Macrodynamics of debt-financed investment-led growth with interest rate rules

ABSTRACT

This article demonstrates the diverse dynamic possibilities arising out of a simple macroeconomic model of debt-financed investment-led growth in the presence of interest rate rules. We show possibilities of convergence to steady state, and growth cycles around it as well as various complex dynamics. We investigate whether, given this framework, the financial sector can provide endogenous bounds to an otherwise unstable system. The effectiveness of monetary policy in the form of an interest rate rule targeting capacity utilization is examined under this context.

KEYWORDS:

• Growth cycles
• Hopf bifurcation
• interest rate rules
• Minsky
• paradox of debt

JEL CLASSIFICATIONS:

• C62
• C69
• E12
• E32
• E44
• G01

Notes

¹See, for instance, Kindleberger’s (1978) interesting and influential account of financial cycles, or the large number of economic models on financial fragility, which originates in an attempt to model at least some aspect of Minsky’s descriptive account, for example, Andresen (1996, 1999), Arena and Raybaut (2001), Asada (2001), Charles (2008a, 2008b), Chiarella et al. (2001), Datta (2005, 2015), Downe (1987), Fazzari et al. (2001, 2008), Foley (1987, 2003), Franke and Semmler (1989), Gatti and Gallegati (2001), Greenwald and Stiglitz (1993), Guilmi et al. (2009), Keen (1995, 1996), Lagunoff and Schreft (2001), Lavoie (1986–87, 1995), Lima and Meirelles (2007), Meirelles and Lima (2006), Palley (1994), Ryoo (2013a, 2013b, 2013c), Semmler (1987), Setterfield (2004), Skott, (1994, 1995), Taylor and O’Connell (1985), Taylor and von Arnim (2008), and Vercelli (2000).

²I am grateful to the referee for pointing this out.

³An alternative view, however, might be found in Charles (2015) and Ryoo (2013a) which looks at the effect of debt on decisions related to borrowing, financing and investment and discusses conditions under which Minsky’s financial instability hypothesis can be revived.

⁴See, for instance, the basic framework found in (Kalecki, 1971, ch. 7) or (Lavoie, 2014, ch. 5.3.6).

⁵Profits are defined net of interest payments. I am grateful to the referee for pointing out an ambiguity regarding the definition of profits in an earlier version of this study.

⁶An individual capitalist might earn either profits, or interest income, or both.

⁷Lavoie et al. (2004) offer a reconciliation of this debate by suggesting an alternative interpretation of the “post Keynesian” investment function, where the normal rate of capacity utilization is determined endogenously, depending on the actual rate of capacity utilization. For more on this debate, see Commendatore (2006), Hein et al. (2011), Skott (2010), and the critique of Duménil and Lévy (1999) model by Lavoie and Kriesler (2007).

⁸At the microeconomic level of a firm, gearing ratios typically exclude from the denominator interest payments. At the macroeconomic level, however, given a constant share of wages (and therefore, profits plus interest payments) in national income, the profits are ceteris paribus inversely proportional to interest payments. Hence, in order to avoid double counting the impact of interest payments on the gearing ratio, we consider the denominator gross of interest payments. I am grateful to the referee for pointing this out.

⁹See, for instance, Abrahams and Zhang (2009) and Kalapodas and Thomson (2006) for a discussion of the process of credit risk assessment.

¹⁰This is, in fact, one of the primary contentions of the Fisher–Minsky hypothesis; see, for instance, Fisher 1932, 1933, and Minsky 1975, 1982, 1986, 1994.

¹¹The past few decades have seen monetary authorities of many countries around the world shifting to some form of an interest rate rule targeting inflation, in the lines suggested by Taylor (1993) and more generally referred to as the “New Consensus in Macroeconomics” or NCM (Clarida and Gertler, 1997; Clarida et al., 1998, 2000; Judd and Rudebusch, 1998; Woodford, 2002). This form of interest rate rule targeting inflation has, however, come under severe criticism in the post Keynesian literature (e.g., Arestis and Sawyer, 2004, 2008; Arestis et al., 2005; Fontana and Palacio-Vera, 2002), especially in the context of the transmission mechanism of these rules. We contend that our strategy of directly targeting capacity utilization (partly because our model is cast in real terms) avoids some of the problems with regard to the transmission mechanism raised in these post Keynesian critiques. In this sense, our rule might be considered a contribution to the larger literature on post Keynesian alternatives (Lavoie, 2014; Nishi, 2015; Rochon, 2007; Rochon and Setterfield, 2007; Wray, 2007), to NCM interest rate rules.

¹²A situation of full capacity utilization, where u* = 1 might bring the economy too close to the full employment, adversely affecting the authority of the capitalists and the state.

¹³See, for instance, Butler and Waltman (1981), Cushing (1984), Feng and Hinson (2005), Koch (1974), Gardini et al. (1989), Hofbauer and So (1994), Hsu et al. (2001), Korobeinikov and Wake (1999), Loladze et al. (2004), Smith (1982); a collection of results for a class of such systems might be found in Zeeman (1993) and Zeeman and Zeeman (2002); for a more general discussion in the context of dynamic possibilities in three-dimensional differential equation systems, see Kuznetsov (1997).

¹⁴We should also note that the strength of this feedback would depend on the policy parameter, l. A higher value of l can set off an overshooting dynamics by strengthening this negative feedback effect. This might eventually destabilize the dynamics of the system.

¹⁵In fact, if the monetary authorities in our model target full capacity utilization, then the rate of investment in the steady state of our model would algebraically coincide with that of Harrod (1939) model. However, as we clarified above, the monetary authorities do not typically target full capacity utilization.

¹⁶For instance, the economies where financial crises and large-scale defaults are common might be more sensitive to such worsening of the borrower profile than the economies where financial crises are a rare occurrence.

¹⁷The existence of such a stable limit cycle for appropriate configuration of parameters might be verified by various methods, for instance, by following the method outlined in Kuznetsov (1997) and Edneral (2007), or by using any standard bifurcation software such as XPPAUT or MATCONT. It is beyond the scope of this study as well as a digression from its central theme, however, to actually predict whether such cycles will occur. Such a prediction would require a more careful empirical examination of the data and a calibration exercise.

¹⁸As mentioned above, the macroeconomic feedback effects are analyzed by isolating each effect, ignoring the impact of other effects.

¹⁹It should be noted here that we are interpreting the term “Hopf bifurcation” in Lemma 1 in a limited sense of emergence of purely imaginary roots. A stronger interpretation, in the sense of emergence of limit cycles would require fulfillment of nondegeneracy conditions. Further, one also needs to take into account the dependence of the first Lyapunov coefficient on a second parameter, for instance, the rate of adjustment of the rate of investment by the private sector, h. Any conclusion regarding emergence of limit cycles from Hopf bifurcation must preclude destruction of these limit cycles due to the presence of a codim 2 bifurcation like the Bautin bifurcation (cf. Kuznetsov {1997, ch. 8, sect. 8.3}, Guckenheimer and Kuznetsov [2007a]). We leave an investigation into these concerns for future research.

²⁰It should be mentioned here that many of the dynamics mentioned below might be observed from a suitable numerical simulation exercise, using any standard bifurcation software such as XPPAUT or MATCONT.

²¹This should be the case, for instance, in an economy characterized by too little competition, where firms have little incentive to adjust their rate of investment based on information on current values of variables.

Additional information

Notes on contributors

Soumya Datta

Soumya Datta is Assistant Professor, Faculty of Economics, South Asian University, New Delhi, India.