article and some analytical results that shed new light on the formal aspects of Samuelson's 1988 model. We also discuss how it historically links up with business cycle models advanced by John Hicks, Nicholas Kaldor, Roy Harrod and Richard Goodwin and examine how far Samuelson's use of the term secular stagnation differs from Larry Summers's recent reconstruction of it.

Multiplicity and not necessarily heterogeneity: implications for the long-run degree of capacity utilization

The paper discusses the implications of disaggregation within the post-Keynesian debate on the long-run convergence of the degree of capacity utilization toward the normal one. The debate is related to the emergence of Harrodian instability inside multiplier–accelerator models and has been characterized by two “opposite” positions: the supermultiplier (SM) and the neo-Kaleckian approaches. These approaches solve the instability issue differently, but both share the postulate that an equilibrium position is such only if the desired state of firms is realized. In the long run, the economy converges toward a fully adjusted position where the realized degree of capacity utilization is equal to the normal/desired one. In this paper, we develop an Agent Based—Stock Flow Consistent version of the SM model showing that once multiplier–accelerator mechanisms are explicitly reproduced in a multi-firm economy, the accumulation process can be stable without requiring any convergence between the actual and normal rate. Conversely, the modeled economy displays two emergent properties: the fluctuations of the business cycle arise endogenously, and the long-run aggregate degree of capacity utilization persistently fluctuates around a level lower than the normal one. To this extent, the quasi-steady state corresponds to a situation where the desired state of agents is not realized and single elements are not in equilibrium, but the aggregate is. Finally, we compare outcomes produced from the model according to different scenarios on firms' heterogeneity and network symmetries.

Keynesian Without the Policy: Why the Business Cycle is all about Business Confidence and Finance

<p>Many of Keynes´s ideas and concepts are proven correct in this paper. The demand side, mainly business investments, drives the economy. Business firms steer the business cycle via profit expectations and animal spirits. Injections to and withdrawals from the circular flow of income are multiplied throughout the economy in accordance with Keynes´s multiplier. A sudden and sharp rise in households´ saving rates has a detrimental effect on aggregate demand, in line with Keynes´s paradox of thrift. Finance, not saving in the S=I sense, is the necessary condition for business investments and economic growth to be realized. Keynes´s finance motive thus makes money endogenous, contradicting the textbook result that exogenous money steers aggregate demand, contradicting the mainstream loanable funds theory and putting into question the Keynesian theory of sticky prices as a condition for real growth. However, a crucial omission in Keynes´s productive writings is the lack of an accelerator tying income to investment. Some of his followers such as Paul Samuelson tried to remedy that by developing multiplier-accelerator models. The problem with them is that the accelerator lacks micro foundations, in specific disregarding business confidence. Linking macro accounting identities with empirical national accounts data for five major economies produces the finding that business firms explain more than all aggregate expenditure growth during a 25-year period. Thus, it is concluded that business confidence is the root of the business cycle. Making the accelerator account for business confidence casts new light on the perhaps most well-known Keynesian “truth”: active fiscal policy as a main force stabilizing the business cycle. With business confidence being the endogenous and ubiquitous variable driving the business cycle, it turns out that any exogenous factor has the possibility to affect it. Policy needs to be viewed as a competing factor to the factor(s) driving the cycle in the other, destabilizing direction. The more powerful those factors are (e.g., a deadly virus), the tougher it gets for policy to “win” the competition, turning business confidence around. This leads up to the paper´s main conclusion: the worse the economy, the stronger is the case for active fiscal policy, but the lesser is the chance for it to succeed.</p>

Building blocks of a heterodox business cycle theory

A key characteristic of heterodox theories of the business cycle is their focus on endogenous business cycle mechanisms. This paper provides an overview and comparison of four models in heterodox business cycle theory: multiplier-accelerator models, Goodwin models, Minskyan debt-cycle models, and momentum trader models. A representative model from each theory is formulated as a two-dimensional predator-prey system in continuous time, which allows us to identify the different stabilizing and destabilizing mechanisms. We argue that the theories are substantially competing, as they posit different mechanisms that explain cycles, but we also argue that these mechanisms are not mutually exclusive. We suggest that heterodox economists work toward a synthesis.

ПОДОЛАННЯ ОБМЕЖЕНЬ ТА ВВЕДЕННЯ ПОВЕДІНКОВИХ АСПЕКТІВ У МОДЕЛІ МУЛЬТИПЛІКАТОРА-АКСЕЛЕРАТОРА САМУЕЛЬСОНА

Background. This article critically examines the limitations of traditional macroeconomic modeling, with a particular focus on the dynamic stochastic general equilibrium (DSGE) models and their predecessors. By scrutinizing their shortcomings in predicting and comprehending economic crises that are highlighted in numerous research papers and addressing contemporary challenges, the article calls for a fundamental revision of these models. To overcome their limitations, the article puts forward a novel approach that integrates insights from behavioral economics and incorporates real-life agents into macroeconomic models aiming to contribute to the advancement and refinement of macroeconomic modeling. Methods. The paper centers its analysis on Samuelson's multiplier-accelerator model, a prominent framework in macroeconomics, highlighting its inherent deficiencies and proposing potential improvements through the application of behavioral economics insights. Results. By dissecting the model's core assumptions, such as the consumption function, private investment, and government spending, the article argues for the integration of real agents with bounded rationality, ‘animal spirits’, expectations of future income, consumer sentiment, and segmentation of households and firms into distinct categories. By adopting a more realistic representation of human behavior, macroeconomic models can provide more accurate forecasts and better policy guidance. Conclusions. The article states that the incorporation of behavioral factors into macroeconomic models is indispensable for advancing our understanding of complex economic phenomena. By incorporating a more nuanced and realistic representation of economic agents and their decision-making processes, these models can overcome their existing limitations and contribute to the development of more robust and effective economic policies.

ANALYSIS OF FOREIGN DIRECT INVESTMENT FLOW IN THE REPUBLIC OF KAZAKHSTAN BASED ON THE ACCELERATOR MODEL

Foreign direct investments play a vital role in the economy of the Republic of Kazakhstan. Nowadays, foreign direct investments are considered to be one of the key aspects in economic integration of countries through creation and facilitation of beneficial links between various countries and economies. The purpose of the paper is to analyze the flow of foreign direct investment in the economy of the Republic of Kazakhstan and its impact on the gross domestic product using the theory of the multiplier-accelerator. While conducting the research the following scientific methods were employed: comparative analysis, analysis and synthesis, content analysis, logical, statistical, and mathematical, graphic. As a result of the undertaken research the features of the applying the multiplier-accelerator model were studied. Based on the collection of statistical data on the inflow of foreign investment and GDP in the Republic of Kazakhstan in the period from 2005-2021, an accelerator line was built. The main findings obtained in the course of the study made it possible to assess the impact of the inflow of foreign direct investment on the volume of gross domestic product, determine the cumulative effect and determine promising directions for the development of investment activity in the Republic of Kazakhstan.

Revisiting a Macroeconomic Controversy: The Case of the Multiplier–Accelerator Effect

This paper presents the bibliometrics of a Keynesian and neoclassical discussion about the multiplier–accelerator effect. Having its oldest roots in the 1930s, there was a special emphasis in the 1960s and 1970s on discussions regarding the dependence of current investment on economic growth (the accelerator effect). Through a bibliometric analysis, we also consider the Hicks–Samuelson contribution, also known as the multiplier–accelerator model. We identified, among other things, the most relevant authors on the topics, the economic areas that have been contributed to the most through keyword analysis, and the most notable contributions through citation analysis. We concluded that several areas in economics have taken advantage of the discussion around the multiplier–accelerator effect, especially the discussion on the business cycle, structural dynamics, and public finance.

A two-stroke growth cycle model for a small open economy

The Hicksian multiplier–accelerator model with a floor and/or a ceiling stands as one of the most successful representations of the economy capable of generating endogenous business cycles. In the present paper, we take some of the main insights of this literature as starting points to develop a continuous-time growth-cycle model for a small open economy. Our main innovation lies in assuming that capital accumulation is constrained only from above by the growth rate compatible with equilibrium in the balance-of-payments, i.e. the dynamic Harrod trade multiplier. It is shown that the obtained piecewise second order differential equation is a so-called two-stroke oscillator. Conditions under which the model produces periodic or aperiodic trajectories are studied analytically and through numerical simulations. An initial assessment of the statistical properties of the time-series indicates that they exhibit high kurtosis and negative skewness.

Assessment of the influence of foreign investment on social and economic development of the country and the region based on the example of the Yaroslavl Region

Introduction. The process of foreign investment flow occurs in an independent world market of financial resources. Its operation depends on the national investment policies of governments, the political global balance, the macroeconomic indicators of different countries, and the investment environment. Within the investment process between host countries and economic agents willing to develop joint business operations with foreign partners, foreign investments may have a controversial influence on regional economies. The recipient state should pursue a sensible policy of foreign investment control, assess the positive and negative influence of foreign investments using macroeconomic indicators and various economic and mathematical models in order to apply the positive effects of foreign investments for the balanced and sustainable development of regions. Today five economic and mathematical models are used in the Russian Federation to assess the influence of foreign investments and they only assess the influence of direct foreign investments and are used solely at the federal level (calculations are not conducted at the level of the regions of the Russian Federation, and base values are not taken into account). The subject of the study is the system of relations in the Russian Federation and in the studied region (Yaroslavl Region) concerning the attraction of foreign investment. Purpose. The purpose of this work is to evaluate the influence of foreign investments on the economy of a host country using the analysis of economic and mathematical models and on the economy of the Yaroslavl Region in 2013 and 2018 using a modified multiplier-accelerator model. Methodology. General scientific research methods were used as the methodological basis for this work, including comparative, economic-statistical, and expert evaluation methods. In this work we systematised the base values in order to use the multiplier-accelerator model at the level of the regions of the Russian Federation. Conclusions. It was concluded that using the multiplier-accelerator model and taking into account the factor of direct foreign investment, it is possible to conduct minimal calculations to get a balance between domestic and direct foreign investment in order to accelerate the economic growth of the regions of the Russian Federation.

Bifurcations and Arnold Tongues of a Multiplier-Accelerator Model

Abstract In this paper, we investigate the bifurcations of a multiplier-accelerator model with nonlinear investment function in an anticyclical fiscal policy rule. First, we give the conditions that the model produces supercritical flip bifurcation and subcritical one, respectively. Second, we prove that the model undergoes a generalized flip bifurcation and present a parameter region such that the model possesses two two-periodic orbits. Third, it is proved that the model undergoes supercritical Neimark–Sacker bifurcation and produces an attracting invariant circle surrounding a fixed point. Fourth, we present the Arnold tongues such that the model has periodic orbits on the invariant circle produced from the Neimark–Sacker bifurcation. Finally, to verify the correctness of our results, we numerically simulate an attracting two-periodic orbit, a stable invariant circle, an Arnold tongue with rotation number 1/7 and an attracting seven-periodic orbit on the invariant circle.

Revisiting Samuelson\u2019s models, linear and nonlinear, stability conditions and oscillating dynamics

In this work, we reconsider the dynamics of a few versions of the classical Samuelson’s multiplier–accelerator model for national economy. First we recall that the classical one with constant governmental expenditure, represented by a linear second-order difference equation, is able to generate oscillations converging to the equilibrium for a wide range of values of the parameters, and give its analytic solution for all the possible cases. A delayed version proposed in the recent literature, represented by a linear third-order difference equation, is also considered. We show that also this model is able to produce converging oscillations, and give a complete analysis of the stability region of the equilibrium. A new simple nonlinear model is proposed, showing that it keeps oscillatory behavior, although coupled with other dynamics related to global effects. Our analysis confirms that the seminal work of Samuelson and simple modifications of it, may give powerful tools in the study of the business cycles.

Economic and environmental impacts of decarbonisation through a hybrid MRIO multiplier-accelerator model

ABSTRACT This paper analyses the impacts of decarbonisation in three energy-intensive sectors/institutions (electricity generation, road transport, and household consumption) on four economic and environmental variables (value added, employment, energy consumption, and emissions). In our basic scenario, the EU is supposed to complete the decarbonisation of the selected sectors in 30 years, whereas in the rest of the world these sectors will be 30% decarbonised. We hypothesise that emissions and employment will fall once renewable sources of energy replace fossil fuels. Yet, in the meanwhile, massive investments are needed to build the required infrastructure. To compute the full impact, we apply a multiplier-accelerator model to a global multiregional hybrid input–output table derived from EXIOBASE3. In the EU, such a decarbonisation reduces yearly energy consumption, CO2 emissions, and employment by 22%, 19%, and 4%, respectively. Thus, additional measures are necessary to avoid global warming and absorb unemployment.

Joan Robinson Never Understood Any Part of Keynes’s Liquidity Preference Theory of the Rate of Interest in the General Theory

Keynes‘s first paragraph in his letter of the 9th of November,1936, is the following two lines: “I beg you not to publish. For your argument as it stands is most certainly nonsense.” Anyone who reads this correspondence will soon realize that it was simply impossible for Joan Robinson to have aided or contributed in any way to the development of the General Theory between 1930 and February, 1936, given the nature of these exchanges. Keynes is very specific as regards his Liquidity preference theory of the rate of interest: “You do not seem to realize that if you are right the whole theory of liquidity preference has to be thrown overboard…Such a conclusion cannot be brought in as a tacit inference from an unargued obiter dictum,”(Keynes,1936,CWJMK,Vol.14, p.146). Over the course of the two month correspondence from September 8th, 1936 till November 13th 1936, Keynes spent a great deal of time and effort trying to correct her many errors about his Liquidity Preference Theory of the Rate of Interest. J. Robinson compounded her original errors by making more additional errors due to her attempt to argue that Keynes was mistaken. Keynes finally realized that J. Robinson simply did not know what she was talking about. R. Skidelsky accused Roy Harrod of covering up certain aspects of Keynes’s life in his 1951 biography of Keynes in order to ”protect” Keynes’s reputation. This is correct, although Skidelsky overlooked Harrod’s additional failure to cover Keynes’s original multiplier-accelerator model of August, 1938 and Keynes’s careful tutoring of Harrod in correspondence, between July and September, 1935, of Keynes’s IS-LM model, which is presented by Keynes formally in the General Theory in chapter 21 in Part IV on pages 298-299. Unfortunately, Skidelsky has done exactly what he condemned R. Harrod of doing in 1951. Skidelsky never covered these exchanges between J M Keynes and Joan Robinson in the period between September and November, 1936 in any published work of his in the 20th or 21st centuries. It is then straightforward to show that other claims related to the General Theory made by Robinson can’t possibly follow ,given her complete and total ignorance of Keynes’s Liquidity preference theory of the rate of interest.

J. M. Keynes Made It Clear in His Correspondence to J. Robinson between September 8th to November 9th, 1936 that She Was Completely Ignorant of His Liquidity Preference Theory of the Rate of Interest: It Is Simply Impossible that Joan Robinson Was “…One of J.m. Keynes’ Most Brilliant Students, Who Helped Him Draft the Original of His General Theory.”

J. M. Keynes Made It Clear in His Correspondence to J. Robinson between September 8th to November 9th, 1936 that She Was Completely Ignorant of His Liquidity Preference Theory of the Rate of Interest: It Is Simply Impossible that Joan Robinson Was “…One of J.m. Keynes’ Most Brilliant Students, Who Helped Him Draft the Original of His General Theory.”

An expanded multiplier-accelerator model

Abstract. This paper revisits the standard multiplier-accelerator model, as advanced by Samuelson. While borrowing on the main assumptions of the multiplier-accelerator, we check the validity of Keynesian theory. Using higher-order difference equations and advanced-level mathematical techniques we solve the tax-augmented multiplier-accelerator model, as well as the open economy one. We find that the values of equilibrium national income are identical to the simple national-income model in the absence of the accelerator. We solve the simple multiplier-accelerator model both in present terms and withprolonged consumption. We solve for equilibrium consumption, tax, and imports which are unaffected by the accelerator. All results conform to Keynesian theory where investment, government spending and exports have a favorable multiplying effect on national income through their respective multipliers. The accelerator coefficient affects neither those multipliers, nor the income and the non-income tax multipliers. Expanding the multiplier-accelerator by the volume of foreign trade, taxation or both does not change the values of Keynesian variables. Adding an accelerator leaves optimal values unaffected but, more importantly, reinforces Keynesian theory. Keywords. Multiplier, Accelerator, Open economy, Difference equations, Keynesian national-income model, Tax multiplier, Exports multiplier. JEL. E12, C02, E21, E22.

A Nonsmooth Extension of Samuelson’s Multiplier-Accelerator Model

Dynamical-systems approaches have historically been used in business-cycle theory to generate sustained oscillations in macroeconomic variables. We aim to contribute to this literature by extending the original Samuelson multiplier-accelerator model with a discontinuous stabilization policy in terms of government expenditure. We show that the nonsmoothness yields dynamics in terms of periodic orbits and irregular fluctuations, not found in the original Samuelson model. We also note with particular interest that our model is able to generate localized nonstationary dynamics, which is in contrast to the most standard models found in the literature.

Multiplier–Accelerator Interaction in the Presence of an Underground Economy and Taxation

This article introduces the underground economy into a standard multiplier-accelerator model with linear progressive income taxation. The main results are that this introduction increases the instability of the overall economy towards chaos, that tax policy plays a critical role in preserving stability even if in the sense of a uniform cycle and that the operation of the accelerator may be countering the negative effect of tax evasion on tax revenue. JEL Classification: O17, E32, H24

Real and financial market interactions in a multiplier-accelerator model: Nonlinear dynamics, multistability and stylized facts.

In the present paper, we investigate the dynamics of a model in which the real part of the economy, described within a multiplier-accelerator framework, interacts with a financial market with heterogeneous speculators, in order to study the channels through which the two sectors influence each other. Employing analytical and numerical tools, we investigate stability conditions as well as bifurcations and possible periodic, quasi-periodic, and chaotic dynamics, enlightening how the degree of market interaction, together with the accelerator parameter and the intervention of the fiscal authority, may affect the business cycle and the course of the financial market. In particular, we show that even if the steady state is locally stable, multistability phenomena can occur, with several and complex dynamic structures coexisting with the steady state. Finally, simulations reveal that the proposed model is able to explain several statistical properties and stylized facts observed in real financial markets, including persistent high volatility, fat-tailed return distributions, volatility clustering, and positive autocorrelation of absolute returns.

On the exponential stability of Samuelson model on some classes of times scales

We prove the remarkable property that the exponential stability of the Samuelson model is invariant under the times scales R and h Z whenever 0 < h ≤ 1 . We characterize the domains of stability for these time scales and we also give sufficient conditions for stability on a class of mixed times scale. We prove analogous results for the Samuelson model in an open economy. Our methods are based on a spectral characterization of exponential stability due to Potzsche, Siegmund and Wirth and a multiplier accelerator model on time scales due to Bohner, Gelles and Heim.

DISCRETE TIME OR CONTINUOUS TIME, THAT IS THE QUESTION: THE CASE OF SAMUELSON’S MULTIPLIER-ACCELERATOR MODEL

A basic problem in economic dynamics is the choice of continuous-time or discrete-time in mathematical modeling. In this paper, we study the continuous-time Samuelson’s multiplier-accelerator model and compare this continuous-time model with its classical discrete-time model. We find that although time scales do not affect the probability of return to equilibrium solution in Samuelson’s multiplier-accelerator model, but time scales have an influence on the perfect symmetry of periodic motion.