Emergent Macroeconomics: Deriving Minsky’s Financial Instability Hypothesis Directly from Macroeconomic Definitions

ABSTRACT

Though Minsky developed a compelling verbal model of the ‘Financial Instability Hypothesis' (FIH), he abandoned his early attempts to build a mathematical model. I show that the essential characteristics of Minsky's hypothesis are emergent properties of a complex systems macroeconomic model which is derived directly from macroeconomic definitions, augmented by the simplest possible assumptions for relations between system states, and the simplest possible behavioural postulates. I also show that credit is an essential component of aggregate demand and aggregate income, given that bank lending creates money. Minsky's Financial Instability Hypothesis is thus derived from sound macrofoundations. This stylized complex-systems model reproduces both the core predictions of Minsky's verbal hypothesis, and empirical properties of the real world which have defied Neoclassical understanding, which were not predictions of Minsky's verbal model: the occurrence of a ‘Great Moderation' — a period of diminishing cycles in employment, inflation, and economic growth — prior to a ‘Minsky Moment' crisis; and a tendency for inequality to rise over time. The simulations in this paper use the Open Source system dynamics programme Minsky, which was named in Minsky’s honour.

KEYWORDS:

• Minsky
• financial Instability Hypothesis
• Complexity
• system dynamics
• credit
• debt
• macroeconomics

JEL CODES:

• C60
• C61
• C62
• E11
• E12
• E31
• E40
• E44
• F47
• G01
• G12
• G51
• N11
• N12
• Y1

Acknowledgements

The author would like to thank two anonymous reviewers for their very insightful comments.

Disclosure Statement

No potential conflict of interest was reported by the author(s).

Notes

1 The Perron-Frobenius theorem is a result in pure mathematics that incidentally shows that the tatonnement process that Walras thought would lead to an equilibrium price vector cannot converge to that equilibrium. The result is best explained by Blatt, who, as Professor of Mathematics, developed a scholarly critique of economics in his later years. His brilliant book Dynamic Economic Systems: A Post Keynesian Approach (Blatt 1983) was out of print for decades, but it was re-released for Kindle in 2019. I highly recommend it to Post Keynesian economists.

2 ‘Obviously, in order to be able to posit to ourselves any problems at all, we should first have to visualize a distinct set of coherent phenomena as a worthwhile object of our analytic efforts. In other words, analytic effort is of necessity preceded by a preanalytic cognitive act that supplies the raw material for the analytic effort. In this book, this preanalytic cognitive act will be called Vision’ (Schumpeter 1954, p. 41).

3 In what follows, I work exclusively in terms of continuous time using differential equations, rather than the more conventional Post Keynesian practice of discrete time using difference equations. I explain this methodological choice in Appendix A.

4 This is commonly called ‘labour productivity’, but the expression ‘output to employment ratio’ is more strictly correct.

24 In Keen (1995) I used the unemployment rate as the input to the ‘Phillips curve’ function, and a hyperbolic function form for the function borrowed from Blatt (1983), to avoid the possibility of the model generating an unemployment rate below 0 per cent. Here I the use the employment rate $\lambda$ (the ratio of employment L to the entire population N), which empirically is of the order of 60 per cent. This allows the use of a linear ‘Phillips curve’, without running the risk of generating an employment rate greater than 100 per cent, or a wages share greater than 100 per cent, as can be seen from the simulations in Figures 1 and 2.

25 A referee questioned the use of a profit-driven investment function, excluding other determinants ‘such as the leverage ratio and capacity utilisation’ that are commonplace in Post Keynesian equations. This was done just to develop the simplest possible model, to illustrate that the complex dynamics displayed emanate from the structure of the model, rather than any specific assumptions made in it. Obviously in a more elaborate and realistic model, such additional determinants should be included, as well as a nonlinear (and multi-factor) Phillips curve.

5 While the behavioural equations in the model are linear, the multiplication of one system state by another generates structural nonlinearities that generate its complex behavior. See Appendix B for details. Nonlinear behavioural relations are introduced later in the paper.

6 The dependence of the model on the investment decisions of capitalists shows that this is a demand-driven model, even though only the demand of capitalists for investment goods is explicitly modelled (workers and bankers are assumed to consume all their incomes). Giraud and Grasselli (2019) show that consumption demand from workers can be explicitly modelled (with investment treated as a residual), while Grasselli and Nguyen-Huu (2018) show that both investment and consumption demand can be modelled, with inventories treated as the residual variable in a necessarily more complicated model.

7 These are a proxy for inflation in this non-price model. Inflation is considered later in this paper.

8 Fontana points out many of the problems that a period-based analysis causes when one attempts to logically analyse processes of change out of equilibrium, including the fact (also noted by Hicks 1981) that during a period, expectations must be considered to be constant, and the change in expectations must occur between periods. Period analysis thus inhibits the analysis of dynamic processes, even though it is an advance over comparative statics.

9 If this is still difficult to grasp, think in terms of the formal definition of a derivative, which is ${\displaystyle \frac{d}{\mathrm{d}t}f\left(t\right)=\underset{\mathrm{\Delta }t\to 0}{lim}\frac{f\left(t+\mathrm{\Delta }t\right)-f\left(t\right)}{\mathrm{\Delta }t}}$. As $\mathrm{\Delta }t\to 0$ then the number of transactions $f\left(t+\mathrm{\Delta }t\right)-f\left(t\right)$ also goes to zero, but it is the ratio that gives you the derivative. The slope of the tangent derived this way gives you the rate of change on an annual basis.

10 Since a loan is not income, it cannot be shown as a transfer along the same row of a Moore Table.

11 The magnitude of the flows A to F in Table 4 can be different to those in Table 3.

12 I prefer to describe this as ‘Bank Originated Money and Debt’, since it is more meaningful to non-specialists — and it has a great acronym (BOMD).

13 All flow definitions and parameter values are detailed in Appendix C.

14 These are widely used in engineering, and state the response time of a system using its fundamental time units. See https://en.wikipedia.org/wiki/Time_constant for a simple explanation.

15 The parameters were deliberately chosen to generate a borrower with a lower propensity to spend than the lender. In the Loanable Funds model, this means that an increase in the debt to GDP ratio causes GDP to fall, while a decrease causes GDP to rise. This emphasises the irrelevance of debt and credit in a Loanable Funds world.

16 Actual banks of course charge fees, but the ‘Fee’ in this model is one for the mythical function of intermediation, which is crucial only in the minds of Neoclassical economists.

17 This addresses an issue raised in Pottier and Nguyen-Huu (2017, pp. 634–38), about how to characterize the endogeneity of money in the Keen model: it is the consequence of bank lending simultaneously expanding the assets and liabilities of the banking system. Without this, the change they note in the level of aggregate monetary savings of the household and banking sectors would not be possible.

18 The source of the pre-Flow of Funds data is the US Census publication Historical Statistics of the United States Colonial Times to 1970, series X393–409: Net public and private debt by sector, p. 989, and X-580–587. All banks: principal assets, p. 1019.

19 This model also does not deal with Minsky’s correct observation that there are two price levels in capitalism. A model with two price levels can also be derived in this definitional manner, but that is beyond the scope of this paper.

20 As with Lorenz’s model of turbulence, this model is intended as a stylized representation of the underlying processes, rather than a model for empirical fitting to actual data. However, as Grasselli and Maheshwari (2017) showed, even a stylized linear Goodwin model does a reasonable job of replicating the cyclical data of major OECD economies. A similar data-fitting exercise with this model is a topic for future research.

21 The actual rates of change are exponential, given the dependence of the rate of change of D at time t on its value at time t.

22 This confusion exists in statistical services, where ‘Debt’ and ‘Credit’ are both used to refer to the stock of outstanding debt. See, respectively, https://fred.stlouisfed.org/series/TCMDO and https://fred.stlouisfed.org/series/TOTBKCR.

23 Though Ohanian described his Figure 4 as being ‘updated from Chari, Christiano, and Kehoe (2008)’, no such chart appears in that paper — which, amusingly given its stock-flow errors, is entitled ‘Facts and myths about the financial crisis of 2008’. The nearest in data terms is Figures 1A (p. 13), which they use to dismiss the claim that ‘Bank lending to nonfinancial corporations and individuals has declined sharply’ (p. 1) via a melange of obvious stock-flow confusions:

Figure 1A displays weekly data on the total amount of bank credit for all US commercial banks …  Bank credit consists of the aggregate amount of assets held by these banks excluding vault cash. As is clear from these figures, bank credit has not declined during the financial crisis. Indeed, bank credit appears to have risen relative to trend in the month of September. (Chari, Christiano, and Kehoe 2008, p. 2)