Modeling financial instability

Asada, Toichiro Article Modeling financial instability Intervention. European Journal of Economics and Economic Policies Provided in Cooperation with: Edward Elgar Publishing Suggested Citation: Asada, Toichiro (2012) : Modeling financial instability, Intervention. European Journal of Economics and Economic Policies, ISSN 2195-3376, Metropolis-Verlag, Marburg, Vol. 09, Iss. 2, pp. 215-232, https://doi.org/10.4337/ejeep.2012.02.06 This Version is available at: https://hdl.handle.net/10419/277245 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in EconStor may be saved and copied for your personal and scholarly purposes. You are not to copy documents for public or commercial purposes, to exhibit the documents publicly, to make them publicly available on the internet, or to distribute or otherwise use the documents in public. If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by/4.0/ Modeling financial instability Toichiro Asada* In this paper, we reconsider Minsky’s financial instability hypothesis from the point of view of mathematical macrodynamic modeling. We start from a simple prototype small scale model of private debt and income with fixed prices. This system is similar to the Lotka-Volterra predator-prey system, in which private debt plays the role of predator and income plays the role of prey. Then, we extend the model step by step by introducing variable prices, inflation expectation, public debt and a budget equation of the consolidated government including the central bank. We also study the effect of macroeconomic stabilization policies by means of monetary and fiscal policies. JEL classifications: E12, E31, E32, E44, E52, E62 Keywords: Minsky’s financial instability hypothesis, Lotka-Volterra system, private debt, income, public debt, inflation expectation, stabilization policy 1. Introduction In contrast to the claim of mainstream (Neoclassical) teaching that the capitalist economy is inherently stable, the American Post Keynesian economist Hyman Minsky (1919 – 1996) proposed the financial instability hypothesis, which means that the financially dominated capitalist economy is inherently unstable (cf. Minsky 1975, 1982 and 1986). It seems that the credibility of Minsky’s hypothesis has been rapidly increasing in recent times, since we * Chuo University. Thanks are due to the valuable comments by two anonymous referees. Needless to say, however, only the author is responsible for possible remaining errors. During this research, the author was financially supported by the Japan Society for Promotion of Science (Grant in Aid (C) 20530160) and the Chuo University Grant for Special Research. Correspondence Address: Toichiro Asada, Faculty of Economics, Chuo University, 742-1 Higashinakano, Hachioji, Tokyo 192-0393, Japan, e-mail: [email protected]. Received 21 January 2012, accepted 24 April 2012 © InterventIon 9 (2), 2012, 215 – 232 216 Intervention. European Journal of Economics and Economic Policies experienced the Japanese long term deflationary depression in the 1990s and the 2000s after the bubbly prosperity in the 1980s, the Latin American and Asian currency crises in the 1980s and the 1990s, and the global financial crises in the USA and Europe that were initiated by the so called ›subprime mortgage crisis‹ of the US economy in 2008 after the prosperous period of the US economy in the 1990s and the 2000s. It looks as if the world economy in the recent 30 years has been faithfully tracing Minsky’s scenario of financial instability hypothesis. In this paper, we shall try to present some formal mathematical models that are inspired by Minsky’s ideas. This paper is organized as follows. In section 2, we restate Minsky’s financial instability hypothesis by referring to Minsky’s own writings. In section 3, we interpret Asada’s (2001) very simple fixed price dynamic model which is expressed by a Lotka-Volterra type two-dimensional system of nonlinear differential equations, which can reflect Minsky’s perspective of a financially driven business cycle called ›Minsky cycle‹. In section 4, we interpret the extended three-dimensional model by introducing price flexibility following Asada’s (2004) procedure, and show that the increase of price flexibility tends to destabilize rather than stabilize the macroeconomic system in this model contrary to the teaching of the mainstream macroeconomics. Minsky’s financial instability hypothesis means that the financially-driven capitalist economy is inherently unstable. But, according to Minsky (1986), the stability/ instability of the system is by no means independent of the macroeconomic policies of the government and the central bank. That is to say, the appropriate policy mix of the fiscal and monetary policies by the government and the central bank can contribute to ›stabilize an unstable economy‹ if we quote from the title of Minsky’s (1986) book. In sections 5 and 6, we present the further extended higher dimensional models that can study the effects of monetary and fiscal stabilization policies analytically. These models are designed to study theoretically what kind of policy mix is appropriate or inappropriate from the point of view of macroeconomic stabilization. We also argue that the analytical conclusions that are derived from these models are quite consistent with the experience of the Japanese economy under the serious deflationary depression in the 1990s and the 2000s, which are called the ›lost twenty years‹. Section 7 is devoted to some concluding remarks.1 1 Sections 3 and 4 are in fact restatements of the author’s previous papers (Asada 2001 and 2004). Availability of these papers is limited among non-Japanese scholars, although these papers are written in English. This is the reason why we sketch the outline of these papers briefly, although we are forced to omit the detailed formulations because of the lack of the space. Main contributions of this paper are sections 5 and 6, which introduce the effect of monetary and fiscal policies into the basic models that are sketched in sections 3 and 4. Asada: Modeling financial instability 217 2. Minsky’s financial instability hypothesis restated Minsky (1975, 1982 and 1986) asserts that the process of endogenous business cycles inevitably entails the endogenous changes of the form of investment financing such that ›Hedge finance → Speculative finance → Ponzi finance‹. Minsky interprets the meanings of these forms of financing as follows. »If realized and expected income cash flows are sufficient to meet all the payment commitments on the outstanding liabilities of a unit, then the unit will be hedge financing. However, the balance-sheet cash flows from a unit can be larger than the expected income receipts so that the only way they can be met is by rolling over or even increasing debt; units that roll over debt are engaged in speculative finance and those that increase debt are engaged in Ponzi finance.« (Minsky 1986: 203) Under the depression process, economic agents become quite pessimistic so that they refrain from investment expenditure, and the repayment of the existing debt and hedge finance dominate in such an environment. As the amount of debt decreases, investment activities become more vigorous, and more bold speculative finance becomes dominant. At the last stage of the prosperity, economic agents become excessively optimistic and they become to be engaged in the Ponzi finance that heavily relies on large amount of borrowing. However, the default of a part of economic agents triggers off the financial crises and the economy rushes into the serious depression. Under the depression process, the hedge finance becomes dominant again. In this way, the waves of pessimism and optimism are repeated reciprocally. This is the essence of Minsky’s financial instability hypothesis. Minsky’s hypothesis forms a striking contrast to the mainstream ›rational‹ expectation hypothesis. Let us quote from Minsky’s writings again:2 »Financing is often based on an assumption ›that the existing state of affairs will continue indefinitely‹ (GT: 152), but of course this assumption proves false. During a boom the existing state is the boom with its accompanying capital gain and asset revaluations. During both a debt-deflation and a stagnant recession the same conventional assumption of the present always ruling is made; the guiding wisdom is that debts are to be avoided, for debts lead to disaster. As a recovery approaches full employment the current generation of economic soothsayers will proclaim that the business cycle has been banished from the land and a new era of permanent prosperity has been inaugurated. […] But in truth neither the boom, nor the debtdeflation, nor the stagnation, and certainly not a recovery of full-employment growth can continue indefinitely. Each state nurtures forces that lead to its own destruction.« (Minsky 1975: 128) Such a typical scenario of the process of financially-driven business cycles that was presented by Minsky is called a ›Minsky cycle‹. 2 The abbreviation ›GT‹ in this quotation means Keynes’s (1936) General Theory. 218 Intervention. European Journal of Economics and Economic Policies 3. Minsky cycle as a Lotka-Volterra like system Minsky himself did not formulate formal mathematical models that reflect his basic idea on the ›financial instability hypothesis‹. However, a lot of mathematical models that were inspired by Minsky’s idea have been produced up to now since the seminal paper by Taylor and O’Connell (1985) was published.3 In this section, we shall summarize the essence of the model that was presented by Asada (2001) as a typical example of such mathematical models. This approach interprets the ›Minsky cycle‹ as a kind of Lotka-Volterra system of mathematical biology, which is based on the dynamic interaction of predator and prey.4 The reduced form of a system of equations that was presented by Asada (2001) consists of the following two-dimensional system of differential equations: (a)  d f d y=1( , ) , (b)  y f d y=2( , ; ) α ; α > 0, (1) where a dot over the symbol is time derivative, and the meanings of the symbols are as follows: d = D / K = private debt-capital ratio, Y = Y / K = income-capital ratio, D = stock of the real debt of the private firms, K = real capital stock that is owned by the private firms, Y = real national income, α = parameter that reflects the adjustment speed of the disequilibrium in the goods market. Variable y is used as a surrogate variable that reflects the degree of the utilization of capital stock and the rate of employment (1 – rate of unemployment) in the labor market.5 In this simplified version of the model, fixed prices are assumed, and the government’s economic activity and international transaction are abstracted from.6 Furthermore, each partial derivative in this model becomes as follows because of some economic reasons (cf. Asada 2001):7 3 Following examples are some of such works. Arena/Raybaut (1998), Asada (2001, 2004 and 2006), Bhaduri (2011), Charles (2008a and 2008b), Charpe et al. (2011), Delli Gatti/Gallegati (1995), Foley (1987), Jarsulic (1990), Keen (2000), Kuroki (1994), Pally (1996) and papers in Semmler (ed.) (1989). Nasica (2000) provides an excellent survey of the related topics. 4 See Gandolfo (2009, ch. 23) for the exposition of the Lotka-Volterra system. Goodwin (1967) is a very famous contribution as a quite interesting application of this system to macrodynamic economic theory. It must be noted, however, that our formulation is the only partial formalization of Minsky’s analytical scheme. For example, it is not clear whether the subprime crisis fits our Lotka-Volterra like model well. 5 This procedure, which was adopted by Franke/Asada (1994) can simplify the analysis by saving one state variable, the rate of employment (e). Although this procedure is not a precise method but only an approximation, we can justify this kind of simplification due to high correlation between the two variables y and e (see Franke/Asada 1994). 6 Later, we shall interpret the extended models that can treat the price movement and macroeconomic stabilization policies by the government including the central bank. 7 Asada (2001) showed that we have a set of inequalities (2) if gy , | gd | in equation (3) and the firms’ marginal propensity of internal retention are sufficiently large. Asada: Modeling financial instability 219 f f d f f y f f d 11 1 12 1 21 2 0 0 0= ∂ ∂ < = ∂ ∂ > = ∂ ∂ </ , / , / , f f y f f f f 22 2 11 22 12 21 0 0= ∂ ∂ > − > − + + − / , ( ) ( ) ( ) ( ) . (2) Equation (1.a) can be derived from the fact that the firms’ investment expenditure that exceeds the firms’ internal finance must be debt-financed.8 Equation (1.b) expresses the ›quantity adjustment‹ process in the goods market disequilibrium, which implies that the rate of utilization of the capital stock fluctuates according as the excess demand in the goods market per capital stock is positive or negative. In both equations (1.a) and (1.b), the following investment function is incorporated: g g y d g g y g g e y e e = − = ∂ ∂ > = ∂ ∂ − < − ( , , ) ; / , / ( ) ρ π ρ π ρ π 0 0 , g g d d= ∂ ∂ </ 0 , (3) where g K K= = / rate of investment (rate of capital accumulation), ρ = nominal rate of interest, π e = expected rate of price inflation, and ρ – π e = expected real rate of interest. Asada (2001) derived this type of investment function with debt effect from the expected profit maximization behavior of the firms by using the ›principle of increasing risk‹ suggested by Kalecki (1937 and 1971), which means that firms’ risk increases as the investment expenditure increases. In the simplified model in this section, fixed prices are assumed so that we have π e = 0. Furthermore, in this section, we assume that the central bank always acts to keep the nominal rate of interest ρ to be constant, which means a lack of the active monetary policy. Therefore, π e and ρ do not enter into the system of equations (1) as variables. In this model, the change of the private debt-capital ratio  d becomes an increasing function of the income-capital ratio y ( f12 > 0), because the increase of y induces the increase of debt financing through the rise of the investment expenditure g. On the other hand, the change of the income-capital ratio  y becomes a decreasing function of the debt-capital ratio d ( f21 < 0), because the increase of d induces the decrease of the investment expenditure, which contributes to the reduction of the excess demand in the goods market through the decrease of effective demand. These characteristics imply that we can consider the system of equations (1) as a ›Lotka-Volterra‹ like system, in which the variable d plays the role of the predator and the variable y plays the role of the prey. Asada (2001) proved that the cyclical fluctuations occur and in particular, the closed orbits around the equilibrium point exist at some range of the parameter value α by means of the Hopf bifurcation theorem.9 Figure 1 illustrates a typical closed orbit of income and private debt that is produced in this system and the time trajectories of two variables corresponding to four phases of the closed orbit. The cyclical fluctuations of income and private debt in Figure 1 can be considered as a typical example of the ›Minsky cycle‹. 8 It is assumed that the firms are debtors and the capitalists are creditors, and the issues of new shares are abstracted from. 9 See Gandolfo (2009, ch. 24) for the exposition of the Hopf bifurcation theorem. 220 Intervention. European Journal of Economics and Economic Policies Figure 2 illustrates two types of bifurcation that can emerge in this system.10 Figure 2 (a) is an example of the ›subcritical‹ Hopf bifurcation. In this case, the closed orbit exists in the range of the parameter value α at which the equilibrium point is locally stable and the closed orbit itself is unstable. Figure 2 (b) is an example of the ›supercritical‹ Hopf bifurcation. In this case, the closed orbit exists in the range of the parameter value α at which the equilibrium point is locally unstable and the closed orbit itself is stable. Figure 1: Emergence of Minsky cycle Source: Asada (2001: 81) Figure 2: Subcritical Hopf bifurcation (a) and supercritical Hopf bifurcation (b) Source: Asada (2001: 83) 10 Here we omit the detailed interpretation how to derive Figures 1 and 2 because of the lack of the space. (a) (b) Asada: Modeling financial instability 221 Both of the above mentioned two types of Hopf bifurcation are economically meaningful. The ›subcritical‹ case corresponds to the ›corridor stability‹ in the sense of Leijonfufvud (1973), which means that this system is immune from small shocks that can contain the initial position inside the ›corridor‹ (stable region), but it is vulnerable to large shocks that leave the initial condition outside the ›corridor‹.11 In the ›supercritical‹ case, the time trajectory of the variables that starts from the initial condition other than equilibrium point converges to the limit cycle, and the cyclical fluctuations persist indefinitely. 4. An extension to the model with flexible prices In this section, we introduce price flexibility into the model of the previous section following Asada’s (2004) procedure. We can formulate this extended model by means of the following three dimensional system of differential equations. (a)  d f d y e = > 10( , , ; ) ; π ε ε , (b)  y f d y e = > 20( , , ; ) ; π α α , (c)  π γ ε γ ef y= > 30( ; , ) ; , (4) where the meanings of the symbols d, y, and α are the same as those in the previous section, and the meanings of other symbols are as follows, π e = expected rate of price inflation, ε = parameter that reflects the price adjustment speed, γ = parameter that reflects the adjustment speed of price expectation. Furthermore, the following properties of the partial derivatives as well as a set of inequalities (2) in the previous section are assumed. f f f f f f y e e 13 1 23 2 32 3 0 0 0= ∂ ∂ > = ∂ ∂ > = ∂ ∂ >/ , / , / π π . (5) We can derive equation (4.c) as follows. In this extended model, the rate of price inflation π becomes an endogenous variable that fluctuates according to the following standard type of the expectations-augmented price Phillips curve. π ε π ε = − + >( ) ;y y e0. (6) As for the price expectation formation, the following ›adaptive‹ expectation formation hypothesis (or the ›backward-looking‹ expectation formation hypothesis) is adopted.  π γ π π γ e e = − >( ) ; 0 . (7) Under the absence of the central bank’s active commitment to inflation targeting like the Japanese economy under deflationary depression during the 1990s and the 2000s, it is likely 11 See also Asada (2010) for the interpretation of the ›corridor stability‹. 222 Intervention. European Journal of Economics and Economic Policies that the people who do not have any definite information form their inflation expectation adaptively. This is the rationale of the hypothesis included in equation (7). Substituting equation (6) into equation (7), we have  π εγ γ ε ey y f y= − =( ) ( ; , ) 3, (8) which is nothing but equation (4.c). In this model, the nominal rate of interest is still kept constant by the central banker’s passive monetary policy. Nevertheless, the real rate of interest becomes a variable rather than constant through the variable expected rate of price inflation, so that the variable π e enters into equations (4.a) and (4.b) through the investment function (3). Both of the rates of change  d and  y become increasing functions of π e (that is, f13 > 0 and f23 > 0) because of the following reasons. The increase of π e implies the decrease of ρ – π e, which induces the increase of the rate of investment and the increase of the debt financing of its expenditure as well as the increase of effective demand. We can consider the increase of the parameter value ε or γ as the increase of the ›price flexibility‹. Asada (2004) proved analytically, however, that the increase of price flexibility in this sense tends to destabilize rather than stabilize the economic system contrary to the teaching of the mainstream economic theory, because the following destabilizing positive feedback mechanism is intensified by the increase of the parameter values ε and γ which contributes to intensify the amplitude of macroeconomic fluctuations. π ρ π π π e e e g y↓⇒ − ↑⇒ ↓⇒ ↓⇒ ↓⇒ ↓( ) . (FM1) Figures 3 and 4 summarize the result of Asada’s (2004) numerical simulations that support the above analytical conclusion. Incidentally, we pointed out in the previous section that the variable d plays the role of ›predator‹ and the variable y plays the role of ›prey‹ in the dynamic interaction between these two variables like the Lotka-Volterra system of mathematical biology. The role of the variable π e is, however, not so simple. It follows from the system of equations (4) that both of the following results (A) and (B) apply. a) π e is the food for d and y. b) y is the food for π e. This means that the relationship between two variables π e and y is not a simple predator-prey relationship and these variables share their destiny. This is the source of the destabilizing positive feedback mechanism that is described schematically by the causal relationships (FM1). Asada: Modeling financial instability 229 Proposition 1 in the previous section also applies to this extended system. Furthermore, we can show analytically that the large value of the parameter θ (value of θ that is close to 1) is a stabilizing factor and the small value of θ (value of θ that is close to 0) is a destabilizing factor.21 This means that the appropriate policy mix is the combination of the active monetary policy with sufficient credibility and the fiscal policy that attaches importance to the employment consideration rather than public debt consideration. The opposite policy mix is inappropriate. If the policy mix is inappropriate, the equilibrium point becomes dynamically unstable, and in this case the deflationary depression, in which the nominal rate of interest is stuck at its lower bound, is likely to occur like in the Japanese economy in the 1990s and the 2000s. The intuitive explanation of this conclusion is as follows. Suppose that the government expenditure responds actively to the changes of real national income (employment). Then, the following stabilizing negative feedback mechanism will work. y v y↓⇒ ↑⇒ ↑⇒ ↑(effective demand per capital stock) . (FM2) On the other hand, the following two destabilizing positive feedback mechanisms will work if the government expenditure responds to the changes of the stock of public debt excessively. y T K b v y↓⇒ ↓⇒ ↑⇒ ↓⇒ ↓⇒ ↓( / ) (effective demand per capital stock) , (FM3) b v y T K H p b↑⇒ ↓⇒ ↓ ↓ ↓⇒ ↑,( / ) ,( / ) . (FM4) These destabilizing feedback mechanisms produce the paradoxical situation in which the decrease of the government expenditure per capital stock induces the decrease of real national income per capital stock (employment) and the increase of debt-capital ratio, contrary to the government’s subjective intention. This theoretical reasoning is consistent with the experience of the Japanese economy in the 1990s and the 2000s, which are called the ›lost twenty years‹. We already noted that the destabilizing ›anti Domar condition‹ was satisfied in Japan in this period. In fact, in Japan in this period of serious deflationary depression with high unemployment, the sharp increase of the public debt-capital ratio b coexisted with the decrease rather than increase of both of government expenditure-capital ratio v and income-capital ratio y together with the decline of the growth rate of money stock (cf. Asada 2011). These apparently paradoxical behaviors of some key variables in Japan in recent twenty years are quite consistent with the theoretical reasoning of the model in this section. 21 In this paper the mathematical proofs are omitted because of the lack of space. Full mathematical proofs will be presented in another paper of the author. 230 Intervention. European Journal of Economics and Economic Policies 7. Concluding remarks In this paper, we presented some dynamic models that can contribute to formalize Minsky’s idea of financial instability hypothesis, and furthermore presented some models that can contribute to the dynamic analysis of the macroeconomic stabilization policies by means of the monetary and fiscal policies. We hope that these models can successfully give an answer to the question »what policy mix is appropriate to stabilize an inherently unstable economy in the sense of Minsky?« References Arena, R., Raybaut, A. (1998): Credit and financial markets in Keynes’ conception of endogenous bsiness cycles: An interpretation, in: Abraham-Frois, G. (ed.), Non-linear Dynamics and Endogenous Business Cycles, Berlin: Springer, 147 – 156. Arestis, P., Sawyer, M. (2008): A critical reconsideration of the foundations of monetary policy in the New Consensus Macroeconomics framework, in: Cambridge Journal of Economics, 32(5), 761 – 779. Asada, T. (2001): Nonlinear dynamics of debt and capital: A Post-Keynesian analysis, in: Aruka, Y., Japan Association for Evolutionary Economics (ed.), Evolutionary Controversies in Economics: A New Transdisciplinary Approach, Tokyo: Springer, 73 – 87. Asada, T. (2004): Price flexibility and instability in a macrodynamic model with a debt effect, in: Journal of International Economic Studies, 18(March), 41 – 60. Asada, T. (2006): Stabilization policy in a Keynes-Goodwin model with debt accumulation, in: Structural Change and Economic Dynamics, 17(4), 466 – 485. Asada, T. (2010): Central banking and deflationary depression: A Japanese perspective, in: Cappelo, M, Rizzo, C. (eds.), Central Banking and Globalization, New York: Nova Science Publishers, 91 – 114. Asada, T. (2011): Macrodynamics of public debt accumulation and fiscal-monetary policies: An inappropriate policy mix, in: Watanabe, K. (ed.), Money, Finance and Income Distribution, Tokyo: Nihon Keizai Hyoron-sha, 3 – 30 (in Japanese). Asada, T., Chiarella, C., Flaschel, P., Franke, R. (2010a): Monetary Macrodynamics, London: Routledge. Asada, T., Chiarella, C., Flaschel, P., Mouakil, T., Proaño, C., Semmler, W. (2010b): Stabilizing an unstable economy: On the proper choice of policy measures, in: Economics: The OpenAccess, Open Assessment E-Journal, 3(21), 1 – 43. Asada, T., Flaschel, P., Mouakil, T., Proaño, C. (2011): Asset Markets, Portfolio Choice and Macroeconomic Activity: A Keynesian Perspective, Basingstoke, U.K.: Palgrave Macmillan. Bhaduri, A. (2011): A contribution to the theory of financial fragility and crisis, in: Cambridge Journal of Economics, 35(6), 995 – 1014. Charles, S. (2008a): Corporate debt, variable retention rate and the appearance of financial fragility, in: Cambridge Journal of Economics, 32(5), 781 – 795. Asada: Modeling financial instability 231 Charles, S. (2008b): Teaching Minsky’s financial instability hypothesis: A manageable suggestion, in: Journal of Post Keynesian Economics, 31(1), 125 – 138. Charpe, M., Chiarella, C., Flaschel, P., Semmler, W. (2011): Financial Assets, Debt and Liquidity Crises: A Keynesian Approach, Cambridge: Cambridge University Press. Delli Gatti, D., Gallegati, M. (1995): Financial fragility and fluctuations: Keynesian views (and an addendum), in: Economic Notes, 24(3), 513 – 554. Domar, E. (1957): Essays in the Theory of Economic Growth, Oxford: Oxford University Press. Foley, D.K. (1987): Liquidity-profit rate cycles in a capitalist economy, in: Journal of Economic Behavior and Organization, 8(3), 363 – 377. Franke, R., Asada, T. (1994): A Keynesian model of the business cycle, in: Journal of Economic Behavior and Organization, 24, 273 – 295. Galí, J. (2008): Monetary Policy, Inflation, and the Business Cycle: An Introduction to the New Keynesian Framework, Princeton: Princeton University Press. Gandolfo, G. (2009): Economic Dynamics, Fourth Edition, Berlin: Springer. Goodwin, R.M. (1967): A growth cycle, in: Feinstein, C.H. (ed.), Socialism, Capitalism and Economic Growth, Cambridge: Cambridge University Press, 54 – 58. Hein, E. (2007): Interest rate, debt, distribution and capital accumulation in a Post Keynesian model, in: Metroeconomica, 58(2), 310 – 339. Isaac, A.G. (2009): Monetary and fiscal interactions: Short-run and long-run implications, in: Metroeconomica, 60(1), 197 – 223. Jarsulic, M. (1990): Debt and macrostability, in: Eastern Economic Journal, 15(3), 91 – 100. Kalecki, M. (1937): The principle of increasing risk, in: Economica, 4(16), 440 – 447. Kalecki, M. (1971): Selected Essays on the Dynamics of the Capitalist Economy, Cambridge: Cambridge University Press. Keen, S. (2000): The nonlinear economics of debt deflation, in: Barnett, W.A., Chiarella, C., Keen, S., Marks, R., Scnabl, H. (eds.), Commerce, Complexity, and Evolution, Cambridge: Cambridge University Press, 83 – 110. Keynes, J.M. (1936): The General Theory of Employment, Interest and Money. London: Macmillan. Kuroki, R. (1994): Growth and debt accumulation, in: Aoki, N., Shiraiwa, K., Takahashi, Y. (eds.), Proceedings of the International Conference on Dynamical System and Chaos, Singapore: World Scientific, 399 – 403. Leijonfufvud, A. (1973): Effective demand failures, in: Swedish Journal of Economics, 75(1), 27 – 48. Minsky, H. (1975): John Maynard Keynes, New York: Columbia University Press. Minsky, H. (1982): Can ›It‹ Happen Again?: Essays on Instability and Finance. Armonk, New York: M.E. Sharpe. Minsky, H. (1986): Stabilizing an Unstable Economy, New Haven: Yale University Press. Nasica, E. (2000): Finance, Investment and Economic Fluctuations: An Analysis in the Tradition of Hyman P. Minsky, Cheltenham, U.K.: Edward Elgar. Pally, T. (1996): Post-Keynesian Economics: Debt, Distribution and the Macroeconomy, London: Macmillan. Semmler, W. (ed.) (1989): Financial Dynamics and Business Cycles: New Perspectives, Armonk, N.Y.: M. E. Sharpe. 232 Intervention. European Journal of Economics and Economic Policies Setterfield, M. (2009): Macroeconomics without the LM curve: An alternative view, in: Cambridge Journal of Economics, 33(2), 273 – 293. Taylor, J.B. (1993): Discretion versus policy rules in practice, in: Carnegie-Rochester Conference Series on Public Policy, 39(December), 195 – 214. Taylor, L., O’Connell, S.A. (1985): A Minsky crisis, in: The Quarterly Journal of Economics, 100 (Supplement ), 871 – 886. Woodford, M. (2003): Interest and Prices: Foundation of a Theory of Monetary Policy, Princeton: Princeton University Press.