Friends, Romans, countrymen, lend me your ears;
I come to bury Caesar, not to praise him.
The evil that men do lives after them;
The good is oft interred with their bones;
So let it be with Caesar. (Marc Antony’s funeral oration in Shakespeare’s Julius Caesar, Act III, Scene II)
Introduction
As aficionados of Shakespeare know, Marc Antony’s speech was ironic: his aim really was to praise Caesar. My intention, however, really is burial: the multiplier-accelerator model of business cycles really does need to be buried, as an “evil that men do” which should not have lived on even during the lives of the Caesars of economics who gave birth to it—specifically, Alvin Hansen, Paul Samuelson (Samuelson 1939; Samuelson 1939) and John Hicks (Hicks 1949; Hicks 1950). We should instead resurrect in its place the “Growth Cycle” model of one of the neglected greats of economics, Richard M. Goodwin (Goodwin 1966; Goodwin 1967). Difference equation methods, which are integral to the multiplier-accelerator model and which still dominate economic modelling, should also give way to differential equations and system dynamics. In making this argument, I showcase Goodwin’s model and extensions of it in the Open Source system dynamics program Minsky.
Zombienomics: the undead Multiplier-Accelerator model should die
The Australian economist John Quiggin coined the term Zombie Economics to characterize ideas that should have died out in economics, but nonetheless persist (Quiggin 2010). Most of Quiggin’s nominations of Zombie economic ideas were the application of faulty economic theories (such as the “Efficient Markets Hypothesis”) to economic policy (such as the deregulation of finance markets). The multiplier-accelerator model has not led to specific policies. However, it has helped to mislead economists about the manner in which economic dynamics should be practised, and in so doing it has possibly caused as much harm as any specific misguided economic policy.
The continuing citations of the source articles by Samuelson (Samuelson 1939; Samuelson 1939)—64 citations for “Synthesis” and 356 for “Interactions”, according to the Web of Science database, with the latter paper clearly undergoing a unfortunate revival in popularity since the start of the millennium—are proof that the Multiplier-Accelerator model still walks amongst us is (see Figure 1).
Figure 1: Citations over time of “Interactions between the multiplier analysis and the principle of acceleration”
Equally significant is the model’s presence as Chapter 11 in Quantitative Economics with Python (Sargent and Stachurski 2020), an Open Source online textbook co-authored by the “Nobel” Prize-winning economist , Thomas Sargent. The multiplier-accelerator model does not play a significant role in modern economics in general, or DSGE modelling in particular, but it is indicative of the poor attention to realism, and obsession with faux and dated analytic techniques, that Paul Romer (another recipient of what I prefer to call the “Faubel Prize in Economics”) (Mirowski 2020) rightly savages in his brilliant but unfortunately unpublished monograph “The Trouble with Macroeconomics” (Romer 2016).
Much of the equilibrium-fixated methodology and pedagogy that our book hopes to replace with system dynamics methods and training originate in the teaching materials written and seminars run by Sargent and his followers. As well as being dominated by equilibrium methods, the fundamental mathematical techniques in both Quantitative Economics with Python and its “advanced” companion Advanced Quantitative Economics with Python (Sargent and Stachurski 2020) are restricted to difference equations, rather than differential equations. In fact, differential equations are not mentioned at all in the “Advanced” text, and are noted just once, in passing, in Quantitative Economics with Python, when complex numbers are discussed. The mention is in relation to the use of complex numbers in determining the properties of the multiplier-accelerator model:
“Useful and interesting in its own right, these concepts reap substantial rewards when studying dynamics generated by linear difference equations or linear differential equations. For example, these tools are keys to understanding outcomes attained by Paul Samuelson (1939) [93] in his classic paper on interactions between the investment accelerator and the Keynesian consumption function, our topic in the lecture Samuelson Multiplier Accelerator.” (Sargent and Stachurski 2020, p. 47).
Samuelson’s paper was indeed a classic: a classic mistake, which should finally be laid to rest. Sargent and Stachurski set out the model’s derivation as follows:
“The model combines the consumption function
with the investment accelerator
and the national income identity
• The parameter 𝑎
is peoples’ marginal propensity to consume out of income…
• The parameter > 0 is the investment accelerator coefficient…
Equations (1), (2), and (3) imply the following second-order linear difference equation for national income:
”
(Sargent and Stachurski 2020, p. 189)
To analyze the model, they set 𝐺𝑡 and 𝛾 to zero, and apply the method of characteristic equations, which converts the difference equation:
into the quadratic:
The roots of this quadratic are:
These roots generate several different classes of behaviour—damped oscillations, explosive growth, explosive oscillations, explosive growth—depending on the magnitudes of its parameters. But these are meaningless characteristics of a meaningless model, as can easily be shown using a more sophisticated mathematical technique, of converting a high order scalar difference equation to a system of first order vector difference equations.
In general, to convert an nth order difference equation to a set of first order equations, you define a vector whose components are:
The model can now be restated using a matrix of coefficients:
The advantage of this technique over the characteristic equation approach is that it imposes a check on the validity of a model, before a characteristic equation is derived: for a model to be valid, the determinant of , where I is the identity matrix, must be zero. If it is not, then the model’s equilibrium is zero. If we consider an equilibrium vector , then it must be true that:
If then cannot be inverted, and can have non-trivial values. If then can be inverted, and the only solution is “the trivial solution”, and therefore there is something wrong with the model: it is asking a question whose only general answer is “zero”.
The matrix form of the multiplier-accelerator model is shown in Equation :
This fails the non-trivial solution test:
Therefore, there must be something wrong with derivation of the multiplier-accelerator model itself.
There are in fact at least two things wrong, the most serious of which is the mis-specification of actual investment in Equation . The national income identity describes the sum of actual consumption and actual investment (and actual government spending , the last of which is omitted in the analysis). Actual investment is defined as the change in the capital stock, and in a discrete-time model investment in time is added to capital stock at time to create the capital stock for period +1:
If we want to relate this to the term in Equation , which fundamentally defines desired investment rather than actual investment, then we need to relate the capital stock to output . The simplest way to do this is to presume a linear capital to output ratio 
, so that:
To instead use Equation as the expression for investment in year t, as is done in the “multiplier-accelerator model”, the following equation must hold:
The only way this can be guaranteed to hold for any non-zero values of , are that ; the only way to guarantee that it holds for non-zero values (when in general ) are that . This is the primary reason why this model only has the trivial solution: it is asking the question “under what conditions can actual investment be guaranteed to equal desired investment, when both are different linear functions of change in output between different years?”. The answer is “when output is zero, and therefore when investment never occurs”. Clearly, this is not the basis on which to erect a model of cycles!
The other problem with the “model” is its treatment of time, which is an unavoidable consequence of the discrete-time formulation of the model. The definition of Consumption in Equation , relates it to the last time period’s income . This would be valid if the time period was of the order of a week to a month: it is reasonable to assume that aggregate consumption is a function of the previous week to month’s income, given that the vast majority of consumers are wage-earners living from paycheck to paycheck. But with a time-dimension measured in weeks or months, the relation for investment makes no sense: investment has a time horizon of years, not months—let alone weeks. Since investment is the driving factor in this “model”, its time dimension must dominate, in which case it makes no sense to relate consumption to last year’s income: it should be treated as related to this year’s income instead:
If we combine this reasonable postulate for consumption in a discrete-time model with the definition of actual investment in Equation via the truncated national income identity 
(ignoring for simplicity), we get
This is a first-order growth relationship, not a model of cycles.
If economics even remotely resembled a science, it would consign the multiplier-accelerator model to its rubbish heap. Since it is not, I have zero faith that this “model” will be abandoned: economists will continue teaching it, regardless of the fact that it has rotten foundations. True progress in dynamics will only come from those outside the mainstream paradigm, and in disciplines like system dynamics. In the remainder of this chapter I want to alert genuine practitioners of dynamics to the existence of a model that has impeccable foundations, which can be used as the basis for well-grounded structural models of capitalism, but which—predictably—has been ignored by mainstream economists. This is Richard Goodwin’s “Growth cycle” model (Goodwin 1967). Unlike the “multiplier-accelerator model”, this model is mathematically valid (the proof is left as an exercise for the reader!), and as such it can be used as the foundation for more realistic models.
Goodwin’s Growth Cycle model and the Keen-Minsky extension
In contrast to the prominence and fawning treatment given to Samuelson’s model, Goodwin’s model was published only in a single-page precis to a supplementary (conference proceedings) volume of the leading mainstream journal Econometrica (Goodwin 1966), as a brief chapter in an edited book (Goodwin 1967), and as a chapter in a book of Goodwin’s collected essays (Goodwin 1982). The Web of Science database records zero citations of this paper in any form. This is of course wrong—I have personally cited it in numerous times, as has Grasselli (Grasselli and Costa Lima 2012; Grasselli and Maheshwari 2017) and several other authors (Landesmann, Goodwin et al. 1994; Harvie, Kelmanson et al. 2007; Flaschel 2015; Giraud and Grasselli 2019)—but it indicates the risible lack of attention paid to this model compared to Samuelson’s.
Goodwin developed his model as a way of expressing Marx’s unexpected cyclical model of growth in Capital I, Chapter 25:
Or, on the other hand, accumulation slackens in consequence of the rise in the price of labour, because the stimulus of gain is blunted. The rate of accumulation lessens; but with its lessening, the primary cause of that lessening vanishes, i.e., the disproportion between capital and exploitable labour power. The mechanism of the process of capitalist production removes the very obstacles that it temporarily creates. The price of labour falls again to a level corresponding with the needs of the self-expansion of capital, whether the level be below, the same as, or above the one which was normal before the rise of wages took place. (Marx 1867, p. 437)
While its origins in Marx may put some readers off, far from being based on any necessarily “Marxist” vision of capitalism, and in contrast to the logically false “multiplier-accelerator model”, Goodwin’s growth cycle can be derived from the impeccable foundations of uncontestably true macroeconomic definitions. We start from the definitions of the employment rate , which is the ratio of the number of people with a job to the total population ; and the wages share of GDP , which is the total wage bill divided by GDP :
Simple calculus turns these static definitions into dynamic statements that are also true by definition: “the employment ratio will rise if employment grows faster than population”; and “the wages share of GDP will grow if wages grow faster than GDP”. Using for , these statements are:
These dynamic definitions can be turned into a model via one more definition, and a set of genuinely simplifying assumptions. We define the ratio of output to labour ; we assume a constant capital to output ratio ; we assume all profits are invested, so that gross investment equals profits (this simplifying assumption is relaxed in the subsequent model); depreciation occurs at a constant rate ; a uniform real wage applies; there is a linear relationship between the employment rate and the rate of change of real wages; and both the output to labour ratio and population grow at the exogenously given rates and respectively. We also define the profit share of output and the gross investment to output ratio :
These assumptions let us expand out the rates of change expressions for and (the rate of change of is by assumption):
Feeding these into Equation gives us the basic Goodwin model:
This model generates both growth and cycles, as the title of Goodwin’s paper states. Figure 2 illustrates the basic dynamics of this model in the Open Source system dynamics program Minsky (which can be downloaded from https://sourceforge.net/projects/minsky/).
Figure 2: The basic Goodwin model in Minsky
This is using a system dynamics program to express a set of differential equations. Precisely the same dynamics can be shown by using Minsky in the traditional causal diagram approach of system dynamics:
InvestmentàRate of change of CapitalàOutputàEmploymentàRate of change of the wageàWagesàProfitàInvestment
In this method, the employment rate and wages share of GDP become calculated variables, while the capital stock , wage rate , output to labor ratio and population are defined by integral blocks—see Figure 3.
Figure 3: Goodwin’s growth cycle model as a flowchart
I used Goodwin’s model as the foundation for my model of Minsky’s Financial Instability Hypothesis (Keen 1995), taking my lead from Blatt’s observation that Goodwin’s model was remarkably successful “Considering the extreme crudity of some of the assumptions underlying this model”, and that its main weakness of “an equilibrium which is not unstable (it is neutral) … can be remedied [by the] introduction of a financial sector, including money and credit as well as some index of business confidence” (Blatt 1983, p. 210).
Minsky thought of the economy in historical rather than merely logical time, with history determining current expectations, and with feedbacks from current conditions changing both the economy and expectations over a cycle:
The natural starting place for analyzing the relation between debt and income is to take an economy with a cyclical past that is now doing well. The inherited debt reflects the history of the economy, which includes a period in the not too distant past in which the economy did not do well. Acceptable liability structures are based upon some margin of safety so that expected cash flows, even in periods when the economy is not doing well, will cover contractual debt payments. As the period over which the economy does well lengthens, two things become evident in board rooms. Existing debts are easily validated and units that were heavily in debt prospered; it paid to lever… (Minsky 1977, p. 10)
A period of tranquil growth thus leads to rising expectations, and a tendency to increase leverage. As Minsky put it in his most famous sentence:
Stability ‒ or tranquility ‒ in a world with a cyclical past and capitalist financial institutions is destabilizing. (Minsky 1977, p. 10).
Minsky’s basic vision was clearly tailor-made for dynamic modelling, but he failed to do this himself, primarily because he chose a poor foundation for it—specifically, Samuelson’s multiplier-accelerator model! (Minsky 1957). I used the far better foundation of Goodwin’s model, and extended it to consider financial dynamics by:
- Redefining profit to be net of interest payments as well as of wages; and
- Introducing a nonlinear investment function based on the rate of profit.
As with Goodwin, a Minsky model can be derived directly from macroeconomic definitions, once it is accepted that banks create money when they create loans (McLeay, Radia et al. 2014), and that that newly created money adds to aggregate demand and income (Keen 2015). We then add the definition of to our fundamental macroeconomic identities, where D is the level of private debt.
The simplest assumption for the causal process behind change in debt is that new debt is used to finance investment in excess of profits—something which has been empirically confirmed by, of all people, Eugene Fama (Fama and French 1999), one of the main promulgators of the Efficient Markets Hypothesis (Fama 1970; Fama and French 2004). Profits are now net of interest payments on debt as well as of wages, while investment is a linear function of the rate of profit:
As with the wages share and the employment rate, the definition of the debt ratio is easily turned into a dynamic statement that “the debt ratio will rise if debt grows faster than GDP”:
We already have from Equation , so only needs to be derived:
Substituting this into Equation yields:
This gives us a 3-dimensional model:
As Li and Yorke proved almost half a century ago, “Period Three Implies Chaos” (Li and Yorke 1975), and that is what this model manifests. There are two meaningful equilibria, a “good equilibrium” with a positive employment rate, wages share of GDP, and a finite debt to GDP ratio, and a “bad equilibrium” (Grasselli and Costa Lima 2012, p. 208) with a zero rate of employment and wages share of GDP and an infinite debt ratio, The former equilibrium is stable for low values of the slope of the investment function, with one negative and two complex eigenvalues with zero real part. However, as the slope of the investment function steepens, the two complex eigenvalues develop a positive real part, and “good equilibrium” becomes unstable—but remains an attractor for the early part of the model’s trajectory. The model then demonstrates the chaotic behavior first observed in fluid dynamics and described as the “intermittent route to chaos” by Pomeau and Manneville (Pomeau and Manneville 1980): cycles diminish for a while, only to rise later on—see Figure 4.
Figure 4: The basic Minsky cycle, modelled in Minsky
When I first developed this model (in August of 1992), I saw its characteristic of diminishing and then rising cycles as its most striking feature. This was not a prediction of Minsky’s verbal model: though he expected a set of cycles before an ultimate one that would lead to a debt-deflationary crisis like the Great Depression—in the absence of “big government” (Minsky 1982, p. xxix)— he made no claim that the cycles themselves would get smaller before the crisis. Nor was it a feature of the economic data at that time. This coincidence inspired what I thought at the time was the rhetorical flourish with which that paper concluded:
From the perspective of economic theory and policy, this vision of a capitalist economy with finance requires us to go beyond that habit of mind that Keynes described so well, the excessive reliance on the (stable) recent past as a guide to the future. The chaotic dynamics explored in this paper should warn us against accepting a period of relative tranquility in a capitalist economy as anything other than a lull before the storm. (Keen 1995, p. 634)
Then reality imitated the model: there was indeed a period of diminishing cycles in the employment rate, growth rate and inflation rate, which Neoclassical economists dubbed “The Great Moderation”, and for which they took the credit (Stock and Watson 2002; Bernanke 2004; Srinivasan 2008). Then there was a crisis, which Neoclassical economists dubbed “The Great Recession”, and which they blamed on exogenous shocks (Ireland 2011).
In contrast, rather that requiring two independent explanations for real world phenomena, this simple model captures the essential features of recent economic data—including the rise in the private debt ratio, and the fall in workers’ share of GDP (see Figure 5)—in one inherently nonlinear system.
Figure 5: Reality imitates the Keen-Minsky model
This extremely simple and well-grounded model clearly provides a better foundation for dynamics than the equilibrium-fixated, difference equation models that dominate Neoclassical macroeconomics today. That will not stop Neoclassicals persisting with DSGE modelling, but the unreasonable effectiveness of these simple models should encourage critics and student rebels to ignore the intellectual backwater of Neoclassical economics, and to develop well-grounded system dynamics models of capitalism instead.
Modelling Money, and the Coronavirus, in Minsky
Though Minsky has some obvious advantages over existing system dynamics programs—the mathematics-oriented GUI, using variables names as well as wires to build equations, the unique capacity to format text using LATEX, overloading of mathematical operators to reduce clutter, the embedding of plots in the design canvas, plots that update dynamically where parameters can be varied during a simulation, etc.—its main is its capacity to model financial dynamics using interlocking double-entry bookkeeping tables called Godley Tables. These take statements of flows between financial accounts and generate systems of differential equations that are guaranteed to be correct. It is also much easier to edit financial flows using a Godley Table than it is to edit them when they are defined using the standard system dynamics flowchart interface.
For example, Figure 6 shows the financial flows in a simple model of the reality that bank loans create deposits—the opposite of the textbook story in which banks are passive “intermediators” who lend out deposits (McLeay, Radia et al. 2014). The table simply records flows between one bank account and another, with Minsky checking that “Assets minus Liabilities minus Equity equals Zero” (the final column in the table).
Figure 6: Godley Table for a simple model of the macroeconomics of Bank Originated Money and Debt (McLeay, Radia et al. 2014)
Neither differential equations nor the customary stock and flow blocks of standard system dynamics programs appear in a Godley Table, but in the background, Minsky turns these flow entries into ODEs of the financial system that are guaranteed to be consistent. Each equation below is the sum of the relevant column in the Godley Table above:
The model is completed by defining the individual flow components using flowchart operators. Figure 7 shows a simulation run of this “Bank Originated Money and Debt” model in which flows are related to the levels of accounts via the engineering concept of time constants. The rates of lending and repayment are varied during the simulation by altering the value of the time constants for lending and repayment, using sliders that are intrinsic to every parameter in Minsky.
Figure 7: A simulation run of the Bank Originated Money and Debt model
In addition to being an excellent foundation for monetary stock-flow consistent models (Lavoie and Godley 2001; Lavoie 2014), Godley Tables can be used whenever a model has the requirement that the entities being modelled cannot be in two states at one time, so that flows between system states are exclusive: a flow must go from one state to another. In the context of the current Coronavirus crisis, they can be repurposed to model a pandemic, since the “Susceptible, Exposed, Infected, Recovered, Dead” or SIERD epidemiological models also have that requirement.
The basic SIR model of susceptibility, infection and recovery (Kermack, McKendrick et al. 1927 [1997]) can be seen as an extension of the predator-prey model, in which the consequence of predation is not death but infection. In the basic predator-prey model, an assumed exponential growth of the prey population x at a rate is reduced by a constant times , the prey population, so that . Interaction between the predator and prey is thus shown as a multiplicative relationship.
In modelling a pandemic, the population N is normally treated as a constant, since it changes far less rapidly than the epidemic spreads. The rate of change of the fraction of the population that is infected depends on the interactions of those infected I with those susceptible S, which in turn depends on the frequency of both groups in the overall population, and , and the transmissibility of the disease, which is modelled by the parameter :
Since population is treated as constant, this reduces to:
Since the increase in those infected is equal to the fall in those who are susceptible, the rate of growth of those infected is the negative of the rate of decline of those susceptible, minus the recovery rate R, which is modelled as a parameter times the number infected:
Figure 8 shows this model implemented in Minsky, using time constants rather than parameters. The Godley Table’s tabular format makes it easy to see the interrelations between the Susceptible, Infected and Recovered compartments. Flowchart tools are only needed to define the flows themselves (and future versions will allow these to be defined off the canvas, using standard LATEX equation notation).
Figure 8: Simple SIR model of a pandemic
The Godley Table interface also makes it very easy to extend this model to a more realistic situation in which there is a more complicated transmission chain—see Figure 9. Other comparmentalizations—such as dividing the susceptible population into the general public and medical staff, including quarantined versus non-quarantined, hospitalized versus non-hospitalized, etc.—are equally straightforward to add and define.
Figure 9: SEIRD model developed by editing Godley Table of SIR model
A 3rd order revision of the multiplier-accelerator model
I hesitate to write this section, because I wish to bury, not merely the invalid multiplier-accelerator model itself, but also the practice of using difference equations to model the economy, when continuous time system dynamics methods are so much more suitable (Keen 2006). However, it would be intellectually dishonest not to note that the multiplier-accelerator model can be saved to some degree by doing what Hansen, Samuelson and Hicks did not do: by paying proper attention to the causal process between their hypothetical equation for desired investment, and actual investment, capital stock, and output.
In this model, I use Samuelson’s (Samuelson 1939) function for desired investment, which he modelled as a lagged response to changes in consumption in the previous two years:
Here c is the desired “incremental capital to output ratio” (ICOR) (Walters 1966) and s the savings rate. I then assume that these investment plans are carried out, so that this becomes the change in capital in year , which is added to the existing stock in year to yield the capital stock in year .
Using the accelerator relation between capital and output, his results in a third order difference equation for Y:
Though I do not wish to encourage the further development of this model, it certainly has many interesting characteristics when compared to Samuelson’s invalid 2nd order model. Firstly, it is a meaningful model: the determinant of minus the first-order vector form of this equation is zero, as is required. Secondly, its characteristic equation is
This is easily factored into three components which are also easily interpreted: the first means that any sustained level of output is an equilibrium; the second root determines the growth rate, and the third creates cycles which remain smaller than and proportional to the growth rate.
Thirdly, in a very non-Neoclassical (and pro-Keynesian!) result, an increase in the savings rate causes a fall in the rate of economic growth. Also, for sustained growth to occur, c—which determines desired investment—must substantially exceed the actual ICOR. With a lower level for c or a slightly higher value for s, a non-equilibrium set of initial conditions leads to a convergence to a new, higher equilibrium level. See Figure 10 for a comparison of two simulations with slightly different savings ratios.
Figure 10: Cyclical growth in the 3rd order Multiplier-Accelerator Model, with a higher savings rate meaning lower growth
Conclusion
I fervently hope that dynamics has a better future in economics than it has had a past. But the odds are not good. We should be under no illusion that the methodology we champion will be resisted by Neoclassical economists, who have, over time, and largely unconsciously, turned equilibrium from the unfortunate compromise in methodology that Jevons, Marshall and even Walras knew it to be, into a religion about the tendencies of actual capitalism.
Almost fifty years ago, the authors of the Limits to Growth (Meadows, Randers et al. 1972) naively expected that the system dynamics methodology that Forrester had developed (Forrester 1968; Forrester 1971) and that they had applied would be welcomed by economists, as a way of escaping from the dead-end of having to pretend that equilibrium applied in order to model dynamic processes. They were unprepared for the ferocity of the attack on their methodology by Neoclassical economists, and most prominently by William Nordhaus (Nordhaus 1973; Forrester, Gilbert et al. 1974; Nordhaus, Stavins et al. 1992).
Since then, economics has, if anything, gone backwards. As the 2018 recipient of “The Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel” Paul Romer observed, in his working paper “The Trouble With Macroeconomics”, mainstream macroeconomic modelling is so divorced from reality today that it deserves to be called not merely “post-modern” but “post-real”:
Lee Smolin begins The Trouble with Physics (Smolin 2007) by noting that his career spanned the only quarter-century in the history of physics when the field made no progress on its core problems. The trouble with macroeconomics is worse. I have observed more than three decades of intellectual regress…
Macroeconomists got comfortable with the idea that fluctuations in macroeconomic aggregates are caused by imaginary shocks, instead of actions that people take, after Kydland and Prescott (1982) launched the real business cycle (RBC) model…
In response to the observation that the shocks are imaginary, a standard defense invokes Milton Friedman’s methodological assertion from unnamed authority that “the more significant the theory, the more unrealistic the assumptions (p.14).” More recently, “all models are false” seems to have become the universal hand-wave for dismissing any fact that does not conform to the model that is the current favorite. The noncommittal relationship with the truth revealed by these methodological evasions … goes so far beyond post-modern irony that it deserves its own label. I suggest “post-real.” (Romer 2016).
Critical perspectives like Romer’s from within the mainstream might give us hope, but the belief that he criticizes—that the economy can and indeed should be described as an equilibrium system occasionally disturbed by exogenous shocks—is still the majority belief within the mainstream. An example of the ferocity with which this belief is held is V.V. Chari’s defence of DSGE (“Dynamic Stochastic General Equilibrium”) models before the US Congress in 2010, after their abject failure to anticipate the “Great Recession” of 2008:
All the interesting policy questions involve understanding how people make decisions over time and how they handle uncertainty. All must deal with the effects on the whole economy. So, any interesting model must be a dynamic stochastic general equilibrium model. From this perspective, there is no other game in town… A useful aphorism in macroeconomics is: “If you have an interesting and coherent story to tell, you can tell it in a DSGE model. If you cannot, your story is incoherent.” (Chari 2010, p. 2)
From the perspective of a genuine mathematician, this is nonsense: the addiction to equilibrium modelling is the main weakness of economics, not its strength. The brilliant applied mathematician John Blatt put it this way in 1983:
In defense of this concentration on equilibrium and the neglect of true dynamics, there are two arguments:
1. Statics or (what comes to much the same thing) balanced proportional growth is much easier to handle theoretically than true dynamic phenomena. A good understanding of statics is a necessary prerequisite for the study of dynamics. We must learn to walk before we can attempt to run.
2. In any case, while no economic system is ever in strict equilibrium, the deviations from such a state are small and can be treated as comparatively minor perturbations. The equilibrium state is, so to speak, the reference state about which everything turns and toward which the system gravitates. Market prices fluctuate up and down, but there exist “natural prices” about which this fluctuation occurs, and these natural prices can be determined directly, by ignoring the fluctuations altogether and working as if strict equilibrium obtained throughout.
Such arguments did carry a great deal of conviction two hundred years ago, when the basic ideas of the science of economics were being formulated for the first time. However, it is impossible to ignore the passage of two hundred years. A baby is expected to first crawl, then walk, before running. But what if a grown-up man is still crawling? At present, the state of our dynamic economics is more akin to a crawl than to a walk, to say nothing of a run. Indeed, some may think that capitalism as a social system may disappear before its dynamics are understood by economists. (Blatt 1983, pp. 4-5. Emphasis added)
When I first read this passage, I regarded it as an excellent piece of hyperbole. Now, almost 40 years later, as capitalism itself is in intensive care thanks to Covid-19, and with signs of climate change abounding in phenomena like the unprecedented wildfires in Australia in 2019-20 (Dowdy, Ye et al. 2019), it is beginning to feel amazingly prescient. This makes the task of establishing genuinely dynamic, non-equilibrium methods in economics even more pressing, despite the near-religious defence of equilibrium modelling by mainstream economists themselves.
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