Financial and Nuclear Meltdowns: the structural instability of critical processes

1. Vienna 15 February 2012 Financial and Nuclear Meltdowns:the structural instability of critical processes Alessandro Vercelli DEPFID University of Siena

2. Analogies September 2008:financial “tsunami”that triggered the“meltdown” of the financial system March 2011:real tsunamithat triggered thepartial meltdown of the nuclear reactors 1,2,3, of the Fukushima1 plant many other terminological and factual analogies: chain reaction, multiplier, instability, stress tests, fragility, contagion, self-regulation vs discretionary regulation, regulatory capture.. The analogy is not restricted to the terminology: -nuclear reactors and financial systems are characterized by a similar sort of complex dynamics leading to similar failures and regulation problems -both are characterized by huge long-term investments and short-term profit seeking

3. Purpose The analogies may be inspiring to understand better: nuclear accidents: understandable also by a layman having some experience of financial phenomena Causes and consequences { financial crises: concrete perception of the consequences and risks passive regulation (self-regulation) mechanisms regulation failures { active regulation rules and their compliance Policy { assessment risk { management

4. Structure of the presentation • Complex dynamics of a nuclear reactor • Nuclear safety • The complex dynamics of a monetary economy • Financial safety • Passive and active regulation in finance and nuclear energy generation • Management of hard risks and precautionary policies

5. 1st Part The Complex dynamics of nuclear reactors

6. The nuclear plant Fukushima1 1st Part The Complex dynamics of nuclear reactors

7. Reactor of Fukushima1 Typical BWR nuclear reactor of the Fukushima1 type Core:where the nuclear fuel bars are contained and the nuclear chain reaction occurs Moderator (water): to slow down the chain reaction Control rods: to regulate and control the chain reaction

8. The nuclear fission nuclear energy generation Nuclear fission { nuclear weapons Microphysics:when a heavy nuclide or isotope is hit by a neutron its nucleus breaks into two or more “fission fragments” releasing a great amount of energy in the form of heat and radiation The most important example for energy generation is that of uranium-235: when hit by a “free” neutron 235U + neutron → fission fragments + 2.4 neutrons + 192.9 MeV

9. nuclear fissions and nuclear chain-reactions The formula above shows: • a nuclear reaction releases a great amount of energy: almost 200 millions of eV (electronvolts): hundreds of millions more than a chemical reaction • each of the neutrons ejected may hit nearby nuclides triggering new fission events → nuclear chain reactionreleasing a great amount of energy in a continuous way • the trouble is that a nuclear chain reaction also releases dangerous radioactive decay of fission fragments radiation { energy in the form of radiation: gamma rays and neutrinos

10. The macrophysics of nuclear reactors The difficult challenge of nuclear engineering is the management of produce great amounts of energy in a continuous way nuclear plants able to{ avoid any release of radiation outside the plants This is very difficult since the optimal equilibrium is extremely unstable: the analysis focuses on the dynamics of a population of free neutrons N that reproduces itself according to the “effective neutron multiplication factor” k=Nt+1/Nt expresses the average number of neutrons released by one fission that bring about another fission

11. The dynamics of the core (discrete time) we can express the dynamics of Nt: Nt = kNt-1 + N’( 2 ) whereN’ (exogenous flow of neutrons) is assumed constant and k is the effective multiplication factor and plays a crucial role: when k<1, the system is subcriticaland cannot sustain a chain reaction: → the system is stable but the energy released rapidly fades away → the equilibrium number of free neutrons N* is given by: N*=N’/(1-k),( 3 ) where 1/(1-k) may be defined as the” multiplier” of exogenous neutrons that determines the equilibrium population of neutrons

12. The criticality of a nuclear reactor when k>1 the system is supercritical: the chain reaction increases exponentially the number of fissionsand thus also the population of neutrons → this progressively amplifies the energy released in a growingly uncontrollable way The chain reaction may be exploited for a sustainable production of energy only in the borderline case: whenk=1the system is critical:the number of free neutrons remains constant in astationary process of energy release The only useful state of the core is thus a structurally unstable bifurcation path

13. Graphical representation The dynamic behaviour of the reactor’s core under the three different hypotheses mentioned above may be represented in a simplified way as in the graphs 1a,b,c we measure on the ordinates axis Nt+1 and on the abscissa axis Nt the equation ( 2 ) has a slope that depends on k, while the locus of possible equilibrium values (stationary since the exogenous neutron generation rate N’ is constant) is represented by the line at 45 degrees (where Nt+1=Nt)

14. Nt+1 Nt+1 Nt+1 N* Nt Nt Nt Fig.1: The dynamic regimes of a nuclear reactor a) subcritical case: k<1 b) critical case: k=1 c) supercritical case: k>1

15. The dynamics of the core (discrete time) The subcritical case in fig.1a is characterized by a stable equilibrium N* that is a function of the rate of exogenous generation of neutrons N’: N* = N’/(1-k)( 3 ) The supercritical case represented in fig.1b has no realizable equilibrium while the population of free neutrons grows exponentially In the critical case there is no equilibrium (while it is indeterminate in the extreme case N’=0) the critical case is a singularity that is structurally unstable (in the sense of Andronov): an infinitesimal perturbation of k is sufficient to transform the system in supercritical or subcritical → oscillations around the critical state

16. The determinants of k The fine tuning of k is very difficult since the physical processes underlying the aggregate value of k are probabilistic and are subject to complex dynamics The parameter k depends on the following factors: k = Pi Pfη - Pa - Pe( 4 ) where Piis the probability that a particular neutron strikes a fuel nucleus Pf is the probability that the stroked nucleus undergoes a fission ηis the average number of neutrons ejected from a fission event (it is between 2 and 3 for the typical fuel utilized in nuclear plants: 235U and 39Pu) Paisthe probability of absorption by a nucleus of the reactor not belonging to the fuel Peis the probability of escape from the reactor’s core. In other words, the product of the first three variables measures the strength of the fission chain reaction, and thus of the energy release, while the probability of absorption and escape measure the average leakage from the system

17. Fluctuations of k and their regulation In consequence of the probabilistic nature of its underlying process, k necessarily fluctuates off its critical (desired) value: “the system is never in equilibrium” K < 1→ the efficiency in energy generation declines, K > 1→ exponential increase in energy generation in the form of heath and radiation: this may easily jeopardize the safety of the reactor → a nuclear reactor requires reliable regulation mechanisms that keep the average fluctuations of k at the critical value while containing their amplitude

18. Active regulation The crucial active regulation instrument is given by the “control rods”: a small shift of the control rod inward or outward the reactor core produces a swift change in the number of fission events Control rods are good enough for routine howeverthe criticality of the dynamic process implies that the reaction to unexpected contingencies may trigger a sequence of events that make the reactor uncontrollable e.g.the accident occurred at the Chernobyl Nuclear Power Plant: a system test meant to improve safety led to a rupture of the reactor vessel and a series of explosions that destroyed reactor 4

19. Self-regulation: passive safety mechanisms high probability of regulation mistakes under unexpected events: →passive safety mechanisms, i.e. independent of human decisions a crucial mechanism of self-regulation is provided by the moderator: most moderators become less effective with increasing temperature → if the reactor overheats the chain reaction tends to slow down e.g. regular water, that is used as moderator in the majority of reactors, starts to boil sizably reducing the effective multiplier however self-regulation may fail: e.g. there may be anunexpected leakage of water or steam or a failure of the system to pump new water into the reactoras in the case of Fukushima1

20. “redundant” passive security mechanisms in case of failure of a mechanism the same role may be played by another one redundancywould increase safety iff failure probability of passive mechanisms were independent; unfortunately their failure probabilities may be not independent in consequence of a major shock Fukushima1, e.g., endured the earthquake in March 2011 but had its power and back-up generators knocked out by a 7- meter tsunami lacking electricityto pump waterneeded to cool the core, engineers vented radioactive steam into the atmosphere to release pressure, leading to a series of explosions that blew out concrete walls around the reactors back-up diesel generatorsthat might have averted the disaster were positioned in a basement, where they weresubmerged by sea water

21. Major incidents Major nuclear incident =defone that either resulted in loss of human life or more than US$50,000 of property damage (def by the US federal government) More than 100 major nuclear power plant accidents have been recorded since 1952, totalling more than US$21 billion in property damages Nuclear industry claims that new technology and improved oversight made nuclear plants much safer, but57 major accidents occurred since 1986 It was claimed that these accidents occurred in badly managed old-fashioned nuclear plants as in Chernobyl (1986); however two thirds of these accidents occurred in the US and the worst of all, the Fukushima1 disaster, in the technologically advanced Japan

22. After Fukushima1 The French Atomic Energy Agency (CEA) admitted that technical innovation cannot eliminate the risk of human errors in nuclear plant operation An interdisciplinary team from MIT estimated that, given the expected growth of nuclear power from 2005 – 2055, at least four serious nuclear power accidents would be expected in this period:Fukushima1 is only the first After Fukushima deep and extensive revision of energy policy: -many countries stopped construction of new plants including Germany, Italy, Switzerland and France -all the other countries are revising and severely downsizing the programs of construction of new plants including Japan,USA and the UK Although the disruptions provoked by the Great Recession are not inferior, the financial system and regulation policies did not undergo a similar process of radical revision

23. Arguments pro nuclear energy Taking account of the high risks intrinsic in the production of nuclear energy we may wonder why it has been developed so much and risks to be further developed a) clean: GHGs emissions as renewables arguments: relatively {b) cheap: less than renewables c) safe: less casualties and radiation than with fossil fuels Counter-arguments: a) estimates that take account of the entire life cycle of a nuclear plant, including its construction, its decommissioning, and waste disposal, find a much higher average level of GHGs emissions in between renewables and fossil sources (see, e.g., the meta-study by Sovacool, 2010)

24. Arguments against nuclear energy b) the favourable cost estimates are criticized for not taking full account of - the entire life cycle of the plant - the scarcity of the fuel similar to that of oil - the external diseconomies - the crucial role of an arbitrary high rate of discount c) the belief in nuclear safety underestimates the number of casualties brought about by nuclear energy because: -Accidents under-reported -Difficult to establish the probabilistic cause-effect nexus even in the short run -It does not take into account the long-run effects of radiation on human health

26. 2° Part The Complex dynamics of financial systems

27. The Complex dynamics of a monetary economy I want to show that a monetary economy is characterized by a complex dynamics that shows deep analogies with that of a nuclear reactor, although the complex dynamics of a sophisticated monetary economy is more elusive as it is characterized by a plurality of interacting criticalities However, the complex dynamics of a nuclear reactor and its crucial criticality is fully recognized by nuclear physics and nuclear plants engineering on the contrary, the complex dynamics of the financial system is generally ignored, even denied, by mainstream economics and finance In both cases the issue of control of complex dynamics is taken lightheartedly and the risks originating from week, late or mismanaged control of critical processes are greatly underestimated

28. Nuclear and economic chain reactions In a nuclear reactor the chain reaction is based on the alternation between free neutrons N hitting nearby nuclides, fission of nuclides F hit by free neutrons, and free neutrons N’ejected from the hit nuclides N-F-N’… in a monetary economy the chain reaction is based on the alternation between flows of commodities sold C, flows of money M from the buyer to the seller, and flows of commodities C’ bought with the money received C-M-C’…

29. The income-expenditure view From the point of view of economic units the economic chain reaction translates in the alternation of income flows yit received e.g. by a certain unit m from other units and expenditure flows eit financed by previous income flows: ymt –emt –ynt – ent – yqt … we get a chain reaction whose “strength” is given by cit = eit+1 / yit where c may be interpreted as the marginal propensity to spend (consume) from flows of income (with a time lag)

30. The aggregate real system: the multiplier taking account of exogenous expenditure e’ we may easily derive from the only constraint of alternation of income and expenditure in a money economy the Kahn-Keynes “multiplier”model (Kahn, 1931 and Keynes, 1936; derivation in Sordi-Vercelli, 2005 and 2012) the cumulative effects of this alternation triggered by an impulse e’ representing the exogenous expenditure converge towards: y* = e’/(1- c) where c is the propensity to consume and m = 1/(1- c) isthe so calledKahn-Keynes“income multiplier”

31. The multiplier as subcritical dynamics In the Kahn-Keynes multiplier y* = e’/(1- c) c plays the same role of the “effective multiplication factor” k in the equations describing the dynamic behaviour of a nuclear reactor: N*= N’/(1-k) the propagation process is dynamically stable sincec < 1 The analogy with the subcritical caseof a nuclear chain reactoris strikingasthe propagation process has a similar dynamic structure (see fig.2a) (Leo Szilard was probably influenced by the income multiplier)

32. The subcritical case and the role of saving In this simple model of income generation the stability of the real system is assured by a positive saving rate: normal case However, in the last decades the saving rate greatly diminished in developed countries progressively pushing the real economic system towards a critical regime, so reducing its stability In a few countries, and most notably in the US, the saving rate became slightly negative just before the outbreak of the subprime crisis in 2007 The stabilizing role played by the saving rate crucially depends on the simplifying assumption that all the investment is exogenous however, this assumption restricts the validity of the model to the short period as capital accumulation is ignored Taking capital accumulation into account the plausibility of a critical and supercritical regimes increases

33. Et+1 Et+1 Et+1 Y* Yt Yt Yt Fig.2 Dynamic regimes of a monetary economy a) subcritical case: c<1 b) critical case: c=1c)supercritical case: c>1

34. The acceleration principle As soon as we consider the impact of endogenous investment on the income-expenditure chain reaction, the potential instability of the process becomes evident, as first pointed out by Harrod (1939) Theendogenous investment Itis assumed to be given by the “acceleration principle”: it depends on the change of income according to a proportionality factor v generally called capital coefficient: It = v(Yt – Yt-1) The “chain reaction” brought about by the interaction between multiplier and accelerator is an unstable path that we may assimilate to the critical path of a nuclear reactor

35. The multiplier-accelerator model When It=Stthe aggregate expenditure Etis equal to the aggregate income in the previous period Yt-1 and the system operates under a critical regime under these conditions the economic system is characterized by what Harrod called a warranted rate of growth g=s/v; from the assumption of criticality: v(Yt – Yt-1) = sYt from which we derive immediately : (Yt – Yt-1) / Yt = s/v this steady state is a“critical process” or a razor’s edge (see fig 2b): a further increase of expenditure over income, however small, would render the system supercritical determining an unsustainable rate of growth (see fig 2c): however, in this case the real system would soon impact on the full employment barrier bouncing back towards a subcritical regime: self-regulation at a cost

36. The role of credit The instability of the economy crucially depends on the financial side of the income-expenditure process: in a modern monetary economy, an excess of endogenous investment over saving in a given period is made possible by the credit system A persisting excess of investment over saving or, more in general, of expenditure over income has to be financed through borrowing → to understand the intrinsic criticality of contemporary financialized economies we have thus to focus on the financial side of transactions and economic decisions

37. The credit multiplier The first monetary chain reaction that has been explored in the economics literature is rooted in thealternation between credit and bank deposits: additional credit translates in additional bank deposits that justify the concession of further credit and so on According to the monetarists, this process explains the money supply M as determined by the monetary base B believed to be under the control of monetary authorities The credit multiplier may be expressed in the following way: M = B(1 + γ)/(α+β+γ) where α is the legal reserve ratio β the excess reserves ratio γ the currency drain ratio when α+β=1the system does not multiply (no chain-reaction): 100% reserve system when α+β<1 the system is subcritical and the credit multiplier has a finite value According to the evidence produced by Koo (2011) the system is currently in a critical state, sometimes even supercritical

38. Credit multiplier and financial chain reaction The nexus between the credit multiplier and financial crises has been emphasized since long For example Friedman and Schwartz observed that “a liquidity crisis in a unit fractional reserve banking system is precisely the kind of event that triggers -and often has triggered- a chain reaction. And economic collapse often has the character of a cumulative process. Let it go beyond a certain point, and it will tend for a time to gain strength from its own development as its effects spread and return to intensify the process of collapse” (Friedman and Schwartz 1963: p.419) In a fractional-reserve banking system, in the event of a bank run, the demand depositors and note holders would attempt to withdraw more money than the bank has in reserves, causing the bank to suffer a liquidity crisis and, ultimately, to default

39. Critique to exogeneous money supply (1) The monetarist belief that money supply is exogenous and controllable fell in disrepute since the early 1980s: It requires a constant velocity of money or at least its independence of the business cycle, while the empirical evidence suggests that these validity conditions are false: the velocity of circulation is quite volatile and strongly pro-cyclical Goodhart, e.g., wrote that the money multiplier model is 'such an incomplete way of describing the process of the determination of the stock of money that it amounts to misinstruction‘ (Goodhart 1984, p.188) and that ‘almost all those who have worked in a [central bank] believe that this view is totally mistaken; in particular, it ignores the implications of several of the crucial institutional features of a modern commercial banking system....’ (Goodhart, 1994, p.1424)

40. Money and the monetary base:money supply is endogenous Source: [Notes on Mishkin Ch.14 - P.18]

41. The money multiplier is endogenous

42. Critique to exogeneous money supply (2) The credit multiplier has been rejected in particular by the advocates of an endogenous money theory advanced since long and subscribed among others by Schumpeter and later many post-Keynesians (in particular Basil Moore) Endogenous money theory states that the supply of money is credit-driven and determined endogenously by the demand for bank loans, rather than exogenously by monetary authorities In this case the analogy with nuclear reactor’s instability is even stronger The trouble with criticality is that, even in the absence of significant external shocks, a small change from within the system may be sufficient to trigger an unstable chain reaction (e.g. stability destabilizing in Minsky)

43. The liquidity criticality (1) financial inflowyt In a given period t, each economic unit is characterized by a { financial outflowet The ratio: k=et/yt that I call liquidity ratio is a significant index of a unit’s current financial conditions as it affects both its liquidity and solvency (see Vercelli, 2011) It is also a financial multiplication factor (the analogous of c in the multiplier): also in this case the critical state is the only one sustainable in the long run, while a deviation from it tends to increase up to a threshold its value may be higher than unity and may persist in such a state for a relatively long time →in this case the financial system is supercritical: a supercritical financial process is often called a “bubble”

44. The liquidity criticality (2) A supercritical process is made possible by credit: creates inflows ex nihilo for the borrower in the expectation that its consequent increase in outflows will generate in the future higher inflows that will permit the repayment of debt with an interest the increase in the extant credit of the private sector typically happens in the period of vigorous expansion of the economy when the euphoria of the agents leads them to seek a higher leverage When the ensuing financial bubble(s) burst(s) the system becomes suddenly subcritical in order to reduce the leverage in this simple formalization the critical path may be identified with Minsky’s period of tranquillity when the system is characterized by stationary expectations (see Sordi and Vercelli, 2011)

45. The liquidity criticality A simple way to explain this sudden change is to assume that during the expansion and the boom the units adopt extrapolative expectations while as soon as the crisis is triggered and during the period of depression the expectations are regressive From: Sordi, S. and A.Vercelli, Heterogeneous expectations and strong uncertainty in a Minskyian model of financial fluctuations, 2010, DEPFID Discussion Paper, forthcoming in JEBO

46. The solvency criticality In order to understand the sudden switch from a supercritical dynamics to subcritical dynamics and vice versa, we have to introduce asecond source of criticality that interacts with the first one The current value of the multiplying factor affects its expected values the sum of which determines the solvency of the economic unit: where r is the discount factor and k* is the solvency ratio When k* < 1 the unit has a positive net worth and is solvent; k* = 1 is the critical value beyond which the unit becomes insolvent since its net worth is negative and is going to be bankrupt unless it is very rapidly bailed out To avoid this fate, the economic units have a desired value of the insolvency ratio k* = 1 – μ sufficiently far from the critical value to withstand unexpected contingencies

47. Financial instability hypothesis: a model We are now in a position to restate the core of the FIH with the aid of a simple model interaction between the liquidity ratio and the solvency ratio (cash-flow approach), ( 1 ) α > 0 ( 2 ) β > 0 This elementary Lotka-Volterra model is based on: Vercelli, A., A perspective on Minsky moments: Revisiting the Core of the Financial Instability Hypothesis, in Review of Political Economy, vol.23(1), 2011, pp.49-67

48. Definition of Minsky moment and Minsky process This Lotka-Volterra model produces clockwise cycles that have properties very similar to those described by Minsky in the FIH kt 2 3 5 A B 1 ω A Minsky moment A-B Minsky process 1 4 6 1-μ 1 k*t

49. Financial fluctuations: dynamic and structural instability kt P 1 ω ω’ k*t 1-μt 1-μt’ 1

50. Sequence of financial cycles (→long cycle) The degree of instability and fragility reached in the final stage of a financial cycle depends on the characteristics of preceding cycles gravity and length of the last crisis Tends to grow in proportion to { time distance from the last great crisis The average safety margin tends to grow progressively: germs of a successive “great crisis”: In the last century long financial cycles of about 30 years: trough-to-trough: 1930-1950, 1950-1982, 1982- 2010?