Tuesday, May 26, 2020


A predator–prey model to explain cycles in credit-led economies

Óscar Dejuán and Daniel Dejuán-Bitriá

Keywords: business cycles; financial instability; predator–prey models; post-Keynesian economics

Published in print:Mar 2018

Category:Research Article


Pages:159–179

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This paper develops a predator–prey model to explain cycles in credit-led economies. The predator is the part of the financial sector that issues credit money for non-output transactions. It increases the indebtedness ratio and inflates bubbles that eventually have a negative impact on the real rate of growth (the prey). From this basis, we build a couple of models that may lead to self-contained or explosive cycles. Even in the first case, there is a risk of a financial collapse when certain variables move far away from their long-term equilibrium positions. In order to tame the cycle and avoid extreme positions, governments should ban the expansion of credit money for the purchase of assets and introduce permanent checks to risky credit.

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1 INTRODUCTION

This is a theoretical paper whose backdrop is the credit boom leading to the financial crash of 2007 and the first great recession of the twenty-first century. This crisis witnesses the ‘financial instability hypothesis’ of Minsky (1964; 1982; 1986; 1992). It also shows that the ‘originate-to-distribute model of banking,’ which characterizes our financialized economy, has accelerated the deterioration of the debt structures. Section 2 revises the key data of this process in the USA – the epicenter of the financial turmoil.

The Minskyan ‘financial instability hypothesis’ is deployed by means of a predator–prey model. This model was introduced in the natural sciences by Lotka and Volterra. Through a system of differential equations, they captured the systemic interdependency among marine species. In Volterra (1926), the higher the population of whiting (prey), the higher the food ratio and population of sharks (predator). After a certain point, the smaller population of whiting is bound to check the expansion of sharks. The traditional idea of the survival of the fittest is not always true in nature, he concluded.

Goodwin (1967) introduced the predator–prey model to explain the counter-clockwise movement in the employment rate and the labor share in income. A profit squeeze may damage the accumulation process and, therefore, the employment rate. Goodwin's model has prompted numerous extensions to the relation between distribution and accumulation. Goodwin et al. (1984) offer a survey. More recently, Arnim and Barrales (2015) have concluded that the Goodwin–Kalecki model of ‘profit squeeze’ continues to be the preferable approach to explain supply-driven cycles.

Taylor and O'Connell (1985) used a predator–prey model to formalize Minsky's hypothesis of an ongoing climate of financial fragility leading to economic crises. In a nutshell: the endogenous deterioration of the debt structure increases liquidity preference and checks productive investment.

Taylor and O'Connell (1985) was the seminal paper that encouraged post-Keynesian economists to study the dynamic competition between the real and financial sectors of the economy. 1 The new models differ mostly on the variables playing the roles of prey and predator. For Asada (2001; 2011), private debt is the predator, and income (related to capacity utilization) is the prey. In Dejuán and González-Calvet (2005), the predator is the rate of interest, while the prey is the rate of growth of real GDP. Fazzari et al. (2008) and Oreiro et al. (2013) relate the cashflow of firms (inversely related to the rate of interest) to their investment decisions. Taylor (2012) relates Minsky with Goodwin-style cycles.

Without using a proper predatory–prey model, Ryoo and Skott build a variety of stock-flow consistent models to show the relationship between the increasing leverage of firms, the capital gains resulting from the sale of stocks, and the investment decisions that depend on Tobin's q. The final effects on the real economy will depend on whether we adopt a Kaleckian view (capacity utilization closure) or a Kaldorian one (profit share closure). In the Kaldorian version, the real sector itself has an inherent tendency towards cyclical behavior (‘short cycles’), along with the cyclical forces generated by endogenous changes in financial practices (‘long waves’) (Skott 1994; Ryoo and Skott 2008; Skott and Ryoo 2008; Ryoo 2013a; 2013b). 2 Palley (1994; 2011) contrasts the long financial cycles leading to financial crashes with the traditional business cycles. Palley (2013, p. 65) states that credit-led capitalism has developed a ‘predator–prey’ mechanism.

Our paper has also been influenced by Badhuri et al. (2006) and Werner (1997; 2005; 2015). Badhuri et al. confront the real economy (from which output and profits accrue) and the virtual one that inflates bubbles and capital gains. Werner differentiates between the circuit of output transactions and the circuit of non-output transactions (assets). The first circuit is a positive-game. The second circuit is a zero-sum game where bubbles are inflated. He reinstates the ‘quantity theory of credit’ to explain asset inflation.

In our paper, the prey will be the productive sector represented by the rate of growth of real GDP. 3 Since our interest is in the impact of financial forces, we will consider an economy that is growing at the autonomous trend marked by the expansion permanent autonomous demand, with inflation controlled by the central bank. In Section 3 we combine the Keynesian–Kaleckian principle of effective demand (Keynes 1936; Kalecki 1971) and the multiplier-accelerator mechanism. This is the supermultiplier model introduced by Hicks (1950), Serrano (1995), Bortis (1997), Dejuán (2005; 2016), and Serrano and Freitas (2015).

Following Werner (1997), the predator has been identified with the financial sector when it provides credit for non-output transactions. It brings about higher indebtedness ratios and bubbles that (eventually) damage the real economy. Section 4 analyses the forces that affect creditworthiness and their influences on aggregate demand: default rate, indebtedness ratio, burden of debt, vertigo–stampede effects, wealth effects.

In Section 5 (and in the mathematical Appendix 1) we build a variety of predator–prey models leading to self-contained or explosive cycles. Even the first ones may lead to a credit crunch and a recession. This happens when the gap between the current trend of certain variables and their long-term equilibrium rate becomes too broad. Arguably, one of the main contributions of this paper is the presence of gravity centers compatible with the principle of effective demand. The expected growth of permanent demand, provided it endures long enough, is an attractor of the growth of output at full capacity (not full employment). The same rate plus the inflation target fixed by the Central Bank marks the long-term equilibrium growth of credit. In a Sraffian mood, the fundamental value of assets (discounted at the normal rate of profit) becomes a gravity center of asset inflation (Sraffa 1960).

The conclusions of the paper are summed up in Section 6. In order to tame the cycle and avoid extreme positions, governments should ban the expansion of credit money for the purchase of assets and introduce permanent checks to risky credit.

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