Lecture 4 ter

1. Lecture 4 ter “Heterogeneous expectations and strong uncertainty in a Minskyan model of financial fluctuations” Serena Sordi Alessandro Vercelli (sordi@unisi.it) (vercelli@unisi.it) DEPFID-Department of Economic Policy, Finance and Development University of Siena, Siena, Italy

2. This paper restates the Financial Instability Hypothesis (FIH) (Minsky, e.g.: 1975, 1982, 1986) to make it a more manageable instrument of analysis We focus on what we believe to be the “core” of this conceptual framework, i.e., the interaction between the financial conditions of the economic units → main determinant of financial fluctuations The interdependent and intertemporal nature of financial decisions gives a crucial role to the specification of the expectations formation mechanism Issue insufficiently developed in the FIH This is true also for our preceding contributions on the topic: Vercelli (2000, SCED), Sordi-Vercelli (2006, JEBO), Dieci-Sordi-Vercelli (2006, CSF), Vercelli (2009a, 2009b, Levy)

3. Behavioural Rules, Rationality and Heterogeneous Expectations in Financial Fluctuations On expectations Minsky sends back to Keynes Minsky emphasised that the crucial role played by expectations in Keynes’s theory depends strictly on his philosophy of uncertainty as stated in A Treatise on Probability (1921) and developed along his entire intellectual career In Minsky’s interpretation, the insights of Keynes on economic behaviour under strong uncertainty play a crucial role: “Keynes without uncertainty is something like Hamlet without the Prince” (Minsky, 1975, p. 57) .

4. However, Keynes himself has never provided a comprehensive and systematic account of his views on the role of expectations in economic behaviour and his inspiring hints are sparse in different writings In addition he never tried to express his views on expectation formation and revision in analytic terms: this is what we try to do here, taking into account a few crucial assumptions underlying Keynes’s point of view that provide the foundations for the treatment of expectations dynamics in our model

5. Keynes distinguishes between short-term expectations  relative to the proceeds obtainable by the employment of the existing stock of capital (Keynes, 1936, pp. 46, 148)  and long-term expectations that are concerned with investment and the value of capital assets for all their residual life (Keynes, 1936, pp. 47, 147-148, 246) We are here concerned exclusively with long-term expectations since the financial conditions of economic units crucially depend on them rather than on short-term expectations; however even in long-term Expectations the time horizon is short Keynes himself clarifies that, under the conditions of strong uncertainty assumed in the General Theory and in this paper, boundedly rational economic agents take into account a very limited sequence of periods: ‘our basis of knowledge for estimating the yield ten years hence of a railway, a copper mine, a textile factory, the goodwill of a patent medicine, an Atlantic liner, a building in the city of London amounts to little and sometimes to nothing; or even five years hence. In fact, those who seriously attempt to make any such estimate are often so much in minority that their behaviour does not govern the market’ (GT, p.136)

6. The role of conventions The basic principle of long-term expectations formation is that the agents project into the future the current trends (e.g., Keynes, 1936) They are aware that, by adopting this hypothesis, they are liable to systematic mistakes that will emerge ex post; however their attitude is not irrational since they do not know in which direction the future will change A natural way of formalizing this assumption is through the hypothesis of extrapolative expectations excessive dynamic instability However this is not fully satisfactory{ fit for boom, not for crisis

7. We may clarify further this point by recalling a metaphor used by Descartes in his Discourse on the Method (1637, pp. 24-25) to express an illuminating general maxim: “a traveller (…) upon finding himself lost in a forest, should not wander about turning this way and that (…) but should keep walking as straight as he can in one direction, never changing it for slight reasons; for in this way (…) he will at least end up in a place where he is likely to be better off than in the middle of the forest” This prescription clearly assumes strong uncertainty (on the characteristics of the forest) and shows that under these circumstances it is rational to stick to a rigid rule of conduct

8. Extrapolative expectations An extension of this metaphor suggests a specification of expectations for the object of our analysis. Let’s assume that an explorer has to cross a forest of unknown size and dimension to reach a desired destination. It is rational for him to proceed in a straight direction to minimize the risk of getting lost inside the forest. He will then expect that the distance from his base camp will progressively increase according to a principle of extrapolative expectations:

9. Regressive expectations However, he has to take account that his reserves of food are limited so that he will pursue this strategy only up to a well defined threshold (1/2 reserve of food). At that point a rational explorer would go back following the same path in the reverse because he does not know how far he is from the border of the forest and whether he will be able to survive by continuing in the same direction. After that threshold, he has to abandon the pursuit of the original goal since he has to focus on mere survival. He will then anticipate a progressive reduction of the distance from the base camp according to a principle of regressive expectations

10. During the upward phase of the cycle, the economic units try hard to increase their returns, being confident that their financial structure is within the solvency safety margin → this leads the units to increase their financial exposure, until they have to recognise that they have breached the safety margin After this threshold, the focus of economic units switches from the attempt to withstand competition and increase returns to secure their own financial survival: the units try hard to go back to a safe financial structure by deleveraging This attitude may be represented as a shift from extrapolative expectations, projecting a progressive increase of financial exposure, to regressive expectations, projecting a progressive reduction of financial exposure “the illusions of the boom cause particular types of capital- assets to be produced in such excessive abundance that some part of the output is on any criterion, a waste of resources (…) when the disillusion comes, this expectation is replaced by a contrary ‘error of pessimism’” (Keynes, 1936, pp. 321-22)

11. The hypothesis of expectations formation here analysed has a • kinship with the hypothesis of heterogeneous expectations • that has been recently applied in macroeconomic dynamics • This literature has in common the adoption of a weighted average • of two different hypotheses of expectations formation, such as • chartists’ and fundamentalists’ expectations (e.g., Day & Huang, • 1990; Levin, 1997; Brock and Hommes, 1998; Westerhoff • & Reitz, 2003; Chiarella, Dieci & He, 2007, 2009) • extrapolative and rational expectations (e.g., Lines and • Westerhoff, 2010) • extrapolative and regressive expectations (e.g., Westerhoff, • 2006a,b,c; 2008)

12. In the existing literature, heterogeneity of expectations is linked to the heterogeneity of agents; we consider a different source of heterogeneity related to the phase of the cycle: changing macroeconomic circumstances may change the plausibility of different hypotheses of expectations formation leading to the prevalence of one or the other → of course this change of weight feeds back on macroeconomic dynamics Heterogeneity has thus two dimensions: macro-economic environment Heterogeneity due to { agents In our model we explore only the consequences of the first kind of heterogeneity

13. The crucial financial conditions Notation: eit, financial outflows of financial unit i in period t yit, financial inflows of financial unit i in period t fityit  eit r, nominal rate of interest index of “liquidity” index of “solvency”

14. Classification of economic units and link with Minsky’s trinity • Hyper-Hedge units • Speculative units • Hyper-Speculative units • Hedge units • Highly Distressed units • Distressed units i, ‘threshold’ level of financial fragility (“safety margin”)

15. Derivation of the dynamical system of the model • Crucial behavioral assumption for the liquidity index: • The solvency index depends on the expected values • of the liquidity index within the unit’s time-horizon • Once we have specified a mechanism of expectations formation and revision, • from the definition of the solvency index we obtain a second feedback • between the two variables

16. Suppose the economy is initially, in period t 1, in a “tranquil” situation (in the sense of Minsky). In such a period, it is reasonable to assume the unit holds constant (‘flat’) expectations: where a = a(r,T) < 1 is such that However, stability may be destabilizing (Minsky) Net profits are positive and expectations validated: the increasing euphoria and confidence improve expectations → progressive deviation from the initial benchmark led by a mechanism of extrapolative expectations

17. Thus: (*) where We rewrite (*) as a recurrent equation in :

18. The dynamic system The feed-back between liquidity and solvency conditions may be thus represented by the following system 0 < α < 1 0 < a < 1 The equilibrium values are: while the characteristic equation is given by:

19. The dynamic system of the model is the following The equilibrium values are given by: while the characteristic equation is given by:

21. Cycle condition: Stability conditions:

22. The model is highly unstable: the typical dynamics generated by the feedback between the liquidity index and the solvency index of the economic unit are fluctuations of increasing amplitude, implying the collapse of the system

23. Some examples (i = a): With i> a (such that i= a+0.001):

24. The Model with Heterogeneous Expectations To model the hypothesis of heterogeneous expectations suggested above we assume that the representative economic unit forms extrapolative expectations until it reaches its safety margin, beyond which they start to form regressive expectations reflecting the effort to reduce the liquidity index towards its normal value

25. where:

26. Some numerical simulations:

29. The model exhibits sensitive dependence on initial conditions, for example:

30. POLICY IMPLICATIONS (1) Although the model is very simple, we believe that we can draw from it a few policy implications The current debates (e.g. on Basel 3), and the weak measures already taken, point mainly towards an increase in liquid reserves requirements In terms of our model, this translates in a shift leftwards of the solvency line so that, ceteris paribus, the financial robustness of the economy is enhanced However: -liquid reserves are burned in weeks (or days) when the contagion is triggered (September-October 2008) insufficient: we have to avoid the contagion -we should expect an analogous shift leftwards of the (desired) safety margin

31. POLICY IMPLICATIONS (2) We have to prevent financial contagion and financial meltdown This may be done only by stabilizing financial fluctuations independently of the phase of the cycle: floor constraining the amplitude of the cycle by fixing a maximum value of the current financial deficit - f relative to the net worth f* A cap to the leverage would go in the same direction But we should act more in general on the structural factors underlying the propagation process reflected in the parameters of the model that determine unstable financial fluctuations

33. Concluding Remarks We have shown in this paper that a simple mechanism of heterogeneous expectations may clarify the role of expectations in financial fluctuations. Our analysis confirms the crucial role of expectations within the core of the FIH. The simple feedback mechanism considered is sufficient to produce a dynamics of the variables consistent with crucial implications of the FIH. We show in particular that: (1) the widespread use of extrapolative expectations by economic agents brings about a high degree of financial instability that may lead to a serious financial crisis; (2) the use by economic agents of a mix of extrapolative and regressive expectations reduces the dynamical instability of the model but may give rise to complex dynamics

34. Further steps The analysis developed in this paper may be generalised in many directions: • First, in order to study the process of contagion triggered in proximity to the solvency line we have to study the interaction between the financial conditions of economic agents in an agent-based model • Second, we can take account of the heterogeneity of agents by giving different weights to the two mechanisms of expectations formation and by assuming different agents’ attitudes • Third, we can endogenize the shifts of the margin of safety • Fourth, we can make explicit the policy implications of the model: higher reserve requirement insufficient in the absence of ceilings to leverage and general conditions for stabilizing financial fluctuations

35. Financial vs Real systems Finally, we can make explicit the relationship between financial and real variables. The usual way to do it is by interpreting the “core model” as representative of the financial sector only -Keynes: marginal efficiency of capital and multiplier financial sector ↔ real sector{-Minsky: two-price approach to investment and Kaleckian identities -Sordi-Vercelli (2006) it refers to all the units We are looking at our core model in a different way { economy seen from the point of view of finance → “Pure finance economy” ( analogy with the “pure credit economy”: Wicksell, Hicks, Woodford)

36. “pure finance economy” (1) Economic decision making complies with different paradigms: C-M-C point of view of mainstream economics (sovereignty of consumption) Marx { M-C-M’ sovereignty of financial profit barter (cooperative) economy Keynes{ money (entrepreneur) economy Example:M-C-M’-C’-M’’-C’’ → classical dichotomy “real” model:(M-)C-(M’)-C’(-M’’)-C’’ { Modigliani-Miller Polar cases { “pure finance economy”: M(-C)-M’(-C’)-M’’(-C’’)

37. “pure finance economy” (2) Empirical evidence is in between the two extreme polarities but it is approaching progressively to the pure finance polarity: Decision making dominated by portfolio theory (Keynes chap. XVII of the GT): -Real investment iff expected cash flows > cash flows from finance (Keynes) -Employment of labor subordinated to the profitable employment of financial capital → involuntary unemployment (Keynes) -Labor subordinated to capital: flexibility -Consumption subordinated to financial profit → under-consumption → Real growth subordinated to financial growth: stagnation and crisis