13 Whether this growth can be sustained indefinitely is another matter altogether that I do not address in this book. On that front I regard The Limits to Growth (Meadows, Randers et al. 1972) as the definitive reference.

14 Though because keynes hadn't completely escaped from the neocla.s.sical way of thinking, those concepts do occasionally occur in the General Theory, in a very muddled way as the lengthy quote from the General Theory ill.u.s.trates.

15 Blatt also provides an excellent mathematical treatment of investment under uncertainty see Chapters 12 and 13 respectively of Blatt (1983) and Boyd and Blatt (1988).

16 hicks also had savings depending upon the level of output, but output was already determined by the first equation and therefore 'we do not need to bother about inserting Income here unless we choose' (hicks 1937).

17 Total employment is the sum of the number of workers needed to produce investment output and the number needed to produce consumption output, so if labour productivities differ between the two sectors then the breakdown has to be known before total employment is determined.

18 another paper in a mainstream journal makes some similar concessions (hicks 1979).

19 only hicks could see similarities between keynes's work and this bizarre model of a one-commodity economy (bread) which had a market in which prices were set on one day (monday) that then applied for the remainder of the week, and in which there was no model of how the bakery that made the bread was actually manufactured.

20 This is false, as a simple check of the table of contents of the General Theory can confirm: Chapter 19 is ent.i.tled 'Changes in money-wages.' In it, keynes concludes that flexible wages would not eliminate the prospect of deficient aggregate demand.

21 Walras's Law is invalid in a growing economy, as I explained earlier. This section considers when it can't be applied to eliminate one market from the a.n.a.lysis even in the no-growth realm to which it does apply.

22 many neocla.s.sical macroeconomic models to this day are based on IS-Lm and have time-based equations including one for the price level in them that appear superficially dynamic. however, most of these models are solved by a.s.suming that the price level (and everything else) converges to a long-run equilibrium over the medium term, which is a travesty of proper dynamic modeling.

23 mathematicians and system dynamics pract.i.tioners would find the first of these references very strange. It gives a detailed discussion of how to solve a nonlinear model where the solution involves approximating a matrix inversion which can only derive the equilibrium for a model yet makes no mention of standard numerical techniques for simulating systems of differential equations (like the runge-kutta or Levenberg-marquardt methods), which can return the actual time path of a model rather than simply its equilibrium. It's as if economists live in a parallel universe where techniques that are commonplace in real sciences haven't been invented yet.

24 The number in square brackets refers to the page numbers of the online reprint of Frisch's paper, available at www.frisch.uio.no/Frisch_Website/ppIp.pdf.

25 as so often happens in economics, the 'founding father' responsible for this view also contemplated the alternative possibility, that fluctuations were endogenous to the economy, as Schumpeter argued at the time. however, since this was more difficult to model, he left it for others to do later: 'The idea of erratic shocks represents one very essential aspect of the impulse problem in economic cycle a.n.a.lysis, but probably it does not contain the whole explanation [...] In mathematical language one could perhaps say that one introduces here the idea of an auto-maintained oscillation [...] It would be possible to put the functioning of this whole instrument into equations under more or less simplified a.s.sumptions about the construction and functioning of the valve, etc. I even think this will be a useful task for a further a.n.a.lysis of economic oscillations, but I do not intend to take up this mathematical formulation here.' (Frisch 1933: 335). Unfortunately, his successors stuck with his easier-to-model exogenous shocks a.n.a.logy, leaving his sensible suggestion to model endogenous fluctuations to wither on the vine.

26 There's at least one phd in producing such a simulation model I hope some brave student takes that task on one day (brave because it would be a difficult task that would make him highly unpopular with neocla.s.sical economists).

27 Joan robinson, who played a leading role in the Cambridge controversies outlined in Chapter 8, coined the term 'b.a.s.t.a.r.d keynesianism' to describe the neocla.s.sical interpretation of keynes (robinson 1981).

28 Lucas was far from the only exponent of this microeconomic takeover of macroeconomics others who made a significant contribution to the microeconomic hatchet job on macroeconomics include muth, Wallace, kydland, prescott, Sargent, rapping, and latterly Smets and Woodford.

29 of course, an economy without growth hasn't existed, but Friedman extended this belief in the economy tending to full-employment equilibrium over to his model with growth, and he had the same views about the actual economy.

30 Now you know where the 'helicopter Ben' moniker that is applied to Ben Bernanke actually comes from! I would regard this as unfair to Bernanke, were it not for his fawning speech at Friedman's ninetieth birthday, noted later.

31 While inflation did ultimately fall, the policy was nowhere near as easy to implement as Friedman's a.n.a.lysis implied the Federal reserve almost always failed to achieve its targets for money growth by large margins, the relationship between monetary aggregated and inflation was far weaker than Friedman implied, and unemployment grew far more than monetarists expected it would. Central banks ultimately abandoned money growth targeting, and moved instead to the 'Taylor rule' approach of targeting short-term interest rates. See desai (1981) and kaldor (1982) for critiques of the monetarist period.

32 See www.ukagriculture.com/production_cycles/pigs_production_cycle.cfm.

33 None of these made it through to the version of rational expectations that was incorporated into models of the macroeconomy.

34 'erG.o.dic' is a frequently misunderstood term, especially within economics. It is properly defined by the Wiktionary (en.wiktionary.org/wiki/erG.o.dic), and the Wikipedia entry on erG.o.dic Theory (en.wikipedia.org/wiki/erG.o.dic_theory) makes the important point that 'For the special cla.s.s of erG.o.dic systems, the time average is the same for almost all initial points: statistically speaking, the system that evolves for a long time "forgets" its initial state.' This is not the case for complex or chaotic models, which show 'sensitive dependence on initial conditions' (see en.wikipedia.org/wiki/b.u.t.terfly_effect and en.wikipedia.org/wiki/Chaos_theory).

35 I can think of no more apt term to describe the group that led the campaign to make macroeconomics a branch of neocla.s.sical microeconomics. Certainly the neocla.s.sical att.i.tude to researchers who refused to use 'rational expectations' in their models approached the old mafia cliche of 'an offer you can't refuse': 'a.s.sume rational expectations, or your paper won't get published in a leading journal.'

36 This is based on the belief that output would be higher (and prices lower) under compet.i.tion than under monopoly, which I showed to be false in Chapter 4.

37 a rule of thumb that a.s.serts that the central bank can control inflation by increasing real interest rates roughly twice as much as any increase in inflation. See Box 10.1.

38 he noted that 'the first two equations of the model are patently false [...] The aggregate demand equation ignores the existence of investment, and relies on an intertemporal subst.i.tution effect in response to the interest rate, which is hard to detect in the data on consumers. The inflation equation implies a purely forward-looking behavior of inflation, which again appears strongly at odds with the data' (Blanchard 2009: 215).

Chapter 11.

1 The first draft of this chapter, completed in March 2000, began with the sentence 'The Internet stock market boom is the biggest speculative bubble in world history.' This was before the Nasdaq crash of 4 April 2000 when, as luck would have it, I was actually in New York on holiday, and, as one then could, observed the action on a tour of the NYSE (and later in Times Square on the giant Nasdaq screen). For the publication itself, 'is' became 'was,' since the book was sent to the typesetters in November 2000, when the Nasdaq was down 50 percent from its peak, and the bubble was clearly over.

2 Though he avoided bankruptcy thanks to loans from his wealthy sister-in-law (they were never repaid, and she forgave them in her will; Barber 1997), and selling his house to Yale in return for life tenancy.

3 Fisher's theory was first published in another work in 1907; The Theory of Interest restated this theory in a form which Fisher hoped would be more accessible than was the 1907 book.

4 Muslim societies continue with the traditional definition, and therefore prohibit with varying degrees of effectiveness any loan contract in which the lender does not share in the risk of the project.

5 'In a country, such as Great Britain, where money is lent to government at three per cent and to private people upon a good security at four and four and a half, the present legal rate, five per cent, is perhaps as proper as any' (Smith 1838 [1776]: Book II, ch. 4).

6 The best record of the famous early panics is in Charles Mackay's Extraordinary Popular Delusions and the Madness of Crowds. The chronicler of our day is Charles P. Kindleberger.

7 Of course, many of the high-flying companies of 1929 were no longer in the index in 1955, so that anyone who held on to their 1929 share portfolio took far more than twenty-five years to get their money back, and most of the shares they held were worthless.

8 Barber notes that after Fisher came into great wealth when his filing invention was taken over by the Remington Rand Corporation, he was 'eager to add to his portfolio of common stocks and placed himself in some exposed positions in order to do so. At this time, his confidence in the soundness of the American economy was complete' (Barber 1997).

9 Barber observed that among the other reasons was the fact that 'In the 1930s, his insistence on the urgency of "quick fix" solutions generated frictions between Fisher and other professional economists' (ibid.).

10 Almost 90 percent of the over 1,200 citations of Fisher in academic journals from 1956 were references to his pre-Great Depression works (Feher 1999).

11 Strictly speaking, this was supposed to be anything in which one could invest, but practically the theory was applied as if the investments were restricted to shares.

12 Since diversification reduces risk, all investments along this edge must be portfolios rather than individual shares. This concept is important in Sharpe's a.n.a.lysis of the valuation of a single investment, which I don't consider in this summary.

13 In words, this formula a.s.serts that the expected return on a share will equal the risk-free rate (P), plus 'beta' times the difference between the overall market return and the risk-free rate. Beta itself is a measure of the ratio of the variability of a given share's return to the variability of the market index, and the degree of correlation between the share's return and the market index return.

14 There are three variations on this, known as the weak, semi-strong and strong forms of the EMH.

15 As I have explained, however, to Fisher's credit, his failure led to an epiphany that resulted in him renouncing neocla.s.sical thinking, and making a major contribution to the alternative approach to economics that Minsky later developed into the Financial Instability Hypothesis.

Chapter 12.

1 Bernanke went on to rephrase debt deflation using several concepts from neocla.s.sical microeconomics including information asymmetry, the impairment of banks' role as adjudicators of the quality of debtors, and so on. He also ultimately developed a c.u.mbersome neocla.s.sical explanation for nominal wage rigidity which gave debt a role, arguing that 'nonindexation of financial contracts, and the a.s.sociated debt-deflation, might in some way have been a source of the slow adjustment of wages and other prices' (Bernanke 2000: 323). By 'nonindexation,' he meant the fact that debts are not adjusted because of inflation. This is one of many instances of Bernanke criticizing real-world practices because they don't conform to neocla.s.sical theory. In fact, the only country ever to put neocla.s.sical theory on debts into practice was Iceland with disastrous consequences when its credit bubble burst.

2 For a start, Fisher's process began with over-indebtedness, and falling a.s.set prices were one of the consequences of this.

3 There are numerous measures of the money supply, with varying definitions of each in different countries. The normal definitions start with currency; then the 'Monetary Base' or M0, which is currency plus the reserve accounts of private banks at the central bank; next is M1, which is currency plus check accounts but does not include reserve accounts; then M2, which includes M1 plus savings accounts, small (under $100,000) time deposits and individual money market deposit accounts, and finally M3 which the US Federal Reserve no longer measures, but which is still tracked by Shadowstats which includes M2 plus large time deposits and all money market funds.

4 It then grew at up to 2.2 percent per annum until October 1929 (the month of the stock market crash) and then turned sharply negative, falling at a rate of up to 6 percent per annum by October 1930. However, here it is quite likely that the Fed was being swamped by events, rather than being in control, as even Bernanke concedes was the case by 1931: 'As in the case of the United States, then, the story of the world monetary contraction can be summarized as "self-inflicted wounds" for the period through early 1931, and "forces beyond our control" for the two years that followed' (Bernanke 2000: 156).

5 'When prices are stable, one component of the cost [of holding money balances] is zero namely, the annual cost but the other component is not namely, the cost of abstinence. This suggests that, perhaps, just as inflation produces a welfare loss, deflation may produce a welfare gain. Suppose therefore that we subst.i.tute a furnace for the helicopter. Let us introduce a government which imposes a tax on all individuals and burns up the proceeds, engaging in no other functions. Let the tax be altered continuously to yield an amount that will produce a steady decline in the quant.i.ty of money at the rate of, say, 10 per cent a year' (Friedman 1969: 16; emphases added). Friedman went on to recommend a lower rate of deflation of 5 percent for expediency reasons ('The rough estimates of the preceding section indicate that that would require for the U.S. a decline in prices at the rate of at least 5 percent per year, and perhaps decidedly more' p. 46), but even this implied a rate of reduction of the money supply of 2 percent per annum the same rate that he criticized the Fed for maintaining in the late 1920s.

6 These were June 1946 till January 1949, June 1950 till December 1951, 1957/58, June 1974 till June 1975, 197982 and December 2000 till January 2001.

7 See en.wikiquote.org/wiki/H._L._Mencken.

8 The minimum fraction that banks can hold is mandated by law, but banks can hold more than this, weakening the multiplier; and the public can decide to hang on to its cash during a financial crisis, which further weakens it. Bernanke considered both these factors in his a.n.a.lysis of why the Great Depression was so prolonged: 'In fractional-reserve banking systems, the quant.i.ty of inside money (M1) is a multiple of the quant.i.ty of outside money (the monetary base) [...] the money multiplier depends on the public's preferred ratio of currency to deposits and the ratio of bank reserves to deposits [...] sharp variations in the money multiplier [...] were typically a.s.sociated with banking panics, or at least problems in the banking system, during the Depression era. For example, the money multiplier in the United States began to decline precipitously following the "first banking crisis" identified by Friedman and Schwartz, in December 1930, and fell more or less continuously until the final banking crisis in March 1933, when it stabilized. Therefore, below we interpret changes in national money stocks arising from changes in the money multiplier as being caused primarily by problems in the domestic banking system' (Bernanke 2000: 1256).

9 '[T]he reserves required to be maintained by the banking system are predetermined by the level of deposits existing two weeks earlier' (Holmes 1969: 73).

10 Such a sequence has a 1 in 4,000 chance of occurring.

11 The word 'debt' doesn't even appear in the Ireland paper, and while McKibbin and Stoeckel's model does incorporate borrowing, it plays no role in their a.n.a.lysis.

12 Samuel Johnson's aphorism, that something is 'like a dog's walking on his hind legs. It is not done well; but you are surprised to find it done at all,' is one of those phrases that was offensive in its origins since Johnson used it to deride the idea of women preaching but utterly apt in its usage today.

13 An update in February 2011 made no changes to the paper apart from adding an additional eleven works, only one of which a 1975 paper by James Tobin could even remotely be described as non-neocla.s.sical.

14 I actually posted a comment to this effect on Krugman's blog when he announced that he had decided to read Minsky and had purchased this book.

15 A paper based on the model that I described in this chapter (Keen 2011) was rejected unrefereed by both the AER and the specialist AER: Macroeconomics, before being accepted by the Journal of Economic Behavior and Organization.

Chapter 13.

1 The Revere Award recognized 'the three economists who first and most clearly antic.i.p.ated and gave public warning of the Global Financial Collapse and whose work is most likely to prevent another GFC in the future.' More than 2,500 people mainly economists cast votes for a maximum of three out of the ninety-six candidates. I was the eventual winner with 1,152 of the 5,062 votes cast; Nouriel Roubini came second with 566 votes and Dean Baker third with 495 votes. See rwer.wordpress.com/2010/05/13/keen-roubini-and-baker-win-revere-award-for-economics-2/ for full details.

2 From Steve Keen (1995), 'Finance and economic breakdown: modeling Minsky's "Financial Instability Hypothesis"', Journal of Post Keynesian Economics, 17(4): 60735. Copyright 1995 by M. E. Sharpe, Inc. Used by permission.

3 Minsky made it into the AER on one other occasion, but only as a discussant of another paper at its annual conference.

4 The base model he used, known as the Hicks-Hansen-Samuelson multiplier-accelerator model, also derived its cycles from the economic error of equating an expression for actual savings with one for desired investment. See Keen (2000: 8892).

5 This verbal model of perpetual cycles in employment and income distribution was first developed by Marx, and published in Section 1 of Chapter 25 of Volume 1 of Capital (Marx 1867). Marx finished his verbal model with the statement 'To put it mathematically: the rate of acc.u.mulation is the independent, not the dependent, variable; the rate of wages, the dependent, not the independent, variable,' and it is believed that his attempt to learn calculus late in his life was motivated by the desire to express this model in mathematical form (Marx 1983 [1881]).

6 Fama and French give empirical support for this equation, which is rather ironic given their role in promoting the empirically invalid CAPM model of finance: 'These correlations confirm the impression that debt plays a key role in accommodating year-by-year variation in investment' (Fama and French 1999: 1954). In a draft version, they stated this even more clearly: 'Debt seems to be the residual variable in financing decisions. Investment increases debt, and higher earnings tend to reduce debt.'

7 I signed a contract that year with Edward Elgar Publishers to deliver a book ent.i.tled Finance and Economic Breakdown in 2002. That long-overdue book will hopefully be available in 2013.

8 This and later reports are downloadable from www.debtdeflation.com/blogs/pre-blog-debt.w.a.tch-reports/. I ceased writing the monthly report in April 2009, in order to devote more time to fundamental research. The blog posts, however, continued.

9 The authority here is Bill Black of the University of Missouri Kansas City, who as a public servant played a major role in enforcing the law against fraudsters in the aftermath to the Savings and Loans fiasco. See Black (2005a, 2005b); Galbraith and Black (2009).

10 When I use GDP in this context I am referring to GDP as estimated by the income measure, not the production measure.

11 The federal government's fiscal stimulus also played a major role a topic I will consider in more detail in my next book.

12 A variable that is growing at 1 percent per annum will double in roughly seventy years, so a 3 percent rate of growth means that it will double roughly every twenty-three years.

13 It also partly reflects the impact of misguided neocla.s.sically inspired government policies that are trying to return to 'business as usual' by encouraging private credit growth an issue I will consider in much more detail in my next book.

14 I expect that history will judge the period from 1997 to 2009 as one continuous Ponzi scheme with two phases: the Internet Bubble and the Subprime Bubble. A term will be needed to describe the period, and this is my nomination for it.

15 Comparing the two periods is feasible, though changes in statistical standards complicate matters. On the negative side, debt data from the 1920s (derived from the US Census) are annual, whereas those data are quarterly today, so the date of changes can't be pinpointed as well for the 1920s1940s as for today. On the positive side, the measure of unemployment was far less distorted back then than it is today, after all the politically motivated ma.s.saging of definitions that has occurred since the mid-1970s to understate the level of unemployment in the OECD, and especially in the USA.

16 This is why the bankruptcy of Lehman Brothers was so disastrous: they had largely cornered the market for commercial paper, and when they went bankrupt this market collapsed meaning that many ordinary firms could not pay their workers or suppliers.

Chapter 14.

1 Discussed in Chapter 10.

2 The nominated policy failing this time would probably be the alleged deviation from the Taylor Rule after 2001 the case Taylor himself is already making (see Box 10.1).

3 Seppecher's Java-based model is accessible at p.seppecher.free.fr/jamel/.

4 And they incur essentially no costs in doing so the cost of 'producing' a dollar is much less than a dollar. This is the source of Graziani's third stricture that the system can't enable banks to exploit this opportunity for seigniorage.

5 Economists normally say 'agents' here rather than cla.s.ses given the microeconomic focus of neocla.s.sical modeling, and the pejorative a.s.sociation that cla.s.s was given by nineteenth-century politics. I use the term cla.s.ses because social cla.s.ses are an objective reality in capitalism, and because the SMD conditions, as Alan Kirman put it, suggest that 'If we are to progress further we may well be forced to theorise in terms of groups who have collectively coherent behaviour [...] Thus demand and expenditure functions if they are to be set against reality must be defined at some reasonably high level of aggregation. The idea that we should start at the level of the isolated individual is one which we may well have to abandon' (Kirman 1989: 138).

6 To register as a bank, and therefore to be able to print its own notes, 'free banking' banks still had to meet various regulatory requirements, and normally also purchase government bonds of an equivalent value to their initial printing of notes. In what follows, I'm taking these operations as given, and focusing just on the banking operations that followed incorporation.

7 My thanks to Peter Humphreys from the School of Accounting at UWS for advice on how to lay out this table in accordance with standard banking practice.

8 I have ignored interest on workers' deposit accounts simply to make the table less cluttered. They are included in my more technical description of this model in the paper 'Solving the paradox of monetary profits' (Keen 2010), which is downloadable from www.economics-ejournal.org/economics/journalarticles/2010-31.

9 See en.wikipedia.org/wiki/Time_constant for an exposition. These are normally expressed as fractions of a year so that the a.s.sumption that workers turn their accounts over twenty-six times a year means that the time constant for workers' consumption is 1/26 but to simplify the exposition I'm expressing them in times per year instead.

10 This point was disputed by early Circuitist literature, but this was an error of logic due to a confusion of stocks with flows (for a detailed exposition on this point, see Keen 2010: 1012).

11 It is just a coincidence that this equals the equilibrium amount in the firms' deposit accounts a different wage/profit share would return a different profit level.

12 A cash handout of $960 was sent to every Australian over eighteen who had a tax return for the previous year.